Physicochemical Kinetics and Transport at Biointerfaces (Series on Analytical and Physical Chemistry of Environmental Systems, Volume 9)

Physicochemical Kinetics and Transport at Biointerfaces

IUPAC SERIES ON ANALYTICAL AND PHYSICAL CHEMISTRY OF ENVIRONMENTAL SYSTEMS

Series Editors Jacques Buffle, University of Geneva, Geneva, Switzerland Herman P. van Leeuwen, Wageningen University, Wageningen, The Netherlands Series published within the framework of the activities of the IUPAC Commission on Fundamental Environmental Chemistry, Division of Chemistry and the Environment. INTERNATIONAL UNION OF PURE AND APPLIED CHEMISTRY (IUPAC) Secretariat, PO Box 13757, 104 T. W. Alexander Drive, Building 19, Research Triangle Park, NC 27709-3757, USA Previously published volumes (Lewis Publishers): Environmental Particles Vol. 1 (1992) ISBN 0-87371-589-6 Edited by Jacques Buffle and Herman P. van Leeuwen Environmental Particles Vol. 2 (1993) ISBN 0-87371-895-X Edited by Jacques Buffle and Herman P. van Leeuwen Previously published volumes (John Wiley & Sons, Ltd): Metal Speciation and Bioavailability in Aquatic Systems Vol. 3 (1995) ISBN 0-471-95830-1 Edited by Andre´ Tessier and David R. Turner Structure and Surface Reactions of Soil Particles Vol. 4 (1998) ISBN 0.471-95936-7 Edited by Pan M. Huang, Nicola Senesi and Jacques Buffle Atmospheric Particles Vol. 5 (1998) ISBN 0-471-95935-9 Edited by Roy M. Harrison and Rene´ E. van Grieken In Situ Monitoring of Aquatic Systems Vol. 6 (2000) ISBN 0-471-48979-4 Edited by Jacques Buffle and George Horvai The Biogeochemistry of Iron in Seawater Vol. 7 (2001) ISBN 0-471-49068-7 Edited by David R. Turner and Keith A. Hunter Interactions between Soil Particles and Microorganisms Vol. 8 (2002) ISBN 0-471-60790-8 Edited by Pan M. Huang, Jean-Marc Bollag and Nicola Senesi

IUPAC Series on Analytical and Physical Chemistry of Environmental Systems. Volume 9

Physicochemical Kinetics and Transport at Biointerfaces Edited by HERMAN. P. VAN LEEUWEN Wageningen University, Wageningen, The Netherlands ¨ STER WOLFGANG KO Swiss Federal Institute for Environmental Science and Technology (EAWAG), CH-8600 Du¨bendorf, Switzerland

Copyright ß 2004 by IUPAC Published in 2004 by John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (þ44) 1243 779777 Email (for orders and customer service enquiries): [email protected] Visit our Home Page on www.wileyeurope.com or www.wiley.com All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher. Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed to [email protected], or faxes to (þ44) 1243 770620. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Other Wiley Editorial Offices John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA Jossey-Bass, 989 Market Street, San Francisco, CA 94103–1741, USA Wiley-VCH Verlag GmbH, Boschstr. 12, D-69469 Weinheim, Germany John Wiley & Sons Australia Ltd, 33 Park Road, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02–01, Jin Xing Distripark, Singapore 129809 John Wiley & Sons Canada Ltd, 22 Worcester Road, Etobicoke, Ontario, Canada M9W 1L1 Library of Congress Cataloging-in-Publication Data Physicochemical kinetics and transport at biointerfaces / edited by H.P. van Leeuwen, W. Ko¨ster. p. cm. – (IUPAC series on analytical and physical chemistry of environmental systems; . v.9) Includes bibliographical references and index. ISBN 0-471-49845-9 (ppc : alk. paper) 1. Biological interfaces. 2. Chemical kinetics. 3. Biological transport. I. Leeuwen, H. P. van. II. Ko¨ster, Wolfgang. III. Series. QP517.S87P485 2004 571.6’4–dc22 2003060730 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 0471 49845 9 Typeset in 10/12 pt Times by Kolam Information Services Pvt. Ltd, Pondicherry, India Printed and bound in Great Britain by MPG, Bodmin, Cornwall This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production.

Contents List of Contributors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Series Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2

3 4

5

6 7

8 9 10

Physicochemical Kinetics and Transport at the Biointerface: Setting the Stage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . W. Ko¨ster and H. P. van Leeuwen Molecular Modelling of Biological Membranes: Structure and Permeation Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. A. M. Leermakers and J. M. Kleijn Biointerfaces and Mass Transfer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H. P. van Leeuwen and J. Galceran Dynamics of Biouptake Processes: the Role of Transport, Adsorption and Internalisation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. Galceran and H. P. van Leeuwen Chemical Speciation of Organics and of Metals at Biological Interphases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. I. Escher and L. Sigg Transport of Solutes Across Biological Membranes: Prokaryotes . . . . . W. Ko¨ster Transport of Solutes Across Biological Membranes in Eukaryotes: an Environmental Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R. D. Handy and F. B. Eddy Transport of Colloids and Particles Across Biological Membranes . . . . M. G. Taylor and K. Simkiss Mobilisation of Organic Compounds and Iron by Microorganisms . . . . H. Harms and L. Y. Wick Critical Evaluation of the Physicochemical Parameters and Processes for Modelling the Biological Uptake of Trace Metals in Environmental (Aquatic) Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K. J. Wilkinson and J. Buffle

vii ix xi

1

15 113

147

205 271

337 357 401

445

Herman P. van Leeuwen is an electrochemist who obtained his degree in chemistry at the State University of Utrecht, The Netherlands, in 1969. His thesis was in the field of pulse methods in electrode kinetics, and his Ph.D. degree was awarded cum laude (best 5% in The Netherlands) in 1972. He then joined the Colloid Chemistry and Electrochemistry group of Professor J. Lyklema at Wageningen University, where he became a senior lecturer in 1986. His teaching includes analytical/ inorganic chemistry, electrochemistry and environmental physical chemistry. He was appointed Extraordinary Professor at the University of Geneva in 2000. His current major research interests are twofold: (1) ion dynamics and electrokinetics of colloids, and (2) dynamic speciation and bioavailability of metals in environmental systems. He has published some 140 research papers, reviews and book chapters in these fields. He was chairman of the IUPAC Commission on Fundamental Environmental Chemistry from 1995 to 1999, and Chairman of the Electrochemistry Section of the Royal Dutch Chemical Society from 1993 to 2001. Together with J. Buffle, he edits the IUPAC Book Series on Analytical and Physical Chemistry of Environmental Systems, launched in 1992. Wolfgang Ko¨ster studied biology at the Universities of Bielefeld and Tu¨bingen, Germany. Placing emphasis on biochemistry, plant physiology, genetics and microbiology he was influenced by the work of Professor V. Braun, Professor E. Sander and Professor H. Za¨hner. In 1986, he earned his Ph.D. from the University of Tu¨bingen. With a grant from the German Science Foundation (DFG), in 1988 he became a post-doctoral fellow in the laboratory of Professor R. J. Kadner at the School of Medicine, University of Virginia, USA. He was then promoted to a position equivalent to Assistant Professor and the ‘Habilitation’ in Microbiology at the University of Tu¨bingen. Between 1998 and 1999 he held the position of ‘Visiting Scientist’ (Cantarini Fellowship of the Institut Pasteur and Fellowship of the Centre National de la Recherche Scientific (CNRS), France) in the laboratory of Professor M. Hofnung, Institut Pasteur, Paris, France. In 1999, he joined as a Senior Scientist (leading the group Drinking Water Microbiology) the Swiss Federal Institute for Environmental Science and Technology (EAWAG). He gained teaching experience from the Universities of Tu¨bingen and Hohenheim and ETH Zu¨rich by conducting lectures, seminars and practical courses at undergraduate and graduate levels in the areas of microbiology, genetics, biochemistry, molecular biology and environmental science. His major areas of work and interest comprise: (1) survival strategies and molecular detection methods for bacteria in drinking water and environmental habitats, (2) membrane-associated transport phenomena in microbes, with focus on metal transport in bacteria, and (3) bioavailability and ecotoxicity of metals and hydrophobic organic compounds in green algae.

List of Contributors J. Buffle CABE (Analytical and Biophysical Environmental Chemistry/Chimie Analytique et Biophysicochimie de l’Environnement), 30, quai Ernest Ansermet, Universite´ de Gene`ve, CH-1211 Gene`ve 4, Switzerland F. B. Eddy Environmental and Applied Biology, School of Life Sciences, The University of Dundee, Nethergate, Dundee, DD1 4HN, Scotland, UK B. I. Escher Environmental Microbiology and Molecular Ecotoxicology, Swiss Federal Insti¨ berlandstrasse 133, tute for Environmental Science and Technology (EAWAG), U CH-8600 Du¨bendorf, Switzerland J. Galceran Departament de Quı´mica, Universitat de Lleida, Av. Rovira Roure 191, 25198 Lleida, Spain R. D. Handy School of Biological Sciences, The University of Plymouth, Drake Circus, Plymouth, PL4 8AA, UK H. Harms Swiss Federal Institute of Technology, ENAC–ISTE–LPE, Baˆtiment GR, CH1015 Lausanne (EPFL), Switzerland J. M. Kleijn Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, NL-6703 HB Wageningen, The Netherlands W. Ko¨ster Environmental Microbiology and Molecular Ecotoxicology, Swiss Federal ¨ berlandstrasse Institute for Environmental Science and Technology (EAWAG), U 133, CH-8600 Du¨bendorf, Switzerland F. A. M. Leermakers Laboratory of Physical Chemistry and Colloid Dreijenplein 6, NL-6703 HB Wageningen, The H. P. van Leeuwen Laboratory of Physical Chemistry and Colloid Dreijenplein 6, NL-6703 HB Wageningen, The

Science, Wageningen University, Netherlands Science, Wageningen University, Netherlands

viii

LIST OF CONTRIBUTORS

L. Sigg Analytical Chemistry of the Aquatic Environment, Swiss Federal Institute for ¨ berlandstrasse 133, CHEnvironmental Science and Technology (EAWAG), U 8600 Du¨bendorf, Switzerland K. Simkiss School of Animal and Microbial Sciences, University of Reading, Whiteknights, Reading, RG6 6AJ, UK M. G. Taylor School of Animal and Microbial Sciences, University of Reading, Whiteknights, Reading, RG6 6AJ, UK L. Y. Wick Swiss Federal Institute of Technology, ENAC–ISTE–LPE, Baˆtiment GR, CH1015 Lausanne (EPFL), Switzerland K. J. Wilkinson CABE (Analytical and Biophysical Environmental Chemistry/Chimie Analytique et Biophysicochimie de l’Environnement), 30, quai Ernest Ansermet, Universite´ de Gene`ve, CH-1211 Gene`ve 4, Switzerland

Series Preface The main purpose of the IUPAC Series on Analytical and Physical Chemistry of Environmental Systems is to make chemists, biologists, physicists and other scientists aware of the most important biophysicochemical conditions and processes that define the behaviour of environmental systems. The various volumes of the Series thus emphasise the fundamental concepts of environmental processes, taking into account specific aspects such as physical and chemical heterogeneity, and interaction with the biota. Another major goal of the series is to discuss the analytical tools that are available, or should be developed, to study these processes. Indeed, there still seems to be a great need for methodology developed specifically for the field of analytical/physical chemistry of the environment. The present volume of the series focuses on the interplay between organisms and the physical chemistry of the environmental media in which they live. It critically discusses the different physicochemical and biophysical features of the kinetics of processes at the biointerface, with special attention given to aspects such as bioavailability of chemical species, analysis of the necessary mass transfer towards/from the biointerface, routes of transfer through the biomembrane, etc. This volume was realised within the framework of the activities of the former IUPAC Commission on Fundamental Environmental Chemistry of the Division of Chemistry and the Environment. We thank the IUPAC officers responsible, especially the executive director, Dr John Jost, for their support and assistance. We also thank the International Council for Science (ICSU) for financial support of the work of the Commission. This enabled us to organise the discussion meeting of the full team of chapter authors (in Du¨bendorf, Switzerland, 2001) which formed such an essential step in the preparation and harmonisation of the various chapters of this book. The series is indeed being well received, and is growing prosperously. New volumes, on fractal properties of soil particles and physical techniques for micro/nanoparticle characterisation respectively, are in an early stage of preparation. As with all books in the series, these volumes will present critical reviews that reflect the current state of the art and provide guidelines for future research in the field. Jacques Buffle and Herman P. van Leeuwen Series Editors

Preface The idea of broadening the scope of analytical and physical chemistry of environmental systems, to include the interactions of chemical species with living organisms, has been on the priority list of the former IUPAC Commission on Fundamental Environmental Chemistry for some time. It had been recognised that the distribution and transport of chemical components in biotic and abiotic reservoirs is of paramount importance in understanding the effects and fate of organic and inorganic material in environmental systems. The development of mechanistic models for the transport and distribution of chemical components both within and between biotic and abiotic environments requires an integrated approach, with functional links between the various modes of transport of bioactive chemical species and the biophysicochemical processes to which they are subjected. This challenging goal has sparked interest across many fields of research, with the result that much of the key knowledge necessary for progress has become dispersed over several rather poorly interacting disciplines. It is thus timely to integrate these activities, which are all focused essentially on a common broad objective. In doing so, this book will provide the current overall state of the art, as well as highlight key directions for future research. At the end of the 1990s Professor Alex Zehnder (EAWAG/Du¨bendorf CH) and Professor Ronny Blust (Antwerpen University/Belgium) made the first steps towards the creation of this publication. In close cooperation with the chairman of the IUPAC Commission at that time (Dr Herman P. van Leeuwen) it was decided to focus the subject of the book on the physicochemical kinetics of the various processes at the biointerface, and their coupling with the mass transfer of the chemical species involved. This brief would necessarily encompass subtopics such as the structure and permeative properties of biomembranes and their aqueous interfacial layers, the description of diffusive and convective processes at the biointerface, the routes for transport of chemical compounds across membranes, and the biological chemistry of organisms as relevant, for example, for the mobilisation of essential chemicals in the medium. The heart of the book would be on the interphasial region between external medium and organism, and not so much on details of the various chemical conversions inside the organism. A meeting with all prospective chapter authors was hosted by EAWAG/ Du¨bendorf (Switzerland) in early 2001, and the organisation and editing of the book finally came into the hands of the undersigned. It was decided to

xii

PREFACE

create an opening chapter in order to introduce some of the basic physicochemical features of biointerfaces, e.g. those regarding their characteristic spatial organisation and timescales of transport and chemical reactions. Obviously, chemical speciation and bioavailability are elements of inherent importance in this context. Internalisation of chemical species by organisms is considered in itself, on the level of routes of transfer through the biomembrane, as well as in relation to preceding chemical conversions, stimulated or not by specific reactions of the organism. The elements of the different chapters, that span such apparently disparate topics as the statistical thermodynamics of membrane formation and the endocytosis of colloidal particles, are interlinked as much as possible. The book is concluded by a chapter where experimental biouptake data is critically interpreted in terms of available knowledge, so as to provide an impression of the state of the art. The editors would like to express their gratitude to EAWAG/Du¨bendorf (Switzerland) for hosting the preparatory meeting, to the various external reviewers who carefully looked into the draft chapters and, last but not least, to Dr. Raewyn M. Town (Queen’s University of Belfast) for scrutinising all chapters in terms of their scientific and linguistic qualities and the proper use of IUPAC terminology. Herman P. van Leeuwen and Wolfgang Ko¨ster

1 Physicochemical Kinetics and Transport at the Biointerface: Setting the Stage ¨ STER WOLFGANG KO Microbiology, Swiss Federal Institute for Environmental Science and Technology ¨ berlandstrasse 133, CH-8600 Du¨bendorf, Switzerland (EAWAG), U

HERMAN P. VAN LEEUWEN Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, NL-6703 HB Wageningen, The Netherlands

Life has developed in media with very diverse chemical compositions and with a variety of physical conditions, including temperature, pressure and their gradients. Evolution actually implies an optimisation in the functioning of organisms in response to these physical and chemical conditions in which they live. It follows that a change in conditions will give rise to a change in the properties of the organism, and this is known in biology as adaptation. The chemical conditions relevant to survival, evolution and adaptation comprise not only the composition and the chemical dynamics of the medium in which the organism is living, but also the availability of the various chemical species. Therefore the distribution and mobilities of inorganic and organic materials in abiotic and biotic media are of paramount importance in understanding their fate and effects in environmental systems. The present book is concerned with the coupling between environmental media and biota, and focuses on the physicochemical features of processes at their interphases.1 Every living cell, whether it be a unicellular organism on its own or a part of a multicellular organisation, is encircled by a biological membrane. In this context, the terms ‘cell membrane’, ‘plasma membrane’, and ‘cytoplasmic membrane’ are used synonymously. Generally, the interphase between an organism and its environment encompasses the elements outlined in Figure 1. The scheme shows that the cell membrane, with its hydrophobic lipid core, has the most 1 Depending on the context, we sometimes prefer the term ‘interphase’ over ‘interface’ because the latter refers to an infinitely sharp dividing plane between two phases. Organisms generally form boundary layers, e.g. the cell wall, that are characterised by a gradual transition from the biological phase to the medium phase, and if we discuss the volume properties of such layers the term ‘interphase’ is more appropriate.

Physicochemical Kinetics and Transport at Biointerfaces Edited by H. P. van Leeuwen and W. Ko¨ster. ß 2004 John Wiley & Sons, Ltd

2

PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

Cell membrane O(5 to 10) nm Cell wall layer O(up to 10) nm

O r g a n i s m

Electric double layer O(1 to 10) nm

Medium

Diffusion layer O(10 to 100) µm

Figure 1. Schematic outline of the typical dimensions of the various physically relevant layers at the organism/medium interphase: cell membrane, cell wall layer, electric double layer, diffusive depletion layer

prominent function in separating the hydrophilic aqueous medium from the interior of the cell. The limited and selective permeabilities of the cell membrane towards components of the medium, be they nutrients or toxic species, play a key role in the transport of material from the medium towards the surface of the organism. The lipid bilayer has a very low water content and its core behaves quite hydrophobically, while the cell wall is rather hydrophilic, containing some 80% of water. Physicochemically, the cell wall is particularly relevant because of its high ion binding capacity, and the ensuing impact on the biointerphasial electric double layer. The presence of such an electric double layer ensures that the cell

¨ STER AND H. P. VAN LEEUWEN W. KO

3

wall possesses Donnan partition characteristics, leaving only a limited part of the interphasial potential decay in the diffuse double layer of the adjacent medium. Mass transfer phenomena usually are very effective on distance scales much larger than the dimensions of the cell wall and the double layer dimensions. Thicknesses of steady-state diffusion layers1 in mildly stirred systems are of the order of 10
5 m. Thus, one may generally adopt a picture where the local interphasial properties define boundary conditions while the actual mass transfer processes take place on a much larger spatial scale. The availability of chemical species to organisms is defined by a number of basic features, including: . their chemical reactivity, as derived from equilibrium distributions of species and their rates of interconversion; . the supply (flux) of these chemical species to the relevant sites at the surface of the organism, as governed by their mass transport properties and the concentration gradients that arise at the interphase as a consequence of the interplay between chemical reactivity and biological affinity; and . the internalisation of the chemical species, governed by an internalisation rate constant, kint , usually accompanied or followed by some bioconversion process. The actual processes of uptake of chemical species by an organism typically encompass transport in the medium, adsorption at extracellular cell wall components, and internalisation by transfer through the cell membrane. Each of these steps constitutes a broad spectrum of physicochemical aspects, including chemical interactions between relevant components, electrostatic interactions, elementary chemical kinetics (in this volume, as pertains to the interface), diffusion limitations of mass transfer processes, etc. Life on Earth in all its diversity could never have evolved without the existence of lipids that are able to spontaneously arrange in aqueous solutions into structures such as micelles or bilayers. Although the composition of biological membranes varies markedly with their various functions, and with the type of organism and environmental conditions, there is a common structural organisation involving lipid, protein, and carbohydrate components. With only a few exceptions, lipids are arranged as bilayers and constitute the basic characteristic architecture for a variety of biomembranes found in different living organisms. The average thickness of biomembranes is approximately 7 nm. The majority of lipids in the plasma membrane of bacteria (prokaryotes) 1 Such layers are frequently denoted as ‘unstirred’ layers. The term ‘unstirred’ however, is physically incorrect [1], since velocity profiles in liquid media are continuous functions which only approach zero at the actual interface. In gel layers the liquid velocity is generally low, but this is due to their high viscosities.

4

PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

and eukaryotes are comprised of acyl chains (e.g. palmitic acid, stearic acid, oleic acid), which are ester-linked to glycerol. However, many other more complex lipids that contain additional elements like phosphorus, nitrogen or sulfur, may also be found in biomembranes. In addition, hydrophilic components such as small sugars, choline, serine, or ethanolamine are commonly found. Phospholipids containing a phosphate group are ideal amphipathic components, and represent the largest group of membrane lipids. Sterols like cholesterol are almost exclusively found in eukaryotic membranes, where they can make up to 25% of the total lipids. Archaebacteria can exist in the most extreme conditions, and their membrane composition differs from those of the bacteria and eukaryotes. Some unusual components like hopanoids have been found in this group of organisms. Hopanoids are pentacyclic triterpenoids, biosynthetically derived from the linear molecule squalen, which is formed by joining six isopentenyl units. It is assumed that hopanoids may play a role similar to that of sterols in eukaryotic cells. Another common feature of archaeal membranes are acyl chains derived from repeating units of isoprene (e.g. phytanol) which are ether-linked to glycerol or nonitol. The membranes of hyperthermophilic Archaea living at high temperatures are composed of glycerol di-ethers and glycerol tetra-ethers. Lipids containing biphytanyl chains can form monolayers (resembling somewhat the usually found bilayers) with a hydrophobic milieu inside and hydrophilic surfaces outside. They are very stable under extremely high temperatures. Proteins represent another major group of membrane components. They play structural roles and/or are involved in many cellular processes, which are strictly coupled to membranes. Proteins can be either entirely embedded within the bilayer, or they might be firmly anchored (e.g. by a hydrophobic transmembrane segment composed of hydrophobic amino acid side-chains or as lipoprotein), or they can be just associated with the surface. Carbohydrates related to membranes can be found as lipopolysaccharides or as parts of glycoproteins. Sugars are often characteristic determinants of cell surfaces (see below). The great majority of carbohydrates are found in the outer leaflet of a membrane, resulting in an asymmetrical structure. This is especially true for many plasma membranes and the outer membrane of Gram-negative bacterial cells (see below). The membrane is the regulating barrier for exchange of chemical species between the environmental medium and cell interior. It may be practically impermeable to one type of species and highly permeable to another. In the chain of transport steps from the bulk of the medium to the cell interior, the membrane transfer step may thus vary from fully rate-limiting to apparently fast with respect to transport in the medium. The overall rate of this biouptake process is determined by mass transport either in the medium or through the membrane: the actual rate-limiting step will depend on a large variety of factors. Membrane

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transfer rates may be influenced by external chemical conditions, such as pH, ionic strength, presence of surfactants, etc., which alter the permeability features of the membrane, as well as by biological factors like conditioning and adaptation, which may regulate the effectiveness and abundance of transporter functions inside the membrane. An intact and largely undisturbed cytoplasmic membrane or plasma membrane representing the innermost layer enclosing a biological cell is absolutely essential for its vitality. Any major impairment or even a small hole would cause unimpeded exchange of ionic species and thus electrical depolarisation of the membrane, resulting in immediate cell death. This effect can also be generated by certain toxins, which assemble into pores in the membrane. Therefore, channels that are simultaneously open to both sides of the cytoplasmic membrane cannot persist in a living cell. With the help of the atomic force microscopy (AFM) technique, it is possible to obtain three-dimensional images of surface structures at the nanometre scale. Erythrocyte membranes, which are stable during the preparation of an AFM experiment, can be used as a rather basic model with respect to composition and surface structure. This enables a number of details to be visualised, e.g. the deformation of a rhesus monkey erythrocyte membrane caused by an infecting virus (Figure 2). In most cases, however, a given solute approaching the surface of a living cell has to deal with more complex structures, a ‘naked’ membrane surface being highly unusual. In human or animal cells, various glycopeptides and glycosylated proteins are integrated into the lipid bilayer, while most plant (a)

(b)

500 2000 400 1500 300

500

2000

1000 1500 1000

500

400

200 300 200

100

500 0 0

100 0

0

Figure 2. Atomic force microscopy images showing the surface of a rhesus monkey erythrocyte membrane. Damage, such as formation of humps on the peripheral surface and pits in other parts, results from the interaction with virions of the canine parvovirus. (a) edge of erythrocyte; (b) pits on membrane surface. (Source: http://www.ntmdt.ru/ publications/download/211.pdf, Reproduced with permission from Dr Boris N. Zaitser)

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

cells are surrounded by a cell wall composed of polymers of carbohydrates. Bacteria are usually encircled by a sacculus: this peptidoglycan (or murein) sheet contains glycan chains formed by the alternating sugar derivatives N-acetylglucosamine and N-acetylmuramic acid, which are cross-linked by small peptides building a network. Gram-positive bacteria are characterised by multiple layers of peptidoglycan with attached teichoic acids (acidic polysaccharides consisting predominantly of glycerophosphate mannitol phosphate or ribitol phosphate). Alternatively, Gram-negative bacteria possess only a single peptidoglycan layer, but additionally have a second membrane, called the ‘outer membrane’, harbouring various proteins, lipoproteins, and lipopolysaccharides. Moreover, a number of bacterial species produce external capsules or slime layers, while others are capable of building spores that are highly resistant to adverse environmental conditions. This book focuses on the processes that control the transfer of chemicals between environmental media and living organisms. The major driving forces for transport and chemical conversion are contained in the electrochemical potential, that is, the chemical potential difference plus the electrostatic freeenergy change for charged species. Electrical potential differences between the inner and outer boundary of the biological membrane play a crucial role in the various physiological mechanisms. Such potential differences, usually denoted as membrane potentials, derive from differences in permeability of the membrane with respect to ions in the inner and outer media. Common membrane potential expressions, like the Goldman–Hodgkin–Katz equation [2,3] for Naþ , Kþ and Cl
, are valid under steady-state conditions of zero net charge transport: X

zi Ji ¼ 0

(1)

i

where i indexes the permeable ionic species, zi is the charge number of i, and Ji is the flux1 of i across the membrane. Fluxes of charged species are generally the result of gradients in concentration, potential and pressure, which are collect~. ively represented by the electrochemical thermodynamic potential m Application of elementary conservation laws leads to formulation of a general expression for Ji , which is often denoted as the Nernst–Planck equation: Ji ¼
Di grad ci
(zi =jzi j) ci ui grad C þ ci


(2)

1 For convenience, fluxes from the medium towards the organism will be counted as positive throughout this book. Analysis of mass transport in the medium is usually based on a coordinate system with the origin at the interface and a positive axis going outward, leading to a negative sign in fluxes towards the interface.

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Equation (2), where D denotes diffusion coefficient, c concentration, u mobility, C electric potential, and
flow velocity, explicitly shows the diffusion, conduction and flow terms respectively. Within the context of biological systems, transport represented by this Nernst–Planck equation (2) is often referred to as ‘passive’ transport. This qualification is intended to make a distinction from situations where apparently transport takes place in the opposite direction, against a gradient of concentration or potential or pressure. Obviously, such ‘uphill’ or ‘active’ transport requires special conditions, which in biomembrane transport are created by metabolic chemical reactions such as ATP hydrolysis. The coupling of the ionic transport process with the energy providing chemical reaction must be of an asymmetrical nature, in the sense that the production/ consumption of ions at the inner side of the membrane is different from that at the outer side. It has been hypothesised that the asymmetry is in the kinetic features of the interfacial transfer process, in such a way that, in the apparent steady-state, the ratio between influx and efflux is modified. Under such conditions, which essentially are of a nonequilibrium nature, it is possible to realise net uphill ionic transport, and this is the basis of the biologically well-known ionic pumps. The existence of ionic pumps is not in conflict with fundamental transport laws like the Nernst–Planck equation (2): these pumps are generated by the special geometrical and chemically asymmetrical conditions in a biological membrane. In fact, for a rigorous analysis of the pump situation, the Nernst–Planck conservation equation has to be complemented with a chemical source term with a confined spatial distribution. Transport across biological membranes is facilitated by their fluid-like nature. The water content varies strongly from the core to the outer boundary; overall it comes to some 25% by mass. The classical Singer–Nicholson fluid mosaic model represents the biomembrane as a two-dimensional sea of the lipid bilayer, in which proteins and other constituents are floating around. Indeed, most lipid membranes are fluid at physiological temperature, and consequently the lateral mobility of the lipids and proteins is relatively high, whereas the transversal movements (including the flip-flop exchange of lipids between the inner and outer sides) are strongly limited. This feature explains the maintenance of the asymmetry of the membrane with respect to composition and orientation of the ion transporter proteins. As outlined above, this chemical asymmetry is essential for the basic functioning of the biomembrane. Below a certain temperature, the fluid bilayer turns into the crystalline–gel state, in which the lateral mobility of the constituents is greatly diminished. In the fluid state, the lateral diffusion coefficient of lipids in the bilayer structure is O(10
13 ) m2 s
1 (the symbol ‘O’ is used to indicate order of magnitude). Interestingly, it has been shown that the diffusion coefficients of phospholipids may differ greatly from the inner to the outer leaflet of the biomembrane layer [4,5]. Again, this is related to the differences in chemical

8

PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

composition. Lateral transport of lyophobic species like water and ions in the core of the bilayer is not very relevant, because of their extremely low local concentrations. Mobilities of ions in the interphasial region, even inside the stagnant water layer at the actual interface between the aqueous phase and the lipid bilayer, are on the level of that in the bulk solution [6]. As noted above, biouptake involves a series of elementary processes that take place in the external medium, in the interphasial region, and within the cell itself. One of the most important characteristics of the medium is the chemical speciation of the bioactive element or compound under consideration. Speciation not only includes complexation of metal ions by various types of ligands, but also the distribution over different oxidation states, e.g. Fe(II) and Fe(III), and protonation/deprotonation of organic and inorganic acids of intermediate strength. The relationship between speciation and the direct or indirect bioavailability1 of certain species has received a lot of recent attention. Organisms are able to take advantage of a wide range of nutrients, ranging from trace elements to biopolymers such as proteins, DNA, RNA, starch, lignin, etc. Although they are often present in relatively large amounts, these compounds are not always accessible, as illustrated by the following examples: (1) iron, which is an essential nutrient for most living bacteria (lactobacilli being the only notable exception), is the fourth most abundant metal on Earth. However, iron is not readily bioavailable under ‘normal’ physiological conditions. In the environment it is mainly found as a component of insoluble hydroxides; while in biological systems it is chelated by highaffinity iron-binding proteins (e.g. transferrins, lactoferrins, ferritins) or found as a component of erythrocytes (haem, haemoglobin, haemopexin). As a consequence, organisms have evolved a number of different sequestering strategies for this metal. Under anaerobic conditions, ferrous iron can be transported without the involvement of any chelators. Likewise, at pH 3, ferric iron is soluble enough to support growth of acid-tolerant bacteria. At higher pH values, however, iron is mostly found in insoluble compounds. Therefore, a great variety of low-molar-mass iron ligands, socalled siderophores, which bind Fe3þ with very high affinity, are produced by many bacterial species, certain fungi, and some plant species. These chelators are released in their iron-free forms and subsequently transported back into the organism as ferric-siderophore-complexes. Furthermore, a 1 The notion ‘bioavailability’ is used with different meanings. Environmental chemists understand it in terms of the supplying potential of the medium, whereas (micro)biologists relate it to the assimilation properties of the organism. In the case of metal uptake, for example, a certain complex may be fully labile and thus potentially contribute to the supply of free metal ions. In contact with an organism with a modest affinity towards the metal in question the uptake requirements may be so small that such labile complexes are completely unimportant and their lability irrelevant. In microbiological jargon this complex would be ‘not bioavailable’, whereas a chemist would say that this complex is fully available to the organism.

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number of organisms are able to use haem-bound iron from haemoglobin and similar molecules. Some bacterial species can acquire iron that is released by an as-yet unknown mechanism from transferrins or lactoferrins, whereas vertebrates take up the whole iron–protein complex. All these processes involve specific uptake systems in the cell envelope and in the cytoplasmic membrane. (2) although many biopolymers represent an excellent source of nutrients, they are often too large to be transported into a biological cell. A number of species have developed ways to overcome this problem by the secretion of enzymes, which are able to breakdown polymers into their constituents. Many organisms originating from all kingdoms of life are known to use this strategy. So-called exo-enzymes, which are released from the producing cell, can be classified according to their functions (e.g. proteases, lipases, nucleases). Although in some cases these enzymes only carry out a partial degradation, oligomers (e.g. peptides) up to a certain size become ‘bioavailable’ and can then be transported into the cell. In particular, the kinetics of dissociation reactions as preceding steps in the biouptake of organics and metals from complex media have been extensively studied. It is likely that the gap between the concentration of labile species, as measured by a certain dynamic analytical technique [7], and the effective bioavailability of that species will soon be bridged. The role of the adsorption of bioactive species in the cell wall region becomes important as soon as a mechanistic interpretation of biouptake fluxes beyond their mere values in the ongoing steady-state is sought. Back-extrapolation of fluxes to zero time, or even better, analysis of the initial transient behaviour of the flux, will provide more comprehensive information on the molecular details of the internalisation kinetics. Such means will enable distinction between receptor sites (physiologically active) and mere adsorption sites (physiologically inactive), metal ion buffering action of the adsorption sites in the cell wall region, and true nonconditional rate constants of the actual membrane transfer steps. Comprehensive models for the overall biouptake process range from simplifying schemes like the free-ion activity model (FIAM) [8] and the biotic ligand model (BLM) [9] to more differentiated approaches at the level of the Best equation (i.e. Michaelis–Menten control of the uptake and mass transport limitations in the medium) coupled with homogeneous chemical kinetics of formation of the bioactive species in the medium [10–12]. Clearly, the local speciation in the biological interphase may be very different from that in the bulk phase, and this may have a great impact on the nature and rate of bioaccumulation processes. Thus, with the ionic composition of the medium generally being very different from that inside the organism, ion trapping mechanisms may be essential in facilitating efficient transport across the cell membrane.

10 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

In addition to their function as a permeability barrier to the extracellular environment, membranes also fulfil important tasks inside most eukaryotic cells and in some bacteria. One crucial role is the separation of different cell compartments. A few examples of intracellular membranes may illustrate the large variety of membrane functions: . a special type of membrane represents the so-called ‘tonoplast’ that surrounds the vacuoles characteristic of many plant cells. Vacuoles, which can differ in size, help to maintain the osmotic pressure of the cell, and are used as temporary stores for reserve materials or final storage compartments for waste products of the cell metabolism. The central vacuole of a fully differentiated cell can reach an extensive size, thus constituting the major part of the cell’s volume. . the nuclear envelope consists of an outer and an inner membrane surrounding the nucleus, which harbours most of the genetic information of the eukaryotic cell. The nucleus is the location of, for example, replication, transcription, and RNA processing, and the enzymes involved in these vital functions have to be imported from the cytosol. . an extensive intracellular membrane system, the so-called endoplasmatic reticulum (ER) is directly connected to the nuclear envelope. A significant portion of protein synthesis is associated with the ER. . stacks of membranous cistern-like structures (dictyosomes) as well as derived small vesicles and tubules (Golgi vesicles) form the Golgi apparatus. Dictyosomes and Golgi vesicles are involved in intracellular transport and secretion of macromolecules. Exocytosis describes a process in which such vesicles undergo a fusion with the plasma membrane and consequently release enclosed substances into the external medium. Likewise, this membrane flow can occur as a reverse process: endocytosis. In this case invagination of membrane areas leads to intracellular vesicles containing substances from the external medium. This process of ‘budding’ can also occur in the opposite direction, thus delivering cellular components (or membraneenclosed phage particles) to the external medium. . membranes are essential elements of organelles that are exclusively found in plants – the plastids. Among them, the chloroplasts, typical of green plants and algae, display a complex structure. Surrounded by an envelope composed of outer and inner membrane, a complicated system, the thylakoid membranes (see Figure 3), harbours all elements essential for photosynthesis. . a special compartment, also consisting of an outer and inner membrane, is realised in mitochondria. These organelles contain all components for generating energy in the form of adenosine triphosphate (ATP) via oxidative phosphorylation. The examples mentioned above exclusively apply to eukaryotic cells. In prokaryotic cells, intracellular membranes are the exception. However,

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Figure 3. Example of intracellular membrane organisation: a transmission electron microscopy (TEM) image of a section through the thylakoid stack from a chloroplast. (Source: http://www.ru.ac.za/administrative/emu/gr10p6.htm, Reproduced with permission from Dr. R. Cross)

exceptions are known in a few groups of bacteria where complex intracytoplasmic membrane systems result from the invagination of the plasma membrane. Vesicles, tubuli and thylakoid-like structures are reported. Some of them are present in certain phototrophic bacteria. Extensive intracytoplasmic membrane systems are also found in nonphototrophic nitrifying methane-utilising bacteria. Transport processes across membranes can be divided into several categories: . transport of signals in the form of a signal transduction cascade can be achieved by a series of conformational changes in the components involved, or by consecutive modification events (e.g. phosphorylation–dephosphorylation, methylation–demethylation). These processes enable cells to communicate with their environment, and allow them to respond to changing conditions such as pH, osmolarity, pressure, temperature. . uptake of ions and nutrients (mostly molecules of lower molar mass) and the secretion of metabolites and other smaller molecules (e.g. signalling molecules, siderophores) depend on different types of transport systems, which are either using primary energy sources such as ATP or which are coupled to a gradient like the membrane potential. . transport (import and export) of polymers, including proteins, is also mediated by special transport systems which, in many cases, represent multicomponent systems.

12 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

All these transport processes are of comparable importance for an organism in order to adapt to changing conditions and to exist in a given environment. This book focuses on the mass transfer aspects across biomembranes, involving ions, molecules, and particles. Intact membranes are essential for a great variety of vital functions, such as energy-generating processes taking place in the mitochondria of eukaryotes (see above) or at the cytoplasmic membrane of bacteria. In addition, membranes are indispensable for components involved in electron transport chains, and photosynthesis is strictly coupled to the lipid bilayers. Export machineries for proteins, as well as secretion systems for a variety of substances (such as metabolites, signalling molecules, enzymes and extracellular structures) are located in membranes. Moreover, components involved in cell growth and cell division are specifically associated with membranes. In bacteria, a great variety of extracellular structures are anchored in the membranes, which constitute the envelope. Some structures (e.g. pili, fimbriae) take part in cell–cell interaction, adhesion to surfaces, and biofilm formation, others (e.g. flagellae) allow locomotion and mobility. Since so many functions and processes all occur either within, or coupled to, lipid bilayers, it is easy to realise that a fine-tuned balance of embedded and associated components is highly important for the integrity and functionality of all the different types of biomembranes. Therefore, the design and interpretation of test systems and in vitro assays for studying phenomena related to membranes must consider that both the elimination or overproduction of a single membrane protein (or indeed any set of components) may disturb a fragile system and lead to artificial results. The various aspects mentioned above can be summarised as follows: fluxes and distribution of solutes in aqueous solutions and at (or through) hydrophilic/hydrophobic interphases (see Figure 4) can be modelled by following the rules of physics and physical chemistry. In many cases, equations describing transport phenomena can be rather simple, so long as processes like diffusion and osmosis are dominant, and the shapes and surfaces of particles or cells are not very complicated. However, the complexity of the situation increases greatly once parameters like ‘transport against a concentration gradient’, ‘multicomponent systems’, ‘high or low affinity to a substrate’ or ‘complex structures associated with a cell surface’ have to be taken into account. Thus the development of mechanistic concepts and models for the transport and compartmentalisation of chemicals in bioenvironmental systems requires an integrated approach, which provides functional links between processes at different levels of organisation. Indeed, a thorough understanding of environmental processes can only be achieved if studies of the chemistry (e.g. reaction kinetics and mobilisation) and the biology (e.g. transport near and across biological interphases) are combined. Although it is now widely recognised that integration is the way to proceed, these areas of research have to date been the subjects

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diffusion

MY

kd(MY)

ka(MY) kin(M) Mads

M

ka(ML)

kd(ML)

kin(ML) ML

excretion

Figure 4. Schematic representation of the various processes involved in the transfer of metal ions from a complex medium to an organism. The free metal ion and the lipophilic complexes ML are effectively bioactive. Bioinactive complexes MY, present in the medium, can only contribute to biouptake processes via dissociation into M

of the individual disciplines, with little interaction between them. The present book critically summarises and integrates current knowledge of the physicochemical mechanisms, kinetics, transport and interactions involved in processes at biological interphases in environmental systems. It starts with fundamental chapters on the physical chemistry of the structure and permeation properties of the lipid bilayer membrane (Chapter 2), and the basic features of various chemical gradients at the biological interphase and ensuing mass transport from/towards its environment (Chapter 3). The coupling of transport processes in the medium with the actual transfer of chemical species through the cell

14 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

membrane, whether or not this occurs via an adsorbed intermediate, is analysed in Chapter 4 and the role of the chemical speciation of both organic compounds and metals at the biological interphase is discussed in Chapter 5. The biochemical background of transporter functions for the transfer of chemical species across the biological membrane is highlighted for prokaryotes (Chapter 6) and for eukaryotes (Chapter 7). The particular case of transfer of colloids and particles across the biological membrane, known as endocytosis, is reviewed in Chapter 8. The active mobilisation of components in the medium by specific chemical strategies of organisms, with emphasis on mobilisation of organics, is evaluated in Chapter 9. Finally, a number of elements of the foregoing chapters are integrated in Chapter 10, where experimental data for the biological uptake of trace elements from aquatic media are modelled on the basis of knowledge of the speciation and transport parameters of the medium and the cell membrane.

REFERENCES 1. 2. 3. 4. 5. 6. 7.

8. 9. 10.

11. 12.

Levich, V. G. (1962). Physicochemical Hydrodynamics. Prentice Hall, Englewood Cliffs, NJ. Goldman, D. E. (1943). Potential, impedance and rectification in membranes, J. Gen. Physiol., 27, 37–59. Hodgkin, A. L. and Katz, B. (1949). The effect of sodium ions on the electrical activity of the giant axon of the squid, J. Physiol. (Lond.), 108, 37–77. Cevc, G. and Marsh, D. (1987). Phospholipid Bilayers. Wiley-Interscience, New York. van der Wal, A., Minor, M., Norde, W., Zehnder, A. J. B. and Lyklema, J. (1997). Electrokinetic potential of bacterial cells, Langmuir, 13, 165–171. Lyklema, J. (1995). Fundamentals of Interface and Colloid Science. Volume II: Solid–Liquid Interfaces. Academic Press, London. Buffle, J. and Horvai, S. eds. (2000). In Situ Monitoring of Aquatic Systems. Chemical Analysis and Speciation. Vol. 6, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Ltd, Chichester. Morel, F. M. M. and Hering, J. (1983). Principles and Applications of Aquatic Chemistry. Wiley-Interscience, New York. Playle, R.C. (1998). Modelling metal interactions at fish gills, Sci. Total Environ., 219, 147–163. Whitfield, M. and Turner, D.R. (1979). Critical assessment of the relationship between biological thermodynamic and electrochemical availability. In Chemical Modeling in Aqueous Systems. ed. Jenne, E. A., ACS Symposium Series, Vol. 93, pp. 657–680. Hudson, R. J. M. (1998). Which aqueous species control the rates of trace metal uptake by aquatic biota? Observations and predictions of non-equilibrium effects, Sci. Total Environ., 219, 95–115. van Leeuwen, H. P. (1999). Metal speciation dynamics and bioavailability. Inert and labile complexes, Environ. Sci. Technol., 33, 3743–3748.

2 Molecular Modelling of Biological Membranes: Structure and Permeation Properties FRANS A. M. LEERMAKERS AND J. MIEKE KLEIJN Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, NL-6703 HB, Wageningen, The Netherlands

1

2

3

4

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Water and the Hydrophobic Effect . . . . . . . . . . . . . . . . . . . . . 1.2 The Hydrocarbon Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 The Hydrocarbon–Water Interface . . . . . . . . . . . . . . . . . . . . . 1.4 Surfactants and the Surfactant Packing Parameter . . . . . . . . 1.5 Membrane Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Vesicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7 Lipid Phase Behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8 Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.9 Models of Lipid Bilayers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.10 Ensembles in Molecular Modelling . . . . . . . . . . . . . . . . . . . . . The Molecular Dynamic Technique . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 The Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 The Box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 The Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 The Force Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Time and Length Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Dipalmitoylphosphatidylcholine Bilayers . . . . . . . . . . . . . . . . 2.7 Coarse-Grained MD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Monte Carlo Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 The Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 The Box and the Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Pragmatic Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Hybrid MC and MD Approaches . . . . . . . . . . . . . . . . . . . . . . 3.5 Typical Monte Carlo Results . . . . . . . . . . . . . . . . . . . . . . . . . . The Self-Consistent-Field Technique . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 The Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Physicochemical Kinetics and Transport at Biointerfaces Edited by H. P. van Leeuwen and W. Ko¨ster. ß 2004 John Wiley & Sons, Ltd

16 19 20 20 21 24 26 30 30 31 32 33 33 34 35 35 39 40 44 46 46 47 48 48 49 51 52

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4.2 4.3

The Box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 The Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.3.1 Lipids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.3.2 Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.3.3 Ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.3.4 Free Volume and the Pressure . . . . . . . . . . . . . . . . . . . 56 4.4 The Segment Potentials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.5 The SCF Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.6 Phosphatidylcholine Bilayers . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.7 The Lateral Pressure Profile. . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.8 Comparison of SCF and MD for SOPC Membranes. . . . . . 70 4.9 Case Studies: SCF Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.9.1 Effects of the Length of the Hydrocarbon Tails . . . . 74 4.9.2 Lipid Variations: Charged Lipids in Bilayers . . . . . . 75 4.9.3 The Gel-phase of DPPC Bilayers . . . . . . . . . . . . . . . . 76 4.9.4 Mechanical Parameters of Lipid Bilayers. . . . . . . . . . 78 4.9.5 Membrane–Membrane Interactions . . . . . . . . . . . . . . 83 4.9.6 A DPPC Layer as a Substrate for a Polyelectrolyte Brush . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5 Transport and Permeation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.1 Solubility–Diffusion Mechanism . . . . . . . . . . . . . . . . . . . . . . . 86 5.1.1 Equilibrium Aspects: Partitioning . . . . . . . . . . . . . . . . 88 5.1.2 Dynamic Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.2 Pore Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.3 MD Modelling of Mediated Membrane Transport . . . . . . . 97 6 Summary, Challenges and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . 99 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

1

INTRODUCTION

In this review we bring together issues relevant for the structure and permeation properties of biological membranes, from a theoretical, physicochemical perspective. After an introduction concerning the nature of biological membranes, models to evaluate their structural, thermodynamic and mechanical properties will be critically discussed. The input and output of models with molecular detail, in particular the molecular dynamics (MD) and self-consistent-field (SCF) approaches, are analysed. The underlying idea is that all membrane properties should be deducible from that of their constituents. We will pay some attention to the relative importance of intra- and intermolecular forces. Most SCF results that will be presented are updated, i.e. literature results are recomputed using a considerably improved set of interaction parameters. We

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will attempt to cover the complete set of membrane properties that has been considered by SCF modelling to date. The hope is that, eventually, modelling will support measurable system characteristics and predict the unmeasurable ones. With respect to the structure of membranes, we will concentrate on that of phospholipid bilayers, and only briefly mention the work on more complex systems. The review will be biased towards those issues that are relevant to permeation. Our conclusion is that detailed knowledge is available on the structural properties of membranes. The molecularly realistic models mentioned are all in good mutual agreement and indeed complement available experimental data. Structure is only one aspect relevant for transport of molecules across the bilayer; partitioning and dynamics are others. Not surprisingly, significantly less is known about the molecular details that control permeation issues. Indeed, modelling of transport phenomena, especially when specialised molecules are involved, is one of the key challenges for the near future. The fluid mosaic model of the nature of the biological membrane, as put forward by Singer and Nicolson [1] in 1972, is still the starting point for most of the modern work done on biomembranes. The first-order effects described by this model are undisputed. The basis of the biological membrane is a bilayer of lipid molecules, i.e. the lipid bilayer. Computer graphics allow beautiful representations of such a bilayer. The example given in Figure 1 depicts a snapshot of a MD simulation of a bilayer composed of phosphatidylcholine lipids in a slab of water. The fluid mosaic model points further to the role of the lipid molecules. On the one hand, the bilayer forms a barrier to transport for many molecular species that go from one compartment to the other, i.e. the membrane is semi-permeable. The matrix also provides a medium in which protein molecules are incorporated in such a way that they are biologically active. The fluid mosaic model also points correctly to the strongly anisotropic mobility of molecules in this topology. A lipid molecule easily moves around in its ‘own’ monolayer, but it is strongly hindered from flipping from one side to the other (flip-flopping) or jumping out of the bilayer into the aqueous phase. The fluid mosaic model conveniently describes how the constituent molecules are ordered, and it correctly describes, in first order, some of the membrane’s properties. However, it does not give explicit insight into why the biological membrane has a particular structure, and how this depends on the properties of the constituent molecules and the physicochemical conditions surrounding it. For this reason, only qualitative and no quantitative use can be made of this model as it pertains to permeation properties, for example. It is instructive to review the physicochemical principles that are responsible for typical membrane characteristics. In such a survey, it is necessary to discuss simplified cases of self-assembly first, before the complexity of the biological system may be understood. The focus of this quest for principles will therefore be more on the level of the molecular nature of the membrane, rather than viewing a

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

Figure 1 (Plate 1). A molecular view of a small section of a flat lipid bilayer generated by molecular dynamics simulations. The bilayers are composed of 1-stearoyl-2-docosahexaenoyl-sn-glycero-3-phosphatidylcholine lipids, i.e. the sn1 chain is 18 C atoms long and the sn2 chain has 22 carbons, including six cis double bonds. The hydrophobic core is in the centre of the picture, and the hydrated head-group regions are both on top and bottom of the view graph. The head group is zwitterionic and no salt has been added. From [102]. Reproduced by permission of the American Physical Society. Copyright (2003)

membrane as a flexible sheet that can be characterised by a number of mechanical parameters. However, the mechanical parameters must also have a molecular origin. Indeed, the large-scale properties of the bilayer (i.e. the lamellar topology) are essential for the compartmentalisation function of membranes. This has a direct link to transport and permeation. For this reason, we will also give this topic some attention. Lipid assemblies of the lamellar type, such as lipid bilayers, can feature a true phase transition in which the topology does not change. Upon cooling, the bilayer goes from the fluid phase to the gel phase. In the fluid phase, the acyl chains are disordered, in the sense that there is enough free volume around the chains to allow for chain conformation variations. In the gel phase, the acyl chains are more densely packed and believed to be ordered in an all-trans (straight) configuration. For very pure systems, at temperatures below this sharp gel-to-liquid phase transition, there are several other states and distinct transitions detectable (pre-transition, ripple phase, etc.). These phases will not be reviewed here. In biomembranes, many type of lipids (and other molecules) occur, and it is known that for this reason the gel-to-liquid phase transition is

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19

not sharp and occurs over a temperature range of ten degrees or more. In the transition region, there are relatively large density fluctuations, especially when the transition is sharp. These fluctuations lead to pronounced changes in permeation characteristics [2]. As these changes are transient we will not focus on these effects. 1.1

WATER AND THE HYDROPHOBIC EFFECT

Soft condensed matter, e.g. a liquid, is composed of molecules that strongly interact with each other. Without the intermolecular interactions, one only would have gases and, at extreme densities, solids. In all systems that are of interest for biology, water is the main liquid. The water H2 O molecule is very special, and to some extent water has peculiar properties [3]. It has a very low molar mass and, as such, one would expect water to be a gas at ambient conditions, like methane (CH4 ). However, water has the ability to form up to four H-bonds per molecule (each molecule can donate two and accept two Hbonds) and at room temperature is far closer to its freezing temperature than to its critical temperature. Water has a local tetrahedral arrangement dictated by the strongly angular-dependent H-bonds between neighbours. This ‘network’ leaves open voids or free spaces that are equal in size to the water molecule themselves. These voids are stabilised against a collapse by repulsive forces between the molecules, which occur when two water molecules make close contact with each other in an orientation unsuitable for H-bond formation. A realistic picture of water is that H-bonds tend to break and reform easily, and in such a dynamic situation it can be understood that water has a relatively low viscosity. Water is not a particularly good solvent. Not many types of molecules mix with water in all proportions. When a compound has no ability to participate in the H-bonding network, it is likely to be rejected from the water phase. We call these compounds hydrophobic. Hydrocarbon chains are representatives of this class of molecules: hydrocarbons and water strongly segregate. Charged molecules, i.e. ions, are an exception to this rule. The water molecule has a dipole with a fractional negative charge near the oxygen, and a corresponding positive charge halfway between the protons. This dipole will orient in such a way that the molecule is attracted to the ion. As a result, a hydration layer coats the ion. This cluster of molecules dissolves easily, often to very high concentrations, in water. Usually, dissolution of a small amount of one compound in a pure liquid is enthalpically unfavourable and driven by an increase in (mixing) entropy. At room temperature, the opposite is true for the dissolution of a small apolar compound in water. This unexpected behaviour is referred to as the hydrophobic effect [4]. Classically, this effect has been rationalised by ordered water structures around apolar compounds (entropy reduction) and the increase in number

20

PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

of H-bonds supposed to form in this layer (enthalpy gain). This interpretation has its problems. It is not very likely that the apolar compounds that prevent the H-bonding network in water from developing can generate structures that overcompensate this loss. We strongly prefer the less-known interpretation of Besseling et al. [5,6]. These authors argue that dissolving a small apolar compound has the effect that the H-bonding network is deformed (entropy loss). The enthalpic gain is not explained by an increase of H-bonds (this remains constant or can even go down when the network is stretched too much), but by the fact that the additives can screen the unfavourable inter-water contacts discussed above. In this picture, the hydrophobic effect and the density maximum of water at 4 8C are strongly correlated phenomena. It is of interest to mention that, at elevated temperature, the usual thermodynamic behaviour is also found for dissolving apolar entities in water. Irrespective of how the free energy of mixing is split up into an enthalpic or entropic part, in effect it remains very difficult to dissolve much of the apolar compound in water. These thermodynamic subtleties are important for explaining the sensitivity for membranes with respect to temperature. We will not do this here. 1.2

THE HYDROCARBON CHAINS

Hydrocarbons can be viewed as semi-flexible chains. The rotation around a C–C bond can be expressed by the rotational isomeric state scheme. The trans configuration is favoured with respect to gauche conformers by an energy difference of about 1 kT. This means that the persistence length – the length along the contour of the chain in which a free-flying chain in a good solvent can ‘remember’ the direction it is going in – is four to five carbon atoms. Short hydrocarbon chains with a chain length of order 16 carbons can thus be viewed as extremely short polymer chains of just about four segments long. In a hydrocarbon melt, the chains are oriented isotropically. This is not the case for hydrocarbon chains at the hydrocarbon–air interface. These chains have anisotropic conformations and are more ordered. Upon cooling a hydrocarbon phase, the freezing of the liquid starts at the hydrocarbon–air interface and at slightly lower temperature the bulk solidifies. This phenomenon is called surface freezing, and has received considerable attention in recent years [7,8]. The slight (order-induced) increase in density of the acyl chains at the boundary is responsible for this effect. Indeed, the shift in freezing temperature is marginal (only one or two degrees), which indicates that the density change of the ordered top layer differs only slightly from that in the bulk. 1.3

THE HYDROCARBON–WATER INTERFACE

When sufficient amounts of hydrocarbon chains are mixed with water, macroscopic phase separation takes place. The saturation value of hydrocarbon

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molecules in water decreases exponentially with the length of the hydrocarbon chain [4,9]. Typically the free energy penalty to transfer a CH2 group from its own environment to water at around room temperature is of order 1 kT (i.e. the thermal energy) [4]. For this reason, the surface tension between a hydrocarbon phase and water is relatively high (ca. 30 mN m
1) and the interface between these two phases is sharp, that is only one or two times the size of a water molecule. It is instructive to rationalise the latter result from the point of view of energy transfer of a CH2 group to water. As mentioned above, this value is about 1 kT. This means that the thermal energy suffices to allow the transfer of one or two CH2 groups of the hydrocarbon chain to water, but not many more. This means that the protrusion of hydrocarbon fragments into the water phase is also limited to a few CH2 groups. In other words, the hydrocarbon–water interface is fairly sharp, but it is not a mathematical step-function. The amount of water that can dissolve in an apolar phase is very low (mole fraction of the order of 0.001). The origin of this low value is the loss of H-bond energy when a water molecule enters the hydrophobic phase. This result is only weakly dependent on the acyl chain length. Finally, it is noted that at room temperature all lipid acyl chains are far from their critical points for the water–hydrocarbon unmixing. Therefore the density of the hydrocarbon phase is high. Indeed, the density of a hydrocarbon melt does not differ much from that of water. 1.4 SURFACTANTS AND THE SURFACTANT PACKING PARAMETER There are molecules that dissolve in water (hydrophilic molecules) and molecules that do not (hydrophobic molecules). Of course there are also molecules that chemically combine both entities. These molecules have peculiar mixing properties with water. It is as if these molecules become ‘frustrated’ when mixed with water. They are called amphiphiles or, more frequently, surfactants. Here we are interested in those surfactants that consist of two hydrocarbon chains as the hydrophobic part of the molecule combined with a hydrophilic moiety (usually a charged group), such that these are in a head–tail configuration. These molecules tend to show a solubility limit in water, typically near a value that would have been found for the hydrophobic part alone, but the result of supersaturation is not a macroscopic phase separation. Instead, the aggregation is stopped by the hydrophilic part of the molecules [10]. This process, arrested phase separation, is known as self-assembly. The results of self-assembly of lipid molecules into flat bilayer objects are called membranes. Other geometries exist. The start–stop mechanism of self-assembly dictates a specific rule regarding the type of geometries that can form. At least one of the dimensions of these objects, which are generally called micelles, must remain of the size of the surfactant molecule. As not all dimensions of the micelle can grow without bounds, these micelles can be referred to as being mesoscopic in size.

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

It is important to remember that the surfactants in the micelles are in equilibrium with the remaining surfactants in solution. The concentration of free surfactants is known as the critical micellisation concentration (c.m.c.). The molecules in these objects are mobile, and they can exchange with molecules in the bulk. Furthermore, the micelle concentration and the size and shape of the micelles may be a function of the surfactant concentration. Typically, the main effect of increasing the overall surfactant concentration is that the number of micelles increase. The secondary effect is that the free surfactant concentration increases slightly and, because of this, the micelle size adjusts. When the number of surfactants per micelle increases, it can result in some type of packing frustration. When the aggregation number is no longer compatible with the micellar shape, shape changes are implemented. This leads to cylindrical or lamellar-shaped micelles at surfactant concentrations well above the c.m.c. In this review, we are mostly interested in lamellar topologies, i.e. membranes. Israelachvili and co-workers [11] argued that in order to have stable bilayers the averaged shape of the molecule should be a cylinder. This means that the so-called surfactant parameter S ¼
=‘ao (where ‘ is the all-trans length of the hydrophobic tail, ao is the area occupied by the hydrophilic head group, and
is the volume occupied by the tails) assumes a value of S  1. Straightforward geometry tells us that cylindrical micelles are favourable when S  1=2, and spherical micelles should be expected when S  1=3. This rule of thumb works very well indeed. It predicts, for example, that surfactants with one tail, for which S  1=3, will tend to form micelles, but surfactants with the same head group, i.e. with same ao , on to which two similar tails of length ‘ are connected will be more likely to form membranes. This is because now
is larger by a factor of two and thus S  2=3. Although the following will not add to the proof of the effectiveness of the surfactant parameter approach, it is instructive to mention the implicit assumptions made in it (see also Figure 2). . the first approximation is that the area per molecule a can be defined. There are two counter acting forces that control this area. Firstly, there is the tendency to minimise hydrocarbon–water contacts. The free energy contribution of this is fh (a) ¼ ~ga. Here, ~g is the surface tension between the hydrocarbon phase and the water phase. This tends to decrease the area per molecule. Secondly, pressing head groups near to each other gives repulsive forces that may be of an electrostatic or steric origin. A generic form for this repulsion is fr (a) ¼ k=a, where k is a constant modulating this repulsion (that is, a function of ionic strength, etc.) and can, in principle, weakly depend on the surfactant tail length or micelle shape. The sum of these contributions: ft (a) ¼ fh (a) þ fr (a) may be optimised to give the parea ffiffiffiffiffiffiffiffi per molecule. The optimal area per molecule is found when a ¼ ao ¼ k=~g. Variations in this area are typically small. This means that membranes are laterally rather incompressible.

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:-(

Incompressible

:-(

:-)

:-(

Only small protrusions

:-)

:-(

No interdigitation

:-) :-(

Tails semi-flexible

Figure 2. This figure gives a schematic illustration of various fluctuations that exist in lipid bilayers. From top to bottom: (1) the increase in area and concomitant reduction in membrane thickness is strongly damped. (2) Up and down movements of the lipids are restricted to small amplitudes, i.e. much less than the tail length. (3) Interpenetration of lipids into the opposite monolayer is, in first approximation, forbidden. (4) Conformations of the lipid tails have only few gauche defects, so that the tail is only slightly curved. Reproduced from (58) with permission from the Biophysical Society

. lipid protrusions, i.e. movements of lipids in membranes in the normal direction of the membrane surface, are small as compared with the length of the amphiphile (cf. the width of the oil–water interface discussed above). This allows in principle for a definition of (an intrinsic) membrane thickness and membrane volume (necessary for the estimation of partition coefficients of additives). . in a typical aggregate the chain may have a number of gauche defects which will reduce its effective length. Nevertheless, the thickness of the bilayer is still expected to scale linearly with the extended length of the tails, ‘. . in addition, there is the issue of the volume occupied by the tails in an aggregate. Above, it was argued that hydrocarbons strongly segregate from water. This means that the density of the hydrocarbon phase is high; the acyl chains pack rather densely. Inside a membrane the density is not necessarily

24

PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

equal to the bulk density of the corresponding hydrocarbon phase because the apolar tails in the aggregated amphiphiles are anisotropically oriented. However, as a first approximation, one can equate these densities. This means that the volume occupied by the surfactant tails
is under water– hydrocarbon phase segregation control. . chains from one leaflet do not interpenetrate (interdigitate) into the opposite leaflet. Although there is no obvious (free-energy) argument why this is generally the case, it is common belief that it is (in first order) true. . cooperative lateral movements of many lipid molecules, usually called undulations, do not frustrate the packing arguments. This means that these fluctuations are on a length scale that is large as compared with the size of the lipid molecules (or, equivalently, the membrane thickness). A detailed justification of the surfactant parameter approach is still the subject of theoretical investigations, and we will return to several issues below. We mention that the surfactant parameter approach is consistent with the fluid mosaic model of Singer and Nicolson. It tells us that the self-assembly of amphiphiles is driven by the strong segregation of water and hydrocarbon chains, and that packing effects dominate the self-assembly process. All of the above considerations have sometimes led to a too rigid picture of the membrane structure. Of course, the mentioned types of fluctuations (protrusions, fluctuations in area per molecule, chain interdigitations) do exist and will turn out to be important. Without these, the membrane would lack any mechanism to, for example, adjust to the environmental conditions or to accommodate additives. Here we come to the central theme of this review. In order to come to predictive models for permeation in, and transport through bilayers, it is necessary to go beyond the surfactant parameter approach and the fluid mosaic model. Of course it is extremely challenging to build a molecular model for the bilayer which incorporates all of the above properties, and which includes the important fluctuations. From a physicochemical point of view, it is clear that such a model should accurately represent the size and shape of the surfactants. This is necessary because we have seen that the packing effects are important. Such a model should be able to work at very high densities of strongly interacting molecules. The interactions are both of the short-range type (hydrophobic–hydrophilic) as well as of a longer-range type (electrostatics, van der Waals). Below we will discuss only those methods that are powerful enough to do so. 1.5

MEMBRANE TENSION

The combination of the first and second laws of thermodynamics exactly defines the equilibrium of a system. Of course, many biological systems are

F. A. M. LEERMAKERS AND J. M. KLEIJN

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not in equilibrium, and not even in so-called steady-states. It is not known by how much such dynamically evolving bilayers differ structurally from equilibrated ones. In the following sections of this review, we are going to assume that the bilayers have come to a thermal equilibrium. The simple reason for this is that such a bilayer system is unequivocally defined. For obvious reasons, we need to introduce surface contributions in the thermodynamic framework. Typically, in interface thermodynamics, the area in the system, e.g. the area of an air–water interface, is a state variable that can be adjusted by the observer while keeping the intensive variables (such as the temperature, pressure and chemical potentials) fixed. The unique feature in selfassembling systems is that the observer cannot adjust the area of a membrane in the same way, unless the membrane is put in a frame. Systems that have self-assembly characteristics are conveniently handled in a setting of thermodynamics of small systems, developed by Hill [12], and applied to surfactant self-assembly by Hall and Pethica [13]. In this approach, it is not necessary to make assumptions about the structure of the aggregates in order to define exactly the equilibrium conditions. However, for the present purpose, it is convenient to take the bilayer as an example. Let us consider, for example, a flat symmetrical bilayer of which the area is large, so that end-effects can be ignored. Finite size effects are important, and will be discussed in the following section. The membrane is freely floating in solution, i.e. it is not supported by a frame. Combination of the first and second laws of thermodynamics gives for the difference of internal energy dU of a bulk system with membranes with area A: X mi dni þ gdA (1) dU ¼ TdS
pdV þ i

where S is the entropy, T the temperature, p the pressure, V the volume, i is the index pointing to molecular components and m the chemical potential. The intensive variable associated with the membrane area is the surface tension g. In principle, the last term seems to be redundant, because the first three terms should already cover any energy change (in a macroscopically homogeneous bulk). In other words, we have introduced extra knowledge of the existence of membranes. The last term is thus some kind of ‘hidden’ contribution. It is often more convenient to control the temperature than to control the entropy, and therefore it is more convenient to switch to the Helmholtz energy F ¼ U
TS, for which we can write: X mi dni þ gdA (2) dF ¼
SdT
pdV þ i

It will be clear that the membrane is free to adjust its area. Let the system be closed, i.e. let the number ni of molecules in it be fixed. Let the temperature

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

T and volume V also be fixed. In this case the system minimises its Helmholtz energy. This can be done by adjusting its surface area: 

qF qA

 ¼g¼0

(3)

T , V , {ni }

This leads to the equilibrium condition that the membrane tension is zero. For stability reasons it is necessary that q2 F =qA2  0, or equivalently that qg=qA  0. To understand this, it may be convenient to consider an off-equilibrium membrane under tension. A finite tension leads to a bilayer in which the area per molecule is slightly larger than the optimal one. This also means that the thickness is slightly reduced. A finite tension means thermodynamically that it is unfavourable to have a large surface area. As a response, the system will try to reduce its area. When doing so, the area per molecule goes down, the membrane thickness must increase (the loss of material to the bulk can often be ignored) and, as a consequence, the membrane tension is reduced. Exactly the opposite will occur for membranes with a negative surface tension. Sufficiently rigorous models of equilibrated flat bilayers must therefore necessarily have the tension-free state of the bilayer as a constraint. There is a discussion in the literature about the effect of undulation entropy on the equilibrium membrane tension [14,15]. Formally, undulations are included in the surface tension, and thus we need not worry about this. However, if in some model the two are artificially decoupled, one may allow for a very small (positive) surface tension as the equilibrium structure. In other words, the entropy (per unit area) from undulations should compensate for the tension (excess free energy per unit area). 1.6

VESICLES

Flat bilayers only exist in lamellar phases (or in theoretical models). In practice, end-effects are important, and can be eliminated by closing the bilayer into vesicles, known in biology as liposomes. Closing a vesicle introduces curvature energy into the system. It is important to discuss this aspect in some depth. Any curved interface can be described by determining at each point of the surface, two radii of curvature R1 and R2 [16,17]. Typically, we will be interested in a large radius of curvature (R very much larger than the membrane thickness), and therefore it is convenient to define two small parameters: the total curvature J ¼ 1=R1 þ 1=R2 , and the Gaussian curvature K ¼ 1=R1 R2 . Both J and K are invariant upon interchanging the numbering. For a spherical object, R1 ¼ R2 ¼ R and J 2 ¼ 4K ¼ 4=R2 . For cylindrical vesicles one R is infinite and thus K ¼ 0 and J ¼ 1=R.

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Helfrich has shown [18] that the surface tension of a curved interface can be expressed as a Taylor series up to second order in the radius of curvature: 1
K g ¼ go þ kc (J
Jo )2 þ k 2 1 1
K ¼ go þ kc Jo2
kc Jo J þ kc J 2 þ k 2 2

(4)


are (phenomenoThe mean bending modulus kc and the saddle splay modulus k logically) mechanical parameters specific for a particular interface. A molecular model is necessary to give an interpretation to these parameters. We will show this below. Equation (4) also allows for a finite so-called spontaneous curvature Jo ¼ 1=R1o þ 1=R2o . For a particular membrane, the Jo (sphere) ¼ 2Jo (cylinder). When a lipid bilayer is composed of just one type of lipid, it must be true that the flat bilayer is stable against small curvature fluctuations. In other words, for reasons of symmetry one should expect that for such a bilayer Jo ¼ 0. In principle, the situation may be fundamentally different for membrane systems which are composed of more than one type of amphiphile. In this case it is, at least in principle, feasible that the flat bilayer is unstable against curvature fluctuations. When a small curvature is imposed, one may witness an uneven partitioning of the various lipids between the inner and outer leaflet of the curved bilayer. Although the two lipids may differ in their surfactant parameter (and thus there may be a thermodynamic driving force for uneven partitioning), entropy strongly counteracts any strong segregation of the lipids. As a result, we must expect that the reshuffling of the lipids is modest and the spontaneous curvature remains strictly zero. However, when entropy cannot counteract a major sorting of the lipids, e.g. when the lipids laterally segregate due to unfavourable lateral interactions, one may expect a nonzero spontaneous curvature. This may be the case when a mixed bilayer membrane is near its gel–liquid phase transition temperature, or when the chemistry of the mixed surfactants is sufficiently different, e.g. when surfactants with fluorinated carbon tails are mixed with hydrogenated ones [19]. Systems of this type, i.e. lipid systems, which are composed of components that laterally segregate, may however, prefer to form two types of vesicles, each composed of one type of lipid only. This again counteracts the nonzero value of Jo for each vesicle. In biological systems, one often observes membrane structures with nonzero spontaneous curvatures, e.g. in mitochondria. This type of bilayer structure is also essential in various transport related processes such as endo- and exocytosis (see Chapter 8 of this volume). These curved membrane systems may be stabilised by protein aggregation in the bilayer, or may be the result of the fact that biological membranes are constantly kept off-equilibrium by lipid transport and/or by (active) transport processes across the bilayer. These interesting

28

PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

subjects are not yet within reach of state-of-the-art molecular modelling techniques. In model systems for bilayers, one typically considers systems which are composed of one type of phospholipid. In these systems, vesicles very often are observed. The size of vesicles may depend on their preparation history, and can vary from approximately 50 nm (small unilamellar vesicles or SUVs) up to many mm (large unilamellar or LUV). Also one may find multilamellar vesicular structures with more, and often many more than, one bilayer separating the inside from the outside. Indeed, usually it is necessary to follow special recipes to obtain unilamellar vesicles. A systematic way to produce such vesicles is to expose the systems to a series of freeze–thaw cycles [20]. In this process, the vesicles are repeatedly broken into fragments when they are deeply frozen to liquid nitrogen temperatures, but reseal to closed vesicles upon thawing. This procedure helps the equilibration process and, because well-defined vesicles form, it is now believed that such vesicles represent (close to) equilibrium structures. If this is the case then we need to understand the physics of thermodynamically stable vesicles. For lipid bilayers, equation (4) can be simplified. Above we have seen that the flat unsupported bilayer is without tension, i.e. g(0, 0) ¼ 0, and therefore the first two terms must cancel: go ¼
12 kc Jo2 . As argued above, Jo ¼ 0, and thus also the third term drops out. The remaining two terms are proportional to the curvature to the power two. For a cylindrical geometry only, the term proportional to J 2 is present. For spherical vesicles, the two combine into one:
)J 2 . The curvature energy of a homogeneously curved bilayer is ( 12 kc þ 14 k found by integrating the surface tension over the available area:
] sphere gAs ¼ 4p [2kc þ k 1 gAs =L ¼ 2p [ kc J] cylinder 2

(5)

In a cylindrically curved bilayer, the area per unit length As =L is of course used. The terms in the square brackets are necessarily positive, and therefore there is
> 0. Considering the importance a constraint on spherical vesicles that 2kc þ k of the two bending moduli, it is rather surprising that estimates for these quantities are very rare. The few experiments on phospholipids point to kc values ranging between 10 and 40 kT [21]. To date, there is no experiment which
. Again, molecular modelling is needed to leads directly to reliable values for k gain insight into these quantities.
controls the memIt is believed that the Gaussian bending modulus k brane topology. In particular, a negative value of this constant is needed for stable bilayers. A positive value will induce nonlamellar topologies, such as
is negative for bicontinuous cubic phases. Therefore, it is believed that k membranes.

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). As The total curvature energy of a spherical vesicle is given by 4p(2kc þ k all experimental data on phospholipids indicate that kc is not small, one is inclined to conclude that the vesicles are thermodynamically unstable: the reduction of the number of vesicles, e.g. by vesicle fusion or by Ostwald ripening, will reduce the overall curvature energy. However, such lines of
is sufficiently negative to allow the thought overlook the possibility that k overall curvature free energy of vesicles to remain small.
is only slightly larger than zero, one can envisage that the When 2kc þ k mixing entropy of the vesicles can compensate for the curvature energy. Accounting for the mixing entropy, which, for dilute solutions, is proportional to lnj of the vesicle solution, equilibrium vesicles are expected when
) ¼ 0. Equivalently, j ¼ exp[
4p(2kc þ k
)=kT]. Fmix ¼ kTlnjy þ 4p(2kc þ k y Safran showed [22] that when the vesicles are thermodynamically stabilised by translational entropy, the vesicle size decreases with decreasing lipid concentration with a power-law R(j) / j0:25 . Experimentally, a smaller power-law exponent is found [23]. The reason for this is that vesicles are not rigid and can assume shape fluctuations, often referred to as undulations. The effect of undulations may be understood from the observation that a membrane may be characterized by a membrane persistence length x. The persistence length is the length along the surface over which the membrane can ‘remember’ its orientation. Orientational information is lost due to the fact that the bilayer is not rigid but semi-flexible. It is known that the persistence length is an exponential function of the mean bending modulus x  ‘m exp(kc =kT ) [24,25]. Here ‘m is a molecular length. When we consider two points on the surface that are closer together than x, we know they are on a piece of the bilayer that may be considered approximately flat. However, when the two points are further apart than x, the local orientation of the bilayer on these two points is uncorrelated. This means that when a bilayer closes on length scales larger than x, the curvature energy must vanish. One way to
, and thus the curvature energy implement this idea is to allow both kc and k of the vesicle, to depend on the radius of the vesicle. For example, one can write the renormalised mean bending modulus of the form kc (R) ¼ kbare
ln( ‘Rm ), c bare is the unnormalised mean bending modulus (all coefficients are where kc ignored for the sake of the argument). When R  x, it is clear that the renormalised constant vanishes. Such renormalisation leads to the conclusion that fluctuation-induced stabilisation of vesicles occurs when R  x. Usually, one assumes that this argument leads to the prediction that only very large vesicles can exist, because of the very strong dependence of x(kc ) and the relatively high
is of the same order of values of kc reported in the literature. However, when
k magnitude as kc , the argument may well explain the thermodynamic stability of the vesicle. In conclusion, lipid vesicles that are fully equilibrated (freeze–thaw procedure) may be stabilised by both translational as well as undulational entropy.

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

Taking both contributions into account leads to the prediction [26,27] that R(j) / j0:12 . Recent experiments are consistent with this [23]. 1.7

LIPID PHASE BEHAVIOUR

Besides the regulation of the surface area, surfactant (lipid) aggregates have the extra degree of freedom of choice of topology. Above, we have already discussed the formation of curved bilayers or vesicles and mentioned the possibility of formation of (spherical) micelles. Other aggregates are also possible, i.e. in some systems, spherical, cylindrical or lamellar micelles (membranes) may form. These objects can float either randomly in solution or they can be ordered in a liquid-crystalline array, leading to, for example, a cubic-, a hexagonal-, or a lamellar phase. On top of these phases there may be various phases in which saddle-shaped surfaces occur, such as double diamonds (cubic) and sponge phases. A phase diagram is therefore rather crowded and complex. Nomenclature exists to refer to particular phases: for example, phases with lamellar topology are referred to by the letter L. The liquid-crystalline phase of the bilayers is known as the La phase and the gel phase is Lb . Extra labels on the latter may refer to packing variations of the tails in the various gel phases. The sponge phase L3 is locally lamellar, but this phase has ‘handles’ in between the bilayers. Hexagonal phases are referred to using the letter H. Again, indices may refer to cases where the head groups are on the outside or are in the inside (inverted hexagonal) of the cylindrical objects. Isotropic phases, i.e. dilute micellar phases, are assigned the letter I. However, in this review, we will not need this nomenclature extensively, as we are mainly interested in La phases. It is important for the theoretical understanding of the formation of various topologies that these aggregates have entropic contributions on the scale of the objects, i.e. on a much larger scale than set by the molecules. These cooperative entropic effects should be included in the overall Helmholtz energy, and they are essential to describe the full phase behaviour. It is believed that the mech
and Jo , control the phase behaviour, anical parameters discussed above: kc , k where it is understood that these quantities may, in principle, depend on the overall surfactant (lipid) concentration, i.e. when the membranes are packed to such a density that they strongly interact. 1.8

COMPLEXITY

It is necessary to elaborate on yet another essential aspect of biological membranes, i.e. their ‘complexity’. This keyword points to the large number of different molecules that are usually found in the biological membrane. First of all, there is a large variety of lipid molecules. The lipid composition of the biological membranes varies from one species to another, and is adapted to meet the needs of organs, cells, organelles, etc. The variations in the head–tail

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overall structure are large. There are differences in hydrocarbon chain length, chain branching, number and position of unsaturated bonds, hydrophilic head group size, charge, etc. There may be other lipid components, such as cholesterol, modulating the physical properties of the bilayers. Most of all, there are proteins embedded into the bilayer or associated with it. The complexity of the biological membranes poses huge problems for the molecular modelling of these objects. Without doubt, the complexity is there for good reasons. For example, the many protein molecules facilitate the chemical reactions and transport events. From a physicochemical point of view, we are still far from a full understanding of complexity; why is there such a variety of lipids and additives (other than proteins) in the biological membrane? Trying to understand model systems is a good way to start, followed by gradually increasing the complexity. This is the route that will be followed in this review. Firstly, the focus will be on ‘simple’ membranes composed of just one type of (saturated) lipids. After that we will consider the effect of number and position of unsaturated bonds, lipid mixtures and the effects of additives. When we arrive at this stage, we can also address permeation issues. 1.9

MODELS OF LIPID BILAYERS

From the above, it will be clear that molecular modelling of lipid bilayers is a challenging task. Models are tailored to give insight into many different aspects. Here we will concentrate mainly, but not exclusively, on models that feature lipid molecules, of which both the hydrophilic as well as the hydrophobic parts are taken into account. The models should reproduce self-assembly, and there should be both a relevant driving force for phase separation and a realistic stopping mechanism. The results should be at least qualitatively consistent with the surfactant parameter approach and the fluid mosaic model. Most importantly, the model should go beyond these approaches by including as many of the aforementioned fluctuations as possible. For such a model, there is hope that it may give predictive insight into the membrane structure and performance, e.g. into permeation issues. It will be rather obvious that models that satisfy these requirements will require the use of a computer to do the detailed work of dealing with all the molecules and the forces between them. Apart from this, there is usually a considerable amount of information that needs to go into the formulation of the problem before one can get something useful out. In this review, we will demonstrate that the ‘break-even point’ has been passed convincingly by several but not all modelling approaches in recent years. To elaborate on this, we will discuss both the in- and output of these models. A further issue is the quality of the results. It will not come as a surprise that the quality of the information gain depends nonlinearly on the computation time that one is willing or able to spend on the problem. There are highly

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detailed models in which very subtle information (on a particular aspect) is obtained. There are more pragmatic models in which it is rather easy to scan some part of the parameter space and gain qualitative insight. How these models work and why these models work, what the limitations are, etc., will be discussed next. Basically, there are two types of molecular approaches: molecular simulations and self-consistent-field (SCF) methods. We will discuss these two approaches in order. The molecular simulations will include molecular dynamics (MD), and Monte Carlo (MC) simulation. Moreover, we will briefly discuss the recently developed dissipative particle dynamics (DPD) method. Like SCF, the last technique is not exact, because not all excludedvolume (packing) correlations are properly accounted for, but it may be used to obtain dynamical information on much longer timescales than can be reached by MD. 1.10

ENSEMBLES IN MOLECULAR MODELLING

The molecular modelling of systems consisting of many molecules is the field of statistical mechanics, sometimes called statistical thermodynamics [28,29]. Basically, the idea is to go from a molecular model to partition functions, and then, from these, to predict thermodynamic observables and dynamic and structural quantities. As in classical thermodynamics, in statistical mechanics it is essential to define which state variables are fixed and which quantities are allowed to fluctuate, i.e. it is essential to specify the macroscopic boundary conditions. In the present context, there are a few types of molecular systems of interest, which are linked to so-called ensembles. . the canonical ensemble: (N, V , A, T) systems, where the number of molecules N, the volume V, the area A, and the temperature T, are fixed, and, as a consequence, the internal energy of the system can fluctuate, . the grand canonical ensemble: (m, V , A, T) system, which allows transfer of molecules from a reservoir with fixed chemical potentials to the system and back, but which restricts the spatial dimension in the system, . the constant-pressure/surface-tension ensemble: (N, p, g, T)-systems, where both the volume and the area of the system may vary (in order to keep the pressure and the surface tension constant), but where both the number of molecules and the temperature remain fixed. The relative importance of fluctuations, e.g. in the membrane area, as is possible in a (N, p, g, T ) ensemble, becomes larger when the system that is under investigation is smaller. For macroscopic systems, the fluctuations in such quantities are negligible, but, for some of the modelling techniques that are restricted to small systems, one cannot avoid dealing with it. Of course, for a (N, p, g, T ) ensemble in which both the volume and the surface area are allowed

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to fluctuate, one can compute the time-average of these quantities. Using these averaged quantities subsequently to specify macroscopic boundary conditions in a canonical ensemble, one typically will recover structural characteristics of the system that match those of the (N, p, g, T ) ensemble. The reverse can also be done. One can perform computations in a canonical ensemble, compute, e.g. the pressure or the surface tension, and subsequently adjust the boundary conditions iteratively until these intensive variables assume the ‘equilibrium’ values of e.g. p ¼ 1 atm and g ¼ 0.

2 2.1

THE MOLECULAR DYNAMIC TECHNIQUE THE STRATEGY

The strategy in a molecular dynamics simulation is conceptually fairly simple. The first step is to consider a set of molecules. Then it is necessary to choose initial positions of all atoms, such that they do not physically overlap, and that all bonds between the atoms have a reasonable length. Subsequently, it is necessary to specify the initial velocities of all the atoms. The velocities must preferably be consistent with the temperature in the system. Finally, and most importantly, it is necessary to define the force-field parameters. In effect the force field defines the potential energy of each atom. This value is a complicated sum of many contributions that can be computed when the distances of a given atom to all other atoms in the system are known. In the simulation, the spatial evolution as well as the velocity evolution of all molecules is found by solving the classical Newton equations of mechanics. The basic outcome of the simulation comprises the coordinates and velocities of all atoms as a function of the time. Thus, structural information, such as lipid conformations or membrane thickness, is readily available. Thermodynamic information is more expensive to obtain, but in principle this can be extracted from a long simulation trajectory. For example, the average kinetic and potential energy in the system is easily obtained from the velocities and the pair interactions. The notoriously difficult part is the evaluation of the entropy. To compute the entropy, it is necessary to know the probability that each distinguishable state can occur in the system. The ‘book-keeping’ to find this probability distribution is not feasible – even more so because in a typical MD run only a part of the possible and allowed configurations of the system is sampled. All known alternatives to compute the entropy are also computationally expensive. Correspondingly, it is very hard to compute, the Helmholtz energy, for example. Fortunately, it is straightforward to obtain differences between Helmholtz energies, upon small changes in the system. Therefore, it is not too difficult to calculate the pressure (tensor) and/or the surface tension, for example. For details we refer to the literature [30].

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The strong point of molecular dynamic simulations is that, for the particular model, the results are (nearly) exact. In particular, the simulations take all necessary excluded-volume correlations into account. However, still it is not advisable to have blind confidence in the predictions of MD. The simulations typically treat the system classically, many parameters that together define the force field are subject to fine-tuning, and one always should be cautious about the statistical certainty. In passing, we will touch upon some more limitations when we discuss more details of MD simulation of lipid systems. We will not go into all the details here, because the use of MD simulation to study the lipid bilayer has recently been reviewed by other authors already [31,32]. Our idea is to present sufficient information to allow a critical evaluation of the method, and to set the stage for comparison with alternative approaches. 2.2

THE BOX

There are several commercial packages that realise the above strategy for molecularly realistic systems. It is useful to discuss some of the limitations. Ideally, one would like to do simulations on macroscopic systems. However, it is impossible to use a computer to deal with numbers of degrees of freedom on the order of Nav . In lipid systems, where the computations of all the interactions in the system are expensive, a typical system can contain of the order of tens of thousands of particles. Recently, massive systems with up to a million particles have been considered [33]. Even for these large simulations, this still means that the system size is limited to the order of 10 nm. Because of this small size, one refers to this volume as a box, although the system boundaries are typically not box-like. Usually the box has periodic boundary conditions. This implies that molecules that move out of the box on one side will enter the box on the opposite side. In such a way, finite size effects are minimised. In sophisticated simulations, i.e. (N, p, g, T)-ensembles, there are rules defined which allow the box size and shape to vary in such a way that the intensive parameters (p, g) can assume a preset value. The finite size of the box has several important consequences. One of them is that the area of the membrane piece is only of the order of 100 nm2 . It is expected that the membrane is, on this length scale, roughly flat, i.e. the area is small as compared with the persistence length x for the bilayer. Interestingly, however, in recent simulations the first signs of fluctuations away from the flat bilayer structure (undulations) have reportedly been found by MD simulations [33]. The periodic boundary conditions applied in the system have the consequence that one bilayer leaflet can interact in the normal direction with the other leaflet, not only through the contact region in the core of the bilayer, but also through the water phase. To minimise artifacts, one should systematically increase the size of the water phase. However, this is expensive, especially if the main interest is in the behaviour of the lipids. Another solution is to cut off the

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permitted range of interactions, to be smaller than the typical box-size. But then salient features in, for example, spatially varying water densities or water orientation in the normal direction, may remain undetected and have an effect in the simulations. These effects can influence, e.g. the pressure measurements. Physically, it means that a simulation focuses not on isolated membranes but on a stack of membranes as in, for example, a lamellar phase, where the membranes interact with each other. 2.3

THE MOLECULES

Many MD packages contain some basic organic chemistry to accurately define the molecule structure including the positions of H-atoms. For an illustration of the level of detail of how lipids can be represented, we will refer to Figure 3. Many packages can also make use of crystallographic data, such that one can position the molecules to relative coordinates given by the unitcell data characteristics. Then it is rather trivial to build a bilayer of lipid molecules that can serve as a reasonable initial guess configuration for the simulation run. An example is given in Figure 4. The bilayer is positioned in, for example, a pre-equilibrated water phase, by removing the water molecules at the positions of the lipid molecules. Finally, one should introduce ions in the system. These ions are necessary to screen the electrostatic interactions. As very accurate input data are needed for a successful MD run on lipid systems, it is not surprising that most of the simulations done are for a very limited number of systems for which these are available. Phosphatidylcholine (PC) bilayers have been and still are popular [31,33–41], but, nowadays, other types of lipid bilayers are under investigation as well [42–46]. MD studies on lipid mixtures, as well as a lipid bilayer including some protein-like object, give all kinds of additional problems that we will touch upon below. 2.4

THE FORCE FIELD

The full description of the interactions in the system that are included in the simulations is called the force field. A typical potential function of the system features extremely simplified forms (for example, harmonic terms) for the various contributions: ! 2 X1  X Aij Bij X qi qj b 0 k þ þ
r
b V¼ ij ij 2 ij 4p"0 rij r12 r6ij ij i<j i<j bonds  2 h  io X1 X f n þ kijkl 1 þ cos n fijkl
f0ijkl kyijk yijk
y0ijk þ 2 angles dihedrals

(6)

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

Figure 3 (Plate 2). Representation of molecular structure in MD simulations. Shown here is the SOPC lipid, discussed in the text. The numbers at each atom indicate the partial charge on the atom. The space-filling picture on the left gives insight into the van der Waals radii of the various groups, and thus into the shape of the molecule. Reproduced from (58) with permission from the Biophysical Society

Here the atoms in the system are numbered by i, j, k, l ¼ 1, . . . , N. The distance between two atoms i, j is rij , q is the (partial) charge on an atom, y is the angle defined by the coordinates (i, j, k) of three consecutive atoms, and f is the dihedral angle defined by the positions of four consecutive atoms, "o is the dielectric permittivity of vacuum, n is the dihedral multiplicity. The potential function, as given in equation (6), has many parameters that depend on the atoms involved. The first term accounts for Coulombic interactions. The second term is the Lennard–Jones interaction energy. It is composed of a strongly repulsive term and a van der Waals-like attractive term. The form of the repulsive term is chosen ad hoc and has the function of defining the size of the atom. The Aij coefficients are a function of the van der Waals radii of the

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Figure 4 (Plate 3). Typical snapshot of a start configuration in MD simulation. Figure 1 (Plate 1) resulted from the equilibration of this initial guess. From [102]. Reproduced by permission of the American Institute of Physics. Copyright (2003)

two atoms si , sj and interaction energy "ij between the two atoms. The Bij coefficient is also a function of the two radii and the interaction energy "ij . The third term in equation (6) deals with stretching of bonds. The spring constant kbij is only nonzero when i and j share a bond and boij is the equilibrium bond length. The fourth term accounts for the energy penalty of bending of a bond away from the preferred angle yoijk . For small differences, again a harmonic assumption is taken and the constant kyijk is the force constant for the angle deformation, and is only nonzero when i, j and k are consecutive atoms in the molecule along a chain. The final term accounts in a similar way for the rotation around bonds, and depends on four consecutive atoms. We note that modern force fields and simulation packages may use extra and/or more complicated forms of the potential V. The first and second terms in equation (6) are rather expensive in terms of computer power needed. They include the interaction of all atoms with all other

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

atoms. This becomes a problem for large systems. As the interaction energy decreases with the distance between the atoms, it is reasonable to cut them off at some distance. The decay of the van der Waals term of the Lennard–Jones contribution is fast, and the cut-off distance is set to a few times the size, s, of the atoms involved. The electrostatic contribution decays very slowly (1/r), and in the literature there are a number of suggestions to deal with this contribution accurately and economically. One of the problems is that the box size can be small as compared with the decay length. Then the Ewald method [30] can be used to sum the contributions of neighbouring boxes. At present, this methodology is still under development for the modelling of charged membranes. In the integration scheme, not only the potential energy in the system, but also the potential energy felt by a particular atom, is needed. This value is trivially found, similar to an equation as given by equation (6) by selecting only those terms in which atom i occurs. It is instructive to see that the kinetic energy does not occur in equation (6), and that equation (6) only depends on the coordinates of the atoms which are unambiguously known at a given moment in time. The Newton equation F ¼ ma is conveniently cast in the form:


qV q2 ri ¼ mi 2 qt qri

(7)

and of course there is one such equation for each atom i. The number of parameters that occur in equations (6) and (7) is huge, and it should be noted that there is a whole industry in finding acceptable values for a balanced force field. Ideally, one would like to have one correct parameter set which can be used to solve all problems, and one would like to have a theoretical justification for these values, e.g. from quantum mechanics, or unambiguous justification of the parameters from spectroscopic data. However, in practice the situation is not so. Many of the parameters are chosen quite empirically, and if they can be obtained from spectroscopic data or from ab initio quantum mechanics, this still may not guarantee good results in a potential form that contains simplified (harmonic) contributions. Therefore, there is a large number of force fields available. One force field tends to perform better for intermolecular interactions. The other one is tuned to represent intramolecular forces accurately. Therefore the optimum force field may depend on the type of problem at hand. An example of a force field used in lipid systems is the ‘optimised parameters for liquid systems’ (OPLS) [47,48]. In such force fields, polarisable atoms are usually given partial charges (cf. in equation (6) or Figure 3). These partial charges may be found from quantum mechanical analysis, and obviously these values differ per force field. Of course the water molecules should be treated with more than average care. Several water models exist and have been applied to lipid systems [49]. There are, for example, a single point charge model (SPC) [50], an extended single point charge model (SPC/E),

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and a TIP water model, of which the first one is popular because of economic reasons. See, for example, [51] for a critical evaluation of parameters for the modelling of alkanes. It is not unimportant to realise that there are several possible ways to implement the Newton equation in an MD simulation. It is not trivial to make sure that all degrees of freedom, e.g. very fast C–H vibrations, or much slower conformational changes, have their proper share of the internal energy. One MD-‘dialect’ may be superior to the other in, e.g. distributing the energy in such a way that the temperature is constant. It would take too long to discuss all the options, so we will only mention that well-known packages such as GROMOS [52], CHARMM [53] and AMBER [54] are widely available. New developments are still being made, such as the collisional dynamics method [55]. In this method, the atoms experience collisions with ghost particles. These collisions are an efficient way to distribute the energy in the system, and the method has the property that all degrees of freedom are at the same temperature. 2.5

TIME AND LENGTH SCALES

To integrate the equations of motion in a stable and reliable way, it is necessary that the fundamental time step is shorter than the shortest relevant timescale in the problem. The shortest events involving whole atoms are C–H vibrations, and therefore a typical value of the time step is 2 fs (10
15 s). This means that there are up to one million time steps necessary to reach (real-time) simulation times in the nanosecond range. The ns range is sufficient for conformational transitions of the lipid molecules. It is also sufficient to allow some lateral diffusion of molecules in the box. As an iteration time step is rather expensive, even a supercomputer will need of the order of 106 s (a week) of CPU time to reach the ns domain. Of course there are many phenomena that equilibrate on the nanosecond timescale. However, the majority of relevant events take much more time. For example, the ns timescale is much too short to allow for the self-assembly of a set of lipids from a homogeneously distributed state to a lamellar topology. This is the reason why it is necessary to start a simulation as close as possible to the expected equilibrated state. Of course, this is a tricky practice and should be considered as one of the inherent problems of MD. Only recently, this issue was addressed by Marrink [56]. Here the homogeneous state of the lipids was used as the start configuration, and at the end of the simulation an intact bilayer was found. Permeation, transport across a bilayer, and partitioning of molecules from the water to the membrane phase typically take also more time than can be dealt with by MD. We will return to this point below. A typical MD simulation usually consists of two parts. The first part is an equilibration time (ca. 1 ns) starting with a reasonably accurate initial configuration (see, for example, Figure 4), which is followed by a production run.

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Considering the relatively short equilibration phase, one should always be alert for possible artifacts that originate from the choice of the initial configuration of the system. In particular, if for equilibration, a considerable adjustment of the area of the membrane is necessary, it may take a very long time before this is completed. An example where this is an issue, is the level of interdigitation of the lipid tails. If the simulations are started in a fully noninterdigitated state, significant chain interdigitations may never be found – not even in the production phase. There can also be hindered equilibration effects that have their origin in finite box size effects. For example, if the number of lipids on each side of the bilayer is taken to be of order 30 to 100, which is reasonable, a fluctuation in this number is not expected to occur in the simulation, because this would be too large an overall perturbation. Cooperative movements of many molecules at the same time, which occasionally may be necessary before equilibration is a fact, may also be very slow. 2.6

DIPALMITOYLPHOSPHATIDYLCHOLINE BILAYERS

From the above, one may be left with the impression that the MD technique has major problems. It is important to realise that there are relatively straightforward ways to systematically improve the method. In the future, the force fields will become more accurate, the computer power will increase and allow larger box sizes and longer (real-time) simulation times. Even today, MD simulations are the closest to this ‘ideal’ situation as compared with other methods. To show this, we will present and discuss some typical results readily available in the literature. Here we will select systems simulated in the constantpressure constant-surface-tension ensemble, i.e. with a temperature, pressure and surface tension control. MD simulations need a sufficiently accurate initial guess for the bilayer structure in order to find relaxation of the structure in the nanosecond range. X-ray diffraction techniques can be used to determine the electron density profile across the bilayer to high precision, and, from these, the required input data can be extracted. However, typically for X-ray diffraction experiments it is necessary to have oriented bilayers, and therefore most results are available for systems with very little water between them. These results are of interest for lipid membranes that strongly interact. Indeed, fully hydrated bilayers are expected to have a slightly different structure. In 1996, Nagle et al. [38] reported the (X-ray) structure of a highly hydrated DPPC bilayer. One problem is that in the fully hydrated state the bilayers do not remain perfectly flat. The shape of the bilayer may be sinusoidally deformed, i.e. it can undulate up and down, and therefore the intrinsic membrane structure is blurred and an ‘averaged’ one is found. Nagle took these undulations into account, and, as a result, there are accurate numbers for the structural parameters of DPPC layers. For example, the area per lipid molecule is a0 ¼ 0:629  0:013 nm2 .

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The number of water molecules per lipid molecule is 29.1 when the equilibrium (centre to centre) distance (swelling limit) between bilayers is 6.72 nm. These data serve also as an accurate test for MD methodology (including the force field). Rand and Parsegian have collected accurate structural parameters for many other lipid systems [57]. From this perspective it is not surprising that most simulations are done on DPPC bilayers, albeit that, from a biological perspective, other lipids, e.g. partially unsaturated lipids, are perhaps more relevant. DPPC bilayers have been extensively reviewed in the literature [31,36], and therefore we will visit this system only briefly. The MD simulation results that easily attract attention are snapshots. From these, it is easy to tell how the molecules are distributed in the box at a particular point of time in the simulation. See Figure 1 for a typical example. These snapshots are important to obtain a good idea of how order parameters and density profiles follow from the positions of the atoms. However, these structural parameters can only reliably be found after sufficient averaging over a large number of such snapshots. Of course, one can find many MD results in the literature, and it is always arbitrary to pick one of those. We choose to present some good results from a simulation by Berger and co-workers [58]. They paid attention to particular values of the force-field parameters, such that the lipid densities were in accordance with experimental observations, and therefore we should interpret the result depicted for the atom distribution profiles as given in Figure 5 to be rather accurate. In Figure 5, the overall water profile, the overall lipid distribution, as well as that of the CH2 , CH3 groups and several head-group fragments, are plotted. It is of interest to discuss some highlights, because we will return to these when discussing corresponding distributions that result from more approximate modelling attempts. The water profile penetrates into the bilayer just up to the glycerol units. Thus, in MD, one does not find any water molecules in the hydrophobic core. The atom density of the lipid shows a dip in the core. The shape of the dip correlates with the distribution of the CH3 groups. These groups have a large volume per atom. As a result of the dip, the profiles suggest that the two monolayers do not overlap greatly (the tails do not interdigitate much). If this were the case, one would expect a bimodal distribution for the CH3 groups. However, there are plenty of chains that cross the symmetry plane and the CH3 is nicely unimodal. The distributions of the head-group fragments are depicted only on the righthand side of Figure 5. Obviously the CO groups that originate from the glycerol backbone are between the PC head group and the hydrocarbon chains. Interestingly, the average position of the P and that of the N are at approximately the same z-coordinate. This means that the average P–N vector is almost parallel to the membrane surface. Close inspection shows that the N profile is significantly wider than that of the phosphate. This reflects the higher mobility

42

PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 50 Lipid

r

no. of atoms/V

40 CH2

30 Water

20

PO4

N(CH3)3

10 0

CH3

0

1

2

CO

3 z / nm

4

5

6

Figure 5. Profiles across the bilayer of the total lipid density of DPPC, the water density and the densities of certain lipid groups as obtained from MD simulations by Berger et al. [58]. The profiles are found by taking the time average over the last 300 ps of the simulation. The densities for the lipid head-group components are only shown on one side for clarity. The origin of the z-axis is arbitrarily positioned on the left of the bilayer. On the y-axis, the atom density in atoms per nm3 is given. Redrawn from [58] by permission of the Biophysical Society

of this group, which is expected because it is positioned at the end of the head group. There is a tendency for the distribution of the N group to be bimodal, something which will be discussed below. From these overall profiles, it is not easy to extract conformational properties, other than that it will be clear that the lipid molecules are strongly anisotropically oriented in the bilayer. For this, other characteristics are much more appropriate. It is possible to define an order parameter which indicates how much the lipid tails are oriented normal to the membrane: 1 S ¼ h3 cos2 W
1i 2

(8)

Here the angular brackets mean that the ensemble average is taken, and the angle W can be defined and computed for each bond in the molecule. When a bond is perfectly aligned normal to the bilayer surface, the order parameter assumes a value of unity. In a random orientation, the order parameter is zero. Bonds that are perfectly aligned parallel to the surface gives a negative order parameter of S ¼
0:5. Such order parameters can also be obtained from deuterium NMR measurements, and therefore one frequently finds predictions for these order parameters in the literature. The order parameter profile that belongs to the tails of the lipid membrane as given in Figure 5 is shown in Figure 6. There is a consensus in the literature about the typical patterns found in the order parameter profile along the chain in the phospholipid bilayer. The order

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0.2 S

0.1

0

0

2

4

6 8 10 12 Carbon atom number

14

16

Figure 6. Variation of the orientational order parameter S along the hydrocarbon chains of the lipids of DMPC lipid bilayers, according to MD simulations of Berger et al. [58]. The line is drawn to guide the eye. The spheres are experimental values obtained by Seelig and Seelig [59] using 2 H-NMR spectroscopy. (Numbering of C-atoms from the head group to the CH3 terminal group). Redrawn from [58] by permission of the Biophysical Society

is relatively high for hydrocarbon chain segments near the glycerol backbone, and slowly decreases toward the ends of the tails, which are more randomly oriented. The absolute value of the order parameter profile is also correct, as can be seen by the satisfactory comparison with data from Seelig and Seeling [59]. It is important to note that the absolute value of the order parameter is of course strongly dependent on the value of the area per lipid in the membrane. In these simulations, the area found is sufficiently close to the experimental data, i.e. a0 ¼ 61 nm2 . Although not an easy task, it is possible to compute, for example, the electrostatic potential profile across the bilayer. In Figure 7, we give an example for DPPC, as reported by Tieleman and Berendsen [49]. In MD many atoms and molecules contribute to the electrostatic potential, because of the partial charges assigned to them. From such an exercise, it turns out that the electrostatic potential assumes very large values of several hundred mV. This is in line with experimental data, where it has been found that the magnitude of the dipole potential of biomembranes is typically several hundreds of millivolts [60] – the hydrocarbon core being positive with respect to the aqueous phases. The surface potential of most biomembranes is of the order of tens of millivolts. As seen in Figure 7, simulations also indicate that the electrostatic potential in the membrane is positive with respect to the aqueous phase. The region
1 < z < 1 is the hydrophobic core of the bilayer, where the effective dielectric permittivity is low (and thus potentials are high). In the aqueous parts of the system, the potential drops rapidly to very low values. This is because the presence of the water molecules, which can orient to compensate for the high potentials (i.e. they have a high dielectric permittivity).

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 0.8

y/ V

0.6

0.4

0.2

0

−3

−2

−1

0 z / nm

1

2

3

Figure 7. The total electrostatic potential profile across the DPPC bilayer as given by Tieleman and Berendson [49]. Redrawn by permission of the American Institute of Physics

Tu et al. [61] analysed the dynamics of water molecules in the vicinity of the bilayer. Water molecules remain bound to the phosphate and carbonyl groups on a 10 ps timescale. The lipid molecules change their conformations more slowly. Only at the hydrocarbon chain ends are there some isomerisation events on the 10 ps timescale. Then, over the period of 100 ps, water molecules can diffuse away from the lipid. Also the centre of mass of the hydrocarbon chains rattles vertically and laterally. On the nanosecond timescale the lipid molecules experience rotational and translational motion (rattling in a cage, no large-scale movement across the box), and the head group can undergo major conformational changes. We need to go to much longer times to see partitioning and transport across the bilayer. It is therefore not possible to use MD to model all relevant processes for transport and permeation. We will return to this in Section 5. 2.7

COARSE-GRAINED MD

Even when the computer ‘power’ will increase significantly, it is not easy to greatly exceed the 10 ns timescales in MD simulations. This is a problem, because many relevant membrane problems in which major lipid rearrangements are necessary have much longer characteristic times. One way of proceeding is to be pragmatic and simplify the models that one is willing to work on. Indeed, in an all-atom MD simulation, most of the simulation time is used to accurately follow the C–H vibrations. This is no longer needed if united atoms are used where a CH2 - or a CH3 group (or in fact several of these groups) are merged together in effective (spherical) units, sometimes called segments. As a result, it is possible to use larger time-steps in the integration of the Newton equations. Of course, for such artificial units, new force-field parameters are

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necessary. The values of the effective interactions between the segments must be chosen such that the physical behaviour on the length scales of the segments is similar to that of the more detailed simulations. The process of ‘integrating’ out the short time-scale events is known as coarse graining. An interesting simulation on coarse-grained lipids is reported by Lipowsky and co-workers [62]. These authors used surfactants that are composed of just a few beads and simplified potentials, similarly to those used in surfactant studies performed by Smit and co-workers [63]. One of the results that was reported is an estimate of the stretching modulus of a model bilayer. We will discuss this point below, where similar properties are reported to have been obtained by the SCF theory. One aspect of MD simulations is that all molecules, including the solvent, are specified in full detail. As detailed above, much of the CPU time in such a simulation is used up by following all the solvent (water) molecules. An alternative to the MD simulations is Brownian dynamics (BD) simulation. In this method, the solvent molecules are removed from the simulations. The effects of the solvent molecules are then reintroduced into the problem in an approximate way. Firstly, of course, the interaction parameters are adjusted, because the interactions should now include the effect of the solvent molecules. Furthermore, it is necessary to include a fluctuating force acting on the beads (atoms). These fluctuations represent the stochastic forces that result from the collisions of solvent molecules with the atoms. We know of no results using this technique on lipid bilayers. Coming from the field of rheology, there is yet another interesting technique to model complex fluids. This technique is called dissipative particle dynamics (DPD) and has recently been applied to (model) lipid bilayers. The fundamental trick here is that the lipids are represented by a set of soft beads, with either hydrophilic or hydrophobic properties that are linked according to the lipid architecture. For soft beads (particles), the appropriate interaction potentials differ fundamentally from the usual Lennard–Jones ones. In DPD, the interaction curve between beads does not have the usual ‘hard-core’ part, and it also lacks an attractive well at small separation. Instead, a weak repulsion, linear with respect to the centre-to-centre distance, is implemented. This potential then allows the molecules to interpenetrate each other to some extent. The weakness of the potential has the big advantage that long time steps can be used in the simulation. This then opens up the possibility of covering significantly longer evolution times than MD. In principle, one should map the DPD potentials to the force fields in atomistically realistic MD simulations. How accurately this can be done is not yet known exactly. A strong point of DPD simulations is that the simulations conform to Navier–Stokes hydrodynamics. Qualitatively, the bilayer structures that result from DPD simulations are reasonable [65]. In the simulation box, it is possible to find a stable bilayer in which the head groups shield the apolar core from the water phase. This means that the model effectively features a start-and-stop mechanism for

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

Figure 8 (Plate 4). Typical snapshot of DPD simulation results [64]. The hydrophobic part of mixed bilayers of DPPC-like lipids and up to 0.8 mole-fraction of the non-ionic surfactant C12 E6 (left) and 0.9 (right). The surfactant C12 chains are represented by grey curves, and the lipid C15 chains are black. The hole in the left conformation is transient; on the right they are stable. Reproduced by permission of the Biophysical Society

self-assembly. A recent simulation of a mixture of lipids and surfactants clearly proves that the DPD method has additional value [64]. When a bilayer of such a mixture was kept under a finite lateral tension, it was possible to visualise and analyse the formation of pores or holes. A graphical representation is given in Figure 8. It is clear that bilayers that lose their integrity also lose their biological functions. These holes were attributed to the presence of the surfactants, and were therefore interpreted to be relevant for the toxic effect of surfactants for bacteria. Of course the possibility that there are transient holes or water channels is relevant for transport and permeation. Such spontaneous fluctuations may determine to some extent the permeability of the bilayer for hydrophilic compounds. We will return to these phenomena below.

3 3.1

THE MONTE CARLO TECHNIQUE THE STRATEGY

In many simulations that use a time trajectory to sample membrane properties, it is the equilibrium situation that one is interested in, rather than the dynamics themselves. The dynamics are then just a by-product that is only used to judge the degree of equilibration.

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When dynamic properties are not one’s main interest, one can consider alternatives to obtain solutions for the equilibrium properties of complex molecular systems. As equilibrium fluctuations can be used to estimate the response of a system when it is slightly off equilibrium (Onsager reciprocal relation [66]), it is still of interest to discuss these alternatives in this review. In the MD simulation, the system can only evolve towards equilibrium by a dynamic path (trajectory), through all kind of possible states of the system (phase space). In a Monte Carlo (MC) simulation technique, the trajectory is typically nonphysical. For example, it is possible to suggest and implement conformational changes, or large changes in system properties, from one MC step to the other. There is no limitation at all on the type of changes that can be made in the system before an evaluation of the system’s energy takes place. In order to prevent ad hoc changes in the system from leading to a random mixing of all molecules (this is often the maximum in the entropy of the system), there is a simple rule which can tell whether or not the changes are accepted or rejected. If the potential energy V in the system is decreased, the suggested move is favourable, and the changes are accepted. If, however, the potential energy V increases, which is unfavourable for the system, the move is either rejected or accepted. This is how the choice is made: (1) Let the potential energy increase be DV > 0, then the Boltzmann factor P ¼ exp (
DV =kT) is a number smaller than unity. (2) Next a random number is generated between 0 and 1. (3) If this number is smaller than P, the move is accepted (and implemented). If it is larger than P, then the suggested changes in the system are rejected, and the old state is counted once more (for taking appropriate averages). This strategy, known as the Metropolis scheme, guarantees that the MC trajectory evolves towards equilibrium [30]. Drawing of the random numbers guarantees, for example, that the system can escape from a local minimum, i.e. that it can sample all relevant system configurations. 3.2

THE BOX AND THE MOLECULES

One can apply the MC technique to the same molecular model, as explored in MD. One can use the same box and the same molecules that experience exactly the same potentials, and therefore the results are equally exact for equilibrium membranes. However, MC examples of this type are very rare. One of the reasons for this is that there is no commercial package available in which an MC strategy is combined with sufficient chemistry know-how and tuned force fields. Unlike the MD approach, where the phase-space trajectory is fixed by the equations of motion of the molecules, the optimal walkthrough phase space in an MC run may depend strongly on the system characteristics. In particular, for densely packed layers, it may be very inefficient to withdraw a molecule randomly and to let it reappear somewhere else in

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the system. Excluded-volume constraints will almost certainly reject the move. Snake-like movements (reptation) would be more efficient, as would small conformational changes within a molecule (typical moves that are done in a MD simulation). Also, the water phase poses huge problems for MC simulations. We recall that the interactions between the water molecules (H-bonds) are very strong, and that each water molecule has, on average, four of these ‘contacts’. It is necessary to invent ingenious MC moves in order to prevent a significant reduction of H-bonds in the water network upon a series of random changes in the positional and orientational distribution of the water molecules. Again, the acceptance probability for such system changes is expected to be small. It is the ingenuity of the researcher to implement efficient trajectories through phase space that can make the difference between failure and success. The lack of guidance as how to design the MC trajectories also explains the lack of commercial MC packages. 3.3

PRAGMATIC APPROXIMATIONS

As the dynamics of the system are removed from the model, it is no longer necessary to allow the molecules to ‘live’ in a continuous space. Instead, the use of lattices – discrete sets of coordinates on to which the molecules are restricted – is popular. Digital computers are of course much more efficient with discrete space than with continuum space. The use of a lattice implies that one removes all properties that occur on shorter length scales than the lattice spacing from the model. This is no problem if the main interest is in phenomena that are larger than this length scale. With the Monte Carlo technique, a very large number of membrane problems have been worked on. We have insufficient space to review all the data available. However, the formation of pores is of relevance for permeation. The formation of perforations in a polymeric bilayer has been studied by Mu¨ller by using Monte Carlo simulation [67] within the bond fluctuation model. In this particular MC technique, ‘realistic’ moves are incorporated, such that the number of MC steps can be linked to a simulated time. 3.4

HYBRID MC AND MD APPROACHES

In principle, MC algorithms can be tuned for particular systems and can thus be more efficient than MD for obtaining equilibrium distributions. An interesting idea is to use MC simulations to obtain accurate initial guesses for subsequent MD simulations. Already as early as 1993, Venable and co-workers [68] used a scheme for efficiently sampling configurations of individual lipids in a mean field. These configurations were then used to develop the initial conditions for the molecular dynamic simulations.

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3.5

49

TYPICAL MONTE CARLO RESULTS

Monte Carlo may be used to study the lateral distribution of lipid molecules in mixed bilayers. This of course is a very challenging problem, and, to date, the only way to obtain relevant information for this is to reduce the problem to a very simplistic two-dimensional lattice model. In this case, the lipid molecules occupy a given site and can be in one of the predefined number of different states. These pre-assigned states (usually about 10 are taken), are representative conformations of lipids in the gel or in the liquid state. Each state interacts in its own way with the neighbouring molecules (sitting on neighbouring sites). Typically, one is interested in the lateral phase behaviour near the gel-to-liquid phase transition of the bilayer [69,70]. For some recent simulations of mixtures of DMPC and DSPC, see the work of Sugar [71]. Levine and co-workers [72,73] have considered an ensemble of chains end-grafted on a plane and the space is represented by an ingenious (highcoordination lattice suitable for representing saturated as well as unsaturated acyl chains. In the MC simulation, only moves that could realistically take place, i.e. small conformational changes, etc., are incorporated, and, for this reason, one can optimistically connect the MC trajectory with a time-axis. Although this is not completely unrealistic, there always is some ambiguity in how this mapping is done. A number of very interesting predictions that compare favourably to that of MD simulations as well as experimental observations, were drawn. For example, the average order of the chains as a function of the distance away from the grafting plane can be computed. In Figure 9, a typical example is shown for unsaturated alkyl chains. A pronounced dip in the order profile at 0.3 S 0.2

0.1

0

0

3

6

9 t

12

15

18

Figure 9. A comparison of the order parameter profile as found by MC simulations [72] of model 9/10 cis unsaturated chains in a monolayer (the x-line is to guide the eye) with experimental data obtained from NMR experiments () on the same chains incorporated into a biological membrane. Redrawn from [72] by permission of the American Institute of Physics

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 0.8

0.6

S 0.4 N = 10 13

0.2

15

0

6

9

15

12

19

18

t

Figure 10. Calculated order parameters of the CH2 groups of isolated molecules of linear alkanes with chain length N as indicated, starting from the centre of the molecule towards its end. The ranking number along the chain is indicated by the letter t. MC simulations by Rabinovich and co-workers [74–76]. Copyright (1997) by Elsevier

the position of the double bond is a very characteristic feature. This dip shows that the double bond significantly disturbs the local order in the bilayer. Not all MC simulations are done on a lattice. We would like to mention a particularly interesting study by Rabinovich and Ripatti [74–76], who analysed the conformational states of a short acyl chain with and without unsaturated bonds (see Figure 10) The idea of the simulations is to consider isolated chains with realistic short-range potentials. As the chains are not much longer than their persistence length, they cannot return to themselves. For this reason, there is no need to specify interaction potentials other than those that exist for two neighbouring segments (vibrations), three segments in a row (bending), and those found for four consecutive segments (rotation). The usual Lennard–Jones parameters for the nonbonded interactions are not needed. Many conformations were sampled by the usual MC procedure. The result is of course that there is no preferred orientation of the molecule. Each conformation can, however, be characterised by an instantaneous main axis; this is the average direction of the chain. Then this axis is defined as a ‘director’. This director is used to subsequently determine the orientational order parameter along the chain. The order is obviously low at the chain ends, and relatively high in the middle of the chain. It was found that the order profile going from the centre of the molecules towards the tails fell off very similarly to corresponding chains (with half the chain length) in the bilayer membrane. As an example, we reproduce here the results for saturated acyl chains, in Figure 10. The conclusion is that the order of the chains found for acyl tails in the bilayer is dominated by intramolecular interactions. The intermolecular interactions due to the presence of other chains that are densely packed around such a chain,

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determine the orientation of the molecule to be roughly perpendicular to the membrane surface. The level of alignment is high when the area per molecule is low, and vice versa.

4

THE SELF-CONSISTENT-FIELD TECHNIQUE

The previous result is an important one. It indicates that there can be yet another fruitful route to describe lipid bilayers. The idea is to consider the conformational properties of a ‘probe’ molecule, and then replace all the other molecules by an external potential field (see Figure 11). This external potential may be called the mean-field or self-consistent potential, as it represents the mean behaviour of all molecules self-consistently. There are mean-field theories in many branches of science, for example (quantum) physics, physical chemistry, etc. Very often mean-field theories simplify the system to such an extent that structural as well as thermodynamic properties can be found analytically. This means that there is no need to use a computer. However, the lipid membrane problem is so complicated that the help of the computer is still needed. The method has been refined over the years to a detailed and complex framework, whose results correspond closely with those of MD simulations. The computer time needed for these calculations is however an order of 105 times less (this estimate is certainly too small when SCF calculations are compared with massive MD simulations in which up to 1000 lipids are considered). Indeed, the calculations can be done on a desktop PC with typical

z U(z) for head groups MEAN-FIELD 0 APPROXIMATION

u(z) U(z) for tail segments

Figure 11. A schematic representation of the mean-field approximation, a central issue in the self-consistent-field theory. The arrows symbolically represent the lipid molecules. The head of the arrow is the hydrophilic part and the line is the hydrophobic tail. On the left a two-dimensional representation of a disordered bilayer is given. One of the lipids has been selected, as shown by the box around it. The same molecule is depicted on the right. The bilayer is depicted schematically by two horizontal lines. The centre of the bilayer is at z ¼ 0. These lines are to guide the eye; the membrane thickness is not preassumed, but is the result of the calculations. Both the potential energy felt by the head groups and that of the tail segments are indicated. We note that in the detailed models the self-consistent potential profiles are of course much more detailed than shown in this graph

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CPU times of 100 s or less. The method can additionally provide insight into the mesoscopic behaviour of the bilayer systems, and can deal with polymeric additives. Dynamic information is not directly available, although there are several attempts to reintroduce dynamics in a mean-field framework [77,78]. More so than in ‘exact’ simulations, it is necessary to give details of SCF methods. This is to give an insight into how and when approximations are introduced. Only then it is possible to build a realistic picture of the approach, understand its limitations in terms of conformational detail and loss of information about dynamics, and to interpret the results. 4.1

THE STRATEGY

A central issue in statistical thermodynamic modelling is to solve the best model possible for a system with many interacting molecules. If it is essential to include all excluded-volume correlations, i.e. to account for all the possible ways that the molecules in the system instantaneously interact with each other, it is necessary to do computer simulations as discussed above, because there are no exact (analytical) solutions to the many-body problems. The only analytical models that can be solved are of the mean-field type. The most essential step in a mean-field theory is the reduction of the manybody problem to a scheme that treats just a small number of molecules in an external field. The external field is chosen such that it mimics the effect of the other molecules in the system as accurately as possible. In this review we will discuss the Bragg–Williams approach. Here the problem is reduced to behaviour of a single chain (molecule) in an external field. Higher order models (e.g. Quasi-chemical or Bethe approximations) are possible but we do not know applications of this for bilayer membranes. Needless to say, a simplified model leads to corresponding thermodynamic quantities, i.e. not all correlations are included. However, the thermodynamic framework itself is fully internally consistent. This is an important observation, because such a model can for this reason be of use to establish the thermodynamic feasibility of ‘what-if ?’ questions. Full control over the absolute deviations from the true thermodynamic behaviour is unfortunately not possible. The approach ignores important (cooperative) fluctuations, and it is expected that especially near phase transitions the approach may give only qualitative results. In particular, comparison of SCF results with experiments or with simulation data can lead to insights into how rigorous the method is. It is of interest to mention that, once particular choices are made concerning how the mean-field interactions are incorporated into the model, the corresponding partition function and thermodynamics follow in a straightforward manner. In particular, there exists a method based upon a variational argument, to formulate the best possible corresponding (mean-field) potential fields. We will not go into these details here, but refer to the variational method, as

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explained in standard textbooks [79]. Typically, the optimal potential fields become a function of the average properties of all test molecules in the system (one for each united-atom type). On the other hand, the average properties of a test molecule depend on the actual values of the potentials. This interconnection of dependencies is solved numerically by some iterative process. As soon as the potentials and the densities are mutually consistent, one can evaluate the partition function, and all thermodynamic and structural characteristics are extracted from it. Such a fixed point is called, for obvious reasons, the selfconsistent-field solution, and the models that make use of this strategy are self-consistent-field models. SCF models typically make use of lattice approximations. As dynamics are not an issue, it is not necessary to specify all the potentials in equal detail. Therefore there are many differences between the SCF and simulation methods. Comparing and contrasting both methods remains of interest, because this will give insight into essential and less essential aspects of membrane formation. 4.2

THE BOX

It is important to realise that the SCF technique differs significantly from the simulation methods, due to the above-mentioned averaging procedure and the use of (average) density-dependent, self-consistent external potentials. This averaging should be done over a large number of molecules, or equivalently, over a sufficiently large region. An averaging procedure is only expected to work if the property over which averaging is done does not fluctuate strongly. Therefore, it makes sense to average in planes parallel to the membrane surface, and account for density-and potential gradients perpendicular to this, i.e. in the z-direction. In this section we will restrict ourselves to this approach. In effect, it is assumed that the system is translationally invariant in the x–y directions. As a consequence, the presentation of the results will also differ from that in a MD or MC box, where a full set of molecules can be depicted (as snapshots). In an SCF model, all properties will be presented in, for example, (average) numbers of molecules per unit area of the membrane, or equivalent, i.e. the (average) densities of molecules as a function of the z-coordinate. The ‘box’ thus consists, if one insists, only of one coordinate. For this reason, we can refer to this method as a one-gradient SCF theory or simply 1D-SCF theory. Extensions towards 2D-SCF are available, where lateral inhomogeneities in the bilayer can also be examined [80]. There are even implementations of 3D SCF-like models, but here the interpretation is somewhat more delicate [78]. For computational reasons, it is necessary to discretise the space in such a way that one considers only a finite number of z-coordinates for the segments of the molecules to take positions. Again, the coarse graining is justified as long as the relevant phenomena do not take place on a smaller length scale. Here we consider lattices with sites that fit united atoms, e.g. CH2 units. The

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z-coordinates can be numbered arbitrarily, z ¼
M,
M þ 1, . . . ,
1, 0, 1, . . . , M
1, M, where M is a sufficiently large number such that the membrane can fit into the ‘box’. Typically, we will put the centre of the bilayer on the z ¼ 0 spot. The trick of putting the bilayer in the centre of the coordinate system is a convenient one, in order to remove an uninteresting translational entropy term from consideration. Computational tricks are not included in this review [81]. 4.3

THE MOLECULES

In the SCF technique, there is a straightforward way to account for intramolecular excluded-volume correlations [82], i.e. by generating all possible selfavoiding conformations, albeit a computationally expensive task. Accounting for intermolecular excluded-volume correlations cannot be treated exactly, not even by using up much more CPU time (unless, of course, one is willing to resort to simulations). One of the challenges is to put as many of the effects of intermolecular excluded-volume correlations in to the procedure as possible. From the MC results discussed above, we have learned that for short chains it is sufficient to just account for short-range along-the-chain excluded-volume correlations. For this reason, it is tolerable to generate conformations in a rotational isomeric state scheme (RIS). In this context, we refer to this scheme as a finite memory Markov process: excluded-volume correlations over a distance of four consecutive united atoms are included, i.e. these cannot overlap, but for segments further apart this is not strictly forbidden. This problem is (partially) corrected by a contribution to the segment potential as discussed below. In contrast to the RIS scheme used in MD only discrete angles are included on the lattice typically only those corresponding with the trans (lowest energy) and the two gauche (two local minimums of the energy) conformers. Correspondingly, only the energy difference between the trans and a gauche state becomes a parameter in the model. In calculations discussed below, we will use a value of 0.8 kT for this difference, except when we mention otherwise. 4.3.1

Lipids

Molecules that are restricted with their segments on to lattice sites need a force field with characteristics different from those in MD simulations. For example, restricting atoms on the lattice leads to fixed bond lengths, and the bond length control is not needed. By the same token, the bond angles are fixed and there are no parameters to control this angle. In fact, we will consider models in which all united atoms in the molecule are of equal size, exactly fitting to a lattice site. The number of united atoms, as well as the type of united atoms (polar, apolar, charged, etc.) determines the molecular architecture and the type of interactions felt by the molecule. Instead of Lennard–Jones potentials, the

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square-well potential is popular. This potential assumes a finite value if the segments that interact occupy neighbouring lattice sites. If they are further apart then the interaction is assumed to be zero. In a modern implementation of the SCF approach, GOLIATH [83], detailed architectures of the molecules can be handled. Typically the protons are not explicitly defined, but molecular groups that are large can be split up into a group of beads. In this way, the lipid molecules may have rather realistic structures, i.e. they consist of a glycerol backbone on to which two acyl chains and a head group with accurate composition are linked [84–86], as shown in Figure 12. There are also possibilities for considering organic molecules with various chemical groups and spatial arrangements. Typically, unsaturated bonds in the acyl chains can be mimicked, at first approximation, by forcing a gauche kink in the chain. This way of dealing with lipid unsaturation is, of course, much more approximate than can be done in MD or in MC simulations. 4.3.2

Water

A relevant model of self-assembly of hydrocarbon-based surfactants in aqueous solutions should pay sufficient attention to water. Detailed attention has been given to water in MD simulations [31,36], but much less effort has been spent on water in a realistic SCF model. In many SCF treatments of lipid bilayer systems, the chains are end-grafted on to a surface, and the interaction with water is considered to be so strong that excursions into the water phase are excluded [87–91]. At this limit, the water phase is (almost) completely eliminated from the problem. In this review, we will concentrate on SCF models that include water in the model. Up to very recently, even the most detailed SCF models featured a simplistic water model. Typically, water was a spherical monomer that strongly repelled hydrocarbon segments. The membranes resulting from such a model show large amounts of water in the core. Typically, in the order of 5% of the volume in the core was occupied by water [86]. This value is several orders of magnitude too high. A reasonable model that tackles this problem will be discussed next. The most important aspect of water that should be accounted for in this context is that water and hydrocarbons strongly unmix. In practice, this can be attributed to the strong associative nature of water molecules. This is the rationale of using a model that accounts for lateral (in a lattice layer) association of water monomers forming dimers, trimers, etc. It is assumed that water clusters are in equilibrium with each other, according to the reaction: XN þ X Ð XNþ1 , where X is the concentration of water monomers, and the subscript indicates the cluster size. In fact, each cluster of N-water molecules is given only one amount of entropy of mixing, irrespective of the size of the cluster. The total water density can easily be expressed in terms of the reaction

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

constant K and the concentration of water monomers, if it is assumed that K does not depend on N. A natural consequence worth mentioning is that the cluster size distribution depends very strongly on the local water concentration. We consider a system with K >> 1. At positions where the water density is low (i.e. in the centre of the bilayer), one can have only free monomers, and large clusters do not exist. On the other hand, in the aqueous phase where the water density is high, almost all water molecules are incorporated in (large) clusters. As a consequence, the free monomer density in the bulk remains very low. Of course, the free monomers in the aqueous bulk are in equilibrium with the free monomers in the bilayer in the same way as in the classical model. The larger clusters prefer the bulk and avoid the membrane core. A typical value of K ¼ 100 is sufficient to remove most of the water from the membrane interior. One can argue that the value of K should be related to the strength of an H-bond in water. Then, a much larger K value should be appropriate. However, this is not implemented for computational reasons. 4.3.3

Ions

In biologically relevant systems, the ionic strength is not extremely low, and the charges in the head-group region are largely screened. The screening by positively or negatively charged ions influences the conformational properties of the ionic head groups and, to a lesser extent, that of zwitterionic head groups. The Gouy–Chapman theory [3] describes the distribution of ions near a charged interface. The classical Gouy–Chapman theory, including a Stern-layer, cannot account for relevant features such as penetration of ions in the head-group region, but it gives the distribution of ions in the immediate surroundings of the bilayers. The self-consistent-field model as elaborated on below may be viewed as an extremely sophisticated Gouy–Chapman model. On top of the use of the Poisson–Boltzmann equation for the charged groups, it has the chain statistics and volume constraint effect (e.g. the Stern concept) included automatically. 4.3.4

Free Volume and the Pressure

One usually distinguishes two types of lattice models. The first type may be called lattice-gas models. In this case, the number of molecules in the system is less than the number of available sites. In other words, there are vacant sites. The second type of lattice models may be called lattice fluids. In this case, all lattice sites are filled exactly by the molecular components in the system; the system is considered to be incompressible. It is easily shown that a two-component incompressible lattice–fluid model can be mapped on a one-component lattice gas one. In other words, it is possible to interpret vacant sites to be occupied by a ‘ghost’

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particle. The chemical potentials in the lattice fluids and the chemical potential and pressure in the lattice–gas model can be related to each other. This can be generalised to more components in the system. Below we will see that a sufficiently general model for the lipid bilayer system should account for some free volume (unoccupied lattice sites) in the bilayer core. If this is not done, then the lipid bilayer system will change spontaneously into the gel phase (at all reasonable temperatures). The choice of lattice-gas versus lattice-fluid models also has consequences for the natural choice of the type of parameters used. Let us consider the squarewell potential as an example. In a lattice-gas model where only one type of molecules, A, exists, there is only one relevant parameter accounting for the particle–particle contacts, i.e. UAA . Neither the interaction energy of a particle with a vacant site, nor the interaction between vacant sites, will contribute to the total energy in the system. In a lattice-fluid system there are two molecular species, A and B. As a consequence, there are UAA , UAB and UBB contact energies. However, the total number of contacts in the system is fixed, because all lattice sites are exactly occupied. It can be shown that in this system one can use Archimedes-like parameters. These parameters, known as the Flory– Huggins (FH) interaction parameters, combine the three energies mentioned above. For convenience, the FH parameter is normalised by the thermal energy kT, and, for technical reasons, it is multiplied by the lattice coordinationZ number Z: wAB ¼ 2kT ½2UAB
UAA
UBB . The reference is the UAA and the UBB contact energies, and therefore the wAA and wBB quantities have a numerical value of zero. A positive w-value means that A and B repel each other. In fact, the difference between the lattice-gas and lattice-fluid parameters is a difference of reference energy only. When, for example, the B-units are interpreted as vacant sites, we have UAB ¼ UBB ¼ 0 and wAB ¼
ZUAA =(2kT). We note that a particular choice for the reference energy is inconsequential for the properties of the system under consideration, and the set of wAB can always be converted into the appropriate U parameters. For historical reasons, the incompressible lattice-fluid system description is used, even if the distribution of one of the components is coupled to the distribution of vacant sites. Constant ‘pressure’ SCF calculations are the same as constant chemical potential calculations for the vacant sites. These conditions are used below. 4.4

THE SEGMENT POTENTIALS

Unless one is willing to become involved in many intricacies, a lattice model with united atoms (segments) features segments which are all of equal size. The price we have to pay for this is that there is no unique way to convert from lattice units to real space coordinates. We will discuss this point in the ‘Result’ sections in more detail.

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In a lattice model, the only way to discriminate between various segment types is by assigning to each segment type a unique set of interactions, e.g. of the nearest-neighbour type parameterised by Flory–Huggins parameters, or of electrostatic origin influenced by the charge and polarisability of the various fragments of the molecule. These segment-type dependent interactions lead to segment-type dependent potentials. Typically, the segment potentials are used in Boltzmann-like weighting factors which influence the molecular distributions. Without going into too much detail, we can note the segment potentials are composed of four terms. For a unit of type A they are given by: uA (z) ¼ u0 (z) þ
A ec(z)   X 1 1 þ kT wAB ½jB (z
1) þ jB (z) þ jB (z þ 1)
jbB
"rA E(z)2 3 2 B (9) The first term is a contribution to the segment potential that does not depend on the segment type. The value of this term is chosen such that the predicted density of molecules in the system is consistent with the incompressibility constraint: X

jx (z) ¼ 1

(10)

x

which applies in each layer z. The second term in equation (9) is the usual electrostatic term. Here vA is the valency of the unit and e is the elementary charge, and c(z) is the electrostatic potential. This second term is the well-known contribution accounted for in the classical Poisson–Boltzmann (Gouy–Chapman) equation that describes the electric double layer. The electrostatic potential can be computed from the charge distribution, as explained below. The third term is the one that accounts for the short-range nearest-neighbour contact energies, parameterised by the Flory–Huggins parameter introduced above. The summation is over all segment types in the system. Here the approach is used that nearest-neighbour contacts can be made with segments that reside in the same – or in one of the adjacent – layers. This implies an a priori weighting of contacts of l1 ¼ 1=3. We note that we here assume that the lattice cell is not isotropic, i.e. the size in the x and y direction is not the same as the size in the z-direction. We will discuss this below. The volume fraction jB (z) is equal to the probability of finding a segment of type B in layer z. The quantity jbB is the probability of finding this segment type in the homogeneous bulk with whichPthe system is in equilibrium. In the bulk all densities add up to unity as well: x jbx ¼ 1.

F. A. M. LEERMAKERS AND J. M. KLEIJN

59

The fourth term is a polarisation term. Here E(z) ¼
qc=qz is the electric field at position z. In previously published SCF results for charged bilayers, this last term is typically absent. It can be shown that the polarisation term is necessary to obtain accurate thermodynamic data. We note that all qualitative results of previous calculations remain valid and that, for example, properties such as the equilibrium membrane thickness are not affected significantly. The polarisation term represents relatively straightforward physics. If a (united) atom with a finite polarisability of "rA is introduced from the bulk where the potential is zero to the coordinate z where a finite electric field exists, it will be polarised. The dipole that forms is proportional to the electric field and the relative dielectric permittivity of the (united) atom. The energy gain due to this is also proportional to the electric field, hence this term is proportional to the square of the electric field. The polarisation of the molecule also has an entropic consequence. It can be shown that the free energy effect for the polarisation, which should be included in the segment potential, is just half this value –12 "rA E 2 . If for each segment in the system the proper segment potential (according to equation (9)) is computed, one can evaluate easily the overall potential energy in the system. This result is comparable with the first two terms of equation (6) for MD. As discussed above, the bond length is fixed and the RIS scheme is used to control the chain flexibility. For a particular conformation c of a molecule, the positions of all (united) atoms in space as well as the chain conformers are known. The potential energy of this conformation is therefore just the sum of the contributions, as given by equation (9) for all the united atoms and a particular energy quantity per gauche bond in the chain. The statistical weight for this conformation is proportional to the Boltzmann factor containing this segment potential: c

Pci / e
ui =kT

(11)

The next step is to generate all possible  and allowed conformations, which leads to the full probability distribution Pci . The normalisation of this distribution gives the number of molecules of type i in conformation c, and from this it is trivial to extract the volume fraction profiles for all the molecules in the system. With these density distributions, one can subsequently compute the distribution of charges in the system. The charges should be consistent with the electrostatic potentials, according to the Poisson equation: q"(z)E(z) ¼ q(z) qz

(12)

where "(z) is the local dielectric constant that is dependent on the local composition. From equation (12), the electrostatic potential is extracted, and, together

60

PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

with the density profile information, equation (12) is recomputed. What follows has been explained above. The potentials and the densities should be consistent with each other, and these solutions are found routinely by computer. Of course, such a solution should also obey the compressibility conditions. The formalism sketched above has been used in the literature in more or less the same detail by many authors [87–92]. The predicted membrane structure that follows from this strategy has one essential problem: the main gel-to-liquid phase transition known to occur in lipid membranes is not recovered. It is interesting to note that one of the first computer models of the bilayer membrane by Marcˇelja [93] did feature a first-order phase transition. This author included nematic-like interactions between the acyl tail, similar to that used in liquid crystals. This approach was abandoned for modelling membranes in later studies, because this transition was (unfortunately) lost when the molecules were described in more detail [87]. The reason for the failure of such an SCF model to predict a gel-to-liquid phase transition is known. The coupling of the single-chain behaviour to the external field is insufficient to induce some cooperative phenomenon necessary for this transition to occur. In the Marcˇelja approach, this coupling was made through a Mayer–Saupe (thermotropic) potential. In this case, the interaction energy is made more attractive for the tails when they are aligned normal to the membrane than when they do not line up. This is reasonable for the molecule as a whole, as may be judged from conformational phase transitions that take place in polymer brushes in the presence of Mayer–Saupe interactions [94], but the ordering efficiency becomes too weak when it is applied on the CH2
CH2 level. It can be shown that in order to recover a cooperative gel-to-liquid phase transition, one should include conformational entropy effects (lyotropic effects). Indeed, it was shown that anisotropic lateral interactions are not necessary for the transition. The solution for the problem was found by introducing weighting factors for placing the bonds of the molecule in the system. It may be of interest to qualitatively explain the origin of the effect. In the derivation of the mean-field partition function, it is necessary to know the probability for inserting a chain molecule in a given conformation into the system. The classical way to compute this quantity is by approximating it by a product of the local volume fractions of an unoccupied site (averaged over lattice layers). It was realised that, besides the density information, information on the bond distributions is also available. The bond distribution gives information on the average local order. Using this information, it becomes possible to more accurately access the vacancy probability. For example, if many chains are perfectly aligned, e.g. in the z-direction, the probability of the test chain also placing its segments in the z-direction becomes strongly enhanced. The oriented molecules leave an open corridor in the direction of the director. In terms of the vacancy probability, it is an event that it is enhanced with respect to the classical mean-field prediction. As a result, the test

F. A. M. LEERMAKERS AND J. M. KLEIJN

61

molecule is likely to follow the average orientation of its neighbours. For very densely packed chains, this effect may introduce a cooperative phase transition. The SCF theory that accounts for the anisotropic placing of segment bonds is called SCAF (self-consistent anisotropic field) theory [95]. It is now realised that in a SCAF analysis the chain statistics are done in a quasi-chemical approximation (on a pair-level). Typically, the interactions are still implemented on the Bragg–Williams level, as outlined above (but this is not a matter of principle). Theories that combine the SCAF approach (lyotropic effects) with anisotropic Mayer–Saupe (thermotropic) interactions do not exist. Such a model in combination with a realistic model for water (based upon the quasi-chemical approximation), may well become a next generation of SCF modelling. 4.5

THE SCF SOLUTION

In practice, the scheme as explained above is not implemented. The consecutive generation of all possible chain conformations is a very expensive step. The reason for this is that there are of the order of Z N number of conformations, where Z is the lattice coordination number. A clever trick is to generate a subset of all possible conformations and to use this set in the SCF scheme. This approach is known in the literature as the single-chain mean-field theory, and has found many applications in surfactant and polymeric systems [96]. The important property of these calculations is that intramolecular excludedvolume correlations are rather accurately accounted for. The intermolecular excluded-volume correlations are of course treated on the mean-field level. The CPU time scales with the size of the set of conformations used. One of the obvious problems of this method is that one should make sure that the relevant conformations are included in the set. Typically, the set of conformations is very large, and, as a consequence, the method remains extremely CPU intensive. There exists a less-dangerous method which has the additional advantage that it is computationally extremely cheap. In an RIS scheme, it suffices to know the exact positions of four consecutive segments. Ignoring any longerrange correlations along the chain allows the use of a Markov scheme to generate conformations. In this scheme the combined statistical weight of the full set of conformations is evaluated using a computation time that is linearly proportional to the number of segments in the molecule. This trick is the basis for the huge gain in CPU time. Again, the MC simulations have indicated that such a Markov process is legitimate. The SCF solution, i.e. the condition that the segment densities and the segment potentials are consistent with each other, is found for a canonical ensemble. This means that the number of molecules of each molecule type is fixed. As explained above, membranes should be modelled in a (N, p, g, T), i.e.

62

PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

in a fixed surface tension (g ¼ 0) and fixed pressure ensemble. Both the pressure and the surface tension can be evaluated as a function of the composition, that is, the number of lipid molecules per unit area in the system. Typically, an extra iteration of the composition is needed to evolve to an equilibrium tension-free membrane. Unless otherwise mentioned, we will present results for membranes that are free of tension. With respect to SCF models that focus on the tail properties only (typically densely packed layers of end-grafted chains), the molecularly realistic SCF model exemplified in this review needs many interaction parameters. These parameters are necessary to obtain colloid-chemically stable free-floating bilayers. A historical note of interest is that it was only after the first SCF results [92] showed that it was not necessary to graft the lipid tails to a plane, that MD simulations with head-and-tail properties were performed. In the early MD simulations (i.e. before 1983) the chains were grafted (by a spring) to a plane; it was believed that without the grafting constraints the molecules would diffuse away and the membrane would disintegrate. Of course, the MD simulations that include the full head-and-tails problem feature many more interactions than the early ones. The set of parameters, i.e. the force-field parameters used in the SCF calculations, are listed in Table 1. We will not discuss all of them. The most important one is the repulsion between water and hydrocarbon. The value of this FH parameter is set to wH2 O, C ¼ 0:8. One should remember however that in Table 1. Parameters used in (most of) the SCF calculations as presented in this chapter H2 O

V

C

CH3

N

P

O

Na

Cl

"r


80 0

1 0

2 0

2 0

10 1

10 –0.2

10 0

10 1

10 –1

w

H2 O

V

C

CH3

N

P

O

Na

Cl

0 2.5 0.8 0.8 0 0.5 0 0 0

2.5 0 2 1 2.5 2.5 2.5 2.5 2.5

0.8 2 0 0.5 2.6 2.6 2 2.6 2.6

0.8 1 0.5 0 2.6 2.6 2 2.6 2.6

0 2.5 2.6 2.6 0 0 0 0 0

0.5 2.5 2.6 2.6 0 0 0 0 0

0 2.5 2 2 0 0 0 0 0

0 2.5 2.6 2.6 0 0 0 0 0

0 2.5 2.6 2.6 0 0 0 0 0

H2 O V C CH3 N P O Na Cl

In the first row the relative dielectric constant for the compound is given. In the second row the valency of the unit is given. The other rows give the values for the various FH parameters. Remaining parameters: the characteristic size of a lattice site 0.3 nm; the equilibrium constant for water association: K ¼ 100; the energy difference for a local gauche conformation with respect to a local trans energy: DU tg ¼ 0:8 kT; the volume fraction in the bulk (pressure control) of free volume was fixed to jbV ¼ 0:042575

F. A. M. LEERMAKERS AND J. M. KLEIJN

63

the calculations the water–cluster approximation has been implemented. Consistent with this model is a fairly low repulsion between water and hydrocarbon. The parameter has been chosen in order to find the predicted critical micellisation concentrations for surfactants that match experimental ones [97]. In Table 1, the interaction parameters of the unoccupied sites V with the real segments in the system are all positive and relatively high. Again, the reason for having interaction parameters for these ‘contacts’ originates from the Archimedes-like FH parameters. The effect of the relatively high values is that the vapour phase is a bad solvent for all components in the system. The parameters shown in Table 1 must still be considered preliminary. For example, several interactions between two polar compounds are assigned the athermal w ¼ 0 value. This ideal value is chosen in order to keep the set as simple as possible. We also kept the system exactly symmetrical with respect to the interactions of the Na and Cl ions. Again this is a simplification of the real system. One undoubtedly has an asymmetry with respect to the interaction with the hydrophobic core for these two ions. This in itself will generate an electrostatic potential at the membrane–water interface. These ion-specific effects may be studied systematically and are relevant for permeation and transport phenomena. 4.6

PHOSPHATIDYLCHOLINE BILAYERS

A selection of the predictions of the equilibrium structure of DPPC bilayers as found by numerical self-consistent-field calculations is given in the following figures. In a series of articles, the SCF predictions for such membranes were published, starting in the late 1980s. As discussed above, we will update these early predictions for the theory outlined above with updated parameter sets. The calculations are very inexpensive with respect to the CPU time, and thus variations of the parameter-set will also provide deeper insight into the various subtle balances that eventually determine the bilayer structure – the mechanical properties as well as the thermodynamic properties. The saturated PC molecule differs (apart from the length of the tails) from the SOPC molecule depicted in Figure 12 only with respect to the double bond, which is replaced by a single one. In this figure, each unit that is included in the SCF model is drawn. The corresponding parameters are collected in Table 1. From this it is clear that a united atom approach is implemented. This means that the protons are not explicitly included. Note that, in contrast to the recent work of Meijer [84–86], the end groups of the acyl chains now have double the volume as compared with CH2 groups. This is realised by a branching point at the CH2 group on the last but one position in the chain. Furthermore, the CH3 group is given some small repulsion with the CH2 groups to specify that these units differ significantly. The overall density profiles across the DMPC bilayer are given in Figure 13 (see also refs. [84–86,92,95,98]). Together with these profiles, the water-density

64

PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES NC 3

+

PO 4

–

C=C 9 10

5

i ii

1

iii

1

sn2 sn1 10

5

15

Figure 12. A typical example of the level of detail used to represent molecules in the SCF calculations: sn1-stearoyl-2-oleoyl-phosphatidylcholine. The open squares are the CH2 groups, the light grey squares on the end of the tails represent the CH3 groups. The C C unsaturation (cis and on position 9) along the acyl chain is indicated. The mid-grey w squares represent oxygen. The darkest grey square is the phosphate. The nitrogen atom as well as the three surrounding carbons in the choline group (CH3 ) are striped. The numbering of the carbons along the sn1 and sn2 tail (1–18) and the carbons in the glycerol backbone (i, ii, iii) are indicated. The positive charge is located at the nitrogen, and the negative charge is distributed over the five units of the phosphate group

Water

DMPC 0.8

j Head

0.4

CH3 0 −20

−10

0 z

Free volume 10

20

Figure 13. The overall density (volume fraction) profile for DMPC bilayers is shown here. Apart from the distribution of the overall DMPC molecules, the density distribution of the head-group units (including the choline group, the phosphate group and the oxygens of the glycerol unit), and the end groups of the lipid tails are also indicated. In addition, the free-volume profile and the water profile are depicted

profile is given. In line with data from the MD simulations, the SCF method predicts that the water molecules only penetrate into the head-group region, and that the water density in the core is reached already in the region of the glycerol backbone. In the model there is also a component which is interpreted as free volume. The parameters were chosen such that the amount of free volume in the core of the bilayer is slightly higher than in the water phase. The free volume density in water is fixed to the equilibrium value found for the water–vapour coexistence calculations: jbv ¼ 0:042575. This value was fixed, which implies, from a lattice-gas perspective, that the pressure was fixed to some reference value, i.e. p ¼ 1.

F. A. M. LEERMAKERS AND J. M. KLEIJN

65

In the interfacial region between the hydrophobic core and the water phase, there is always a small increase in free volume. The increase is not particularly large, and we are not aware of attempts in MD simulations to measure this small drop in local density. As can be seen from Figure 13 the distribution of head groups is almost as wide as the width of the hydrophobic core. On the one hand, this is because we have collected several head-group units in this overall head-group distribution. On the other hand, there are a number of protrusion fluctuations that are automatically ‘excited’ in the computations. The end groups of the hydrocarbon tails are depicted separately in Figure 13. In line with data from MD simulations, we see a significant spread of the end groups throughout the core. This means that there are considerable fluctuations in conformations of the tails. The atom density dip, as found above in the MD simulation, correlates with the distribution profile of the CH3 units. In reality, the CH3 groups are rather voluminous, and thus conversion of the MD data to volume fractions, or the SCF data to atom densities, leads to the conclusion that the SCF results are at least qualitatively consistent with the MD predictions. The membrane thickness can be defined in many ways. The z-axis is in units of a lattice-cell dimension. As can be seen, the thickness is 20 to 30 lattice units. In principle, the size of a lattice unit can still be chosen. When this value is scaled to the size of a water molecule, i.e. 0.3 nm, a bilayer thickness of the order of 6 nm is obtained. However, a C–C bond in the hydrocarbon chain is significantly shorter, and taking this (i.e. 0.15 nm) as a measure for the lattice size, a P–P distance of approximately 20 lattice units corresponds with a size of order 3 nm. Of course some average is more appropriate. To dissolve the conversion problem from lattice units to real space coordinates it is necessary to compare the results to accurate simulations or experiments. Comparison of MD results, for example as presented in Figure 5, and the SCF result shown in Figure 13 suggests that a more accurate scaling of the size of a lattice site should be around d ¼ 0:2 nm. This value is indeed between the size of a water molecule and that of a C–C bond. We will use this value below to convert from lattice units to real coordinates. Using this value, the bilayer thickness given by the cross-membrane P–P distance for the membrane given in Figure 13 is approximately 4 nm. A more detailed investigation of the DMPC bilayer is given in Figure 14. In this figure, the distributions are split up into two groups, depending on which side the choline group of the lipid is positioned. In this way it is possible to illustrate how much the chains from opposite monolayers interact with each other. The average position of the CH3 groups of the chains is approximately at the centre of the bilayer, albeit that the end groups belonging to chains that have the head group on the positive side have a positive average position. Surprisingly, however, the maximum in the end-point distribution is positioned slightly on the opposite side.

66

PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

CH2

0.6 j

0.4

0.2 CH3

P 0 −20

−10

0 z

N 10

20

Figure 14. Volume-fraction profiles of parts of the DMPC molecules for lipids that have the head group at positive coordinates (continuous lines) and at negative coordinates (dashed lines). The centre of the bilayer is positioned at z ¼ 0. The phosphate group, the nitrogen of the choline group and the CH3 groups of the tail ends, as well as the other hydrocarbon units, are indicated

Now we can discuss the interdigitation issue in more depth. The key point is that there is undoubtedly some interdigitation, but that this remains relatively limited. The two monolayers are thus not completely independent. A limited interpenetration should also be expected from entropic considerations. Below we will see that the chain ends are not particularly highly ordered. Thus the chains do not have a clear memory as to which side of the bilayer they ‘belong’. In previous SCF calculations, the interpenetration is likely to have been overestimated. This is because the interpenetration is sensitive to the detailed properties of the CH3 groups. These groups have a larger volume and are expected to be more hydrophobic than CH2 groups. These properties are represented in the parameter set discussed above (and not present in previous ones). The quantitative results depend to some extent on the details of the parameter set. However, it is virtually impossible to completely remove all the overlap between opposing monolayers. This is of course an important observation for the ability of the bilayer to absorb additives in the core. We will return to this issue below. The orientation of the head group can also be deduced from Figure 14. In line with results published in SCF results of Meijer et al. [85], and also in line with all MD simulations of PC layers, the head group is laying flat. This flat orientation is very much promoted by the zwitterionic nature of the head group. The acyl groups connected to the nitrogen group may even push the choline group towards the membrane core. However, entropically it is expected that the end group can be positioned more freely and thus will have a wider distribution. For this reason, the choline group can be found on both sides of

F. A. M. LEERMAKERS AND J. M. KLEIJN

y

67

0.05

0.006

0.025

0.003

0

0

−0.025

−0.05 −30

q

−0.003

−20

−10

−0.006 0 z

10

20

30

Figure 15. The electrostatic potential (V) profile (dashed line; left ordinate) and the overall charge (in units of elementary charges) profile (continuous line; right ordinate) across the DMPC bilayer, as found by SCF calculations

the phosphate group. Meijer [84] has shown that with increasing ionic strength the bimodal character of the N profile becomes more pronounced. This result is also in accordance with experimental observations. It has been reported that in PC crystals both conformations of the head group are present [99]. The charge distribution and the electrostatic potential profile across the DMPC bilayer are much more complex that one would intuitively expect. The electrostatic potential profile is presented in Figure 15. It is slightly positive on the outer side of the bilayer as well as in the membrane core. A region with negative electrostatic potential is found at the position of the phosphate group. The electrostatic potential profile must be zero throughout the bilayer, as long as the phosphate and the choline group have identical z-positions. These identical positions do not occur, and thus there is a potential profile and a charge distribution which remains finite, albeit that the local charge density as well as electrostatic potentials are small. The differences between the electrostatic potential profiles as found by SCF calculations and that of MD simulations (cf. Figure 7) are large. First of all, there is a huge difference in absolute value. Furthermore, the SCF results are more detailed. It is instructive to discuss these disparities. For this we need to return to the force fields used in both methods. In MD, many segments have partial charges, and therefore they all contribute to the electrostatic potential. In SCF, these partial charges only occur on the groups which carry an effective charge. All the other contributions are ‘hidden’ in the Flory–Huggins parameters and the local dielectric permittivities, and as such do not show up in the charge distribution and the mean-field electrostatic potential. For this reason, it is not a surprise that the two methods give different results. Perhaps it remains worthwhile to note that both methods indicate that the electrostatic potential in

68

PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 0.0015 j

Cl 0.001 Na

0.0005

0 −30

Figure 16.

−20

−10

0 z

10

20

30

The distribution of the ions across the DMPC bilayer

the core is positive with respect to that in the water phase, in accordance with experimental data. The distributions of the ions (Na and Cl) follow the electrostatic potential profile accordingly, as is seen from Figure 16. Of course the ions have a strong preference for the aqueous phase. Nevertheless, they have to partition inside the membrane to some extent. Because the electrostatic potential is positive inside, the negative ions have a small preference for the membrane interior over the positive ions. It should be noted that this preference is solely the result of the electrostatic potential, because the size and the nonelectrostatic interactions were chosen to be identical for the two ions. A more realistic model can discriminate between the ions with respect to the intrinsic affinities for oil and water, respectively. The electrostatic potential profile in the water phase is of course well understood, and follows exactly the Gouy–Chapman theory [3]. For sufficiently low electrostatic potentials (smaller than 25 mV), there is an pffiffiffiffi exponential decay with a decay length given by the Debye length kD  3= js where js is the volume fraction of ions that is proportional to the concentration of ions. The order parameter is directly available from the calculations and the SCF results are given in Figure 17. The absolute values of the order parameter are a strong function of head-group area. Unlike in most SCF models, we do not use this as an input value; it comes out as a result of the calculations. As such, it is somewhat of a function of the parameter choice. The qualitative trends of how the order distributes along the contour of the tails are rather more generic, i.e. independent of the exact values of the interaction parameters. The result in Figure 17 is consistent with the simulation results, as well as with the available experimental data. The order drops off to a low value at the very end of the tails. There is a semi-plateau in the order parameter for positions t ¼ 6
14,

F. A. M. LEERMAKERS AND J. M. KLEIJN 0.4

69

sn2

S

sn1 0.3

0.2

0.1

0 0

2

4

6

8 t

10

12

14

16

Figure 17. Order parameter profile for the two tails of DMPC bilayers. The chain closest to the head group is named sn1 and the other one sn2. Segments closest to the glycerol backbone are numbered t ¼ 1, and the chain ends are t ¼ 16. The lines are drawn to guide the eye

and there is a maximum in the order parameter at chain segments near the glycerol backbone. Together with the known positions of the chain segments and the order along the chain, we can deduce that the central region in the bilayer is slightly more disordered than the outer part of the core. Such a result is relevant for the mechanism of incorporation of foreign objects in the bilayer. The two chains in the lipid bilayer are not identical, because they are positioned asymmetrically with respect to the PC head. It turns out that the tail closest to the head group is buried less deep in the bilayer than the other chain [98]. The difference is not very large; it amounts to about half a segment size. From this difference, we can rationalise the disparities in order between the two tails. The chain that is pulled out will be stretched most, and the order tends to be higher than the other chain. Below we will see that the differences in the behaviour of the tails can become larger if there are differences between the tails, e.g. with respect to the degree of unsaturation. 4.7

THE LATERAL PRESSURE PROFILE

Recently, the lateral pressure profile in a bilayer has been discussed in the context of partitioning of proteins in bilayers [100]. It is argued that this pressure profile can be used to rationalise the effects of additives on the membrane properties. Here a note of caution is necessary. It is not possible to define the lateral pressure profile through a bilayer unambiguously. The reason for this problem is that the local pressure not only has contributions that come from the local densities (this property is uniquely defined), but also from

70

PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

interaction between molecules. As molecules typically do not occupy the same coordinate, the method of keeping track of binary, tertiary, etc., interactions becomes somewhat arbitrary. All choices that one can make to do this are equally good. For example, all results of thermodynamic observables that result from moments over the lateral pressure profile and moments over the derivatives of the lateral pressure profile, such as the surface tension and the mechanical parameters of the bilayer, can be shown to be independent of this choice [16,101]. The fact that the lateral pressure profile is ill defined indicates that this property is not a useful one to be monitored or to be discussed in the context of partitioning of additives in membranes. For this reason, we will neither discuss the lateral pressure profile further, nor give an example of the lateral pressure profiles. For one and the same membrane we can generate many strongly varying lateral pressure profiles [16,101]. 4.8

COMPARISON OF SCF AND MD FOR SOPC MEMBRANES

In biological membranes, the class of fully saturated PC lipids is just one of many. Indeed, variations in the lipid architecture are frequently encountered. There are variations with respect to the head-group structure as well as variations in the tail architecture. For example, in the tails, single or multiple unsaturated bonds are very common. There is relatively little knowledge about the role of lipid unsaturation in biomembranes. There are relatively few MD simulations on bilayers composed of lipids with unsaturated bonds. Nevertheless, single unsaturation as well as multiple unsaturated chains have been of some interest. For a recent review see reference [102]. We will now present a selection of the results. We will also take this opportunity to compare the results from the MD simulations with those from the SCF calculations. In Figure 1 we showed a snapshot of a typical MD result for a membrane composed of lipids of the type 1-stearoyl-2-docosahexaenoyl-sn-glycero-3phosphatidylcholine, which has six unsaturated bonds. From a snapshot, it is not possible to understand the role of unsaturation in any detail. However, the averaged density profiles are more informative. In Figure 18, various profiles as found by SCF modelling are compared with corresponding MD results for SOPC bilayers in the hydrated state (see also reference [103]). Before this figure can be discussed, one should realise that in MD simulations the results are typically presented in terms of the density in g cm
3 versus the distance from the centre of the bilayer in nm units. The SCF results are available in terms of dimensionless densities (volume fractions) and the dimensionless distance to the centre of the bilayer (i.e. in lattice units). Implementing the above suggested conversion of 0.2 nm leads to a good match in membrane thickness. The problems with the conversion of volume fractions to densities are not easily resolved, and therefore we need to concentrate on the shape of the distributions and not on the heights of the distributions.

(a)

F. A. 1M. LEERMAKERS AND J. M. KLEIJN Tails

(b)

0.8

1.2

Water

1

0.6

0.8

0.4

Head

r/g cm−3

j

71

Water

Gly 0.2

CH3 V

Tails 0.6

Head

0.4

Gly 0.2

0.015

0.2

Na

0.01

Cl

0.005

r/g cm−3

j

0 P

0.075

j

P

0.1

0.05 N

0.025 −20

−15

−10

−5

0

z

5

10

15

N

0 20

0

−4

−3

−2

−1

0

1

2

3

4

z /nm

Figure 18. Molecular modelling results for hydrated bilayers of 1-stearoyl-2-oleoyl-snglycero-3-phosphatidylcholine PC (SOPC). (a) SCF results. The volume fraction profiles for tails, head group, glycerol backbone, CH3 end-groups and water (top panel), Na and Cl (middle panel) and the P and N atoms of the head group (bottom panel) are presented. Note that the volume fractions are dimensionless densities and that the z coordinate is made dimensionless by the lattice spacing. (b) MD results. Mass density distributions, g cm
3, for the tails, head-group segments, glycerol backbone units and water (top panel), the P and N atoms (bottom panel). In the MD simulation systems there were 48 times two lipids per cell, 24 H2 O molecules per lipid, and altogether there were 20 544 (SOPC) atoms. Mean cross-sectional area per lipid molecule was 0.6624 nm2. The MD trajectories of 1018 ps were computed at T ¼ 303 K. The zero point (z ¼ 0) is the centre of the bilayer: it was calculated during the MD simulations as the middle point between the centres of P–N vectors of the two monolayers (the centre of the P–N vector is the middle of P–N distance). The ratio between the CPU times (MD/SCF) needed to obtain these results is in the order of 105

First of all it is seen that the SCF results are free of any noise, whereas there is plenty of noise in the MD profiles (note, however, that the density profiles on both halves of the bilayer are in this case not averaged; the close resemblance between the profiles on both halves thus indicates that the membranes are well equilibrated). Apart from this, inspection of Figure 18 shows a remarkable resemblance between the two set of predictions. Many details are in semiquantitative agreement. Moreover, many of the features of membranes composed of SOPC resemble those of DMPC discussed above. For example, the width of the membrane–water interface is about 1 nm, i.e. the size of just two to three water molecules. This width is consistent with the scaling arguments mentioned at the beginning of this chapter. A more accurate comparison

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

between the SCF and MD results shows that even the shapes of the head-group profiles match accurately and the distributions of the P and N atoms have the same features. The fact that these two distributions are strongly overlapping means that the PC head group is roughly oriented parallel to the membrane surface, as is the case for DMPC. Of course there are differences. For example, in the SCF calculations a 1:1 electrolyte solution was used, whereas in the MD simulations no salt ions were added. We note that the densities of the two ions, as shown in Figure 18a, are almost the same in the centre of the bilayer. This means that in this case the electrostatic potential in the centre of the bilayer is virtually zero. Other features of the ion profiles are the same as in Figure 16 for DMPC. The noted difference is not attributed to a fundamental difference between DMPC and SOPC bilayers. The difference is caused by the fact that the ionic strength used in the SOPC system (Figure 18a) is 10 times higher than in the DMPC system (Figure 16). The higher ionic strength leads to a more efficient screening of the electrostatic potential. A minor effect already noticed by Meijer and co-workers [84] is that the head-group properties slightly depend on the ionic strength, even in the case of a zwitterionic head group. From the density profiles one cannot really judge the effect of the double bonds; the density profiles for membranes of saturated lipids are very similar to those of unsaturated ones. Therefore it is necessary to consider some of the conformational characteristics of the tails. It is possible to compute the order parameter profile for both the saturated and the unsaturated chains. The order parameter profile for the saturated chain closely follows the results presented in Figure 17 for DMPC membranes for both the SCF and the MD predictions. The order parameter profiles for the unsaturated chain closely follows the MC predictions, as discussed in Figure 9. A pronounced dip is found near the cis double bond. For this reason, we choose here to present complementary data about the conformational properties of the acyl chains. In Figure 19 the root-mean-square positions (fluctuations) of all segments of both tails as a function of the average positions are shown for both modelling techniques. These results are significantly more informative than order parameter profiles. From Figure 19 it is easily seen that towards the tail end the fluctuations increase and that the segments close to the glycerol backbone have the sharpest distributions. The average positions of the first segments of the two tails differ slightly; the sn1 tail is (similarly to in DPPC bilayers) buried slightly deeper in the bilayer than the sn2 tail, as can be judged from the hzi positions of the first segments. In lipid bilayers with saturated tails, the two tails differ only with respect to this small shift. However, in SOPC the unsaturated chain is buried significantly less deep in the bilayer than the saturated one; the unsaturated chain behaves effectively as a shorter chain [104]. The fluctuations tend to increase relatively fast for the free chain ends, especially for the unsaturated tail, i.e. left of the arrow (which indicates the position of the double bond) in Figure 19. The fact that the average end position (CH3 groups) of the saturated

F. A. M. LEERMAKERS AND J. M. KLEIJN

73

5 1.4

(a)

(b)

18 18

4

18

18

RMSZ /nm

RMSZ

1.2 18:1

3 18:0

18:0

1 2

1

18:1

2

2 2

1

0.8 2 1

1

1 0

2

4



6

8

0.6 0

0.5

1

1.5

2

< z >/nm

Figure 19. The root-mean-square (RMS) position of each segment of both acyl chains of SOPC lipids is plotted as a function of the average position of the segment. The sn1 tail is given by the closed symbols, and the sn2 tail is given by the open symbols. Various numbers of the tail segments and of the backbone segments are indicated. The lines are drawn to guide the eye. The arrow points to the position of the unsaturated bond. (a) SCF results (conversion from dimensionless units to real units is approximately a factor of 0.2 nm), (b) MD results (the average over the sides of the bilayer is taken)

tail is near the centre of the bilayer, and because the fluctuations are large, it is again true that there is a significant interdigitation between tails of opposite monolayers. The interpenetration is significantly less for the unsaturated chain. In both the SCF calculations, as well as for the MD results, the two curves in Figure 19 cross each other. The local growth of the fluctuations at the position of the double bond and suppression of fluctuations just around the double bond are both very characteristic of a cis double bond. Similar results are also discussed in some depth in a paper where statistical mechanical calculations are compared with corresponding MD simulations [105]. The mean-field model that is used in the latter study is one where chains of equimolar amounts of saturated and unsaturated bonds are grafted at a density which corresponds with the experimental data. Not all studies agree on the effect of unsaturation. In an MD study made by Heller [106] it was found that around the unsaturated bond there is a region with increased fluctuations, whereas above these regions there were just a few less fluctuations. One can argue that this might be due to an insufficient equilibration of the system. From the modelling results for bilayers composed of unsaturated lipids one can begin to speculate about the various roles unsaturated lipids play in biomembranes. One very well-known effect is that unsaturated bonds suppress the gel-to-liquid phase transition temperature. Unsaturated lipids also modulate the lateral mobility of molecules in the membrane matrix. The results discussed above suggest that in biomembranes the average interpenetration depth of lipid tails into opposite monolayers can be tuned by using unsaturated lipids. Rabinovich and co-workers have shown that the end-to-end distance of multiple unsaturated acyl chains was significantly less sensitive to the temperature than that of saturated acyls. They suggested from this that unsaturated

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

lipids may have a role in providing a temperature-insensitive lipid jacket around protein molecules [102]. Whether it is generally true that membrane proteins are preferentially surrounded by unsaturated lipids remains to be proven. 4.9

CASE STUDIES: SCF RESULTS

We have seen from the above that the simulations and the calculations give a consistent picture of the PC bilayers. The strong and weak points of both methods are now well illustrated, and we can proceed by presenting results for gradually more complex problems obtained by the SCF method. 4.9.1

Effects of the Length of the Hydrocarbon Tails

It is of interest to elaborate on the effect of the tail lengths of the PC lipids on various (overall) membrane parameters. Here we will concentrate on the area per molecule and the compressibility modulus in the range C12 to C16 . Relevant data can easily be obtained from SCF calculations, and the predictions of this theory are presented in Figure 20. In line with experimental data, the area per molecule is almost independent of the length of the tails. Only a very small linear correction is found, which indicates that the longer the tail length the larger is the head group area. As a consequence, the thickness of the bilayer is to a good approximation proportional to the length of the chains. It is necessary to convert the dimensionless area as given in Figure 20 to real areas per molecule. For this, we need to know the cross-sectional area of a lattice site. The first-order approximation of this is d 2 . However, this is only correct for isotropic lattice sites. It can be shown that, consistent with the weighting of the interactions in equation (9) (l1 ¼ 1=3), the area is a factor of three higher: 0.9

(a)

5.4

0.2

1.3

(b)

C16PC

1.1

g

5.3

0.85

0.1 0.9

0.8 12

13

14 t

15

5.2 16

0 0

0.05

0.1 (a − a0)/a0

0.15

d ln a / d g

d ln a/d g

a0

0.7 0.2

Figure 20. (a) The (dimensionless) lateral compressibility (dilatational modulus, elastic area expansion modulus) (left ordinate) and the dimensionless area per molecule (right ordinate) as a function of the tail length (t) of the PC lipids in equilibrium bilayer membranes. The conversion to real compressibilities and areas per molecule is discussed in the text. (b) The (dimensionless) surface tension and the (dimensionless) lateral compressibility as a function of the relative expansion for the C16 PC lipid

F. A. M. LEERMAKERS AND J. M. KLEIJN

75

as ¼ 3d 2 . Again, when we use d ¼ 0:2 nm, as explained above, it is possible to convert the prediction to the area per molecule. One simply needs to multiply the dimensionless areas by 0.12 to obtain the area in units of nm2 . The correspondence with experimental data is satisfactory. The lateral compressibility, i.e. the relative area change upon an imposed membrane tension, decreases slightly more than linearly with the chain length. This means that it is more difficult to expand the membrane surface area of a long-chained lipid than a shorter one. In Figure 20 dimensionless units are used, which means that the surface tension is given in units kT=as . Again, using a lateral dimension of a site, d ¼ 0:2 nm, and the lattice site area as ¼ 3d 2 , means that g ¼ 1 corresponds with about 33 mN m
1 lateral tension. In other words, one needs to apply a lateral tension of order 40 mN m
1 to double the membrane area. This prediction seems to be a factor of about six lower than estimates that were recently reported by Evans and co-workers [107]. These authors use micropipettes to pressurise giant vesicles and obtain values of the order KA ¼ qg=q ln a ¼ 230 mN m
1 . There are also some data on the compressibility modulus, as found by MD simulations on primitive surfactants [62] KA ¼ 400 mN m
1 . In a molecular detailed simulation study on DPPC lipids, Feller and Pastor [40] report a KA value of about 140 mN m
1 . In Figure 20 the surface tension of the bilayer is given as a function of the relative expansion of the bilayer. Of course, when the surface area is increased, the surface tension invariably goes up. The slope of this curve decreases slightly with increasing relative expansion. From this, it is seen that the membrane compressibility increases when the membrane is stretched. 4.9.2

Lipid Variations: Charged Lipids in Bilayers

An important ingredient at the disposal of nature to vary the membrane properties in subtle ways is to make changes in the head-group structure. A PC lipid is zwitterionic and, as such, it is rather inert with respect to variations in ionic strength. We note that the insensitivity with respect to the membrane structure does not imply that the colloidal stability is not affected by the ionic strength. Meijer [84] has shown that it is expected that PC bilayers are only colloid-chemically stable at an intermediate ionic strength; then the electrostatic repulsion is largest. Both at high and low ionic strength attractive contributions may dominate over repulsive interactions. Charged lipids have not frequently been modelled. In simulations, the charges impose significant problems because it is extremely expensive to account for long-range interactions. Also by SCF techniques there has been little work done. Meijer et al. [84] reported on some properties of phosphatidylserine-type lipids. We connect here to these results and present a short survey. In an SCF model the PS lipids are parameterised on the same level of detail as the PC lipids. The extra carboxyl group is modelled with one negative charge with similar properties as a negative ion, on to which

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

24 5.8 dP−P

ao PS

20 5.4 PC

16 5 0

0.2

0.4

0.6

0.8

1

fPS

Figure 21. The area per molecule (left ordinate) and the distance between the phosphate groups on opposite sides of the bilayer of the PC and PS lipids as indicated (right ordinate) as a function of the fraction of PS molecules in equilibrated bilayers composed of mixtures of C16 PC and C16 PS lipids. Reproduced from ref (85) with permission from the American Chemical Society

two oxygens are coupled. For PS, there are two negative charges and one positive charge in the head group. A net negative charge on the head group gives the head group a more hydrophilic nature. This leads to a more hydrated head group that tends to extend more towards the water phase than the PC group. The average phosphate – phosphate distance across the bilayer is a convenient measure for the thickness of the bilayer. This property is presented in Figure 21 for bilayers composed of mixtures of PS and PC lipids. The phosphate of the PS head group is extended more outwards than the phosphate of the PC group. At the same time, the area per molecule increases with an increase of the PS in the bilayer. These effects are shown in Figure 21. It is anticipated that the membranes composed of charged lipids are more sensitive to the ionic strength. Very often in such cases the Debye length is the controlling parameter. As the Debye length is proportional to the square root of the ionic strength, we present in Figure 22 the area as well as the hP
Pi distance as a square root of the ionic strength. The number of molecules per unit area (the inverse of the area per molecule) is inversely proportional to the Debye length (i.e. ðjs Þ
1=2 ). When the area per molecule goes down, the molecules must pack more closely, and thus it is natural to find that the membranes become thicker. This is reflected by the increase in hP
Pi, increasing again with the square root of the ionic strength. 4.9.3

The Gel-Phase of DPPC Bilayers

At sufficiently low temperature, the liquid state of the bilayer is not stable and the membrane abruptly ‘freezes’ into the so-called gel state. The structure of a

F. A. M. LEERMAKERS AND J. M. KLEIJN

77 21

5.9

dP−P

a0

20 5.7

19

5.5

5.3

18 0.02

0.04

0.06

0.08

0.1

js

Figure 22. The average dimensionless area per molecule (left ordinate) and the phosphate – phosphate distance in lattice units across the bilayer (right ordinate) of phosphatidyl serine bilayers as a function of the square root of the ionic strength

bilayer membrane in the gel state has recently been modelled by MD simulations [35,106,108]. To obtain good results, it is necessary to have a constant pressure rather than a constant-area simulation. In the gel phase, the molecules are almost in an all-trans configuration. Only approximately 0.1 gauche torsion was found per acyl chain. The acyl chains can be ordered in several ways with particular tilting angles. The SCF modelling of gel-state membranes has also some history. There are some early works on the gel-to-liquid phase transition [109,110], where the main interest is in the cooperative ordering of the acyl chains. The full problem of thermodynamically relaxed bilayers composed of lecithin-like molecules has been reported by Leermakers et al. more than a decade ago [95]. Although the SCAF model makes use of lattice approximations which become rather restrictive when the molecules go towards the fully ordered state, it was shown that it is possible to generate tensionless membranes in the gel state. Both fully interdigitated gel phases and noninterdigitated ones could be found which depended on the degree of hydration of the bilayers. We will not present these results in this review in more detail. In passing, we note that Schick and co-workers also modelled lipid monolayers using a SCAF-like technique [111]. They go essentially off-lattice by allowing steps in many different directions. By doing so, they found some cooperative tilt direction of the lipid tails as a function of the headgroup area. Such an approach should be applied to the bilayer problem as well. Then gel phases in which the molecules are cooperatively tilted with respect to the membrane normal can be analysed. To our knowledge this has not yet been done.

78

4.9.4

PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

Mechanical Parameters of Lipid Bilayers

In principle, one can analyse the equilibrium fluctuations as found from an MD simulation around the perfectly flat configuration of a bilayer to obtain information on the mechanical properties of the bilayer [14,15]. The finite size of the box is a serious limitation to do this accurately, and results of this type can best be reached using coarse-grained MD simulations. The alternative to learning about the mechanical parameters of the bilayer is to do molecular realistic simulations on nonlamellar geometries (i.e. curved bilayers). Periodic boundary conditions dictate that the (average) shape of the bilayers in MD simulations is flat. This is why such results do not (yet) exist in the literature. The authors are aware of some preliminary MD simulations on primitive surfactants (coarsegrained MD) in which the molecules follow the equations of motion in the presence of some type of bias force. This force is chosen such that it maintains a well-defined local curvature in the bilayer [112]. The strength of the bias gives information on the mechanical resistance of the bilayer against shape changes. Some information on the behaviour of lipids in curved geometries for a molecularly simplistic model is available from MC simulations [113]. Much more work has been done using SCF theory. Above, we argued that a portion of a finite-sized membrane can close upon itself to remove edge effects. In this way, vesicles are formed. The thermodynamic stability of vesicles is still a topic of hot debate in the literature, primarily because there are so many scenarios. The SCF analysis of vesicles leads to information on the mechanical parameters for a particular membrane system. The first point to be made is that the structure of the bilayers changes due to an imposed curvature. These curvature effects are easily monitored in an SCF analysis. Unless one is willing to do a three-dimensional analysis, the method is restricted to homogeneously curved bilayers, i.e. cylindrical or spherically shaped vesicles. Curvature-induced structural changes are best observable when the curvature is extremely high. Curved vesicles composed of lipids with molecular detail were first performed by Leermakers and Scheutjens [114]. The results presented in Figure 23 were obtained with the same parameter-set as discussed in Table 1, but the anisotropic bond-weighting factors were omitted. This means that the bilayers are slightly thinner than given in Figure 13. In Figure 23 the centre of the vesicle is at r ¼ 0. The head groups on the inner leaflet, positioned at r ¼ 20 have a higher local density than the head groups in the outer leaflet. The tails, excluding the CH3 end-groups, show a clear maximum on the outer side of the core region. The CH3 groups, on the other hand accumulate slightly more on the inner side. This shows that two halves of the curved bilayer contain chains that have different conformational properties. The total contribution of the tails, i.e. including the CH2 and CH3 groups, still reaches a maximum in the

F. A. M. LEERMAKERS AND J. M. KLEIJN

79

1 Tails

0.8 j

0.6

0.4 Head

0.2

0

CH3

0

10

20

30

40

50

r

Figure 23. Radial segment density profile through a cross-section of a highly curved spherical vesicle. The origin is at r ¼ 0, and the vesicle radius is very small, i.e. approximately r ¼ 25 (in units of segment sizes). The head-group units, the hydrocarbons of the tails and the ends of the hydrocarbon tails are indicated. Calculations were done on a slightly more simplified system of DPPC molecules in the RIS scheme method (thirdorder Markov approximation), i.e. without the anisotropic field contributions

outer region of the core. These curvature-induced changes in the membrane structure are the locus of some additional free energy in the system. By means of a thermodynamic analysis, one can extract these changes in free energy and obtain information on the mechanical properties of the bilayers. The thermodynamic analysis of curved bilayers is typically done on very weakly curved objects (much less curved then the example shown in Figure 23). This is to guarantee that the free energy of curvature remains quadratic in J and K. The bending modulus that controls the undulation fluctuations kc is known to depend strongly on the length of the hydrocarbon chains. The classical theory of elastic deformation [115] already indicates that the energy needed to bend a plate scales with the third power of its thickness. Such a strong increase of the bending modulus with lipid chain length appears to be consistent with both theoretical SCF computations [116] and with experimental findings [107]. It is also believed that for stable bilayers the Gaussian bending modulus is negative [25]. There is no experimental technique available that points directly to this quantity. It is believed that theoretical predictions may help to understand these matters in more detail. A typical outcome of the Helfrich analysis for charged bilayer systems is presented in Figure 24b–d in combination with experimental results for the dependence of the equilibrium radius of vesicles composed of DOPG and DOPC as a function of the ionic strength in Figure 24a. The vesicle solution was equilibrated using the freeze–thaw method [20], and the size was measured

80

PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 140

(a)

(b) 6.5

R / nm

120

kc/kT 100

DOPG

cW-ion = −2

5.5

80 cW-ion = 0

DOPC 60 0

100

200

300 cNaBr /mM

0

400 (c)

_ k/kT

c

W-ion

0.01

80

= −2

0.02

fs

0.03

0.04

(d)

cW-ion = 0

−5

c

W-ion

= −2

em/kT cW-ion = 0 40

−10

−15 0

4.5 0

0.01

0.02

0.03

fs

0.04

0

0

0.01

0.02

0.03

0.04

fs

Figure 24. (a) Experimental results for the radius of vesicles composed of DOPG and DOPC lipids as a function of the concentration of NaBr. The vesicles were prepared by the freeze–thaw method mentioned above, and the size R was found from dynamic lightscattering analysis. (b) The mean bending modulus as found by SCF calculations for DOPG-like lipids as a function of the ionic strength of 1:1 electrolyte. (c) the Gaussian bending modulus as found by SCF calculations for DOPG-like surfactants as a function
) as of the ionic strength of 1:1 electrolyte. (d) The total curvature energy em ¼ 4p(2kc þ k a function of the ionic strength of 1:1 electrolyte. In b, c and d the two curves illustrate the effect of the solvent quality for the ions (as indicated). Reproduced from (132) with permission from the American Institute of Physics

using dynamic light scattering [23]. The experimental data show that the vesicle size R goes through a minimum for DOPG, and is essentially an increasing function for DOPC as a function of the ionic strength. For computational reasons, the corresponding SCF analysis has been done on a relatively primitive model. The chain statistics is set to the lowest order (i.e. a first-order Markov approximation instead of the RIS scheme). The lipid molecules were modelled as linear chains with a charged head group in the middle of two C18 tails, i.e. with a Gemini-like architecture: C18 M2 C2 M2 C18 . The charge on the head-group units was set to vM ¼
0:25 mimicking DOPG, so that the overall charge was –1. The ionic strength is given by the volume fraction of ions in the bulk, which was varied from 10
4 to 0.04. Interaction parameters were chosen to be as simple as possible (still reflecting the essential amphiphile characteristics): w ¼ 1:6 for water–C as well as ion (M, Na, Cl)–C contacts. In the calculations the affinity of ions for the water phase was varied

F. A. M. LEERMAKERS AND J. M. KLEIJN

81

to show the effect of changes with respect to the ionic properties. Below, results are presented for the athermal interactions, i.e. wion
water ¼ 0 and for attractive interactions between ions and water wion
water ¼
2. The interaction parameter for the M–water contacts was fixed at zero. Lekkerkerker [117] examined the curvature dependence of the free energy of the electric double layer for fixed surface charge density. From this, the electrostatic part of the mean and Gaussian bending moduli of charged bilayers was predicted as a function of the ionic strength. Both the mean bending modulus and the Gaussian bending modulus were found to depend relatively strongly on the ionic strength. With increasing ionic strength, the absolute value
a
of these quantities decreases as a power law (kc / c
a salt and k / csalt ). The power-law exponent is predicted to be a function of the surface charge density. At high surface charge density, a ¼ 0:5, whereas at low surface charge density a value of a ¼ 1:5 was reported. One problem with these early predictions is that the surface charge density is fixed for all values of the imposed curvature J and K and the value of the ionic strength. Thus the model does not allow for curvature-dependent head-group areas and local charge compensation mechanisms such as the penetration of the ions in between the charged head groups. Indeed, for lipid membranes, one should expect that the head-group area, and thus the effective charge density of the bilayer, is a function of the ionic strength. These restrictions do not apply for the SCF analysis. In these calculations, the surface charge density adjusts itself automatically. In the SCF analysis of curved bilayers, it was found that all results could be fitted with the Helfrich equation, without the need to invoke a nonzero J0 . This means that the vesicles are typically stabilised by translational and undulational entropic contributions. This result is consistent with results by Leermakers [114] for uncharged lipid bilayers, and can be rationalised by symmetry arguments as discussed above. In Figure 24b and 24c, the mean and Gaussian bending moduli are plotted as a function of the ionic strength for charged lipid vesicles in a 1:1 electrolyte
) is presolution. For convenience, the total curvature energy em ¼ 4p(2kc þ k sented in Figure 24d. Results are presented for two values of the ion–water interactions. Let us first discuss the ideal case where the ions interact athermally with the solvent (closed spheres). In this case, the predictions of Lekkerkerker [117] are qualitatively recovered: with increasing ionic strength the Gaussian bending modulus becomes less negative, the mean bending modulus is reduced and the overall curvature energy is an increasing function of the ionic strength. Forcing a power law through the data of Figures 24b,c (solid points), however, gives a much lower ionic strength dependence than predicted by Lekkerkerker [117] (a  0:1). The reason for this weak ionic strength dependence is that with increasing ionic strength the area per molecule goes down, which tends to increase the absolute values of the bending moduli.

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

One may argue that the ideal interactions of all ions with water are not physically realistic. For this reason, we have repeated the full analysis with better than athermal solvent conditions. The results of this exercise are given by the open circles in Figure 24b,c,d. Indeed, for this case, the mean bending modulus goes through a minimum as a function of the ionic strength. For the other properties presented in Figure 24, the qualitative behaviour is not affected. We may argue that, with increasing ionic strength, the solvent (water þ ions) becomes a worse solvent for the apolar tails. As a consequence, the membrane thickness increases just slightly more with increasing ionic strength than in the athermal case (not shown). At high ionic strength, the change of the bare bending modulus due to the increase in thickness of the bilayer, dominates over the change of the electrostatic part of the bending modulus. Above we have argued that the equilibrium radius of a vesicle may be related to the persistence length of the bilayer. This implies that the radius of the vesicle kc ). The strong correlation between the curves for DOPG in R  x / exp ( kT Figures 24a and 24b (open circles) strongly indicates that this line of reasoning makes some sense. Using this approach, one can extract from Figure 24a how the bending modulus depends on the ionic strength. Consistent with the SCF results, a very weak ionic strength dependence is found (a  0:06). It is of significant interest to discuss the overall curvature energy (as shown in Figure 24d) as a function of the ionic strength, in somewhat more detail. Consistent with predictions based upon the electrostatic part of the bending moduli [117], it is found that the overall curvature energy goes down with decreasing ionic strength. When the overall curvature energy drops below zero, the vesicles become unstable. The SCF thus predicts that at very low ionic strength, a micellar phase, not the vesicles, becomes the more favourable aggregation state of these lipids. This is consistent with the surfactant parameter arguments mentioned in the introduction. With decreasing ionic strength, the effective size of the head group increases. Therefore, the effective shape of the surfactant becomes less like a cylinder and more like a cone. In other words, the surfactant parameter drops to such a low value that bilayers are not stable. Interestingly, at the point where the curvature energy vanishes, the size of the vesicles is very large, because kc increases with decreasing ionic strength. The transition from the solution with vesicles to a micellar solution is predicted to be a jump-like (first-order) phase transition. Going in the opposite direction, i.e. when we consider the membrane stability
towards zero. Going with increasing ionic strength, we notice the approach of k towards this value, the tendency of the bilayers to form saddle-shaped connections (also called ‘stalks’) between bilayers increases. Saddle-shaped membrane structures also occur in processes like vesicle fusion, endo and exocytosis. The SCF predictions thus indicate that these events will occur with more ease at high ionic strength than at very low ionic strength.

F. A. M. LEERMAKERS AND J. M. KLEIJN

4.9.5

83

Membrane–Membrane Interactions

Invariably, the thermodynamic stability of lipid vesicles in the colloid–chemical sense is an important issue. In this context, it is very important to know how a given bilayer interacts with other bilayers of its kind. In MD simulations, it is virtually impossible to do predictions for isolated, noninteracting bilayers. Typically, one uses experimental data on the equilibrium membrane–membrane spacing when a simulation box is created. Systematic thermodynamic analysis of the effect of the membrane–membrane spacing is not available from simulations. For this, we again have to turn to more approximate SCF modelling. In an SCF technique the partition function is accurately available, and therefore it is straightforward to examine interacting membranes. In Figure 25 we show a prediction of Meijer et al. [85] for DMPC membranes interacting with each other as a function of an applied lateral tension (see reference [85] for the details of the values of interaction parameters used). Membranes under lateral tension have an increased area per molecule, and thus are thinner than equilibrium membranes. As a result, the number of water– hydrocarbon tail contacts is increased, and also the head-group conformation may be altered. As a result of this, one would expect that membranes under tension become more attractive to each other than when they are free of tensions. Basically, this is also what can be extracted from Figure 25. The repulsion at high membrane spacing has an electrostatic origin. When increasing tension is applied to the membrane, the repulsion goes down. The attraction in the curve is due to conformational changes in the head-group region when membranes are in very close proximity. The depth of this minimum is not 0.0008

F int γ(∞)= 0.160 0.0004 0.0 0.087

0

5

7

9

11

D

Figure 25. The free energy of interaction between two DMPC membranes at various degrees of surface tension as indicated. We note that the indicated surface tension is the tension at large membrane–membrane spacing. The salt bulk volume fraction was js ¼ 0:002. Redrawn from [85] by permission of the American Chemical Society

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

affected greatly by the lateral tension. The position of the minimum is a function of the applied tension, as must be expected from the reduced dimensions of the bilayers. The steep repulsion at very close proximity is due to a compression of the bilayers, which is, as explained above, energetically unfavourable. Stress-induced adhesion is also found in experimental systems, as discussed by Helfrich [118]. The typical interpretation of stress-induced adhesion differs significantly from the one given above. It is generally believed that the main effect of an applied tension is to reduce undulations. In the absence of undulations, the corresponding repulsion vanishes and the membranes can attract each other by, for example, van der Waals forces. It should be noted that the interaction free energy of the bilayers reported in Figure 25 is an intrinsic interaction. For a complete picture, one needs to add the van der Waals contribution, but also, more importantly, the contributions due to the undulation. To some extent, these two contributions cancel each other out, and it is expected that the intrinsic effects as discussed above are relevant for the interaction of bilayers at rather close proximity. 4.9.6

A DPPC Layer as a Substrate for a Polyelectrolyte Brush

In many biological systems the biological membrane is a type of surface on which hydrophilic molecules can be attached. Then a microenvironment is created in which the ionic composition can be tuned in a controlled way. Such a fluffy polymer layer is sometimes called a slimy layer. Here we report on the first attempt to generate a realistic slimy layer around the bilayer. This is done by grafting a polyelectrolyte chain on the end of a PC lipid molecule. When doing so, it was found that the density in which one can pack such a polyelectrolyte layer depends on the size of the hydrophobic anchor. For this reason, we used stearoyl C18 tails. The results of such a calculation are given in Figure 26. Because the amount of matter in the form of DPPC lipids in these calculations is about 25 times higher than for the polyelectrolyte modified lipids, it is necessary to rescale the latter densities such that one can understand the interesting aspects. Therefore there are different scales on left and right ordinates in the figures. In Figure 26a, the overall density profiles of both lipids are shown. The DPPC lipids are not much affected by the intrusion of the PEmodified ones. The overall membrane thickness due to the DPPC chains is about equal to the thickness of an unperturbed DPPC bilayer. The conformations of the PE chain are understood from polymer brush theory. In particular, the work on polyelectrolyte brushes has advanced in recent years [119,120]. The distribution of small counterions in the polyelectrolyte layer is such that the charge is almost exactly compensated locally. It is relevant to mention that the charge per segment on the PE chain was set to
¼ 0:25 and

F. A. M. LEERMAKERS AND J. M. KLEIJN DPPC

1

0.008

H2O

(b)

0.006

C PC-P

0.6

18

0.04

0.005

(a)

0.8

j

85

200

0.02

0.0025

j 0.004

q

0.002

−0.0025

y

0

0

0.4

Na 0.2

−0.02

Cl 0

0

j

20

40

z

60

80

0 100

0.006 C

0.0003

0

20

40

z

60

(d)

j 0.0003 0.04

P200 0.00015

j

C PC-P 18

N

0.003

−0.04 100

80

0.06

j

(c)

P

−0.005

C PC 16

200

0.00015

0.02 P N

N

P

0 0

20

40

z

60

80

0 100

0 0

5

10

z

15

0 20

Figure 26. The structural properties of a mixture of C16 PC (DPPC) and stearoyl C18 PC lipids of which there is a polyelectrolyte chain attached to the N of the choline group. The polyelectrolyte (PE) chain is a string of hydrophilic segments, each of which has a charge of
¼
0:25. The amount of lipid is y ¼ 10:1, and that of the PE chain is y ¼ 0:4. In all views graph profiles are shown for only half the bilayer, i.e. starting from the centre of the bilayer (at z ¼ 0). (a) The overall profiles for C16 PC and water are solid lines, left ordinate, and C18 PC
P200 , Na and Cl all dashed lines, right ordinate. (b) The charge distribution, q, left ordinate and electrostatic potential profile, c, right ordinate. (c) Detailed distribution of the PE-modified lipid C18 PC
P200 . The C units and the PE chain are dashed (left ordinate), and the P and N distributions are solid lines (right ordinate). (d) The P and N distributions for the C16 PC lipids, broken lines (left ordinate) and that for the PE-modified lipid, solid lines (right ordinate)

that on the small mobile ions is unity. Therefore the density of polymer is about a factor of four higher than the difference between the density of positive ions and negative mobile ions. This local electroneutrality is illustrated in Figure 26b, where the charge density profile q(z) is plotted. The electrostatic potential profile is rather complex. In the hydrophobic region, the features are similar to those discussed above for the pure DPPC layer cf. Figure 15. The electrostatic potential profile in the PE layer is parabolic, and outside the PE layer the potential is very low, but decays according to the classical Gouy–Chapmann theory, i.e. exponential decay towards zero. In Figure 26c and 26d some more details are plotted for the PE-modified lipid. On the PE chain there are some features deviating from the parabolic profile near the lipid–water interface. We should realise that in the membrane

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there is a positive electrostatic potential, whereas the electrostatic potential in the brush is negative. The relatively high brush density near z ¼ 20 is therefore attributed to electrostatically driven ‘adsorption’. One would intuitively argue that grafting a long hydrophilic tail on the end of the head group would cause the P–N vector to orient towards the membrane normal. This is indeed the case. The distribution of the N is shifted to higher z values than the P group, as is best seen in Figure 26d. In this part of the graph it is shown that the head-group orientation of the unmodified DPPC is surprisingly unperturbed by the presence of the PE chains near the membrane.

5

TRANSPORT AND PERMEATION

To facilitate specific uptake of nutrients and secretion of products, as well as to maintain the ionic concentration gradients and membrane potentials essential for life processes, nature has developed different kinds of more or less specialized transport systems incorporated in the lipid bilayer. However, some types of molecules and ions can pass biomembranes by themselves. Examples are water, oxygen and carbon dioxide (which need to move rapidly into and out of cells), nitrous oxide, and various toxins and drugs. For the explanation of this so-called nonmediated transport, two alternative mechanisms are commonly used. In the first, it is proposed that molecules diffuse across the membrane (solubility–diffusion mechanism), in the other the transport is assumed to take place along water wires or stochastic pores in the lipid bilayer (pore mechanism). In the next subsections we will go into some detail with respect to these two mechanisms, and will discuss the molecular modelling performed in this direction using MD simulations and SCF calculations. In Section 5.3 we will pay attention to the modelling of mediated membrane transport, i.e. the transport through peptide or protein channels, or otherwise catalysed by carriers or transport proteins. 5.1

SOLUBILITY–DIFFUSION MECHANISM

Travel across the lipid bilayer must be an exciting undertaking. The molecular traveller has to go through a complex inhomogeneous soft material. In doing so, the molecule first passes a crowded head-group region that is still rather aqueous. Then, on a length scale of about a nanometre (as soon as the glycerol backbone is passed), the polarity drops to a value that is close to that found in hydrocarbon liquids. Subsequently, a region with a relatively high orientational order is encountered. Near the centre of the bilayer the order gradually diminishes somewhat. After this, the molecule has to move out again through the other half of the bilayer, encountering the similar regions in reverse order. In short, there are gradients in polarity, in electrostatic potential, in packing

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density and orientational order. Not many molecules can readily cope with all these gradients. In 1899, Overton [121], who, of course, at that time had no conception of the structural complexity of biological membranes, recognised that these provide a barrier to the free diffusion of solutes. From numerous investigations on the osmotic properties of both plant and animal cells [121,122], he found that the permeabilities of membranes to different solutes correlate with the water– octanol partition coefficients of the solutes. The resulting Overton rule, implying that solutes that dissolve well in organic solvents (such as hexane or octanol) can penetrate membranes more rapidly than solutes that are less soluble in such solvents, has been for a long time the most important guideline in physiological studies concerning membrane permeability and related issues (see Figure 27). In more recent years it was found, however, that for small nonelectrolytes (e.g. water, ammonia, formamide) the Overton rule does not hold. Their permeabilities are much higher than predicted from the trends seen for larger molecules, and are inversely proportional to their size [123,124]. The ideas of Overton are reflected in the classical solubility–diffusion model for transmembrane transport. In this model [125,126], the cell membrane and other membranes within the cell are considered as homogeneous phases with sharp boundaries. Transport phenomena are described by Fick’s first law of diffusion, or, in the case of ion transport and a finite membrane potential, by the Nernst–Planck equation (see Chapter 3 of this volume). The driving force of the flux is the gradient of the (electro)chemical potential across the membrane. In the absence of electric fields, the chemical potential gradient is reduced to a concentration gradient. Since the membrane is assumed to be homogeneous, the −1 −2

log P (P in m s−1)

−3 −4 −5 −6 −7 −8 −7

−6

−5

−4

−3

−2

−1

0

log K

Figure 27. Relationship between water–hexadecane partition coefficients and membrane permeabilities for a broad selection of solutes. (Data collected by Walter and Gutknecht [124]. Reproduced with permission from the American Chemical Society)

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

concentration profile of the permeant molecule in the membrane is taken to be linear, and the concentration drop going from one side to the other is related to the concentration differences in the solutions at both sides of the membrane, according to the equation: Dcmembrane ¼ KDcw

(13)

with K the water/membrane partition coefficient of the molecule. If any interfacial barriers for the entrance and exit of the membrane are neglected, the permeability P of a solute over the membrane is given by: P¼

KD d

(14)

Here, D is the diffusion coefficient of the solute in the membrane, and d is the thickness of the membrane. In all its simplicity, the above equation shows that both equilibrium and dynamic information is needed for predicting the permeability of biological membranes for particular solutes, and therefore has added value with respect to the Overton rule. The permeation of molecules across membranes, and their distribution in the lipid bilayer are closely related phenomena, but, to describe membrane permeability, knowledge of the diffusive behaviour of the solute in the bilayer must be available as well. Of course, with increasing knowledge of the structure of lipid bilayers and biological membranes, the classical solubility–diffusion model has been refined. The most obvious improvement is to divide the bilayer into different regions (e.g. an inner hydrophobic region and two more hydrophilic outer regions with dielectric properties different to those of the surrounding electrolyte solutions, and with different mobilities for the permeating solutes [127]). Meanwhile, computational methods have reached a level of sophistication that makes them an important complement to experimental work. These methods take into account the inhomogeneities of the bilayer, and present molecular details contrary to the continuum models like the classical solubility– diffusion model. The first solutes for which permeation through (polymeric) membranes was described using MD simulations were small molecules like methane and helium [128]. Soon after this, the passage of biologically more interesting molecules like water and protons [129,130] and sodium and chloride ions [131] over lipid membranes was considered. We will come back to this later in this section.

5.1.1

Equilibrium Aspects: Partitioning

The equilibrium modelling of additives in bilayers is already a challenging task. For example, in MD simulations it is difficult to consider very low loading

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because one can consider only very small systems. Above a certain (still low) concentration of foreign molecules in the bilayer, one should expect serious perturbations of the membrane properties, and the possibility exists that this loading threshold is exceeded by just putting a single foreign molecule in the box. In SCF calculations, one can both investigate the infinite dilution case and study the effects that occur upon increasing the loading. In the former case, the equilibrium membrane properties are not affected, but in the latter one they are. However, for the prediction of partition coefficients from first principles it is necessary that all parameters are known. This situation has not been reached yet. For this reason we can only rely on predictions of trends in partition coefficients for a series of additives in which some parameter is varied systematically. As indicated above, in MD the infinite dilution case cannot be investigated. For hydrophobic small inert units like noble gases, however, it is assumed that their distribution in the bilayer follows the distribution of free volume. An extensive analysis of free-volume-related properties (free-volume fraction, hole size distribution, local order parameters) of the lipid membrane has been given by Marrink et al. [132]. On the basis of MD simulations of a DPPC bilayer, the membrane was divided into four distinct regions with very different free-volume properties, shown in Figure 28. The first region contains the adjacent water layer, the second is the head-group layer, the third comprises the first half of the hydrophobic tails, and the fourth is the centre of the membrane, i.e. the second half of the tails. The largest free-volume fraction is found in the centre of the membrane, with large cavities in which even larger molecules with a diameter of 0.6 nm, like urea, could fit without disturbing the structure. The third region, where the order in the lipid tails is high (cf. the order

Accessible free-volume fraction

0.6

1

2

3

0.5 0.4

4 0.0

3

2

1

0.1

0.3

0.2 0.2

0.28 0.34 0.4 0.6

0.1 0

−2

−1

0

1

2

z / nm

Figure 28. Accessible free-volume fraction profile across a DPPC bilayer for solutes of different sizes (diameters indicated in nm; 0.0 corresponds with the total free volume). Results of Marrink et al. [132]. Redrawn by permission of the American Institute of Physics

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

parameter profile for a DMPC bilayer given in Figure 17), has clearly the lowest free-volume fraction, and is therefore considered to represent the largest resistance to the permeation of small solutes. This view is supported by MD simulations [133,134]. Xiang and Anderson [133] investigated the processes to insert noble gases into the bilayer interior. The unfavourable free energy to generate a cavity in the bilayer was analysed by scaled-particle theory, and the interaction energy between the inserted particle and the lipids in the molecule was determined. They found that it was much more difficult to create a cavity in a membrane with oriented lipids than in an isotropic alkane (dodecane), which suggests a model with an anisotropic surface tension at the noble gas–lipid interface. In these MD simulations the alkyl chains were grafted with a harmonic potential to a plane. In a more recent paper [134], they evaluated, from a series of MD simulations on a DPPC bilayer, the contributions of functional groups like CH3 ,
Cl,
OH and COOH to the free energy for transfer of solutes from water to the ordered-chain region of the bilayer. In an experimental study, the same authors [135] systematically explored the effects of permeant size and shape, using as permeants seven monocarboxylic acids with different chain length and chain branching. Deviations of the permeability coefficients found for permeation across DPPC bilayers from the values predicted by solubility– diffusion theory, were found to correlate with the minimum cross-sectional area of the permeants, which was explained as resulting from lipid-chain ordering. The pronounced size-dependency of bilayer permeation by small solutes has also been analysed in terms of the structure and ordering of the lipid-chain region of bilayers by Mitragotri et al. [136], using scaled-particle theory. The partitioning of polar molecules is restricted to the head-group region and typically remains limited. Since the partitioning of lipophilic molecules in the interior of the bilayer is expected to be relatively high, it can be studied in MD simulations with some confidence. For example, in animal cells the cholesterol/ lipid ratio is relatively high and therefore suitable for MD studies. Indeed, there are quite a number of simulation studies on the effect of cholesterol on lipid bilayers (see the review by Ohvo-Rekila¨ et al. [137] and references therein). The rigid steroid ring system of the cholesterol molecules affects the conformations of the acyl chains, and tends to increase the population of trans conformations and decrease the free-volume fraction. Cholesterol contains one hydroxyl group, which gives this otherwise hydrophobic compound its hydrophilic character and ability to partition in hydrogen-bonding, with water molecules or with the lipid carbonyl and phosphate groups [138]. Simulations further show that the introduction of cholesterol allows for a broader distribution of P–N angles in the lipid head groups. This is caused by the relatively low position of cholesterol in the lipid bilayer, leaving holes in the bilayer surface, which are filled by choline N-groups from neighbouring lipids [139]. This leads to rearrangement of water molecules and changes the electrical properties of the

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bilayer/water interface in the sense that the membrane dipole potential increases. An increase in dipole potential with increasing cholesterol content has experimentally been found for egg phosphatidylcholine monolayers [140]. Furthermore, cholesterol decreases the fluidity of membranes by slowing down large-scale rearrangements and reorientational motions. The experimental observation that the permeability of bilayers for small permeants like water decreases with increasing cholesterol content [141], is probably connected with both the tighter packing of the lipid chains, as well as with the slower dynamics. In the literature, one can find many more interesting MD studies concerning lipid bilayers with additives. In particular, a wealth of MD simulations of such systems is in the field of anaesthetics (for a review see [142]). Many anaesthetics tend to accumulate at the membrane/water interface, implying that their potencies are not related to their ability to cross the membrane. Instead, it seems to be more likely that their functioning is via binding to membrane receptors. Generally, they have an effect opposite to that of cholesterol, i.e. they increase the membrane fluidity and permeability. In Section 4.6 we discussed the partitioning of ions in the bilayer as found from SCF calculations. Bilayers possess an internal dipole potential that favours the partitioning of anions over cations (see Figure 16). This is due to the orientation of molecular dipoles at the bilayer interface, lipid head groups and bound water, rendering the hydrocarbon core positive with respect to either aqueous phase. Apolar molecules may preferentially partition in the core of the bilayer, and then the saturation level is potentially high, especially when the additive is able to separate the two halves of the bilayer. Amphiphiles partition in the outer regions of lipid membranes. The effect of charged surfactants on the orientation of the head group of DMPC as determined by SCF calculations has been reported by Meijer et al. [85]. It should be noted, by the way, that strong partitioning of lipophiles or amphiphiles in the core of the bilayer or the bilayer/solution interface, respectively, slow down trans-bilayer transport. Experimentally determined rates of transport of drug molecules have been analysed in terms of the amphiphilicity and lipophilicity of these molecules, by Bala´z˘ [143]. In Figure 29a we show the well-known result that for alkanes the partition coefficient is a strongly increasing function of the molecular weight. (It should be noted, as mentioned earlier, that SCF calculations can only give trends in partition coefficients.) This result can be explained by realising that by partitioning in the bilayer the alkane gains interaction energy, which scales linearly with the chain length DU ¼ NwC, water . However, the transfer of an additive from the water phase to the membrane phase implies a loss of translational entropy. This loss is given by DS ¼
k log K. The free-energy balance DF ¼ DU
T DS ¼ 0 gives log K / N. This law is followed as shown in Figure 29a. In Figure 29b three typical absorption isotherms are given near the saturation levels of the alkanes in the DPPC membrane. The results presented in this graph

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 8 (a)

(b)

n excN

7

6

log K 5

4

C8 3

2

C24 C4

1 0

5

10

15 N

20

25

0 −0.5

−0.4

−0.3

−0.2

∆m

−0.1

0

0.1

Figure 29. (a) The log of the partition coefficient as a function of the chain length of alkanes CH3 (CH2 )N
2 CH3 (at infinite dilution) in DPPC membranes. The CH3 units are modelled as a double bead, similarly to the DPPC lipids. (b) The absorption isotherm of three alkanes in equilibrated DPPC membranes. The excess number of molecules (multiplied by the chain length) is plotted as a function of the chemical potential of the alkane minus the chemical potential of alkane at saturation (binodal) in water

are highly nontrivial. They show that the absorption of both low- and highmolecular-weight alkanes is limited, whereas, for intermediate chain lengths, the amount of alkanes is unbounded at the bulk saturation conditions. For C8 – an intermediate case – the isotherm is smooth. With an increasing concentration of octane, i.e. with increasing chemical potential, the absorbed amount increases. It is expected that long-range van der Waals interactions, not included in the model calculations, will keep the absorbed amount finite, also at coexistence. For C4 the absorbed amount remains very low. The arrow in Figure 29b points to this low value. In fact, this result is rather surprising, because one may argue that short-chain alkanes can easily penetrate between the tails and expand the bilayer, this behaviour being predicted from polymer brush theory [24]. However, butane has two CH3 groups, which are given small, unfavourable interactions with CH2 groups, see Table 1. For this reason, the incorporation of low-molecular-weight alkanes is limited for enthalpic reasons. This mechanism is expected to limit the concentration of additives in membranes in most, if not all, cases. This is because there are always chemical differences between the additives and the acyl chains. The finite absorbed amount for very large alkanes C24 is expected, because the long chains experience a reduction in conformational entropy when they partition inside the finite-sized bilayer. This is an old result already predicted by Gruen [144]. It is also known that a melt of long chains does not penetrate a brush of short chains (at high grafting densities) [24]. The absorption isotherm is nontrivial in this particular case. Before the finite absorbed amount of the C24 alkane at the binodal, indicated by the arrow in Figure 29b, is found, there is a stepwise growth of the absorbed amount. This jump-wise growth means that there is a first-order phase transition taking place in the layer. Such a stepwise growth of absorbed amount may be expected when

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the transition is from a finite absorbed amount to an infinite absorbed amount, which may be generated by changing the temperature, for example, in a firstorder phase transition. Then, the C24 case is just close to such a transition. The unexpected effect is that the step in the isotherm is found for the case that the absorbed amount at coexistence remains finite. This must indicate that there are two mechanisms active on two length scales that should be considered for the control of additive uptake. One of these is the hydrophobic compatibility. The other one is likely to be the ability of the additive to be compatible with the local order in the bilayer. These data have been collected as an example for this review. More work is needed to understand the physics involved here. The authors do not know sufficiently accurate experimental data on absorption isotherms to test the above predictions. In Figure 30, the partition coefficients are given for a series of molecules with equal overall composition, but which differ in architecture. This graph is reproduced from the work of Meijer and co-workers [86]. The key point here is that the partition coefficient is largely determined by the chain composition, but in addition to this there is a weak contribution to how the various groups in the molecule are linked to each other. The additive, which is just designed to show the potential application of the model, has a positive charged N on one side and a negatively charged P group on the other. In addition, there is a C6 group somewhere along the chain, splitting the chain into two fragments. These fragments can be positioned on the chain in an ortho, a meta or a para position, as depicted in Figure 30. All these variables have their effect on the partition coefficient. The partition coefficient is largest when the C6 group is positioned about halfway up the chain, and in particular when the two chain fragments are

1.0⫻107

o m 8.0⫻106

p K 6.0⫻106 +

o

N

1

4.0⫻106

Cn+1

m

Cm+1 −

P

4

p

2.0⫻106

0

2

4

6

8

10

12

14

n

Figure 30. Partition coefficients for a series of molecules that all have the same overall composition, but in which the architecture is changed systematically. The second chain can either be positioned on the ortho, meta or para position of the C6 -ring

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

in the ortho position. This can be understood, because in this way the C6 group can be positioned near the centre of the bilayer, where the order is lowest, while the two charges can still reach the membrane–water surface. The asymmetry with respect to the C6 group being near the positive or negative chain is interesting. As the positive charge in the PC head group is more mobile, it can adjust to accommodate the negative charge on the ring, irrespective of whether it sits in an ortho, meta or para position. However, the restricted phosphate cannot do the same when the positive charge is positioned at the ring. Then the ortho position is particularly unfavourable. 5.1.2

Dynamic Aspects

Study of the dynamic aspects of permeation processes across lipid bilayers from molecular modelling is still in its infancy. As yet, SCF theory has not been developed to deal with dynamics (modelling of steady-state processes is just starting), whereas the MD technique cannot cover the relevant time frame to simulate the full dynamic process of a particular molecule crossing the lipid bilayer. Despite this limitation, permeation processes may be investigated with MD, using indirect methods. For example, Marrink and Berendsen [129] deduced the rate of permeation of water across DPPC membranes via the computation of the free-energy profile and diffusion rate profile across the bilayer. For the head-group region and adjacent water layer, the diffusion rate profile was obtained by determination of the mean squared displacement of the water molecules in a short time interval (1 to 5 ps trajectories). For the interior part of the bilayer, a force-correlation method was used, in which the autocorrelation function of random forces acting on a water molecule (constrained or inserted as a ghost particle, i.e. without disturbing the configuration) is converted into a local friction coefficient x. This friction coefficient is related to the local diffusion coefficient by Einstein’s well-known equation D ¼ kT=x. From the results (depicted in Figure 31), it is concluded that the rate-limiting step is the permeation of the water molecule through the dense, ordered region of the lipid tails. In the centre of the membrane, where the hydrocarbon tails are disordered (comparable with the situation in liquid alkanes), diffusion is fastest. MD simulations of Bassolino-Klimas et al. [145,146] suggest that cavities play a role in the permeation of small solutes across membranes. In these simulations, occasionally large and rapid displacements of a benzene molecule are observed. The benzene molecule is trapped in a cavity, where it undergoes rattling motions, until a pathway opens to another, nearby cavity. This usually requires a rearrangement of the lipid chains, often involving a gauche–trans transition. Jumps from one cavity to another seem to be of particular importance for diffusion through the best-ordered region of the lipid tails, i.e. near the head-group region. Hopping between voids was already proposed by Lieb and Stein [123] on the basis of the size-dependent permeability of small solutes.

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95

⫻10−5 20

1

2

3

4

3

2

1

D/cm2 s–1

15

10

5

0

−2

−1

0

1

2

z / nm

Figure 31. Diffusion coefficient of water in a DPPC bilayer as a function of position. Results of MD simulations of Marrink and Berendsen [129]. Redrawn by permission of the American Chemical Society

Obviously, the availability of large enough cavities decreases strongly with the size of the solute. We have already discussed another explanation of the relationship between permeation rate and solute size, based completely on solubility, i.e. the size-selectivity of solute partitioning in the ordered lipidchain region [133–136]. 5.2

PORE MECHANISM

Experimental results have shown that the solubility–diffusion model is satisfactory for many permeants, but for some solutes it clearly fails. One of the features that will frustrate its applicability is the possibility that thermal fluctuations give rise to the formation of transient water-channels or hydrated pores. The smallest type of short-lived hydrophilic channels may be single strands of hydrogen-bonded water molecules or water threads. When such a channel is somewhat larger, the head groups may also cover the water–tail interface inside the pore. Such a mesoscopic pore can grow to semi-macroscopic size, especially when the membrane is under tension [147]. This mechanism may be considered when the failure of the bilayer under tension is studied. Earlier we discussed the example of such a (stressed) membrane as simulated by DPD [64], where it was shown that surfactants stabilise long-lived pores, giving a mechanism for the toxicity in microorganisms. Mesoscopic pores may in turn provide a mechanism for lipid flip-flop events. Related to the pore mechanism is the process of ion transport over bilayers, as suggested by molecular dynamics simulations by Wilson and Pohorille [131]. These simulations show that permeation of ions into a glycerol 1-monooleate (GMO) bilayer is accompanied by the formation of deep thinning defects in the bilayer, whereby the lipid head groups and water penetrate into the bilayer interior. As the ion passes the mid-plane of the

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

membrane, the deformation switches to the other side, and, while the initial defect slowly relaxes, a defect forms in the outgoing side of the bilayer. During the process, the ion remains hydrated. As discussed earlier, lipid bilayers possess an internal dipole potential, which favours the partitioning of anions over cations. Therefore, the solubility– diffusion model predicts lower permeabilities for cations compared with anions [148]. However, in particular for small cations and relatively thin bilayers, the permeability is much higher than predicted on the basis of this model. Back in 1969, Parsegian [149] calculated the free energy of a small cation located in an aqueous pore, and showed that this is significantly lower than in the hydrophobic part of the bilayer, implying a lower diffusion barrier for crossing the bilayer along a water pore. If the pore-mechanism applies, the rate of permeation should be related to the probability at which pores of sufficient size and depth appear in the bilayer. The correlation is given by the semi-empirical model of Hamilton and Kaler [150], which predicts a much stronger dependence on the thickness d of the membrane than the solubility–diffusion model (proportional to exp(–d) instead of the 1/d dependence given in equation (14)). This has been confirmed for potassium by experiments with bilayers composed of lipids with different hydrocarbon chain lengths [148]. The sensitivity to the solute size, however, is in the model of Hamilton and Kaler much less pronounced than in the solubility-diffusion model. A number of MD studies have been published on permeation along water wires, all devoted to proton permeation through bilayers [130,151,152]. This process is a very special case. Experimental studies [153–155] have shown that protons penetrate bilayers at rates five orders of magnitude faster than other monovalent cations. In contrast to the nonmediated transport of other ions, for protons the rate of this process is so high that it is of physiological significance. Protons can diffuse by a special mechanism not applicable for other cations: hopping along hydrogen-bonded strands of water molecules (see, for example, ref. [156] and references therein). One of the first MD studies in which the hypothesis of proton transport through water pores via hopping over a single strand of water molecules was tested, was performed by Marrink et al. [130]. As the observation of spontaneously formed water channels is still far from accessible in MD studies, a strand of water molecules was gradually induced across a DPPC bilayer (64 DPPC and 736 water molecules in the box). From the forces needed to constrain the pore in the bilayer, its free energy of formation was calculated. After lifting the constraints, it was found that the lifetime of the pore before being dispersed is in the order of a few picoseconds, which would be – according to the authors – just long enough to accommodate the transport of a single proton. However, Venable and Pastor [151] argued that this lifetime is too short to demonstrate the feasibility of proton transport along water wires. Their MD simulations on

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a DPPC bilayer, as well as on a crude model system for a lipid bilayer (water/ octane/water sandwich model), suggest much longer lifetimes of water wires, on the 50–100 ps timescale. In both systems a water wire was inserted, preformed in vacuum under cylindrical constraints. Subsequently, the systems were energy-minimised and subjected to 10 ps of MD with restraints to keep the water molecules in the wire. After this, simulations were performed without restraints until the wire dissipated. In a similar way Zahn and Brickmann [152] studied the breaking of water wires in a DLPE bilayer, and they found an average lifetime of about 90 ns. These authors give a rough calculation of the minimum lifetime to allow proton transport over the hydrophobic core of a DLPE bilayer (6.7 ps), based upon the rate of proton transfer from one water molecule to another (1.2 (ps)
1) and the number of water molecules in a singlefile water pore long enough to bridge this hydrophobic core (8). The obvious conclusion is that water chains are sufficiently stable to allow proton permeation. Conduction along water wires may as well be the dominant mechanism in the permeation of protons in channels; an MD study of proton transport through a gramicidin channel can be found in, for example, [156]. 5.3

MD MODELLING OF MEDIATED MEMBRANE TRANSPORT

The Holy Grail of membrane modelling is without doubt the modelling of molecular realistic biological membranes, including membrane transport systems or systems with other functionalities (like the photosynthetic reaction centre, the respiratory chain and molecular complexes for recognition). Membrane transport systems comprise pores and channels, which only facilitate downhill or passive transport (i.e. movement towards equilibrium), and carriers and pumps, which are able to perform transport uphill. Pores select their transported substrates according to size, while channels are more selective and characteristically transport ions [157,158]. Ion-selective transmembrane protein channels form dynamic structures that rearrange their structure in response to outer influences, such as changes in ion gradients or electric potential across the membrane, and ligand binding. If the different conformational states are characterised by different ion permeabilities (open and closed states), this is called channel gating. Generally, gating is a complex process, involving various intermediate states [159,160]. A well-known example is the potentialdependent opening and closing of Naþ channels in nerve membranes. Ionselective channels can also be formed by molecules other than proteins. These have very specific properties, like a flexible conformation (so that conformational changes connected to ion transport can occur readily), sufficient length, and a hydrophobic exterior (except at the ends of the channel). A well-known example is gramicidine, a pentadecapeptide, of which two molecules in a b-helix conformation form, head-to-head, a transmembrane channel [161]. Cyclic

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PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

oligopeptides with a hydrophobic exterior, like the antibiotic valinomycin, are characteristic ion carriers. A general difficulty that is encountered in MD simulations of mediated transmembrane transport is, again, the timescale of relevant processes. For example, the mediated transport of a single ion across a membrane takes tens to hundreds of nanoseconds, and gating transitions several microseconds. Coarse-grained MD simulations do not provide insight into the delicate balance of forces and interactions involved in the transport. Furthermore, to construct a good starting conformation is especially difficult for the simulation of protein– membrane complexes, since structural information on membrane proteins is still sparse [162]. On the nanosecond timescale, simulation results are still sensitive to details of the starting structure of the proteins. Nevertheless, there are many recent papers concerning MD simulations of lipid bilayers containing biomolecules, among these various articles on proteins and oligopeptides forming transmembrane ion channels, reviewed by, amongst others, Biggin and Sansom [163], Feller [164] and Roux [165,166]. These simulations focus on different aspects, like the testing of channel structures, the effect of the lipid bilayer on the structure and vice versa, the dynamics of ion or water transport, and the identification of structurally relevant features that affect this process: e.g. multiple occupancy and gating. The above-mentioned problems have been dealt with (as fully as possible) by using somewhat simpler molecules to model the functioning of membrane proteins, special techniques, or combining MD simulations with other methods (see the review by Feller [164]). For example, helix bundles of (synthetic) channel-forming peptides have been studied as a model for the bilayer-spanning part of membrane proteins [163,167]. We end this section with an example of a recent MD study of Tieleman and co-workers [168] on the selectivity of a bacterial Kþ channel, KcsA, which is formed by a protein. Experimentally, it has been found that the channel is selective for Kþ , but under certain conditions it is possible for Naþ to pass through it. Furthermore, intracellular Naþ can block the channel. In Figure 32, the structure of the channel is depicted. The starting conformation was built using X-ray diffraction data (which have a relatively low resolution of 0.32 nm), and the missing KcsA side-chain coordinates were added by building stereochemically preferred conformers. A number of amino acid residues at the N and C terminal regions were not included in the simulations. The KscA protein was embedded in a preequilibrated POPC bilayer (116 POPCs in the extracellular leaflet, 127 in the intracellular one), hydrated with 9821 water molecules. All ionisable side-chains were in their default ionisation state, and Cl
ions were added to have a net charge of zero in the system. Van der Waals and electrostatic interactions were cut off at 1.0 and 1.7 nm, respectively. The duration of the simulations (ca. 2 ns, taking about 20 days of CPU time on eight processors) was an order of

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Figure 32. (a) Overview of the simulation system for the bacterial potassium channel KcsA, as used by Shrivastava et al. [168]. The channel consists of four peptide chains (for clarity in the picture only two are given), and is embedded in a lipid bilayer. The structure can be thought of as being made up of a selectivity filter, a central cavity, and a gate at the inner side of the bilayer. (b) Water molecules and Kþ ions in the selectivity filter; SO represents the extracellular mouth. From [168]. Reproduced by permission of the Biophysical Society

magnitude shorter than the estimated time for an ion to pass through the channel. Therefore, only short time- and length-scale motions can be observed, and the study of ion transport concentrates on the passage through the selectivity-filter part of the channel. Another limitation is that the parameters for ion–filter and ion–water interactions are not accurately known, but the authors checked that the results are not dependent on small changes in these parameters. It was found that the structure of the selectivity filter is somewhat flexible and is distorted by the presence of ions; Kþ ions and water translocate between the binding sites in the filter (in either direction) on a subnanosecond timescale, while Naþ remains bound. The distortion of the filter is significantly larger when the smaller Naþ ion is present. The results clearly correlate with the experimentally observed selectivity of the channel. 6

SUMMARY, CHALLENGES AND OUTLOOK

In this review, we have presented a molecular picture of the lipid bilayer system in relation to its permeation properties, as it appears from simulations and from self-consistent field calculations. Of course, it was not possible to go into all the details. In fact, the practicalities are always much more complicated, and the fine details are only of interest to the experts. The level of detail in this review is sufficient to evaluate the state of the art, at least to some extent. We hope that the previous pages have shown that the molecularly realistic models that have been elaborated on by the various

100 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

computational tools start to give a consistent and transparent picture of the lipid bilayer membranes. The computations can help to interpret experimental findings, and the MD snapshots will further guide our intuition. The MD simulations of molecular detail can give all the information that can be known for a small part of an ideal bilayer for fast processes (on the order of 10 ns). The dynamic aspects that take place on longer timescales can be investigated by coarse-grained methods, or with DPD or quasi-dynamic MC simulations. Due to continuously increasing computer power, the field of MD is gradually moving into larger systems and longer (real-time) scales on the one hand, and more complex, biologically relevant systems, e.g. including additives and functional molecules, on the other. Equilibrium properties are surprisingly accurately predicted by molecularlevel SCF calculations. MC simulations help us to understand why the SCF theory works so well for these densely packed layers. In effect, the high density screens the correlations for chain packing and chain conformation effects to such a large extent that the properties of a single chain in an external field are rather accurate. Cooperative fluctuations, such as undulations, are not included in the SCF approach. Also, undulations cannot easily develop in an MD box. To see undulations, one needs to perform molecularly realistic simulations on very large membrane systems, which are extremely expensive in terms of computation time. One can formulate many challenges for the near future. One of these is to include dynamics in SCF calculations in a convincing way. The advantage of SCF is that the technique is computationally extremely efficient. Therefore it is more easy to sample large parts of the parameter space, and, by doing so, one can understand the regularities of particular problems. Some first initiatives to take the approach into the world of dynamics have already given interesting results, but these approaches have not yet been applied to lipid bilayers. There is also some work under way to analyse off-equilibrium so-called steady-state distributions of molecules that are exposed to some chemical potential gradients. This development will help us understand many aspects that have to do with the semi-permeable properties of the bilayer membranes. The link from lipid properties to mechanical properties of the bilayers is now feasible within the SCF approach. The next step is to understand the phase behaviour of the lipid systems. It is likely that large-scale (3D) SCF-type calculations are needed to prove the conjectures in the field that particular values of the Helfrich parameters are needed for processes like vesicle fusion, etc. In this context, it may also be extremely interesting to see what happens with the mechanical parameters when the system is molecularly complex (i.e. when the system contains many different types of molecules). Then there will be some hope that novel and deep insights may be obtained into the very basic questions behind nature’s choice for the enormous molecular complexity in membrane systems.

F. A. M. LEERMAKERS AND J. M. KLEIJN

GLOSSARY a a A As BD c.m.c. d DPPC DLPE DMPC DPD DSPC e E f F F int J J0 k kc
k K K K l L m M MC MD ni N N Nav p P P PC PG q

Area per molecule, ao equilibrium area (m2 ) Acceleration (m s
2 ) Surface area of the system (m2 ) Surface area of membrane (m2 ) Brownian dynamics Critical micellisation concentration (mol m
3 ) Thickness of the membrane (m) Dipalmitoylphosphatidylcholine Dilauroylphosphatidylethanol Dimyristoylphosphatidylcholine Dissipative particle dynamics Distearoylphosphatidylcholine Elementary charge 1:6  10
19 (C) Field strength (V m
1 ) Free-energy contribution (J) Helmholtz energy (J) Free energy of interaction (J) Total or mean curvature (m
1 ) Spontaneous curvature (m
1 ) Boltzmann’s constant 1:38  10
23 (J K
1 ) Mean bending modulus (J) Saddle splay modulus (J) Gaussian curvature (m
2 ) Cluster constant used in water model Water/membrane partition coefficient Length of surfactant tail (m) Length of cylinder (m) Mass of particle (kg) Last layer in lattice used in SCF calculation Monte Carlo Molecular dynamics Number of molecules of type i Number of molecules in system Number of segments in chain Avogadro’s number 6:02  1023 (mol
1 ) Pressure (N m
2 ) Probability Permeability (m s
1 ) Phosphatidylcholine (zwitterionic) Phosphatidylglycerol (negatively charged) Charge (C)

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102 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

r rij ri R1 , R2 R S S S SCF SOPC t t T U u vA v V V z Z g e0 erA em kD l x ji js c w

Dimensionless radial coordinate Distance between atoms i and j (m) Position of particle number i (m) Radii of curvature (m) Radius of vesicle (m) Surfactant parameter Entropy of the system (J K
1 ) Order parameter Self-consistent-field 1-stearoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine Time (s) Ranking number of tail segments Absolute temperature (K) Internal energy of the system (J) Self-consistent (segment) potential (J) Valency of component A Volume of surfactant tail(s) (m3 ) Volume of the system (m3 ) Potential energy in MD simulation (J) Layer number Lattice coordination number Surface tension (J m
2 ¼ N m
1 ) Dielectric permittivity of vacuum 8:85  10
12 (C V
1 m
1 ) Dielectric permittivity times segment volume of A (C V
1 m2 ) Total curvature energy of vesicle (J) Debye length (m) A priori step probability in lattice Membrane persistence length (m) Volume fraction of component i Volume fraction of salt Electrostatic potential (V) Flory–Huggins interaction parameter

REFERENCES 1.

Singer, S. J. and Nicolson, G. L. (1972). The fluid mosaic model of the structure of cell membranes, Science, 175, 720–731. 2. Papahadjopoulos, D., Jacobson, K., Nir, S. and Isac, T. (1973). Phase transitions in phospholipid vesicles fluorescence polarization and permeability measurements concerning the effect of temperature and cholesterol, Biophys. Biochim. Acta, 311, 330–348.

F. A. M. LEERMAKERS AND J. M. KLEIJN 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.

103

Lyklema, J. (1991/1995). Fundamentals of Interface and Colloid Science I–II. Academic Press, London. Tanford, C. (1973). The Hydrophobic Effect: Formation of Micelles and Biological Membranes. John Wiley & Sons, Ltd, New York. Besseling, N. A. M. (1993). Statistical Thermodynamics of Fluids with OrientationDependent Interactions. Applications to Water in Homogeneous and Heterogeneous Systems. Ph.D. Thesis, Wageningen University. Besseling, N. A. M. and Scheutjens, J. M. H. M. (1994). Statistical thermodynamics of fluids with orientation-dependent interactions in homogeneous and inhomogeneous systems, J. Phys. Chem., 98, 11 597–11 609. Beaglehole, D. and Wilson, P. (1993). Thickness and anisotropy of the ice–water interface, J. Phys. Chem., 97, 11 053–11 055. Leermakers, F. A. M. and Cohen Stuart, M. A. (1996). Self-consistent-field lattice gas model for the surface ordering transition of n-hexadecane, Phys. Rev. Lett., 76, 82–85. Shaw, D. G. (ed.) (1989). Hydrocarbons with Water and Seawater. Part II: Hydrocarbons C8 to C38. IUPAC Series on Solubility Data, Vol. 38, Pergamon, Oxford. Evans, D. F. and Wennerstrom, H. (1994). The Colloidal Domain Where Physics, Chemistry, Biology and Technology Meet. VCH Publishers, New York. Israelachvilli, J. N., Mitchell, D. J. and Ninham, B. W. (1976). Theory of selfassembly of hydrocarbon amphiphiles into micelles and bilayers, J. Chem. Soc. Faraday Trans. II, 72, 1525–1568. Hill, T. L. (1991/1992). Thermodynamics of Small Systems (Part 1; Part 2). Dover Publications, New York. Hall, D. G. and Pethica, B. A. (1976). Nonionic Surfactants. Chapter 16. Marcel Dekker, New York. Lindahl, E. and Edholm, O. (2000). Spatial and energetic–entropic decomposition of surface tension in lipid bilayers from molecular dynamics simulations, J. Chem. Phys., 113, 3882–3893. Marrink, S. J. and Mark, A. E. (2001). Effect of undulations on surface tension in simulated bilayers, J. Phys. Chem., 105, 6122–6127. Oversteegen, S. M., Barneveld, P. A., van Male, J., Leermakers, F. A. M. and Lyklema, J. (1999). Thermodynamic derivation of mechanical expressions for interfacial parameters, Phys. Chem. Chem. Phys., 1, 4987–4494. Gibbs, J. W. (1993). The Scientific Papers, Vol. 1. OxBow Press, Oxford, UK. Helfrich, W. (1973). Elastic properties of lipid bilayers: theory and possible experiments, Z. Naturforsch., 28c, 693–703. Jung, H. T., Coldren, B., Zasadzinski, J. A., Iampietro, D. J. and Kaler, E. W. (2001). The origins of stability of spontaneous vesicles, Proc. Natl Acad. Sci. USA, 98, 1353–1357. MacDonald, R. C., Jones, F. D. and Qui, R. (1994). Fragmentation into small vesicles of dioleoylphosphatidylcholine bilayers during freezing and thawing, Biochim. Biophys. Acta–Biomembranes, 1191, 362–370. Seifert, U. and Lipowsky, R. (1995). Morphology of vesicles. In Handbook of Biological Physics. Vol. 1, eds. Lipowsky, R. and Sackmann, E. Elsevier, Amsterdam, pp. 403–460. Safran, S. A., Pincus, P. A., Andelman, D. and MacKintosh, F. C. (1991). Stability and phase behavior of mixed surfactant vesicles, Phys. Rev. A, 43, 1071–1078. Claessens, M. M. A. E., van Oort, B. F., Leermakers, F. A. M., Hoekstra, F. A. and Cohen Stuart, M. A. (2003). Charged lipid vesicles: effects of salts on bending rigidity, stability, and size, submitted to Biophys. J.

104 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39.

40. 41. 42. 43.

de Gennes, P. G. and Taupin, C. (1982). Microemulsions and the flexibility of oil/ water interfaces, J. Phys. Chem., 86, 2294–2304. Helfrich, W. (1990). Elasticity and thermal undulations of fluid films of amphiphiles. In Liquids at Interfaces. eds. Chavrolin, J., Joanny, J. F. and Zinn-Justin, J., Elsevier, Amsterdam, pp. 209–237. Herve, P., Roux, D., Bellocq, A. M., Nallet, F. and Gulik-Krzywicki, T. (1993). Dilute and concentrated phases of vesicles at thermal equilibrium, J. Phys. II, France, 3, 1255–1270. Simons, B. D. and Cates, M. E. (1992). Vesicles and onion phases in dilute surfactant solutions, J. Phys. II, France, 7, 1439–1451. Hill, T. L. (1986). An Introduction to Statistical Thermodynamics. Dover Publications, New York. Safran, S. A. (1994). Statistical Thermodynamics of Surfaces, Interfaces, and Membranes. Addison Wesley, Reading, UK. Allen, M. P. and Tildesley, D. J. (1987). Computer Simulation of Liquids. Clarendon Press, Oxford. Tieleman, D. P., Marrink, S. J. and Berendsen, H. J. C. (1997). A computer perspective of membranes: molecular dynamics studies of lipid bilayer systems, Biochim. Biophys. Acta-Biomembranes, 1331, 235–270. Scott, H. L. (2002). Modeling the lipid component of membranes, Curr. Opin. Struct. Biol., 12, 495–502. Lindahl, E. and Edholm, O. (2000). Mesoscopic undulations and thickness fluctuations in lipid bilayers from molecular dynamics simulations, Biophys. J., 79, 426–433. Zubrzycki, I. Z., Xu, Y., Madrid, M. and Tang, P. (2000). Molecular dynamics simulations of a fully hydrated dimyristoylphosphatidylcholine membrane in liquid-crystalline phase, J. Chem. Phys., 112, 3437–3441. Venable, R. M., Brooks, B. R. and Pastor, R. W. (2000). Molecular dynamics simulations of gel phase lipid bilayers in constant pressure and constant surface area ensembles, J. Chem. Phys., 112, 4822–4832. Tobias, D. J., Tu, K. and Klein, M. L. (1997). Atomic-scale molecular dynamics simulations of lipid membranes, Curr. Opin. Colloid Interf. Sci., 2, 15–26. Pastor, R. W. (1994). Molecular dynamics and Monte Carlo simulations of lipid bilayers, Curr. Opin. Struct. Biol., 4, 486–492. Nagle, J. F., Zhang, R., Tristram-Nagle, S., Sun, W. J., Petrache, H. I. and Suter, R. M. (1996). X-ray structure determination of fully hydrated L-alpha phase dipalmitoylphosphatidylcholine bilayers, Biophys. J., 70, 1419–1431. Hyvonen, M. T., Rantala, T. T. and Ala-Korpela, M. (1997). Structure and dynamic properties of diunsaturated 1-palmitoyl-2-linoleoyl-sn-glycero-3phosphatidylcholine lipid bilayer from molecular dynamics simulation, Biophys. J., 73, 2907–2923. Feller, S. E. and Pastor, R. W. (1999). Constant surface tension simulations of lipid bilayers; the sensitivity of surface areas and compressibilities, J. Chem. Phys., 111, 1281–1287. Chiu, S. W., Clark, M., Balaji, V., Subramaniam, S., Scott, H. L. and Jakobsson, E. (1995). Incorporation of surface tension into molecular dynamics simulation of an interface: a fluid phase lipid bilayer membrane, Biophys. J., 69, 1230–1245. Damodaran, K. V., Merz, K. M. Jr and Gaber, B. P. (1992). Structure and dynamics of the dilauroylphosphatidylethanolamine lipid bilayer, Biochemistry, 31, 7656–7664. Damodaran, K. V. and Merz Jr, K. M. (1994). A comparison of DMPC and DLPE based lipid bilayers, Biophys. J., 66, 1076–1087.

F. A. M. LEERMAKERS AND J. M. KLEIJN 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62.

105

Raghavan, K., Reddy, M. R. and Berkowitz, M. L. (1992). A molecular dynamics study of the structure and dynamics of water between dilauroylphosphatidylethanolamine bilayers, Langmuir, 8, 233–240. Perera, L., Essmann, U. and Berkowitz, M. L. (1996). Role of water in the hydration force acting between lipid bilayers, Langmuir, 12, 2625–2629. Lopez Cascales, J. J., Garcia de la Torre, J., Marrink, S. J. and Berendsen, H. J. C. (1996). Molecular dynamics simulation of a charged biological membrane, J. Chem. Phys., 104, 2713–2720. Jorgensen, W. L., Madura, J. D. and Swenson, C. J. (1984). Optimized intermolecular potential functions for liquid hydrocarbons, J. Am. Chem. Soc., 106, 6638–6646. Jorgensen, W. L. and Tirado-Rives, J. (1988). The OPLS potential functions for proteins. Energy minimizations for crystals of cyclic peptides and crambin, J. Am. Chem. Soc., 110, 1657–1666. Tieleman, D. P. and Berendsen, H. J. C. (1996). Molecular dynamics simulations of a fully hydrated dipalmitoylphosphatidylcholine bilayer with different macroscopic boundary conditions and parameters, J. Chem. Phys., 105, 4871–4880. Berendsen, H. J. C., Postma, J. P. M., Gunsteren, W. F. and Hermans, J. (1981). Intermolecular Forces. Reidel, Dordrecht. Chiu, S. W., Clark, M. M., Jakobsson, E., Subramaniam, S. and Scott, H. L. (1999). Optimization of hydrocarbon chain interaction parameters: application to the simulation of fluid phase lipid bilayers, J. Phys. Chem. B, 103, 6323–6327. van Gunsteren, W. F. and Berendsen, H. J. C. (1987). Groningen Molecular Simulation (GROMOS). Brooks, B. R., Bruccoleri, R. E., Olafson, B. D., States, D. J., Swaminathan, S. and Karplus, M. (1983). CHARMM: a program for macromolecular energy minimization and dynamics calculations, J. Comput. Chem., 4, 187–217. Weiner, S. J., Kollman, P. A., Case, D. A., Singh, U. C., Ghio, C., Alagona, G., Profeta, S. and Weiner, P. (1984). A new force field for molecular mechanical simulation of nucleic acids and proteins, J. Am. Chem. Soc., 106, 765–784. Lemak, A. S. and Balabaev, N. K. (1996). Molecular dynamics simulation of a polymer chain in solution by collisional dynamics method, J. Comput. Chem., 17, 1685–1695. Marrink, S. J., Lindahl, E., Edholm, O. and Mark, A. E. (2001). Simulation of the spontaneous aggregation of phospholipids into bilayers, J. Am. Chem. Soc., 123, 8638–8639. Rand, R. P. and Parsegian, V. A. (1989). Hydration forces between phospholipid bilayers, Biochim. Biophys. Acta, 988, 351–376. Berger, O., Edholm, O. and Jahnig F. (1997). Molecular dynamics simulations of a fluid bilayer of dipalmitoylphosphatidylcholine at full hydration, constant pressure and constant temperature, Biophys. J., 72, 2002–2013. Seelig J. and Seelig A. (1974). Dynamic structure of fatty acyl chains in a phospholipid bilayer measured by DMR, Biochemistry, 13, 4839–4845. Kleijn, J. M. and van Leeuwen, H. P. (2000). Electrostatic and electrodynamic properties of biological interphases. In Physical Chemistry of Biological Interfaces. eds. Baszkin, A. and Norde, W., Marcel Dekker, New York, pp. 49–63. Tu, K., Tobias, D. J. and Klein M. L. (1995). Constant pressure and temperature molecular dynamics simulation of a fully hydrated liquid crystal phase dipalmitoylphosphatidylcholine bilayer, Biophys. J., 69, 2558–2562. Goetz, R. and Lipowsky, R. (1998). Computer simulations of bilayer membranes; self-assembly and interfacial tension, J. Chem. Phys., 108, 7397–7409.

106 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78.

79. 80. 81.

Smit, B., Hilbers, P. A. J., Esselink, K. Rupert, L. A. M. van Os, N. M. and Schlijper, A. G. (1991). Structure of a water–oil interface in the presence of micelles – a computer-simulation study, J. Phys. Chem., 95, 6361–6368. Groot, R. D. and Rabone, K. L. (2001). Mesoscopic simulation of cell membrane damage, morphology change and rupture by nonionic surfactants, Biophys. J., 81, 725–736. Venturoli, M. and Smit, B. (1999). Simulating the self-assembly of model membranes, Phys. Chem. Comm., 10. Onsager, L. (1996). World scientific series in 20th century physics. In The Collected Works of Lars Onsager. Vol. 17, eds. Hemmer, P. C., Holden H. and Ratkje, S. K., World Scientific Publishing Co., New Jersey. Mu¨ller, M. and Schick, M. (1996). Structure and nucleation of pores in polymeric bilayers; a Monte Carlo simulation, J. Chem. Phys., 105, 8282–8292. Venable, R. M., Zhang, Y. H., Hardy, B. J. and Pastor, R. W. (1998). Molecular dynamics simulations of a lipid bilayer and of hexadecane: an investigation of membrane fluidity, Science, 262, 223–226. Pink, D. A., Green, T. J. and Chapman, D. (1981). Raman scattering in bilayers of saturated phosphatidylcholines and cholesterol. Experiment and theory, Biochemistry, 20, 6692–6698. Mouritsen, O. G. (1991). Theoretical models of phospholipid phase transitions, Chem. Phys. Lipids, 57, 179–194. Sugar, I. P., Thompson, T. E. and Biltonen, R. L. (1999). Monte Carlo simulation of two-component bilayers: DMPC/DSPC mixtures, Biophys. J., 76, 2099–2110. Levine, Y. K., Kolinski, A. and Skolnick, J. (1993). A lattice dynamics study of a Langmuir monolayer of monounsaturated fatty acids, J. Chem. Phys., 98, 7581–7587. Levine, Y. K. (1993). Monte Carlo dynamics study of cis and trans unsaturated hydrocarbon chains, Mol. Phys., 78, 619–628. Rabinovich, A. L. and Ripatti, P. O. (1997). Intramolecular ordering of the bonds of hydrocarbon chains of lipids. Computer simulation, Biophysics, 42, 143–151. Rabinovich, A. L. and Ripatti, P. O. (1997). A theoretical study of the intramolecular ordering of the bonds of cis-octadecene chains, Biophysics, 42, 879–887. Rabinovich, A. L. and Ripatti, P. O. (1997). A theoretical study of the intramolecular ordering of the bonds of trans-octadecene chains, Biophysics, 42, 889–895. Fraaije, J. G. E. M. (1993). Dynamic density functional theory for microphase separation kinetics of block copolymer melts, J. Chem. Phys., 99, 9202–9212. van Vlimmeren, B. A. C., Maurits, N. M., Zvelindovsky, A. V., Sevink, G. J. A. and Fraaije, J. G. E. M. (1999). Simulation of 3D mesoscale structure formation in concentrated aqueous solution of the triblock polymer surfactants (ethylene oxide) 13(propylene oxide)30(ethylene oxide)13 and (propylene oxide)19(ethylene oxide)33(propylene oxide)19. Application of dynamic mean-field density functional theory, Macromolecules, 32, 646–656. Chandler, D. (1987). Introduction to Statistical Thermodynamics. Oxford University Press, Oxford. Leermakers, F. A. M., Scheutjens, J. M. H. M. and Lyklema, J. (1990). Statistical thermodynamics of association colloids. IV. Inhomogeneous membrane system, Biochim. Biophys. Acta, 1024, 139–151. Evers, O. A., Scheutjens, J. M. H. M. and Fleer, G. J. (1990). Statistical thermodynamics of block copolymer adsorption. 1. Formulation of the model and results for the adsorbed layer structure, Macromolecules, 23, 5221–5233.

F. A. M. LEERMAKERS AND J. M. KLEIJN 82. 83. 84. 85. 86.

87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102.

107

Guerin, C. B. E. and Szleifer, I. (1999). Self-assembly of model nonionic amphiphilic molecules, Langmuir, 15, 7901–7911. Meijer, L. A. and Leermakers, F. A. M. (1998). GOLIATH: Self-Consistent Field Implementation Dedicated to Self-Assembly. Wageningen University. Meijer, L. A., Leermakers, F. A. M. and Lyklema, J. (1994). Head-group conformations in lipid bilayer membranes, Recl. Trav. Chim. Pays-Bas, 113, 167–175. Meijer, L. A., Leermakers, F. A. M. and Lyklema, J. (1995). Modeling the interactions between phospholipid bilayer membranes with and without additives, J. Phys. Chem., 99, 17 282–17 293. Meijer, L. A., Leermakers, F. A. M. and Lyklema, J. (1999). Self-consistent-field modeling of complex molecules with united atom detail in inhomogeneous systems. Cyclic and branched foreign molecules in dimyristoylphosphatidylcholine membranes, J. Chem. Phys., 110, 6560–6579. Gruen, D. W. R. (1980). A statistical mechanical model of the lipid bilayer above its phase transition, Biochim. Biophys. Acta, 595, 161–183. Cantor, R. S. and Dill, K. A. (1986). Theory for the equation of state of phospholipid monolayers, Langmuir, 2, 331–337. Szleifer, I., Ben-Shaul, A. and Gelbart, W. M. (1986). Chain statistics in micelles and bilayers: effects of surface roughness and internal energy, J. Chem. Phys., 85, 5345–5358. Ben-Shaul, A. and Gelbart, W. M. (1994). Statistical Thermodynamics of Amphiphile Self-assembly: Structure and Phase Transitions in Micellar Solutions. Chapter 1. Springer, Berlin. Dill, K. A., Naghizadeh, J. and Marqusee, J. A. (1988). Chain molecules at high densities at interfaces, Ann. Rev. Phys. Chem., 39, 425–461. Leermakers, F. A. M., Scheutjens, J. M. H. M. and Lyklema, J. (1983). On the statistical thermodynamics of membrane formation, Biophys. Chem., 18, 353–360. Marcˇelja, S. (1974). Chain ordering in liquid crystals. II. Structure of bilayer membranes, Biochim. Biophys. Acta, 367, 165–176. Amoskov, V. M. and Birshtein, T. M. (2000). Homeotropic and planar structures in liquid-crystalline polymer brushes, Vysomolekul. Soedin. A B, 42, 612–626. Leermakers, F. A. M. and Scheutjens, J. M. H. M. (1988). Statistical thermodynamics of association colloids. III. The gel to liquid phase transition of lipid bilayer membranes, J. Chem. Phys., 89, 6912–6924. Szleifer, I., Ben-Shaul, A. and Gelbart, W. M. (1990). Chain packing statistics and thermodynamics of amphiphile monolayers, J. Phys. Chem., 94, 5081–5089. Leermakers, F. A. M. and Scheutjens, J. M. H. M. (1990). Statistical thermodynamics of association colloids. V. Critical micelle concentration, micellar size and shape, J. Coll. Interf. Sci., 136, 231–241. Leermakers, F. A. M. and Scheutjens, J. M. H. M. Statistical thermodynamics of association colloids. I. Lipid bilayer membranes, J. Chem. Phys., 89, 3264–3274. Hauser, H., Pascher, I., Pearson, R. H. and Sundell, S. (1981). Preferred conformation and molecular packing of phophatidylethanolamine and phosphatidyl choline, Biochim. Biophys. Acta, 650, 21–51. Cantor, R. S. (1999). Lipid composition and the lateral pressure profile in bilayers, Biophys. J., 76, 2625–2639. Oversteegen, S. M. and Leermakers, F. A. M. (2000). Thermodynamics and mechanics of bilayer membranes, Phys. Rev. E, 62, 8453–8461. Rabinovich, A. L., Ripatti, P. O., Balabaev, N. K. and Leermakers, F. A. M. (2003). Molecular dynamics simulations of hydrated unsaturated lipid bilayers in

108 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

103.

104. 105. 106. 107. 108. 109. 110.

111. 112. 113. 114. 115. 116. 117. 118. 119.

the liquid-crystal phase and comparison to self-consistent field modeling, Phys. Rev. E, 67, 011909. Leermakers, F. A. M., Rabinovich, A. L. and Balabaev, N. K. (2003). Selfconsistent field modeling of hydrated unsaturated lipid bilayers in the liquidcrystal phase and comparison to molecular dynamics simulations, Phys. Rev. E, 67, 011910. Rabinovich A. L. and Ripatti, P. O. (1991). On the conformational, physical properties and functions of polyunsaturated acyl chains, Biochim. Biophys. Acta-Lipid. Metabol., 1085, 53–62. Fattal, D. R. and Ben-Shaul, A. (1994). Mean-field calculations of chain packing and conformational statistics in lipid bilayers: comparison with experiments and molecular dynamics studies, Biophys. J., 67, 983–995. Heller, H., Schaefer, M. and Schulten, K. (1993). Molecular dynamics simulation of a bilayer of 200 lipids in the gel and in the liquid-crystal phases, J. Phys. Chem., 97, 8343–8359. Rawicz, W., Olbrich, K. C., McIntosh, T., Needham, D. and Evans, E. (2000). Effect of chain length and unsaturation on elasticity of lipid bilayers, Biophys. J., 79, 328–339. Tu, K., Tobias, D. J., Blasie, J. K. and Klein, M. L. (1996). Molecular dynamics investigation of the structure of a fully hydrated gel-phase dipalmitoylphosphatidylcholine bilayer, Biophys. J., 70, 595–608. Nagle, J. F. (1980). Theory of the main lipid bilayer phase transition, Ann. Rev. Phys. Chem., 31, 157–195. Marsh, D. (1991). Analysis of the chainlength dependence of lipid phase transition temperatures: main and pretransitions of phosphatidylcholines; main and non-lamellar transitions of phosphatidylethanolamines, Biochem. Biophys. Acta– Biomembranes, 1062, 1–6. Schmid, F. and Schick, M. (1995). Liquid phases of Langmuir monolayers, J. Chem. Phys., 102, 2080–2091. Den Otter, W. K. and Briels, W. J. (2003). The bending rigidity of an amphiphilic bilayer from equilibrium and nonequilibrium molecular dynamics, J. Chem. Phys., 118, 4712–4720. Baumgartner, A. (1994). Asymmetries of a curved bilayer model membrane, J. Chem. Phys., 101, 9060–9062. Leermakers, F. A. M. and Scheutjens, J. M. H. M. (1989). Statistical thermodynamics of association colloids. II. Lipid vesicles, J. Chem. Phys., 93, 7417–7426. Love, A. E. H. (1907). Lehrbuch der Elastizita¨t. Teubner Verlag, Wiesbaden, Germany. Szleifer, I., Kramer, D., Ben-Shaul, A., Roux, D. and Gelbart, W. M. (1988). Curvature elasticity of pure and mixed surfactant films, Phys. Rev. Lett., 60, 1966–1969. Lekkerkerker, H. N. W. (1990). The electric contribution to the curvature elastic moduli of charged fluid interfaces, Physica A, 167, 384–394. Helfrich, W. (1995). Handbook of Biological Physics. Tension-Induced Mutual Adhesion and a Conjectured Superstructure of Lipid Membranes. Chapter 14. Elsevier, Amsterdam. Zhulina, E. B., Borisov, O. V., van Male, J. and Leermakers, F. A. M. (2001). Adsorption of tethered polyelectrolytes onto oppositely charged solid–liquid interfaces, Langmuir, 17, 1277–1293.

F. A. M. LEERMAKERS AND J. M. KLEIJN

109

120. Borisov, O. V., Leermakers, F. A. M., Fleer, G. J. and Zhulina, E. B. (2001). Polyelectrolytes tethered to a similarly charged surface, J. Chem. Phys., 114, 7700–7712. ¨ ber die allgemeinen osmotischen Eigenschaften der Zell, ihre 121. Overton, E. (1899). U vermutliche Ursachen und ihre Bedeutung fu¨r die Physiologie, Vierteljahrsschr. Naturforsch. Ges. Zuerich, 44, 88–114. ¨ ber die osmotischen Eigenschaften der lebenden 122. Overton, E. (1895). U Pflanzen und Tierzelles, Vierteljahrsschr. Naturforsch. Ges. Zuerich, 40, 159–201, 1895. 123. Lieb, W. R. and Stein, W. D. (1969). Biological membranes behave as non-porous polymer sheets with the respect to the diffusion of non-electrolytes, Nature, 224, 240–243. 124. Walter, A. and Gutknecht, J. (1986). Permeability of small nonelectrolytes through lipid bilayer membranes, J. Membr. Biol., 90, 207–218. 125. Hanai, T. and Dayton, D. A. (1966). The permeability to water of bimolecular lipid membranes, J. Theor. Biol., 11, 1370. 126. Finkelstein, A. and Cass, A. (1967). Effect of cholesterol on the water permeability of thin lipid membranes, Nature, 216, 717–718. 127. Aguilella, V., Belaya, M. and Levadny, V. (1996). Ion permeability of a membrane with soft polar interfaces. 1. The hydrophobic layer as the rate-determining step, Langmuir, 12, 4817–4827. 128. Sok, R. M., Berendsen, H. J. C. and van Gunsteren, W. F. (1992). Molecular dynamics simulation of the transport of small molecules across a polymer membrane, J. Chem. Phys., 96, 4699–4704. 129. Marrink, S. J. and Berendsen, H. J. C. (1994). Simulation of water transport through a lipid membrane, J. Phys. Chem., 98, 4155–4168. 130. Marrink, S. J., Ja¨hnig, F. and Berendsen, H. J. C. (1996). Proton transport across transient single-file water pores in a lipid membrane studied by molecular dynamics simulations, Biophys. J., 71, 632–647. 131. Wilson, M. A. and Pohorille, A. (1996). Mechanism of unassisted ion transport across membrane bilayers, J. Am. Chem. Soc., 118, 6580–6587. 132. Marrink, S. J., Sok, R. M. and Berendsen, H. J. C. (1996). Free volume properties of a simulated membrane, J. Chem. Phys., 104, 9090–9099. 133. Xiang, T. X. and Anderson, B. D. (1999). Molecular dissolution processes in lipid bilayers: a molecular dynamics simulation, J. Chem. Phys., 110, 1807–1818. 134. Xiang, T. X. and Anderson, B. D. (2002). A computer simulation of functional group contributions to free energy in water and a DPPC lipid bilayer, Biophys. J., 82, 2052–2066. 135. Xiang, T. X. and Anderson, B. D. (1998). Influence of chain ordering on the selectivity of dipalmitoylphosphatidylcholine bilayer membranes for permeant size and shape, Biophys. J., 75, 2658–2671. 136. Mitragotri, S., Johnson, M. E., Blankschtein, D. and Langer, R. (1999). An analysis of size selectivity of solute partitioning, diffusion, and permeation across lipid bilayers, Biophys. J., 77, 1268–1283. 137. Ohvo-Rekila¨, H., Ramstedt, B., Leppima¨ki, P. and Slotte, J. P. (2002). Cholesterol interactions with phospholipids in membranes, Progr. Lipid Res., 41, 66–97. 138. Robinson, A. J., Richards, W. G., Thomas, P. J. and Hann, M. M. (1995). Behavior of cholesterol and its effect on head group and chain conformations in lipid bilayers: a molecular dynamics study, Biophys. J., 68, 164–170.

110 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 139. Tu, K., Klein, M. L. and Tobias, D. J. (1998). Constant-pressure molecular dynamics investigation of cholesterol effects in a dipalmitoylphosphatidylcholine bilayer, Biophys. J., 75, 2147–2156. 140. McIntosh, T. J., Magid, A. D. and Simon, S. A. (1989). Cholesterol modifies the short-range repulsive interactions between phosphatidylcholine membranes, Biochemistry, 28, 17–25. 141. Fettiplace, R. and Haydon, D. A. (1980). Water permeability of lipid membranes, Physiol. Rev., 60, 510–550. 142. Pohorille, A., New, M. H., Schweighofer, K. and Wilson, M. A. (1999). Insights from computer simulations into the interactions of small molecules with lipid bilayers. In Membrane Permeability, Vol. 48: 100 Years Since Ernest Overton. eds. Deamer, D. W., Kleinzeller, A. and Fambrough, D. M., Academic Press, San Diego pp. 50–76. 143. Bala´zˇ, S. (2000). Lipophilicity in trans-bilayer transport and subcellular pharmacokinetics, Persp. Drug Discov. Des., 19, 157–177. 144. Gruen, D. W. R. and Haydon, D. A. (1981). A mean-field model of the alkanesaturated lipid bilayer above its phase transition. II. Results and comparison with experiment, Biophys. J., 33, 167–188. 145. Bassolino-Klimas, D., Alper, H. E. and Stouch, T. R. (1993). Solute diffusion in lipid bilayer membranes: an atomic level study by molecular dynamics simulation, Biochemistry, 32, 12 624–12 637. 146. Bassolino-Klimas, D., Alper, H. E. and Stouch, T. R. (1995). Mechanism of solute diffusion through lipid bilayer membranes by molecular dynamics simulation, J. Am. Chem. Soc., 117, 4118–4129. 147. Sandre, O., Moreaux, L. and Brochard-Wyart, F. (1999). Dynamics of transient pores in stretched vesicles, Proc. Natl Acad. Sci. USA, 96, 10 591–10 596. 148. Paula, S., Volkov, A. G., van Hoek, A. N., Haines, T. H. and Deamer, D. W. (1996). Permeation of protons, potassium ions, and small polar solutes through phospholipid bilayers as a function of membrane thickness, Biophys. J., 70, 339–348. 149. Parsegian, A. (1969). Energy of an ion crossing a low dielectric membrane: solutions to four relevant electrostatic problems, Nature, 221, 844–846. 150. Hamilton, R. T. and Kaler, E. W. (1990). Alkali metal ion transport through thin bilayers, J. Phys. Chem., 94, 2560–2566. 151. Venable, R. M., and Pastor, R. W. (2002). Molecular dynamics simulations of water wires in a lipid bilayer and water/octane model systems, J. Chem. Phys., 116, 2663–2664. 152. Zahn, D. and Brickmann, R. (2002). Molecular dynamics study of water pores in a phospholipid bilayer, Chem. Phys. Lett., 352, 441–446. 153. Nichols, J. W. and Deamer, D. W. (1980). Net proton hydroxyl permeability of large unilamellar liposomes measured by an acid–base titration technique, Proc. Natl Acad. Sci. USA, 77, 2038–2042. 154. Elamrami, K. and Blume, A. (1983). Effect of lipid phase transition on the kinetics of Hþ/OH
diffusion across phosphatidic acid bilayers, Biochim. Biophys. Acta, 727, 22–30. 155. Perkins, W. R. and Cafiso, D. S. (1986). An electrical and structural characterization of Hþ/OH
currents in phospholipid vesicles, Biochemistry, 25, 2270–2276. 156. Pome`s, R. and Roux, B. (2002). Molecular mechanism of Hþ conduction in the single-file water chain of the gramicidin channel, Biophys. J., 82, 2304–2316.

F. A. M. LEERMAKERS AND J. M. KLEIJN

111

157. Post, R. L. (1999). Active transport and pumps. In Membrane Permeability: Vol. 48 100 Years Since Ernest Overton. eds. Deamer, D. W., Kleinzeller, A. and Fambrough, D. M. Academic Press, San Diego pp. 397–417. 158. Eisenberg, B. (1998). Ionic channels in biological membranes: natural nanotubes, Acc. Chem. Res., 31, 117–123. 159. Honig, B. H., Hubbell, W. L. and Flewelling, R. F. (1986). Electrostatic interactions in membranes and proteins, Ann. Rev. Biophys. Biochem., 15, 163–193. 160. Schulze, K. D. (1994). Investigations of the channel gating influence on the dynamics of biomembranes, Z. Phys. Chem., 186, 47–63. 161. Arseniev, A. S., Barsukov, I. L., Bystrov, V. F., Lomize, A. L. and Ovchinnikov, Y. A. (1985). 1H-NMR study of gramicidin-A transmembrane ion channel: headto-head right handed single stranded helices, FEBS Lett., 186, 168–174. 162. Werten, P. J. L., Re´migy, H. W., de Groot, B. L., Fotiadis, D., Philippsen, A., Stahlberg, H., Grubmu¨ller, H. and Engel, A. (2002). Progress in the analysis of membrane protein structure and function, FEBS Lett., 529, 65–72. 163. Biggin, P. C. and Sansom, M. S. P. (1999). Interactions of a-helices with lipid bilayers: a review of simulation studies, Biophys. Chem., 76, 161–183. 164. Feller, S. E. (2000). Molecular dynamics simulations of lipid bilayers, Curr. Opin. Coll. Interf. Sci., 5, 217–223. 165. Roux, B. (2002). Theoretical and computational models of ion channels, Curr. Opin. Struct. Biol., 12, 182–189. 166. Roux, B. (2002). Computational studies of the gramicidin channel, Acc. Chem. Res., 35, 366–375. 167. Law, R. J., Tieleman, D. P. and Sansom, M. S. P. (2003). Pores formed by the nicotinic receptor M2d peptide: a molecular dynamics simulation study, Biophys. J., 84, 14–27. 168. Shrivastava, I. H., Tieleman, D. P., Biggin, P. C. and Sansom, M. S. P. (2003). Kþ versus Naþ ions in a K channel selectivity filter: a simulation study, Biophys. J., 83, 633–645.

3 Biointerfaces and Mass Transfer HERMAN P. VAN LEEUWEN Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, NL-6703 HB Wageningen, The Netherlands

JOSEP GALCERAN Departament de Quı´mica, Universitat de Lleida, Av. Rovira Roure 191, 25198 Lleida, Spain

1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Organism–Medium Interphase . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Physicochemical Characteristics . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Ionic Distributions at Biological Interphases . . . . . . . . . . . . . 2.3 Electrodynamics of Biological Interphases . . . . . . . . . . . . . . . 3 General Mass Transfer Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Conservation Laws and the Nernst–Planck Equation. . . . . . 3.2 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 The Impact of Geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Transient and Steady-State Conditions. . . . . . . . . . . . . . . . . . 3.5 Diffusion in Composite Media . . . . . . . . . . . . . . . . . . . . . . . . . 4 Convective Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Convective Diffusion from an Unbounded Laminarly Flowing Liquid to a Planar Surface . . . . . . . . . . . . . . . . . . . . 4.2 Convective Diffusion from a Channelled Laminarly Flowing Liquid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Convective Diffusion from a Liquid to a Moving Spherical Body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Superscripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Subscripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Latin Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Greek Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Physicochemical Kinetics and Transport at Biointerfaces Edited by H. P. van Leeuwen and W. Ko¨ster. ß 2004 John Wiley & Sons, Ltd

114 115 115 117 120 122 122 124 125 125 127 129 130 135 137 141 141 141 142 142 143 143

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1

INTRODUCTION

Life has evolved in media with colourful chemical composition, under a variety of physical conditions, which include temperature, pressure and their gradients (see Chapter 1 of this volume). Evolution implies an optimisation of the functioning of organisms with respect to the physical and chemical conditions in which they live. Likewise, a change of conditions will give rise to a change in the properties of the organism, and this is known as adaptation. The chemical conditions relevant to evolution, adaptation and survival do not only comprise the composition and the chemical dynamics of the medium in which the organism is living. More generally, it is the operational availability of the various chemical species that determines their effect. In general terms, the availability of chemicals is defined by a number of basic features: . the chemical availability as derived from equilibrium distributions of species and their rates of interconversion; . the supply of these chemical species to the relevant sites at the surface of the organism; and . the actual internalisation of the chemical species by the organism, usually followed by some bioconversion process. The second feature is largely concerned with mass transfer of chemicals from the medium to the biosurface or back. It generally involves diffusion (transport due to a concentration gradient), flow (transport due to a pressure gradient), and sometimes also conduction (transport due to an electric potential gradient). Organisms may be actively involved in the efficient organisation of transport processes. This may be realised, for example, by the creation of flow via their own motility, or by tuning the physical structure of their active uptake surface to the transport conditions. This chapter deals with the basic principles of mass transfer, and their application to the specific case of transport to/from biological surfaces. It will do so after an appropriate characterisation of the physicochemical features of the biological interphase between an organism and an aqueous medium. The origin and nature of chemical gradients and ionic distributions near the biointerphase will be outlined, with special emphasis on electric double layers, diffusion layers, and their dimensional and dynamic properties. The mathematical formulation of mass transport processes is derived from basic conservation laws, which include conservation of mass and conservation of momentum. Their application to the mass transport situation, with simultaneous gradients in pressure, concentration and electric potential leads to the well-known Nernst–Planck equation, which comprises individual recognisable terms for diffusion, flow and conduction. The elaboration of this fundamental equation to practical biouptake situations calls for explicit consideration of such aspects

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as the geometrical conditions and the distinction between transient and steadystate transport situations. The combination of flow and diffusion is especially important in many practical transport situations, so, by way of illustration and implementation of the basic equations, some cases of convective diffusion are dealt with, such as diffusion towards planar active surfaces or moving spherical organisms. More pertinent elaboration on the resulting biouptake fluxes can be found in Chapters 4 and 10 of this volume.

2

THE ORGANISM–MEDIUM INTERPHASE

Quite generally, the interphase between an organism and its environment encompasses the elements outlined in Figure 1 of Chapter 1. The scheme shows that the cell membrane, with its hydrophobic lipid bilayer core, has the most prominent function in separating the external aqueous medium from the interior of the cell. The limited and selective permeabilities of the cell membrane towards components of the medium – nutrients as well as toxic species – play a governing role in the transport of material from the medium towards the surface of the organism. While the lipid bilayer has a very low water content, and therefore behaves quite hydrophobically, especially in its core (see Chapter 2 of this volume), the cell wall is rather hydrophilic, with some 90% of water. Physicochemically, the cell wall is particularly relevant because of its high ion binding capacity and the ensuing impact on the biointerphasial electric double layer. Due to the presence of such an electric double layer, the cell wall possesses Donnan-like features, leaving only a limited part of the interphasial potential decay in the diffuse double layer in the adjacent medium. For a detailed outline, the reader is referred to recent overviews of the subject matter [1,2]. Mass transport phenomena usually are effective on distance scales much larger than cell wall and double layer dimensions. Thicknesses of steady-state diffusion layers in mildly stirred systems are in the order of 10
5 m. Thus one may generally adopt a picture where the local interphasial properties define the boundary conditions, while the actual mass transfer processes take place on a much larger spatial scale. 2.1

PHYSICOCHEMICAL CHARACTERISTICS

The chemical and structural features of the membrane and cell wall are extensively discussed elsewhere in this volume (see Chapters 2, 6, 7 and 10). They usually contain numerous charged groups, which, as far as they are not internally compensated by counterions, give rise to the formation of an electric double layer at the interphase. The net charge of membrane surface plus cell wall is counterbalanced by a diffuse charge with opposite sign. This so-called diffuse

116 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

double layer extends into the medium over a distance depending on the electrolyte concentration. In aqueous systems of low salt concentration, for example, rivers and lakes, the diffuse countercharge around the cell wall of a microorganism may extend over distances of the order of 10 nm, whereas, in more saline systems, such as seawater and most body fluids, the compensating charge will be situated at distances less than a nanometre. The charge on bacterial cell walls mostly originates from carboxylic, phosphate and amino groups [1,3,4]. The degree of protonation of these anionic and cationic groups is determined by the pH and the ionic composition of the medium. At neutral pH, almost all bacterial cells are negatively charged, because the number of deprotonated carboxylate and phosphate groups is generally higher than that of the protonated amino groups. The compensating charge mainly consists of (positive) counterions that penetrate the porous wall, and, to a minor extent, of (negative) co-ions that tend to be expelled from it. The thickness of bacterial cell walls is in the range of several tens of nanometres [4]. Electrostatic fields associated with biomembranes arise from several sources. The net charge on the membrane generates a potential at the surface relative to the bulk aqueous phase (the surface or double layer potential). This charge resides in the outer parts of the membrane and arises from charged head groups of phospholipids, adsorbed and penetrated ions, and proteins. It is dependent on the pH and ionic composition of the medium, and should be considered in conjunction with the charges in the cell-wall layer. In the hydrophobic core of the membrane, the net charge density is essentially zero. In most biological systems the double layer potential of membranes is negative, owing to the predominance of negatively charged lipids. These typically constitute 10–20% of the effective lipid area of the membrane (about
0:02 C m
2 [5–7], corresponding with about one elementary charge per 10 nm2 ). Furthermore, most of the membrane proteins have isoelectric points below pH 7. Altogether, this results in z-potentials (i.e. potentials in the electrokinetic slip plane, that is, the outer boundary of the hydrodynamic stagnant layer at the surface, usually some tenths of a nm thick) of
8 to
30 mV [5,7]. Internal membrane potentials are due to the inhomogeneous distribution of charges within the membrane. Lipid bilayers possess a substantial dipole potential arising from the structural organisation of dipolar groups and molecules. These groups are oriented in such a way that the hydrocarbon phase is positive with respect to the outer membrane regions. The magnitude of the dipolar potential is usually large, typically several hundreds of millivolts [5,7,8]. Other internal potentials arise from membrane asymmetry, including differences in adsorption at the two sides of the membrane, and from differences in penetration of ions (see Chapter 2 of this volume). Finally, separation of charge across the membrane gives rise to a transmembrane potential. The transmembrane potential is defined as the electric potential

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difference between the bulk phases at the two sides of the membrane, and results from selective transport of charged species across the membrane. In biological systems it is typically of the order of 10 to 100 mV [6,7]. As a rule, the potential at the cytoplasm side of cell membranes is negative relative to the extracellular physiological solution. The issues of ion permeation and transmembrane potential recur in other chapters of this volume (2, 6 and 10) Typical values for the dimensions of the various layers are included in Figure 1 of Chapter 1. Diffusion layer thicknesses depend on the timescale and hydrodynamic conditions; they will be dealt with in detail in Sections 3 and 4. 2.2

IONIC DISTRIBUTIONS AT BIOLOGICAL INTERPHASES

In the electrochemical literature one finds the Gouy–Chapman (GC) and Gouy–Chapman–Stern (GCS) approaches as standard models for the electric double layer [9,10]. According to the Gouy–Chapman model, the thickness of the diffuse countercharge atmosphere in the medium (diffuse double layer) is characterised by the Debye length k
1 , which depends on the electrostatic properties of the medium: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k
1 ¼ ee0 RT =2F 2 z2 c (1) where F stands for the Faraday constant, c is the concentration of the (supposedly symmetrical) electrolyte, z the ionic charge number (z ¼ zþ ¼
z
) and ee0 the permittivity. Typical values for k
1 are 1 nm for 0:1 mol dm
3 1–1 electrolyte and 10 nm for 10
3 mol dm
3 1–1 electrolyte. In the diffuse part of the double layer, the profile of the electrical Volta potential c [10] is given by an exponential decay function, with k as the mathematical argument: c ¼ c0 exp (
kx)

(2)

where c0 is the electrical potential at the surface. The quantity ee0 k is the capacitance Cd of the diffuse double layer. The applicability of GC and GCS models to biological systems is limited because they completely ignore the interphasial structure with its spatial distribution of charged sites, counterions and co-ions. Nevertheless, in a number of cases, GCS adequately describes the dependence of potential on distance at a lipid membrane surface [11–13]. An obvious first attempt to take into account the three-dimensional distribution of charges in the interphase is to extend the double layer model with a Donnan layer. A Donnan layer contains a number of fixed charges and is accessible for water and dissolved ions. For a biological interphase, the Donnan layer would encompass the head-group charges of

118 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

the membrane lipids, the ionisable sites in the cell-wall layer, and part of the countercharge. The countercharge is generally distributed over the Donnan layer and the diffuse layer, the distribution ratio being dependent on the electrolyte concentration in the medium. A theoretical derivation of the potential in a system with a combination of a Donnan layer and a diffuse layer has been given by Ohshima and Kondo [14–17]. The basic step is to write Poisson’s equation in terms of all relevant charge carriers. For the Donnan layer, it reads: d2 c r þ re ¼
w eD e0 dx2

(3)

where rw represents the space charge density due to the lipid head groups and the charged groups of the cell wall, re that of the electrolyte ions and eD is the relative permittivity of the Donnan layer phase (see Figure 1). For the adjacent diffuse layer in the aqueous phase, the GC approach is maintained. The potential profile can be derived if rw is taken as constant for any x and the distribution of ions that generates re follows a simplified solution of the Poisson–Boltzmann equation [14,17]. Using the continuity of potential and potential gradient across the interphase and taking eD as identical to the relative permittivity e in the surrounding medium, Ohshima and Kondo [17] found: cDm ¼ cD


RT zF cD tanh zF 2RT

(4)

where cDm is the potential at the boundary between the Donnan layer and the medium, and cD is the Donnan potential, corresponding with the limiting situation of the pure Donnan profile (no diffuse layer at all): cD ¼

RT r sinh
1 w 2zFc zF

(5)

The expression for the potential variation with x within the Donnan phase is approximated by [17]:  h i1=4  2 x c(x < 0) ¼ cD þ ðcDm
cD Þ exp k 1 þ ðrw =2zFcÞ

(6)

where k
1 is the Debye length given by equation (1). Figure 1 shows a set of calculated potential profiles for different electrolyte concentrations. For each curve, the asymptotic value on the left is cD , while the intercept with ordinates is cDm . For large c, the profile approaches the step functionality of the pure Donnan model. Note that for low potentials, the ratio

H. P. VAN LEEUWEN AND J. GALCERAN −10

−5

119

x / nm 0

0

5

c = 0.2 mol dm−3 −2

c = 0.1 mol dm−3 c = 0.05 mol dm−3

−4

y / mV

−6

−8 c = 0.02 mol dm−3 −10

−12 c = 0.01 mol dm−3 −14

Figure 1. Potential profile c(x) across the cell wall (x < 0) according to the simplified expression (6) from the Ohshima and Kondo model [15]. The profile within the solution (x > 0) is assumed to follow the usual GC decay expression c ¼ cDm exp (
kx) (equation (2)). Parameters: T ¼ 298 K, z ¼ þ1, e ¼ 78:5, thickness of the Donnan layer ¼ 10 nm, rw ¼
1447 C dm
3 . Curves correspond with c ¼ 0:2, 0:1, 0:05, 0:02 and 0:01 mol dm
3

cDm =cD tends to 1/2 according to equation (4). The diffuse double layer potential is lower than in the pure GC model, because part of the ‘fixed’ charge is already compensated within the Donnan layer phase. In the Ohshima-modified Donnan approach it is assumed that the distribution of fixed charges in the Donnan layer, rw , is homogeneous and that the thickness of this layer is larger than k
1 , resulting in an exponential variation of the potential in the interphase. This feature makes the Ohshima-modified Donnan approach primarily suitable for describing the double layer at the cell wall–solution interface, and less appropriate for the lipid bilayer membrane. For the construction of the full electric potential profile of a biological interphase, the preceding approach is a good starting point. It divides the interphase into different regions, each with its own thickness, permittivity, and fixed charge density, and applies a Poisson–Boltzmann type of approach. At all boundaries between distinguishable layers, we have the Gaussian conditions of continuity, taking into account the differences   in permittivity for the various layers cþ ¼ c
; eþ (dc=dx)þ ¼ e
(dc=dx)
. For the diffuse part of the double layer in the solution, the GC model may be used again. More detailed reviews concerning the electric double layer at biological interphases are given in references [5,11,18,19].

120 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

2.3

ELECTRODYNAMICS OF BIOLOGICAL INTERPHASES

How fast does an electric double layer in a biological interphase and the adjacent solution build up or adjust itself to changing conditions? In other words, what are the characteristic time constants for formation of the interphasial double layer? The time constant, td , for relaxation of the diffuse part of the double layer is determined by bulk properties of the medium: td ¼

ee0 K

(7)

where K is the specific conductivity. In terms of electric equivalent circuitry, the relaxation process corresponds with the discharge of the capacitor with capacitance ee0 (i.e. the dielectric formed by the bulk electrolyte solution) across the solution of resistivity K
1 . In electrical jargon, td represents the RC time constant of the solution, and this indeed governs the rate of interphasial double layer formation. Equation (7) can be rewritten in terms of the ionic diffusion coefficients Di because: K ¼F

X

jzi jui ci ¼

i

F2 X 2 z D i ci RT i i

(8)

in which ui represents the ionic mobilities. For a single symmetrical electrolyte with Dcation ¼ Danion ¼ D, and using equation (1), it follows that: td ¼

1 Dk2

(9)

Thus, the time constant td is directly related to the time necessary for ions to migrate over a distance equal to the Debye length k
1 . For example,
1 for a 10
3 mol dm
3 aqueous electrolyte solution with D ¼ 10
9 m2 s , and 8
1
7 k ¼ 10 m , equation (9) yields a td value of 10 s. Note that k is proportional to the square root of the electrolyte concentration, (see equation (1) ), so that td is inversely proportional to c. Thus, for electrolyte concentrations of the order of 0:1 mol dm
3 , td reaches values as low as 10
9 s. Lipid bilayer membranes, with their apolar cores, generally have extremely poor conductivities. K can be as low as 10
6 V
1 m
1 [20], and also depends on the type of ions transferring the charge across the membrane. The time constant tm (as given by equation (7) with em e0 and Km representing the membrane permittivity and conductivity, respectively) to relax from electric polarisation by conduction through the bilayer is correspondingly large. For a membrane with a relative permittivity of the order of 10 and a thickness of about 10
8 m, the geometrical capacitance is 10
2 F m
2 . Thus, the corresponding time

H. P. VAN LEEUWEN AND J. GALCERAN

121

constant tm is 104 s. This means that on the relevant timescales of biological processes, the double layer at the solution side adjusts instantaneously (td typically 10
9 to 10
7 s), whereas the apolar core of the lipid bilayer may behave as a dielectric that does not allow appreciable passage of charge on timescales below 104 s. In real biological systems, this is generally overruled by specific ionselective permeation processes (e.g. see Chapters 5, 6 and 10). When the bilayer contains ion-transport channels or other transport mediators, the individual channels have conductivities typically of the order 10
11 V
1 m
1 [21]. Realising that such a channel occupies a part of the membrane surface area of the order of 10 nm2 , this corresponds with a local K of about 106 V
1 m
1 . Thus, locally, the relaxation time constant comes down to around 10
8 s, which logically is again in the range of that for electrolyte solutions. Lateral transfer of ionic species through the biointerphasial double layer has only recently received attention. Yet it is a subject of significant relevance, because it may play a crucial role in the interactions of organisms with their surroundings, for example in bacterial adhesion processes, biofilm formation (and removal), etc. As an example, we may refer to a study of bacterial cells of the genus Corynebacterium. The cells are more or less spherical, with diameters of 1.1 and 0:8 mm for the longer and shorter axes, and can be prepared as fairly homodisperse suspensions. Electrophoretic mobilities of Corynebacterium cells are displayed as a function of pH in Figure 2. Via the z-potential and other double layer features, the mobility represents the particle charge (see Chapter 4 in [10]). Thus, the mobility increases with increasing charge in the wall, and with decreasing electrolyte concentration. For the Corynebacterium cells, the mobility versus charge function levels off and becomes quite insensitive to the electrolyte concentrations at higher pH, i.e. at increasing (negative) charge. This behaviour points to surface conduction effects, i.e. tangential displacement of counterions inside the double layer. A comprehensive analysis of the electrodynamic features is accessible by combining mobility data with the dielectric spectra of the dispersed cells [22,23]. As suggested before, the role of the interphasial double layer is insignificant in many transport processes that are involved with the supply of components from the bulk of the medium towards the biosurface. The thickness of the electric double layer is so small compared with that of the diffusion layer d that the very local deformation of the concentration profiles does not really alter the flux. Hence, in most analyses of diffusive mass transport one does not find any electric double layer terms. For the kinetics of the interphasial processes, this is completely different. Rate constants for chemical reactions or permeation steps are usually heavily dependent on the local conditions. Like in electrochemical processes, two elements are of great importance: the local electric field which affects rates of transfer of charged species (the actual potential comes into play in the case of redox reactions), and the local activities

122 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 3

108 u/m2 V-1 s-1

2

1

0

−1 −2 −3 0

2

4

6 pH

8

10

12

Figure 2. Electrophoretic mobility of Corynebacterium versus pH. The general trend of the markers for each KNO3 concentration (D ¼ 0:001; O ¼ 0:01 and  ¼ 0:1mol dm
3 ) is indicated with an auxiliary line. Redrawn from reference [22]

of charged species (different from their values just outside the double layer by some type of Boltzmann factor). These aspects are of primary importance in defining the boundary conditions (see Section 3.2).

3

GENERAL MASS TRANSFER EQUATIONS

3.1 CONSERVATION LAWS AND THE NERNST–PLANCK EQUATION Basic elements of transport equations are the laws expressing conservation of mass and conservation of momentum. The former is self-evident; the latter derives from Newton’s second law (stating that the sum of forces acting on a system equals the rate of production of momentum in that system). For details on the basic premises and features, refer to the specialised literature [24–29]. Let us consider the very general situation where a liquid system is subject to: . a pressure gradient, so that there is a flow of the liquid with velocity v, . a concentration gradient for a certain component i, so that there is diffusion of i, and

H. P. VAN LEEUWEN AND J. GALCERAN

123

. an electric potential gradient, so that the charged components of the system are subjected to conduction (often denoted as ‘migration’ in the electrochemical literature). For this set of stimuli, the general linear flux equation for component i can be formulated as Ji ¼
Di grad ci


|fflfflfflfflffl{zfflfflfflfflffl} diffusion term

zi ci ui grad c þ ci v jzi j

|fflfflfflffl{zfflfflfflffl}

|fflfflfflffl{zfflfflfflffl}

conduction term

flow term

(10)

where subscript i denotes that the magnitude (J for flux, c for concentration, u for mobility and z for charge) corresponds with the species i, and v is the velocity of the solution at the point where the flux is measured. For transport in one dimension, equation (10) reduces to: Ji ¼
Di

dci zi dc
ci ui þ ci v dx jzi j dx

(11)

Equation (10) is known as the Nernst–Planck equation. This equation can be given in all kinds of formulations. Another common one is: Ji ¼


Di ~i þ ci v ci grad m RT

(12)

where the diffusion and conduction terms are contained in the gradient of the ~i . electrochemical potential m Mass conservation for component i implies that at a certain point in space, the time dependence of ci is related to the divergence of the flux of i. It is easily understood that a finite positive divergence in the flux will lead to depletion, i.e. to a lowering of the concentration. This can be expressed as: qci ¼
div Ji qt

(13)

  where div denotes the divergence, i.e. div J ¼ qJx =qx þ qJy =qy þ qJz =qz in Cartesian coordinates, which reduces to dJ/dx in the one-dimensional case. We shall also encounter situations where a chemical reaction influences the concentrations. For a volume reaction of the type j Ð i, the reaction rate for the production of i is given by kf cj (if we assume it to be an elementary reaction), where kf is the forward reaction rate constant, and the rate of consumption of i by a term kb ci , where kb is the rate constant of the backward

124 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

reaction. Then the conservation equation (13) has to be extended with the chemical source terms: qci ¼
div Ji þ kf cj
kb ci qt

(14)

The relative importance of reaction with respect to diffusion can be described in terms of the nondimensional (second) Damko¨hler number [30–36] (also called Thiele modulus), in terms of the reaction layer thickness [37,38] or in terms of lability criteria [39,40]. 3.2

BOUNDARY CONDITIONS

For a given mass transfer problem, the above conservation equations must be complemented with the applicable initial and boundary conditions. The problem of finding the mathematical function that represents the behaviour of the system (defined by the conservation equations and the appropriate set of initial and boundary conditions), is known as a ‘boundary value problem’. The boundary conditions specifically depend on the nature of the physicochemical processes in which the considered component is involved. Various classes of boundary conditions, resulting from various types of interfacial processes, will appear in the remainder of this chapter and Chapters 4 and 10. Here, we will discuss some simple boundary conditions using examples of the diffusion of a certain species taken up by an organism: . fixed concentration at a boundary. If an isolated organism is immersed in a huge volume, then the bulk concentration of the species taken up is constant and its fixed concentration (either at finite or infinite distance) can be used as a boundary condition. In the particular case of fixed zero concentration at the organism surface, we would have the maximum (‘limiting’) flux allowed by the diffusion supply. . fixed flux at a boundary. If a biological internalisation flux can be considered constant along a certain period, then a fixed-flux condition holds at the interfacial boundary. If the species cannot cross a surface (e.g. a ligand of the species taken up not being able to cross a cell membrane), then a zeroflux condition for that species applies. The nonflux condition would also be relevant for the case of an organism in a finite medium, as the internalised species in the medium is not replenished [41]. Obviously, many combinations arise: different boundary conditions for different species on the same surface, different boundary conditions on different adjacent surfaces (mixed boundary conditions) for the same species, prescribed combinations of flux and concentrations at a certain surface, etc.

H. P. VAN LEEUWEN AND J. GALCERAN

3.3

125

THE IMPACT OF GEOMETRY

For an incompressible liquid (i.e. a liquid with an invariant density which implies that the mass balance at any point leads to div v ¼ 0) the time dependency of the concentration is given by the divergence of the flux, as defined by equation (13). Mathematically, the divergence of the gradient is the Laplacian operator r2 , also frequently denoted as D. Thus, for a case of diffusion and flow, equation (10) becomes: qci ¼ Di r2 ci
div(ci v) qt

(15)

which, performing a local balance of matter, is a continuity equation. Like the divergence or the gradient, the Laplacian operator has different forms for different geometrical situations [42]; see Table 1.

3.4

TRANSIENT AND STEADY-STATE CONDITIONS

The general equation of convective diffusion in liquids, equation (15), is a second-order, partial differential equation with variable coefficients. Its solution yields the spatial distribution of ci as a function of time, namely its transient behaviour. On an analytical level, solution of equation (15) into the transient c(t) is possible only for a number of relatively simple systems with well-defined geometry and flow properties. The problem is greatly simplified if the concentration function ci (x, y, z) is essentially independent of time t, i.e. in the steadystate. Then equation (15) reduces to: Di r2 ci
divðci vÞ ¼ 0

(16)

It is useful to point out here that we frequently encounter partial steadystates. An important example is the case where the diffusion process is much faster than a surface process, and thus a quasi-steady-state is reached for the diffusion concentration profile at each changing concentration of the surface. This distinction between different timescales of the processes can lead to a significant simplification of complex problems, see end of Section 4.3 or Chapter 4 in this volume. The derivation of a steady-state solution requires boundary conditions, but no initial condition. Steady-state can be seen as the asymptotic solution (so never mathematically reached at any finite time [43]) of the transient, which – for practical purposes – can be approached in a reasonably short time. For instance, limiting-flux diffusion of a species with diffusion coefficient Di ¼ 10
9 m2 s
1 towards a spherical organism of radius r0 ¼ 1 mm is practically attained at t  r20 =Di ¼ 1 ms.

Variable

x r r r, z

r, y, j

x, y, z

System of coordinates

Planar (1D) Spherical (1D) Cylindrical (1D) Axisymmetrical (2D)

Spherical polar (3D)

Cartesian (3D)

q2 S=qx2 þ q2 S=qy2 þ q2 S=qz2

(qS=qx)ex þ (qS=qy)ey þ (qS=qz)ez

(qS=qx)ex (qS=qr)er (qS=qr)er (qS=qr)er þ (qS=qz)ez qS 1 qS 1 qS er þ ey þ ej r sin y qj r qy qr

r2 S q2 S=qx2 q2 S=qr2 þ (2=r)(qS=qr) q2 S=qr2 þ (1=r)(qS=qr) q2 S=qr2 þ (1=r)(qS=qr) þ q2 S=qz2

q2 S 1 qS 1 q qS 1 q2 S þ þ sin y þ qr2 r qr r2 sin y qy qy r2 sin2 y qj2

grad S

Table 1. Gradient and Laplacian operators for different geometries. S stands for a scalar and ei stands for a unit vector associated to coordinate i

H. P. VAN LEEUWEN AND J. GALCERAN

127

Some transient problems tend to a trivial (and useless) steady-state solution without flux and concentration profiles. For instance, concentration profiles due to limiting diffusion towards a plane in an infinite stagnant medium always keep diminishing. Spherical and disc geometries sustain steady-state under semi-infinite diffusion, and this can be practically exploited for small-scale active surfaces. As steady-state can only be maintained by the concurrence of some pumping energy, it has been associated with many life processes of no change. Conversely, equilibrium would correspond with a no-change situation of ‘death’.

3.5

DIFFUSION IN COMPOSITE MEDIA

For some biological systems, the species that eventually crosses the cell membrane has travelled through different media, each one with its own mass transfer characteristics. As an example, we deal with the case where the two media are the bulk solution and the cell wall (with the separation surface parallel to the cell membrane) with diffusion as the only relevant mass transfer phenomenon in each medium. Apart from having different parameters in the differential equations in each medium (due to the unequal diffusion coefficients), we need to impose two new boundary conditions at the separating plane which we denote as s. The first boundary condition follows from the continuity of the material flux: Ji, s
¼ Ji, sþ

(17)

where sþ and s
indicate opposite sides of the separating surface. The second boundary condition arises from the continuity of chemical potential [44], which implies – under ideally dilute conditions – a fixed ratio, the so-called (Nernst) distribution or partition coefficient, KN , between the concentrations at the adjacent positions of both media: c i , s
¼ KN c i , s þ

(18)

The transient solution can be obtained, for planar or spherical geometry, using Laplace transforms [26,45], but, for simplicity, we restrict ourselves to the steady-state solutions. We consider, then, two media (1 for the cell-wall layer and 2 for the solution medium) where the diffusion coefficients of species i are Di,1 and Di,2 (see Figure 3). For the planar case, pure semi-infinite diffusion cannot sustain a steady-state, so we consider that the bulk conditions of species i are restored at a certain distance di (diffusion layer thickness) from the surface where ci ¼ 0 [28,45], so that a steady-state is possible. Using just the diffusive term in the Nernst–Planck equation (10), it can be seen that the flux at any surface is:

128 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

Medium 2

Medium 1

Di,2

Di,1

s ci,s−

* ci,s+ ci (di) = c i,2

ci (0) = 0

xs di

Figure 3. Outline of the concentration profile of species i due to steady-state diffusion in a composite region with two media

Ji ¼

c  i, 2 xs = Di,1 KN þ ðdi
xs Þ=Di,2 

(19)

where xs denotes the position of the separating plane s. Expression (19) can be physically interpreted as due to the ‘resistance’ to flow generated by each medium due to its length and diffusion coefficient. Although Di,1 is expected to be lower than Di,2 , the fact that xs is  di can result in the practical neglect of the retardation due to the thin wall layer. Expressions analogous to (19) have been used in interpreting analytical techniques with composite media [46]. In the case of semi-infinite diffusion towards a spherical organism of radius r0 , with the surface of separation (concentric with the organism’s surface) at radius rs , the flux at the membrane surface is [26]: Di,1 KN ci,2   Ji ¼  ð1=rs Þ
ð1=r0 Þ
Di,1 KN =rs Di,2 r20

(20)

If rs and r0 are very similar, the previous expression practically reverts to the diffusion in only one medium. If the transported species is volatile, it is convenient to relate the concentration to the pressure via the solubility (or Henry law coefficient), because the steady-state solution does not depend on the particular values of the diffusion

H. P. VAN LEEUWEN AND J. GALCERAN

129

coefficients and of the solubility parameters of each medium [26,44], but on their product, which is known as the permeability of this medium. Other geometries can be substantially more difficult to solve [45], mostly when the one-dimensional approach is not appropriate. The steady-state analytical solution through a multilayer medium towards a disc surface is available [47], but for most problems (especially transient ones) only numerical simulation is feasible.

4

CONVECTIVE DIFFUSION

Let us consider the transport of one component i in a liquid solution. Any disequilibration in the solution is assumed to be due to macroscopic motion of the liquid (i.e. flow) and to gradients in the concentration ci . Temperature gradients are assumed to be negligible. The transport of the solute i is then governed by two different modes of transport, namely, molecular diffusion through the solvent medium, and drag by the moving liquid. The combination of these two types of transport processes is usually denoted as the convective diffusion of the solute in the liquid [25] or diffusion–advection mass transport [48,49]. The relative contribution of advection to total transport is characterised by the nondimensional Pe´clet number [32,48,49], while the relative increase in transport over pure diffusion due to advection is Sh – 1, where Sh is the nondimensional Sherwood number [28,32,33,49,50]. Transport of i due to the flow of the surrounding liquid travelling at a velocity v amounts to ci v so that the total flux Ji resulting from diffusion and flow comes to: Ji ¼
Di grad ci þ ci v

(21)

which is nothing other than the Nernst–Planck equation (10) for the case without the conduction term. We note that for not too high concentrations of i, the diffusion coefficient Di can be considered as a (temperature-dependent) constant. In many biological works, which have tended to focus on the organism rather than on the surrounding medium, the flux coming from the medium and crossing the surface is taken as positive (see Chapter 1). Following this sign convention, and considering the usual absence of flow of the fluid across the surface, the flux reads: Ji (diffusion) ¼ þDi grad ci

(22)

which is just the first term from the Nernst–Planck equation (10). Taking into account that the liquid acting as a medium for the microorganism is incompressible (div v ¼ 0), equation (15) becomes:

130 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

Di

q2 c i q2 c i q2 c i þ þ qx2 qy2 qz2

!



qci qci qci
vx ¼0 þ vy þ vz qx qy qz

(23)

which is the general equation of steady-state convective diffusion. Mathematically, it is a second-order partial differential equation, which can be solved (either analytically or more frequently numerically) for a given a set of boundary conditions that are characteristic for the problem under consideration. In most cases, the velocity profile is known or can be solved prior to (and independently of) the determination of the diffusion profile. Unfortunately, the rigorous solution of most realistic hydrodynamics problems is rather involved (for instance, due to the presence of turbulence) and sometimes it is reasonable to use empirical expressions for the velocity profile. One particular simplification arises when the scale of the turbulence [48] is much larger than the size of the microorganism, which effectively results in a locally linear shear (velocity gradient) [49,51] or, for that matter, a laminar sublayer close to the biological surface [25,52]. Below we shall treat three relevant, although simplified, examples. 4.1 CONVECTIVE DIFFUSION FROM AN UNBOUNDED LAMINARLY FLOWING LIQUID TO A PLANAR SURFACE We consider a plane with length l and width w, which is exposed to a flowing solution with a dissolved component i at a bulk concentration ci . The direction of the bulk stream of flow is parallel to the plane in the direction of the y-axis; the x-axis is perpendicular to the plane, as shown in Figure 4. The bulk velocity of the flow far from the plane is denoted as v. The z-axis is considered immaterial, due to a sufficiently large value of w compared with the dimensions of the velocity and concentration perturbations. l is assumed to be much larger than the diffusion layer thickness (di ). The first step in solving convective diffusion problems is the derivation of the velocity profile. In this case, the flow arriving with velocity v is modified by y x

w

l

Direction of flow

z

Figure 4. Schematic representation of the convective–diffusion problem for an active plane parallel to the direction of flow dealt with in Section 4.1. The liquid flow extends up to x ¼ 1, where its free velocity is v in the direction of increasing y. The leading edge of the plane is the segment x ¼ 0, y ¼ 0, 0  z  w

H. P. VAN LEEUWEN AND J. GALCERAN

131

the leading edge of the plane (y ¼ 0) and develops a velocity profile for which the rigorous solution, attributed to Blasius in 1908 (p. 20 in [25], p. 396 in [53], Chapter 4 in [54]), can be approximated by: vy  0:332v3=2 x=

pffiffiffiffiffi
~y

(24)

vx  0:083ðv=yÞ3=2 x2
~
1=2

(25)

where
~ is the kinematic viscosity of the solution (the quotient between the viscosity and the density, which for aqueous solutions at room temperature is about 10
6 m2 s
1 ). Notice that vx and vy depend on both x and y, but vx =vy (usually small except close to the leading edge, where the Blasius solution is not accurate [50,55]) is independent of v. Exact (continuous line) and approximate (dotted line, given by equation (24) ) profiles of the velocity are depicted in Figure 5. An important concept in fluid mechanics is the hydrodynamic boundary layer (also known as Prandtl layer) or region where the effective disturbance 16 di

ci /ci*

vapprox

0.8

vexact

0.6

d0 8

ci /ci*

108v/m s−1

12

1.0

0.4 4 0.2

0 0

0.1

0.2

0.3 x/mm

0.4

0.5

0.0 0.6

Figure 5. Exact (numerical solution, continuous line) and linearised (equation (24), dotted line) velocity profile (i.e. vy of the fluid at different distances x from the surface) at y ¼ 10
5 m in the case of laminar flow parallel to an active plane (Section 4.1). Parameters: Di ¼ 10
9 m2 s
1 , v ¼ 10
3 m s
1 , and
~ ¼ 10
6 m2 s
1 . The hydrodynamic boundary layer thickness (d0 ¼ 5  10
4 m), equation (26), where 99% of v is reached is shown with a horizontal double arrow line. For comparison, the normalised concentration profile of species i, ci =ci , the linear profile of the diffusion layer approach (continuous line) and its thickness (di ¼ 3  10
5 m, equation (34) ) have been added. Notice that the linearisation of the exact velocity profile requires that di  d0

132 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

of the main flow takes place, with d0 labelling its thickness as seen in Figure 5. It is good to emphasise that the diffusion layer and the hydrodynamic boundary layer are principally different. The former denotes the layer of solution where the concentration of diffusing species is depleted, whereas the latter refers to the layer of solution where the liquid velocity is reduced with respect to the bulk velocity. The d0 (assumed to be much smaller than l or w) can be quantified as the distance from the plane where vy  0:99v, using the exact (numerical) solution. In this problem, d0 can be taken as [53,55,56]: pffiffiffiffiffiffiffiffiffiffi d0  5 ~ny=v

(26)

With the expressions for the velocities, i.e. equations (24) and (25), at hand, one can turn to the diffusion problem and seek to solve equation (23). Apart from dropping the terms with derivatives in the z-direction, it can be shown that the diffusive term q2 ci =qy2 is also relatively small in comparison with q2 ci =qx2 (see p. 87 in [25]). Thus, equation (23) boils down to:

q2 c i qci qci ¼0 þ vy Di 2
v x qx qx qy

(27)

The leading boundary conditions correspond with semi-infinite diffusion with an instantaneous sink of the diffusing species at the plane x ¼ 0: ci (x, y) ¼ 0 ci (x, y) ¼

x¼0

ci

x!1

8y

(28)

8y

(29)

with ci (0, 0) well behaved. Substitution of equations (24) and (25) into equation (27) and further manipulations (see p. 88 in [25] for details), leads to the solution:  3=2 3
1=2 ci =ci ¼ 1
0:373G 1=3, 0:0277D
1 x ~n i ðv=yÞ

(30)

where G stands for the incomplete gamma function: G(a, z) ¼

Z

1

ta
1 exp
t dt

(31)

z

It can be seen that the profile of the concentration (see Figure 6 and dashed line in Figure 5) is largely linear over a wide range of x-values away from the plane. On the other hand, the change in ci with y, at a given x, is of a parabolic nature (see Figure 7). With the complete concentration profile ci (x, y) at hand, it is straightforward to compute the magnitude of the flux Ji towards the plane:

H. P. VAN LEEUWEN AND J. GALCERAN

133

1.0

y = 30 µm

0.8

ci /mol m−3

y = 20 µm 0.6

y = 10 µm

0.4

0.2

0.0 0

4

8

12

16

20

x/µm

Figure 6. Concentration profiles of species i (equation (30)) as a function of the distance from the surface (x) in the case of laminar flow parallel to an active plane (Section 4.1).
1 Parameters: Di ¼ 10
9 m2 s
1 , v ¼ 0:012 m s
1 , ci ¼ 1 mol m
3 , and
~ ¼ 10
6 m2 s

1.0

ci /mol m−3

0.8

0.6

x = 30 µm

0.4

x = 20 µm 0.2 x = 10 µm 0.0 0

250

500 y/µm

750

1000

Figure 7. Concentration profiles of species i (equation (30) ) as a function of the distance from the leading edge (y) in the case of laminar flow parallel to an active plane (Section 4.1). Other parameters as in Figure 6

134 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 2=3

Ji ¼ Di ðqci =qxÞx¼0 ¼ 0:339ci Di

pffiffiffiffiffiffiffi
1=6 v=y
~

(32)

which shows that the diffusive flux of solute i towards a plane in a laminarly flowing solution is proportional to its diffusion coefficient Di to the power 2/3 [48]. Thus, changes in the exponent of Di (sometimes on empirical basis) are linked to the hydrodynamic regime and the contribution of advection. The magnitude of the flux given by equation (32) decreases with increasing distance from the upstream edge of the plane and with decreasing velocity of the liquid according to square root dependencies. Formally, the flux can also be written: Ji ¼ Di ci =di

(33)

where di is the thickness of the diffusion layer of species i. Comparison with equation (32), yields di for the present case of laminar flow along a plane: 1=3

di ¼ 2:95Di

pffiffiffiffiffiffiffi 1=6 y=v
~

(34)

Physically, di represents the distance from the plane where bulk concentration would be recovered if a concentration profile were simply linear with a slope given by the tangent of the true concentration profile at x ¼ 0 (see continuous line in Figure 5). Notice that the boundary (equation (26) ) and diffusion (equation (34) ) layers, in this example, extend as the square root of the distance from the leading edge, i.e. the steady-state thicknesses of the hydrodynamic boundary layer and the diffusion layer increase with increasing distance (y) from the upstream edge, according to parabolic relationships. The flux of i at x ¼ 0, being inversely proportional to di , decreases with increasing y. Figure 8 summarises this typical behaviour. It should be noted that the ratio di =d0 is independent of the coordinate y and the liquid velocity, and that the solution for convective diffusion given by (30) and following equations requires that di =d0 is well below unity, to allow for the approximate expressions of the velocities, equations (24) and (25), to apply. One easily verifies that for small ions and molecules in aqueous systems with D  O(10
9 ) m2 s
1 and
~  O(10
6 ) m2 s
1 , di =d0 is small enough for the approximate treatment developed here to be acceptable. In passing, it is good to emphasise that the above analysis illustrates the limitations of the widely used Nernst diffusion layer concept. This concept assumes that there is a certain thin layer of static liquid adjacent to the solid plane under consideration at x ¼ 0. Inside this layer, diffusion is supposed to be the sole mechanism of transport, and, outside the layer, the concentration of the diffusing component is constant, as a result of the convection in the liquid. We have seen that, in contradiction with this oversimplified picture, molecular diffusion and liquid motion are not spatially separated, and that the thickness

H. P. VAN LEEUWEN AND J. GALCERAN

135 6.0

d0

0.2

4.0

2.0

0.1

104 J/mol m−2 s−1

Boundary or diffusion layer thickness/mm

0.3

Ji di 0.0 0.0

0.5

1.0 y/mm

1.5

0.0 2.0

Figure 8. Variation of the hydrodynamic boundary layer thickness (d0 , equation (26), continuous line), the diffusion layer thickness (di , equation (34), dotted line) and the ensuing local flux (J i , equation (32), dashed line) with respect to the distance from the leading edge (y) in the case of laminar flow parallel to an active plane (the surface is a
1 sink for species i). Parameters: Di ¼ 10
9 m2 s , v ¼ 10
3 m s
1 , ci ¼ 1 mol m
3 , and
6 2
1
~ ¼ 10 m s . Notice that di  d0 (as required for the derivation of the flux equation (32) ), and that the flux decreases when di increases

of the diffusion layer depends on the properties of the diffusing molecules as well as on hydrodynamic characteristics. Needless to say, a formal flux expression like equation (33) becomes meaningful only after combination with the appropriate formulation of the values of di . 4.2 CONVECTIVE DIFFUSION FROM A CHANNELLED LAMINARLY FLOWING LIQUID In some biological cases, liquid is forced to flow inside a channel (e.g. a tube inside an animal, as in gills, for example). The channel can be modelled as a long pipe or cylinder of radius R. The active surface corresponds with r ¼ R (see Figure 9). As usual, we must first solve for the velocity profile. The flow can be taken as laminar for low Reynolds numbers, vR=~
< 2500, where v is the maximum velocity of the flow reached at the centre of the channel (r ¼ 0) [52]. For simplicity, we will consider the particular case where the Poiseuille velocity profile has been fully developed when the solution carrying the active species

136 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

Parabolic velocity profile

r

v R

x

y

Figure 9. Model of convective diffusion inside a tube channel (radius R) towards the walls of the tube considered as perfect active surfaces. A Poiseuille profile for the velocity (equation (35) ) is also schematically shown with arrows on the right-hand side. The maximum velocity v is reached at the centre of the tube (r ¼ 0)

reaches the part of the pipe with the active surface. Thus, the main difference with respect to the previous case is that the velocity profile does not change along the direction y (under steady-state conditions, the incompressible fluid is forced to flow at the same velocity all along y), because no end effects distort the velocity profile. The parabolic Poiseuille profile (including the no-slip condition on the surface at r ¼ R) is:   vy ¼ v 1
r2 =R2

(35)

Via a simple integration of this parabolic profile, one can find a relationship between v and the effective flow rate vf (volume of liquid crossing any section of the channel per unit of time): vf ¼ pR2 v=2

(36)

A further simplification (known as the Le´veˆque approximation [57]), linearises the profile in the vicinity of the surface (where a local coordinate x, perpendicular to the surface, is taken): vy  2vx=R

(37)

Considering also that in the y-direction the rate of mass transport due to convection is much higher than that due to diffusion [58], equation (23) reduces to: Di

q2 c i qx2

!




2vx qci R qy

¼0

(38)

Through a change of variable (see p. 114 in [25]), the concentration profile, for the limiting situation where the active surface is a perfect sink, can be expressed (similarly to equation (30)) as:

H. P. VAN LEEUWEN AND J. GALCERAN

  ci =ci ¼ 1
0:373G 1=3, 2vx3 =(9Di Ry)

137

(39)

Then, we obtain for the flux:  1=3 Ji ¼ 0:678 ci D2i v=ðRyÞ

(40)

As physically expected, the flux diminishes as we move downstream (increasing y) due to the previous depletion at lower y. No direct relation to the viscosity is present, as the flow is forced to go with a constant v (along different y), but the viscosity of the liquid has an indirect effect via Di . The diffusion layer thickness can be computed as: di ¼ 1:474 ðDi Ry=vÞ1=3

(41)

Obviously, this approximate treatment fails when di > R, as then the Le´veˆque linearisation is clearly unapplicable. For an approximation to account for lateral effects of nonactive walls in box-like channels, see ref. [46].

4.3 CONVECTIVE DIFFUSION FROM A LIQUID TO A MOVING SPHERICAL BODY Another case of great practical importance in the bioenvironmental context is the convective–diffusive transport of solutes towards the surface of suspended bodies (or particles) in a liquid medium. We will consider the situation where a spherical body of radius r0 moves with respect to the liquid, which, of course, is mathematically equivalent to the situation of a stagnant particle in a flowing liquid [48]. Figure 10 shows a planar cross-section of the situation and the polar coordinate system relevant to the analysis. As the starting velocity profile (for vr and vy ), we take the simplified regime corresponding with ‘creeping’ flow around the sphere [24], which limits the applicability of the results to parameters corresponding with low Reynolds numbers, i.e. cases where turbulences do not come into play:
< 0:1 vr0 =~

(42)

The field of velocities corresponding with such a regime (which includes ‘no-slip’ of the fluid at the sphere surface) is indicated by the arrows in Figure 10, where the length of each arrow is proportional to the local velocity of the fluid. The perturbation of the bulk velocity extends to quite large distances; for instance, it is necessary to move 75 times the radius r0 from the centre of the sphere normal to the free stream direction of flow in order to obtain 99% of v.

138 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

r

r0 q

Figure 10. Velocity field of creeping flow around a sphere [24]. Each arrow represents the velocity at the origin of the depicted vector. The length of the arrow corresponding with the free velocity v would equal the radius of the sphere

In the steady-state situation qci =qt ¼ 0, and we can use equation (23) as the appropriate starting equation. For the case of diffusion towards a sphere in polar coordinates (see Table 1), this comes to: Di

q2 ci 2 qci þ qr2 r qr

!
vr

qci qci
vy ¼0 qr qy

(43)

where r and y are the two relevant variables. Due to axisymmetry, the elevational angle j is immaterial (not depicted in Figure 10), so that we are left with two essential spatial variables, i.e. r and y. For clarity, we choose again the boundary conditions corresponding with limiting transport (maximum flux): ci (r, y) ¼ 0

r ¼ r0

8y

ci (r, y) ¼ ci

r!1

8y

(44)

H. P. VAN LEEUWEN AND J. GALCERAN

139

The second expression in equation (44) implies that the bulk concentration in the medium is not affected by the consumption of i towards the particle, i.e. the overall depletion is insignificant. In case of the presence of an ensemble of bodies (or particles), this means that the distance between different bodies (or particles) is sufficiently large compared with the steady-state diffusion layer (i.e. the dispersion should be sufficiently diluted). Then an approximate analytical solution of the convective diffusion equation (43), which satisfies the boundary conditions, equation (44), is available under the assumption that the thickness of the diffusion layer di is small compared with the body radius r0 (p. 80 in [25]). As in the example of Section 4.1 (see equation (33)), the results of the derivation can be formally written in terms of the diffusion layer thickness, which now is:



1=3 di 1:29 Di 1 ¼ y
sin 2y r0 sin y vr0 2

(45)

The value of the product v  r0 becomes critical as, on one hand (see condition (42)), it must be low, but on the other it must be high enough to satisfy di  r0 [48]. For instance, Figure 11 (where the end of the diffusion layer is depicted with a discontinuous line) just fulfils both conditions, except in the rear down
1 stream flow if
~ < 10
6 m2 s . Inspection of equations (33) and (45) confirms that the flux Ji is maximal for y ¼ 0. It decreases with increasing y, and tends to zero for y ¼ p, where the depletion layer thickness is no longer small compared to r0 . This result is not practically important, since the fluxes for y close to p are relatively small and hardly count in the total transport rate. It may also be noted that, as a consequence of the approximations in the derivation, the limit v ! 0 of equation (45) does not approach the purely diffusional value given by r0 . The total transport rate (in mol s
1 ) to the whole body (or particle) is found
1 by integration of the flux (in mol m
2 s ) over the total surface area: ð

Ji dA ¼ 2pr20

ðp Ji sin ydy

(46)

0

which, after substitution of equations (33) and (45), yields the average flux: J
i ¼ 0:65(D2i v=r20 )1=3 ci

(47)

It should be highlighted that equation (47) holds for solid particles. In the case of liquid particles, e.g. with emulsions, the convective diffusion process is very different due to interfacial momentum transfer which gives rise to a different velocity profile. Consequently, convective diffusion to/from a liquid particle is more effective than that for a solid particle. Starting again from equation (43),

140 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 0.4

x/mm

0.3

Flow 0.2

0.1

di r0 0.0 −0.4

−0.3

−0.2

−0.1 y/mm

0

0.1

0.2

Figure 11. Position of the diffusion layer limit (dashed line; computed with equation (45) ) for a species diffusing towards a spherical surface (continuous line) when creeping flow coming from the right-hand side is considered. Notice that the ensuing flux will be maximum at positions facing the flow. Parameters: r0 ¼ 10
4 m, Di ¼ 10
9 m2 s
1 , and v ¼ 10
3 m s
1

the following equivalent of equation (47) for a moving particle can be obtained (see page 404 in [25]): 1=2
1=2 1=2 J
i ¼ 0:65Di ci r0 v0

(48)

Z v v0 ¼  m 2 Zm þ Zp

(49)

with:

where Zm and Zp are the viscosities of the medium and the particle, respectively. Literature data seem to suggest that the behaviour of vesicles with a lipid bilayer skin is more close to that of rigid particles [2,12,23]. In many interfacial conversion processes, certainly those at biological interphases, the diffusion situation is complicated by the fact that the concentration at the organism surface is not constant with time (c0i (t) not constant). However, in most cases of steady-state convective diffusion, the changes in the surface

H. P. VAN LEEUWEN AND J. GALCERAN

141

concentration are slow compared to the characteristic time for reaching a steady-state diffusional situation (typically of the order of r20 =D [59] in the spherical case). This means that the thickness of the diffusion layer and the shape of the concentration profile have reached their steady-state properties. Then, it is allowed to apply the flux equations above together with the appropriate expression for di , withci replaced  by the relevant concentration change over the diffusion layer, i.e. ci
c0i (t) . Applying this, by way of example, to the spherical body case, we may write the flux as [9]:   Ji ¼ ms ci
c0i (t) (50) where ms is shorthand notation for the steady-state mass transfer coefficient, which for the case of diffusion towards a rigid spherical body in creeping flow (see equation (47)) is:  1=3 ms ¼ 0:65 D2i v=r20

(51)

Thus, with a variable degree of empiricity, mass transfer coefficients for a number of biologically relevant cases have been described: phytoplankton uptake [60], periphyton uptake [61], coral-reef supply of nutrients [62–64], fixation of carbon at leaf surfaces [65], etc. Due to the difficulties in having rigorous analytical expressions for the flux at any given geometry and flow conditions, in many instances it is convenient to include all the characteristics of the supply in the mass transfer coefficient ms and use expression (50). It must be pointed out that expression (50), stating a linearity between the flux and the difference between bulk and surface concentrations, cannot be – in general – valid for nonlinear processes, such as coupled complexation of the species i with any other species (see Chapters 4 and 10 for a more detailed discussion).

GLOSSARY GC GCS RC

Gouy–Chapman Gouy–Chapman–Stern Resistance–Capacitance

LIST OF SYMBOLS SUPERSCRIPTS * 0

bulk conditions (spherical) surface of the organism

142 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

SUBSCRIPTS D Dm e i m m r, y w x,y,z s þ – 1,2 0

Donnan phase Donnan–medium interphase electrolyte ions charge species i medium membrane polar components of a vector (fixed) wall phase charge Cartesian components of a vector separation surface between different media limit approaching from the right limit approaching from the left labels of media spherical surface of the organism

LATIN SYMBOLS Symbol

Name

Units

Equation

A c D div F grad J K KN k k f , kd l ms

Area Concentration Diffusion coefficient Divergence Faraday constant Gradient Flux Conductivity Nernst distribution coefficient Boltzmann constant Kinetic constants Length of plane Steady-state mass transfer coefficient Gas constant Radius of the cylindrical channel Radius, radial coordinate Temperature Time Ionic mobility Fluid velocity Flow rate Width of adsorbing plane

m2 mol m
3
1 m2 s Operator C mol
1 Operator
1 mol m
2 s
1
1 V m None J K
1 s
1 m m s
1

(46) (1) (8) (13) (1) (10); see Table 1 (10), (22) (7) (18) (1) (14) Figure 4 (50)

R R r T t u v vf w


1

J K
1 mol m m K s
1 m2 V
1 s
1 ms
1 m3 s m

(4) (35), (36) (20) (1) (13) (8), (10) (10) (36) Figure 4

H. P. VAN LEEUWEN AND J. GALCERAN

x y z z

Coordinate normal to the surface Coordinate of main flow Ionic charge Cartesian coordinate

143

m m None m

(3) Figure 4 (1), (6), (10) Figure 4

None m m None F m
1 V N s m
2 rad m
1
1 m2 s J mol
1 C m
3 s V

(31) (33) (26) (1), (3) (1)

GREEK SYMBOLS G di d0 e e0 z Zm , Zp y k
~ ~ m r td c

Incomplete gamma function Diffusion layer thickness Boundary layer thickness Relative permittivity Absolute permittivity of vacuum Electrokinetic potential Medium and particle viscosities Polar coordinate Reciprocal of Debye length Kinematic viscosity Electrochemical potential Density of charge Double layer relaxation time Electrical potential

(49) (43) (1) (24) (12) (3) (7), (9) (3), (4)

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

Kleijn, J. M. and van Leeuwen, H. P. (2000). Electrostatic and electrodynamic properties of biological interphases. In Physical Chemistry of Biological Interfaces. eds. Baszkin, A. and Norde, W., Marcel Dekker, New York, pp. 49–83. Barenholz, Y. and Cevc, G. (2000). Electrostatic and electrodynamic properties of biological interphases. In Physical Chemistry of Biological Interfaces. eds. Baszkin, A. and Norde, W., Marcel Dekker, New York, pp. 171–241. van Grondelle, R. (1985). Excitation-energy transfer, trapping and annihilation in photosynthetic systems, Biochim. Biophys. Acta, 811, 147–195. Harden, V. P. and Harris, J. O. (1952). The isoelectrical point of bacterial cells, J. Bacteriol., 65, 198–202. Cevc, G. (1990). Membrane electrostatics, Biochim. Biophys. Acta, 1031, 311–382. Pethig, R. (1985). Ion, electron, and proton transport in membranes: a review of the physical processes involved. In Modern Bioelectrochemistry. eds. Gutmann, F. and Keyzer, H., Plenum, New York, pp. 199–239. Honig, B. H., Hubbell, W. L. and Flewelling, R. F. (1986). Electrostatic interactions in membranes and proteins, Ann. Rev. Biophys. Biophys. Chem., 15, 163–193. Gawrisch, K., Ruston, D., Zimmerberg, J., Parsegian, V. A., Rand, R. P. and Fuller, N. (1992). Membrane dipole potentials, hydration forces, and the ordering of water at membrane surfaces, Biophys. J., 61, 1213–1223. Bard, A. J. and Faulkner, L. R. (1980). Electrochemical Methods. Fundamentals and Applications. John Wiley & Sons, Ltd, New York.

144 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33.

Lyklema, J. (1995). Fundamentals of Interface and Colloid Science, Vol. II. Solid– Liquid Interfaces. Academic Press, London. McLaughlin, S. (1989). The electrostatic properties of membranes, Ann. Rev. Biophys. Biophys. Chem., 18, 113–136. Cevc, G. and Marsh, D. (1987). Phospholipid Bilayers. Wiley-Interscience, New York. Langner, M., Cafiso, D., Marcelja, S. and McLaughlin, S. (1990). Electrostatics of phosphoinositide bilayer-membranes – theoretical and experimental results, Biophys. J., 57, 335–349. Ohshima, H. and Ohki, S. (1985). Donnan potential and surface-potential of a charged membrane, Biophys. J., 47, 673–678. Ohshima, H. and Kondo, T. (1987). Electrophoretic mobility and Donnan potential of a large colloidal particle with a surface-charge layer, J. Coll. Interf. Sci., 116, 305–311. Ohshima, H. and Kondo, T. (1989). Approximate analytic-expression for the electrophoretic mobility of colloidal particles with surface-charge layers, J. Coll. Interf. Sci., 130, 281–282. Ohshima, H. and Kondo, T. (1991). On the electrophoretic mobility of biological cells, Biophys. Chem., 39, 191–198. Blank, M. (1985). Electrical Double Layers in Biology. Plenum, New York. Baszkin, A. and Norde, W. (2000). Electrostatic and Electrodynamic Properties of Biological Interfaces. Marcel Dekker, New York. Lakshminarayanaiah, N. (1969). Transport Phenomena in Membranes. Academic Press, New York. Haydon, D. A. and Hladky, S. B. (1972). Ion transport across thin lipid membranes: a critical discussion of mechanisms in selected systems, Q. Rev. Biophys., 5, 187–282. van der Wal, A., Minor, M., Norde, W., Zehnder, A. J. B. and Lyklema, J. (1997). Electrokinetic potential of bacterial cells, Langmuir, 13, 165–171. Barchini, R., van Leeuwen, H. P. and Lyklema, J. (2000). Electrodynamics of liposome dispersions, Langmuir, 16, 8238–8247. Bird, R. B., Stewart, W. E., and Lightfoot, E. N. (1960). Transport Phenomena. John Wiley & Sons, Ltd., New York. Levich, V. G. (1962). Physicochemical Hydrodynamics. Prentice-Hall, Englewood Cliffs, NJ. Crank, J. (1975). The Mathematics of Diffusion. Clarendon Press, Oxford. Pedley, T. J. (1997). Introduction to fluid dynamics, Sci. Mar., 61, 7–24. Cussler, E. L. (1999). Diffusion. Mass Transfer in Fluid Systems. Cambridge University Press, Cambridge. Berry, R. S., Rice, S. A. and Ross, J. (2000). Physical Chemistry. Oxford University Press, New York. ¨ ber die Adsorptionsgeschwindigkeit von Gasen an porDamko¨hler, G. (1934). U o¨sen Adsorbentien, Z. Physik. Chem., 169, 222–239. Damko¨hler, G. (1937). Einflu¨sse der Stro¨mung, Diffusion und des wa¨rmeu¨berganges auf die Leistung von Reactionso¨fen. 2. Die isotherme, raumbesta¨ndige, homogene Reaktion erster Ordnung, Z. Elektroch. Bd., 43, 1–13. Boucher, D. F. and Alves, G. E. (1959). Dimensionless numbers, Chem. Eng. Prog., 55, 55–64. Jannasch, H. W., Honeyman, B. D. and Murray, J. W. (1996). Marine scavenging: the relative importance of mass transfer and reaction rates, Limnol. Oceanogr. 41, 82–88.

H. P. VAN LEEUWEN AND J. GALCERAN 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53.

145

Wolf-Gladrow, D. and Riebesell, U. (1997). Diffusion and reactions in the vicinity of plankton: a refined model for inorganic carbon transport, Mar. Chem., 59, 17–34. Galceran, J., Taylor, S. L. and Bartlett, P. N. (1999). Application of Danckwerts’ expression to first-order EC reactions. Transient currents at inlaid and recessed microdisc electrodes, J. Electroanal. Chem., 466, 15–25. Galceran, J., Puy, J., Salvador, J., Cecı´lia, J. and van Leeuwen, H. P. (2001). Voltammetric lability of metal complexes at spherical microelectrodes with various radii, J. Electroanal. Chem., 505, 85–94. Heyrovsky´, J. and Ku˚ta, J. (1966). Principles of Polarography. Academic Press, New York. van Leeuwen, H. P., Puy, J., Galceran, J. and Cecı´lia, J. (2002). Evaluation of the Koutecky´–Koryta approximation for voltammetric currents generated by metal complex systems with various labilities, J. Electroanal. Chem., 526, 10–18. van Leeuwen, H. P. (1999). Metal speciation dynamics and bioavailability: inert and labile complexes, Environ. Sci. Technol., 33, 3743–3748. van Leeuwen, H. P. (2001). Revisited: the conception of lability of metal complexes, Electroanalysis, 13, 826–830. Pinheiro, J. P., Galceran, J. and van Leeuwen, H. P. (2003). Metal speciation dynamics and bioavailability. Bulk depletion influence in biouptake, Environ. Sci. Technol., submitted. Gradshteyn, I. S. and Ryzhik, I. M. (1994). Tables of Integrals, Series and Products. Academic Press, New York. Zoski, C. G., Bond, A. M., Allinson, E. T. and Oldham, K. B. (1990). How long does it take a microelectrode to reach a voltammetric steady-state? Anal. Chem., 62, 37–45. Gnaiger, E. (1983). Symbols and units: toward standardization. In Polarographic Oxygen Sensors. eds. Gnaiger, E. and Forstner, H., Springer-Verlag, Berlin, pp. 352–358. Carslaw, H. S. and Jaeger, J. C. (1959). Conduction of Heat in Solids. Clarendon Press, Oxford. Tomaszewski, L., Buffle, J. and Galceran, J. (2003). Theoretical and analytical characterisation of a flow-through permeation liquid membrane with controlled flux for metal speciation measurements, Anal. Chem., 75, 893–900. Galceran, J., Salvador, J., Puy, J., Cecı´lia, J. and Gavaghan, D. J. (1997). Analytical solution for the steady-state diffusion towards an inlaid disc microelectrode in a multi-layered medium, J. Electroanal. Chem., 440, 1–25. Csanady, G. T. (1986). Mass-transfer to and from small particles in the sea, Limnol. Oceanogr., 31, 237–248. Pahlow, M., Riebesell, U. and Wolf-Gladrow, D. A. (1997). Impact of cell shape and chain formation on nutrient acquisition by marine diatoms, Limnol. Oceanogr., 42, 1660–1672. Adamczyk, Z. and van de Ven, T. G. M. (1982). Particle transfer to a plate in uniform-flow, Chem. Eng. Sci., 37, 869–880. Lazier, J. R. N. and Mann, K. H. (1989). Turbulence and the diffusive layers around small organisms, Deep-Sea Res., 36, 1721–1733. Sˇtulı´k, K. and Pacakova, V. (1987). Theory of electroanalytical flow measurements. In Electroanalytical Measurements in Flowing Liquids. Series eds. Chalmers, R. A. and Masson, M., Ellis Horwood, Chichester, pp. 27–81. White, F. M. (1986). Fluid Mechanics. McGraw-Hill, New York.

146 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65.

Landau, L. D. and Lifshitz, E. M. (1987). Fluid Mechanics. Vol. 6. Pergamon Press, Oxford. Douglas, J. F., Gasiorek, J. M. and Swaffield, J. A. (1985). Fluid Mechanics. Longman Scientific & Technical, New York. Vogel, S. (1994). Life in Moving Fluids: the Physical Biology of Flow. Princeton University Press, Princeton, NJ. Le´veˆque, M. A. (1928). Les lois de la transmission de chaleur par convection, Ann. Mines. Mem. Ser., 13, 201–208. Alden, J. A. (1998). Computational Electrochemistry. Ph.D. Thesis, University of Oxford, UK. Oldham, K. B. and Myland, J. C. (1994). Fundamentals of Electrochemical Science. Academic Press, San Diego. Pasciak, W. J. and Gavis, J. (1974). Transport limitation of nutrient uptake in phytoplankton, Limnol. Oceanogr., 19, 881–888. Ploug, H., Stolte, W. and Jorgensen, B. B. (1999). Diffusive boundary layers of the colony-forming plankton alga Phaeocystis sp – implications for nutrient uptake and cellular growth, Limnol. Oceanogr., 44, 1959–1967. Patterson, M. R., Sebens, K. P. and Olson, R. R. (1991). In situ measurements of flow effects on primary production and dark respiration in reef corals, Limnol. Oceanogr., 36, 936–948. Atkinson, M. J. and Bilger, R. W. (1992). Effects of water velocity on phosphateuptake in coral reef-flat communities, Limnol. Oceanogr., 37, 273–279. Bilger, R. W. and Atkinson, M. J. (1992). Anomalous mass transfer of phosphate on coral-reef flats, Limnol. Oceanogr., 37, 261–272. Wheeler, W. N. (1980). Effect of boundary-layer transport on the fixation of carbon by the giant-kelp Macrocystis pyrifera, Mar. Biol., 56, 103–110.

4 Dynamics of Biouptake Processes: the Role of Transport, Adsorption and Internalisation JOSEP GALCERAN Departament de Quı´mica, Universitat de Lleida, Av. Rovira Roure 191, 25198 Lleida, Spain

HERMAN P. VAN LEEUWEN Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, NL-6703 HB Wageningen The Netherlands

1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Uncomplicated Mass Transfer of the Species Being Taken up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 A Transient Model for Two Parallel Internalisation Routes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 General Model with Two Types of Langmuirian Adsorption Sites Coupled to First-Order Internalisation Processes . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Typical Results for the Case of Two Internalisation Routes . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 A Particular Case: One Internalisation Route and One Adsorption-Only Route. . . . . . . . . . . 2.1.3.1 Transient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3.2 Steady-State. . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 The Steady-State Limit for Two Parallel Internalisation Routes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 The Linear Adsorption Limit . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Model Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Analytical Solution for Steady-State . . . . . . . . . . . . . . 2.3.3 Analytical Solution for the Transient . . . . . . . . . . . . . 2.3.4 The Impact of the Radius . . . . . . . . . . . . . . . . . . . . . . . 2.3.5 The Approach to Steady-State After a Maximum . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Physicochemical Kinetics and Transport at Biointerfaces Edited by H. P. van Leeuwen and W. Ko¨ster. ß 2004 John Wiley & Sons, Ltd

149 150 150

150 153 155 155 155 156 160 160 160 161 162 163

148 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

2.3.6

How Long Does it Take to Reach Steady-State? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.7 Discriminating the Individual Parameters of the Product kKH Through the Cumulative Plot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 The Diffusional Steady-State (dSS) Approach . . . . . . . . . . . 2.4.1 The Essence of the dSS Approach . . . . . . . . . . . . . . . 2.4.2 Linear Adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Langmuirian Adsorption . . . . . . . . . . . . . . . . . . . . . . . 2.4.3.1 One Site Adsorbing and Internalising . . . . . 2.4.3.2 Two Sites: Site 1 ¼ Adsorption þ Internalisation, Site 2 ¼ Adsorption Only . . . . . . . . . . . . . . . . . . . . . . 3 Biouptake When Mass Transfer is Coupled With Chemical Reaction (Complex Media) . . . . . . . . . . . . . . . . . . . . . . . 3.1 Mathematical Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Totally Inert Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Fully Labile Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Partially Labile Complexes. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 The Limiting Supply Flux in the Steady-State Uptake Considering Homogeneous Kinetics . . . . . . . 3.4.2 The Degree of Lability and Lability Criteria . . . . . . . 3.4.3 Combining Supply and Internalisation. . . . . . . . . . . . 3.5 Relationship with the FIAM . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Key Factors and Challenges For Future Research in Biouptake Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Refinements Based on Mass Transport Factors . . . . . . . . . . 4.1.1 Finite Media. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Nonstagnant Media . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.3 Complex Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Refinements Based on Adsorption Processes. . . . . . . . . . . . . 4.2.1 Adsorption Isotherm and Kinetics . . . . . . . . . . . . . . . 4.2.2 Competition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Refinements Based on Internalisation Factors . . . . . . . . . . . 4.3.1 Internalisation Kinetics. . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Efflux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix A: Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Latin Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Greek Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

165

168 170 170 172 175 175

176 178 178 180 180 182 182 183 184 186 190 190 190 192 192 193 193 193 194 194 194 194 195 195 196 196 197 198

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1

149

INTRODUCTION

Biological systems are open to the exchange of matter with their environment. If species from the medium (either nutrients or pollutants) travel towards the membrane and a net increase in their concentration arises in the cell, then an uptake process is occurring. Apart from the obvious importance for the organism itself, there is an impact on the medium (e.g. regulating the fate of pollutants in the environment). Modelling biouptake processes helps in the understanding of the key factors involved and their interconnection [1]. In this chapter, uptake is considered in a general sense, without distinction between nutrition or toxicity, in which several elementary processes come together, and among which we highlight diffusion, adsorption and internalisation [2–4]. We show how the combination of the equations corresponding with a few elementary physical laws leads to a complex behaviour which can be physically relevant. Some reviews on the subject, from different perspectives, are available in the literature [2,5–7]. Here we discuss in some detail a few recent models for biouptake, highlighting their physicochemical basis, especially the diffusive transport involved. Numerical examples are usually taken from the biouptake literature on bacteria and algae, because the uptake occurs across a single membrane and the application of the modelling is simpler; thus no exploration is done of more ‘macroscale’ models based such as those based on compartments [4,8]. The goal is to help the reader in the building up of a coherent picture of the various processes and their mathematical modelling, taking into account their relative importance and the specific equations describing them (e.g. Henry or Langmuir adsorption isotherm). Special attention is paid to analytical solutions – even if their applicability requires simplifying assumptions – as they can provide primary understanding for the main trends in global behaviour. We shall consider spherical microorganisms [9] (see ref. [10] for spheroidal shapes), but the treatment applies equally well to cases of larger organisms where the uptake takes place in individual, well-separated microregions. The planar case can be found by letting r0 tend to infinity. We recall from Chapter 3 (this volume) that planar semi-infinite diffusion without any convection cannot sustain steady-state, which is attainable in practice only for sufficiently small radii. We will first deal with the uptake of a species that diffuses towards the biosurface without coupled chemical reactions in the medium (Section 2) and then move to the case of a coupled reaction (Section 3). Dynamic aspects are then highlighted, because it might not be realistic to assume that the species being taken up is in equilibrium in the medium surrounding the microorganism [11]. The idea of kinetics possibly being relevant was pioneered by Jackson and Morgan [12] and Whitfield and Turner [9], and then experimentally proved by Hudson and Morel [13] with regard to Fe

150 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

uptake. The consideration of further physical phenomena is discussed in Section 4. A list of the symbols used is given in Appendix A. 2 UNCOMPLICATED MASS TRANSFER OF THE SPECIES BEING TAKEN UP 2.1 A TRANSIENT MODEL FOR TWO PARALLEL INTERNALISATION ROUTES 2.1.1 General Model with Two Types of Langmuirian Adsorption Sites Coupled to First-Order Internalisation Processes Let us consider the uptake of a given species, either a nutrient or a pollutant heavy metal or an organic (macro)molecule, etc., which will be referred to as M. M is present in the bulk of the medium at a concentration, c
M , and we assume that the only relevant mode of transport from the medium to the organism’s surface is diffusion. The internalisation sites are taken to be located on the spherical surface of the microorganism or in a semi-spherical surface of a specialised region of the organism with radius r0 (see Figure 1). Thus, diffusion prescribes: " # qcM (r, t) q2 cM (r, t) 2 qcM (r, t) ¼ DM þ qt qr2 r qr

(1)

In the most general case considered here, M is adsorbed on two kinds of sites, labelled ‘1’ and ‘2’. Each adsorption process is assumed to be fast enough (when

Medium

Organism

r0

Mads,1

Minter

M

M

Mads,2

Figure 1. Outline of the uptake model showing the spherical diffusion of species M through the medium towards two different sites where adsorption is followed by internalisation. The radius of the organism is taken as r0

J. GALCERAN AND H. P. VAN LEEUWEN

151

compared with diffusion or the internalisation process) as to be described by a Langmuir (equilibrium) isotherm relating the coverage fraction of each kind of site (y1 and y2 , respectively) and the local concentration of M at the organism surface: cM (r0 , t): y1 (t) ¼

G1 (t) cM ðr0 , tÞ G2 (t) cM ðr0 , tÞ ; y2 (t) ¼ ¼ ¼ Gmax,1 KM,1 þ cM ðr0 , tÞ Gmax,2 KM,2 þ cM ðr0 , tÞ

(2)

where Gj stands for the surface concentration associated with sites of type j, and KM,1 and KM,2 are a type of adsorption constant. The adsorption process can thus be considered as the coordination of M with a finite number of transport sites on the surface of the microorganism [3,11,14,15]. Once adsorbed, we assume that M is internalised following a first-order kinetic process in each of the sites, with internalisation rate constants k1 and k2 respectively [9,16–18]. For each kind of adsorption site, we have an uptake flux given by: Ju, j (t) ¼ kj Gmax , j

cM (r0 , t) KM, j þ cM (r0 , t)

j ¼ 1, 2

(3)

which can be seen as a Michaelis–Menten-like expression, with KM, j called the half-saturation constant or bioaffinity parameter [13,14,19]. Within the hypothesis of adsorption equilibrium, the usual Michelis–Menten coefficient
 KM, j ¼ kdesorption, j þ kj =kadsorption, j  kdesorption, j =kadsorption, j (usually kdesorption, j > kj , due to the fast adsorption process), thus becomes the inverse of the usual Langmuir coefficient [4,13,15] (which is indicative of the stability of the surface complex). For a constant ‘cell quota’ (as amount of M per unit biomass) [20], Ju can be related to the rate of growth of biomass, and equation (3) has been described in the uptake context as a Monod expression [16,21]. Thus, the fundamental boundary condition arising from the flux balance at r ¼ r0 can be written as:   dG1 (t) dG2 (t) qcM (r, t) þ ¼ DM  k1 G1 (t)  k2 G2 (t) dt dt qr r¼r0

(4)

simply expressing that the change in adsorbed amounts follows from the difference between the diffusive supply flux and the internalisation rates. The remaining boundary condition for the diffusion equation (1) is semiinfinite diffusion:

152 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

cM (r, t) ¼ c
M

r!1

t0

(5)

and the initial distribution of M is assumed to be homogeneous: cM (r, t) ¼ c
M

r  r0

t¼0

(6)

As expected from the presence of nonlinear terms in the boundary conditions, no analytical solution for the problem defined by equations (1)–(6) is available to our knowledge, so a numerical strategy is applied here. As seen in ref. [22], the problem given by the differential equation (1) with boundary conditions (4)–(6) can be recast in the form of an integral equation for cM (r0 , t):   ðt DM
1 cM ðr0 , tÞ  c
M pffiffiffiffiffiffiffiffiffiffi dt cM t  pffiffiffiffiffiffiffiffiffiffiffi r0 pDM 0 r0 t  t  ðt  DM cM ðr0 , tÞ dt k1 G1 (t) þ k2 G2 (t) þ  r0 0

G1 (t) þ G2 (t) ¼

(7)

and the numerical solution of this equation can be obtained by discretising the unknown cM ðr0 , tÞ. Once the value of cM (r0 , t) (which for simplicity will be denoted as c0M from now on) is known, any physical quantity of the system can be computed. In particular, the incoming diffusive (or mass transport) flux:  Jm (t) ¼ DM

 qcM (r, t) qr r¼r0

(8)

has been selected in this work as a relevant response function. For the general case considered here, equation (4) can be reorganised as: Jm (t) ¼

dG1 (t) dG2 (t) þ þ k1 G1 (t) þ k2 G2 (t) dt dt

(9)

where fluxes towards the organism are counted positively (see Chapters 1 and 3 of this volume). The bioaccumulated amount, Fu , is the time integral of the uptake flux: Fu (t) 

ðt Ju (t)dt

(10)

0

representing the amount of matter that has been internalised per unit of surface area. The product 4pr20 Fu is the number of moles taken up per individual cell from the beginning of the process, i.e. the cell quota [23]. On the other hand, the total supply from the medium can be defined as:

J. GALCERAN AND H. P. VAN LEEUWEN

Fm (t) 

153

ðt Jm (t)dt

(11)

0

The relationship between the accumulated fluxes can be easily found by integrating the boundary condition (4) as: Fm (t) ¼ Fu (t) þ G1 (t) þ G2 (t)

(12)

which is nothing else than mass conservation of M. 2.1.2

Typical Results for the Case of Two Internalisation Routes

Figure 2 plots the evolution of the incoming fluxes Jm and Ju with time for some typical values from the literature [24,25] and references therein. As expected, the diffusive flux Jm decreases with time and tends towards a steady-state value when converging with Ju . It is noticeable that, in the initial transient, the internalisation flux Ju is much closer to its eventual steady-state 1.00

1.6

0.90

1.4

0.70 1.0

0.60 0.50

0.8 Ju

q

J /10−10 mol m−2 s−1

0.80

q1

Jm

1.2

0.40

0.6

0.30 0.4 0.20

q2

0.2

0.10 0.00

0.0 0

1

2

3

4

5 t/s

6

7

8

9

10

Figure 2. Evolution of diffusive (Jm , continuous line) and internalisation (Ju , circles) fluxes with time for a system with two internalisation sites (Section 2.1.2). Fraction of coverages of each site type, y1 and y2 , are indicated with dashed lines. Parameters: DM ¼ 109 m2 s1 , c
M ¼ 104 mol m3 , r0 ¼ 104 m, KM,1 ¼ 105 mol m3 , KM,2 ¼ 103 mol m3 , Gmax,1 ¼ 108 mol m2 , Gmax,2 ¼ 1011 mol m2 , k1 ¼ 102 s1 and k2 ¼ 1 s1

154 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

value than Jm , whose values are huge for short t. Plots on suitable scales establish that Ju goes through a maximum (of around 9:1735  1011 mol m2 s1 ) for t  148 s, which is slightly larger than the steady-state flux of around 9:1734  1011 mol m2 s1 . Obviously, such a small maximum is irrelevant for practical purposes, but other maxima – for other sets of parameters – could appear to be more prominent. For more detailed discussion on these maxima (for the simpler case of linear adsorption), see Section 2.3.5. It is also seen in Figure 2 that there is no saturation of either of the two kinds of sites (the largest coverage is about 90% for sites of type 1), because cSS M is too small. The shape of the various Ju versus t plots reflects the impact of different maximum coverages for each of the site types. Figure 3 shows a system with the same parameters as in Figure 2, but with Gmax,2 a factor of 1000 higher. At around 0.2 s, sites 1 (with high affinity and same Gmax ) depart from the linear regime of the isotherm; a smaller fraction of the supply accumulates on G1 ; c0M increases more steeply and so does the flux Ju,2 and consequently Ju . Sites of type 2 are always in the linear regime; the curvature of Ju,2 (e.g. at 1.2 s) being due to the progressive achievement of the steady-state concentration

10

2.0 Ju

9

Ju,2

8

1.8 Jm

1.4

7

1.2

6

1.0

5

0.8

4

0.6

3

0.4

2

0.2 0.0 0.0

1

Ju,1

0.5

1.0

1.5

2.0

Ju /10−10 mol m−2 s−1

Jm /10−8 mol m−2 s−1

1.6

2.5

0 3.0

t /s

Figure 3. Plot of fluxes (solving integral equation (7) numerically) for parameters in Figure 2, but Gmax,2 ¼ 108 mol m2 . The individual uptake fluxes for sites of type 1 (Ju,1 , þ ) and sites of type 2 (Ju,2 ,  ) are added to provide the total flux Ju (s). The inflexions in Jm arise from the saturation of sites of type 2 and from the approach to the steady-state

J. GALCERAN AND H. P. VAN LEEUWEN

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c0M  cSS M  KM,2 . When the inflexions in (the increasing) Ju occur, there are also the inflexions of (the decreasing) Jm , because Ju increases with c0M , but Jm decreases with c0M . For a detailed discussion on the effects of the parameters on the fluxes, see ref. [22]. 2.1.3 A Particular Case: One Internalisation Route and One Adsorption-Only Route We deal now with two parallel Langmuir adsorption steps, only one of which is followed by internalisation. Parameters of the site with both adsorption and internalisation will be denoted with subscript 1 (physiologically active site), while the other, with no internalisation, will be denoted with subscript 2 (physiologically inactive site) [2]. 2.1.3.1 Transient The numerical solution of this case can be obtained by setting k2 ¼ 0 in the expressions for the general model of two routes (or ‘mouths’) described in Section 2.1.1. Now, material adsorbed on site 2 simply acts as a reservoir, buffering c0M . 2.1.3.2 Steady-State If one defines the limiting biouptake flux for each site (which would appear for cSS M much larger than each KM, j ) as [26]: Ju
, j (t) ¼ kj Gmax, j

j ¼ 1, 2

(13)

the internalisation flux Ju (for steady-state) can be written as: Ju ¼ k1 Gmax,1

cSS cSS M M ¼ Ju
,1 SS K M, 1 þ c M KM,1 þ cSS M

(14)

which depends only on the parameters of site 1 because, for steady-state fluxes, the adsorption-only route is irrelevant. So, results in this section also apply when there are only internalising sites present. SS can be written: The supply flux Jm     c
 cSS DM c
M cSS cSS SS
M M Jm ¼ J (15) ¼ DM M ¼ 1 M 1  m r0 r0 c
M c
M where:
Jm  DM c
M =r0

(16)

is the limiting supply flux, namely the product of bulk concentration and the mass transfer coefficient DM =r0 (see Chapter 3).

156 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

The result of equating the steady-state fluxes, equations (14) and (15), is sometimes known as the Best equation [9,13,16,27–31] which we normalise to its most elementary parameters [26] (other normalisations have also been suggested [21]): (  1=2 ) (1 þ a þ b) 4b 1 1 J~ ¼ 2b (1 þ a þ b)2

(17)

where J~ is the normalised flux: SS J~  Jm =Ju


(18)

(with Ju
¼ Ju
,1 , if there is a second noninternalising site) a is the normalised bioaffinity parameter: a ¼ KM =c
M

(19)

(with KM ¼ KM,1 , if there is a second noninternalising site) and b the limiting flux ratio:
b ¼ Ju
=Jm

(20)

Equation (17) shows quite elegantly that the biouptake flux is governed by the two fundamental parameters a and b. A set values of J~ is easily
of limiting  derived by using that (1  x)1=2 approaches 1  12 x for x  1. If we consider, by way of example, an organism with a relatively low affinity for M (a  1) in a medium with a relatively high transport flux (b  1), then equation (17) reduces to: (  1=2 ) a 4b 1 1 2 J~ ¼ 2b a

(21)

which, since for this case 4b=a2 is much smaller than unity, approaches J~ ¼ 1=a or

SS Jm ¼ Ju
c
M =KM

(22)

2.2 THE STEADY-STATE LIMIT FOR TWO PARALLEL INTERNALISATION ROUTES Let us now consider the simple case of steady-state, towards which the transient solution tends when t ! 1 but which, for sufficiently small r0 , is practically

J. GALCERAN AND H. P. VAN LEEUWEN

157

reached within a very short time. In this case, the balance of flux, equation (4), can be written as [18]: DM

c
M  cSS cSS cSS M M M ¼ k1 Gmax,1 þ k2 Gmax,2 SS r0 K M, 1 þ c M KM,2 þ cSS M

(23)

This is a cubic equation of the unknown quantity cSS M which is the eventual concentration at the surface of the organism. Then, the resulting steady-state flux can be computed using either side of equation (23). Some insight on the effect of the parameters on the mathematical solution can be gained through a graphical procedure. The basic idea is to plot the uptake and diffusive fluxes as functions of a variable concentration on the surface c0M (i.e. cM (r0 )) and seek their intersection. It is therefore convenient dSS to introduce the ‘diffusive steady-state’ (dSS, see Section 2.4 below) flux, Jm , or flux corresponding to the diffusion profile conforming to the steady-state situation for a given surface concentration c0M : dSS Jm  DM

c
M  c0M r0

(24)

14 12 10 8 6 4

Ju −0.0011

2

−0.0008

−0.0005 cM(r0)/mol m−3

−0.0002

Ju

0 0.0001 −2

J /10−10 mol m−2 s−1

JmdSS

−4 −6

Figure 4. Graphical determination of the three real solutions of the cubic equation (23) corresponding with the steady-state case. The diffusive flux JmdSS (a straight line with negative slope) and the uptake flux Ju are plotted as a function of the variable cM (r0 ) (including physically meaningless negative values). Ju is the addition of two hyperbolae dSS (for Ju,1 and Ju,2 ) with its asymptotes plotted as dashed lines. The intersections of Jm and Ju yield the three solutions, from which one is positive (the physically relevant) and the remaining two real and negative. Parameters as in Figure 2, except r0 ¼ 103 m, Gmax,1 ¼ 5  109 mol m2 , Gmax,2 ¼ 1012 mol m2 and k2 ¼ 10 s1

158 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

As depicted in Figure 4, all the solutions for cSS M can be found graphically at dSS (which is a straight line of slope DM =r0 ) with the each intersection of Jm curve for Ju ¼ Ju,1 þ Ju,2 (which is the sum of two hyperbolae with their corresponding vertical asymptotes at c0M ¼ KM,1 and at c0M ¼ KM,2 ). Due to the positive character of all the physical constants, one concludes that there is only one positive (physically meaningful) solution of equation (23). The above graphical method, where the fluxes are plotted in terms of c0M (in the region c0M > 0), can help in rationalising the impact of several parameters on the steady-state flux (as well as in the graphical solution of the cubic equation with a spreadsheet). Each diagonal line in Figure 5a represents the diffusive flux dSS versus c0M for different c
M values (given by the intercept with the abscissas). Jm As seen in Figure 5a, at low c
M , a small change in c
M implies a large shift SS (upwards) of the ordinate of the intersection (a large change in Jm ) within the
linear region of the Ju curve. On the other hand, at large cM , the impact of changing c
M on the ordinate of the intersection point is low, because in this region the uptake flux approaches its maximum value: Ju
¼ Ju
,1 þ Ju
,2 ¼ k1 Gmax,1 þ k2 Gmax,2

(25)

SS Figure 5b shows the resulting steady-state flux Jm (obtained as the positive SS solution for cM from equation (23)) for a range of c
M values. At low c
M values (usually associated with low cSS M values), there is a linear dependence between SS and c
M , as expected from the linearisation of the Langmuir isotherms (see Jm equation (31), below). At large c
M values, the usual Michaelis–Menten saturating effect of c
M is also seen. From inspection of equation (23), it follows that the effects of r0 and DM dSS are opposed. Three Jm versus cM (r0 ) plots for different ratios DM =r0 are shown as straight lines with different slopes in Figure 5c, converging at a common point at c0M ¼ c
M . Thus, the steady-state flux increases with DM =r0 up to an asymptotic value given by the maximum (at this c
M ) uptake flux c
c
SS ! Ju
,1 KM,1Mþc
þ Ju
,2 KM,2Mþc
< Ju
. The overall effect of changing organism Jm M M SS size (i.e. r0 ) on the Jm can be seen in Figure 5d, which exhibits a sigmoidal c
c
shape (falling practically from Ju
,1 KM,1Mþc
þ Ju
,2 KM,2Mþc
to 0) when the ratio M M spans over a large interval, but could be experimentally seen as practically linear even for certain regular variation ranges of r0 . The same analysis can be performed on the effect of the similar parameters SS increases when any of them k1 , Gmax ,1 , k2 and Gmax,2 . The steady-state flux Jm increases. As seen in Figure 5f for the particular case of Gmax,1 variation, there SS are two asymptotic limits for Jm given by the fixed Ju,2 (at low Gmax,1 ) and by the fixed limiting diffusion value (see equation (16) and Figure 5e).

J. GALCERAN AND H. P. VAN LEEUWEN 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

159

1.2

(a)

(b)

J /10−10 mol m−2 s−1

J /10−10 mol m−2 s−1

1.0

Ju

cM* =

10−4 mol m−3

cM* = 5⫻10−5 mol m−3 0

0.00005

cM* = 2⫻10−4 mol m−3

0.00015

* Ju,1

0.6 0.4

* Ju,2

JmSS

* cM * KM,1 + cM * cM

* KM,2 + cM

0.2

cM* = 1.5⫻10−4 mol m−3

0.0001

0.8

0.0

0.0002

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

(c)

5.0

DM −6 −1 r0 = 2.5⫻10 m s

1.0

DM −6 −1 r0 = 10 m s

Ju

J /10−10 mol m−2 s−1

J /10−10 mol m−2 s−1

3.0 2.0

0.0 0

0.00002

0.00004

0.00006

0.00008

0.0001

J*u

1.00 0.80

J*u,1

0.60 0.40

J*u,2

* cM

* KM,1 + cM

JmSS

* cM

* KM,2 + cM

0.20 0.00 −6

−5

−4

−3

cM(r0)/mol m−3

−2

−1

0

log (r0/ m)

(e)

2.0

J /10−10 mol m−2 s−1

1.5

Gmax,1=2×10−8 mol m−2 Gmax,1=5×10−9 mol m−2

0.5

0.0 0

0.00002

0.00004

0.00006

cM(r0)/mol m−3

0.00008

0.0001

J /10−10 mol m−2 s−1

Gmax,1=2×10−8 mol m−2

1.0

1

(d)

1.20 DM −6 −1 r0 = 5⫻10 m s

4.0

0.9

* /10−3 mol m−3 cM

cM(r0)/mol m−3

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0

(f)

J*m

JmSS

Ju,2

0.5

1.0

J *u,2 1.5

2.0

2.5

3.0

Gmax,1 /10 −8 mol m−2

SS Figure 5. Effect of the model parameters on the steady-state flux Jm illustrated by the graphical procedure (left column), and the corresponding outcome (right column) with rest of parameters as in Figure 4, except Gmax,1 ¼ 5  108 mol m2 for (a)–(d) and DM ¼ 109 m2 s1 for (d). SS dSS (a) Impact of c
M on Jm . Straight lines with negative slope indicate the diffusive flux Jm
for different cM . Circles stand for the uptake flux Ju , sum of two terms like equation (3). Each intersection between a straight line and the quasi-hyperbolic succession of circles SS corresponding with that c
M value. yields the Jm SS on c
M . The maximum values expected for Ju, j at each bulk (b) Dependence of Jm concentration are also depicted. SS dSS . Straight lines indicate Jm at different (c) Impact of the relationship DM =r0 on Jm DM =r0 values.

160 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

2.3 2.3.1

THE LINEAR ADSORPTION LIMIT Model Formulation

For sufficiently low coverages (such as those expected for low bulk concentrations, e.g. trace pollutants), the adsorption isotherms, equation (2), revert to linear ones: G1 (t) cM (r0 , t)  ; Gmax,1 K M, 1

G2 (t) cM (r0 , t)  Gmax,2 K M, 2

(26)

then equation (4) can be written as: KH

  dcM (r0 ) qcM (r)  kKH cM (r0 ) ¼ DM dt qr r¼r0

(27)

with an effective linear (Henry) adsorption coefficient: KH ¼

Gmax,1 Gmax,2 þ KM,1 KM,2

(28)

and an effective internalisation rate constant:    k1 Gmax,1 k2 Gmax,2 Gmax,1 Gmax,2 k¼ þ þ KM,1 K M, 2 K M, 1 K M, 2 k1 Gmax,1 KM,2 þ k2 Gmax,2 KM,1 ¼ Gmax,1 KM,2 þ Gmax,2 KM,1

2.3.2

(29)

Analytical Solution for Steady-State

The steady-state solution associated with equation (27) is: (d) Dependence of JmSS on the logarithm of the radius. Notice that for r0 ! 0, c
c
SS ! Ju
,1 KM,1Mþc
þ Ju
,2 KM, 2Mþc
< Ju
as diffusion is no longer limiting. For r0 ! 1, Jm M M SS Jm vanishes. SS . The straight line indicates JmdSS . Each succession of (e) Impact of Gmax,1 change on Jm circles indicates the uptake flux Ju at a given Gmax,1 (5  109 mol m2 , 108 mol m2 and 2  108 mol m2 ). SS on Gmax,1 (solid line). Notice that for Gmax,1 ! 0, JmSS ! (f) Dependence of Jm SS
Ju,2 (cSS M ) (O) and that Ju,2 (cM ) < Ju,2 ¼ k2 Gmax,2 (dashed line). For Gmax,1 ! 1, SS
^ Jm ! Jm ( )

J. GALCERAN AND H. P. VAN LEEUWEN

cSS M ¼

c
M 1 þ ðkKH r0 =DMÞ

161

(30)

from which the steady-state diffusion flux can be computed as [11,21]: SS Jm ¼

DM c
M c
M ¼ r0 þ (DM =kKH ) (r0 =DM ) þ (1=kKH )

(31)

This expression has been interpreted as the total ‘resistance’, being the sum of the diffusion ðr0 =DM Þ and adsorption þ internalisation (1=kKH ) resistances [11,32] or a combination of permeabilities [19]. If the couple: adsorption þ internalisation is much more effective than diffusion (kKH  DM =r0 ), then cSS M ! 0 and we recover the steady-state maximum uptake flux for a spherical
organism Jm . 2.3.3

Analytical Solution for the Transient

It can be shown (see [33–35]), that the expression for the flux can be expressed in terms of the auxiliary parameters a and b:
 pffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DM r0 þ DM r0  4 DM KH þ kKH2 r0 a pffiffiffiffi 2KH r0
 pffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DM r0  DM r0  4 DM KH þ kKH2 r0 b pffiffiffiffi 2KH r0

(32)

(33)

type of combination of parameter values Thus, if a ¼
b, that is, for a particular

DM r0 ¼ 4 DM KH þ kKH2 r0 : rffiffiffiffiffiffiffiffiffi  SS Jm Jm 1 DM t 1 2 2 p ffiffiffiffiffiffiffiffiffiffiffiffi ffi þ ¼ þ  DM c
M DM c
M p KH r0 pDM t " # pffiffiffiffiffiffiffiffiffi   DM t 4KH 1 1 2 2 DM t F þ    2 2KH KH KH r0 2KH r0 where:
 F(x)  exp x2 erfc(x) For the more general case with a 6¼ b:

(34)

162 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES SS Jm Jm 1 ¼ þ pffiffiffiffiffiffiffiffiffiffiffiffiffi DM c
M DM c
M pDM t pffiffiffiffiffiffiffiffi   pffiffi 2 DM DM a  þ F(a t)  2 KH r0 (a  b) KH r0 a(a  b) KH (a  b) pffiffiffiffi   pffiffi 2 DM DM b F(b t)    2 KH r0 (a  b) KH r0 b(a  b) KH (a  b)

(35)

From the previous expressions, the accumulated uptakes (Fu and Fm , see equation (11)) follow by simple integration [35]. 2.3.4

The Impact of the Radius

Figure 6 shows the evolution of Jm with time, for three different radii. As expected from the enhanced diffusion efficiency, the smaller the radius, the sooner steady-state values are approached. For a large radius of 1 mm, after SS (in practice, with such long 200 s, the value of Jm is still approximately twice Jm times, convection will usually overrule the pure diffusion conditions). It can also be seen in Figure 6 that larger radii yield larger fluxes at intermediSS ate times, while Jm decreases with increasing r0 . Plots at very short times (not 3.00

Jm /10−5 mol m−2 s−1

2.50

2.00

1.50

1.00

0.50

0.00 0

0.1

0.2

0.3

0.4

0.5 t /s

0.6

0.7

0.8

0.9

1

Figure 6. Impact of the microorganism radius, r0 , on the time evolution of the diffusive flux Jm (given by equations (34) and (35)). Three curves are depicted: u (r0 ¼ 10 mm), n (r0 ¼ 100 mm) and þ (r0 ¼ 1 mm). Parameters: KH ¼ 2  105 m, k ¼ 5  105 s1 , DM ¼ 109 m2 s1 , c
M ¼ 1 mol m3

J. GALCERAN AND H. P. VAN LEEUWEN

163

shown here) indicate larger fluxes for smaller radii, as expected from the enhanced diffusion transport towards microbodies. The inversion of the order in the fluxes at intermediate times can be explained as larger radii producing more gradually decreasing fluxes than smaller radii. 2.3.5

The Approach to Steady-State After a Maximum

As seen in Figure 7, the surface concentration c0M attains a maximum, overshooting the steady-state concentration value. It has been shown theoretically [35] that the maximum appears for any combination of parameters’ values. Experimental evidence of the appearance of transient uptake rate maxima (which might be totally or partially related to the maximum predicted by the present uptake model) has already been reported [36–39]. The maximum can be physically understood as a result of the simultaneous settling of two processes: adsorption governing short times (see Section 3.2, below) and internalisation ruling longer times. If only adsorption were present (i.e. k ¼ 0), the final cM ðr0 , tÞ value would be c
M . So, at relatively short times, for the combined processes, the surface concentration ‘aims at’ a value closer to c
M than the eventual cSS M value, overshooting it. After the maximum (longer times), cM ðr0 , tÞ is relatively large, and the corresponding Ju cannot match the

0.25

* cM(r0,t)/cM

0.20 k = 10−2 s−1

0.15

0.10

k = 10−3 s−1

0.05 k = 10−4 s−1 0.00 0

500

1000

1500

2000 t /s

2500

3000

3500

4000

Figure 7. Evolution of cM ðr0 , tÞ=c
M for three different combinations of KH and k yielding a common product 105 m s1 . Curves for k ¼ 102 s1 , k ¼ 103 s1 and
9 2 1 m s k ¼ 104 s1 converge towards cSS M =cM ¼ 0:09. Other parameters: DM ¼ 10 and r0 ¼ 1 mm

164 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

‘exhausted’ diffusive flux Jm (due to the depleted surroundings of the surface). Then, cM ðr0 , tÞ begins to decrease towards cSS M . Such a type of overshoot, a typical transient phenomenon, was already seen for adsorption–internalisation in planar geometry [40] and for the electrodic conversion affected by a slow preceding chemical reaction [41]. Figure 8 shows the fluxes’ evolution in terms of c0M for a given set of parameters. When c0M is low (corresponding with short times), the diffusive dSS flux Jm is much larger than Ju . For reference, Jm (diffusive steady-state flux 0 for the same cM ) has been included in the plot. The intercept corresponding dSS SS with Jm ¼ Ju ¼ Jm yields Jm , as seen in the plots of fluxes versus c0M discussed above in the steady-state case. Although time is not explicitly represented in Figure 8, we can follow the transient evolution towards steady-state on this plot. At t ¼ 0, c0M and Ju are zero and the uptake flux starts from the origin of coordinates; then, with increasing (but still short) t, Ju increases. At short t, Jm is extremely large (in comparison with Ju ), but decreasing until both fluxes (Ju and Jm ) eventually meet at a t which is easily identified as tmax (the time when c0M reaches its maximum value). Indeed, if Ju ¼ Jm , the boundary condition equation (27) prescribes dcM ðr0 , tÞ=dt ¼ 0, which is the condition for the maximum. Thus, while t < tmax , Jm > Ju , with their difference indicating the rate of accumulation 3.00

2.50

J/10−6 mol m−2 s−1

JmdSS 2.00 Jm 1.50

1.00 Ju 0.50

0.00

0

0.1

0.2

0.3

0.4 cM(r0

0.5

0.6

0.7

0.8

0.9

1

,t )/mol s−1

Figure 8. Plots of the fluxes versus cM ðr0 , tÞ. n (Jm ), s (Ju ) and u (JmdSS ). Parameters: c
M ¼ 1 mol m3 , KH ¼ 2  105 m, k ¼ 0:05 s1 , DM ¼ 109 m2 s1 and r0 ¼ 0:1 mm. 3 For t ! 1, the three fluxes converge at the coordinates cSS M  0:909 mol m , SS Jm  9:09  107 mol m2 s1

J. GALCERAN AND H. P. VAN LEEUWEN

165

2.00 1.80

J /10−9 mol m−2 s−1

1.60 Jm

1.40

Ju

1.20 1.00 0.80

JmSS

Ju

Jm

0.60 0.40 0.20 0.00 0

2000

4000

6000

8000 10 000 12 000 14 000 16 000 18 000 20 000 t/s

Figure 9. Plot of the fluxes showing that proximity to steady-state can require huge times. Parameters: KH ¼ 2  105 m, k ¼ 5  105 s1 , DM ¼ 1011 m2 s1 , c
M ¼ 1 mol m3 and r0 ¼ 1 cm

on the organism surface as adsorbate. In the plot, Jm first moves to the right and downwards, but, after cM ðr0 Þ has reached its maximum, moves left towards SS . In the overshoot region (t > 25 s), Jm < Ju (not seen the steady-state value Jm in Figure 8, but obvious in Figure 9 for t > 10 000 s), as the amount of species adsorbed on the surface is decreasing. dSS Further computations show that at very short times, Jm  Jm . For the dSS parameters in Figure 8, Jm > Jm at any time, but this relationship can be inverted at intermediate times for other parameters (such as those of curve KH ¼ 2  105 m in Figure 10). 2.3.6

How Long Does it Take to Reach Steady-State?

Mathematically, steady-state is never reached within a finite time. For practical purposes, however, one can compute the time necessary to reach steady-state by imposing the condition that a given transient magnitude (concentration or flux) differs from the steady-state value in a reasonably low relative proportion [42]. For calculating the proximity to steady-state, the diffusive flux Jm is more convenient than the internalisation flux Ju , because of the continuously decreasing behaviour with time of the former. The approach to steady-state can be extremely slow (see Figure 9), and would lead to considerable error in the determination of the characteristic parameters of the system if an inappropriate transient value is taken as the final

166 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 4

Jm KH = 2⫻10−4 m

J /10−9 mol m−2 s−1

3

2

KH = 2⫻10−5 m KH = 2⫻10−6 m

1 Ju 0 0

10

20

30

40

50 t/s

60

70

80

90

100

Figure 10. Evolution of fluxes with t. Upper curves: diffusive fluxes Jm for three different combinations of KH and k, yielding a common product 109 m s1 . Lines with k ¼ 5  104 s1 , k ¼ 5  105 s1 and k ¼ 5  106 s1 converge towards SS Jm ¼ 109 mol m2 s1 . Lower curve with markers s: internalisation flux Ju for KH ¼ 2  105 m and k ¼ 5  105 s1 . Other parameters: DM ¼ 109 m2 s1 , c
M ¼ 1 mol m3 and r0 ¼ 10 mm

steady-state value. For instance, in Figure 9 the transient flux at t ¼ 104 s is still twice the true steady-state value; this would lead to a 100 % error in the determination of the product kKH via application of equation (31) (see Section 2.3.2 above). The same relative error appears in the case with the smallest k in SS . Figure 10 if the transient flux at t ¼ 80 is taken as Jm If, at large time intervals, flux data do not change within the experimental error, the steady-state hypothesis is the simplest option. A possible check on that hypothesis would be to analyse the data in comparison with the transient behaviour as derived from the general expressions given above for given values of k and KH . The availability of analytical expressions for the transient diffusive flux Jm allows computation of the time necessary for a given proximity to the steadySS state. Results for the particular case of Jm being 10 % greater than Jm are given as a contour plot in Figure 11. The plot can be used for any set of parameters following the model, because it can be demonstrated that three suitable dimensionless variables suffice to describe the model [33]. We have selected the following dimensionless parameters: DM t=r20 (which could be called a dimensionless time), KH =r0 (a dimensionless adsorption parameter) and kr20 =DM (a dimensionless kinetic parameter). The logarithm of the dimensionless adsorption and kinetic parameters have been used as coordinates in Figure 11. Each

J. GALCERAN AND H. P. VAN LEEUWEN

167

4 3 2

log (kr02/DM)

1 −3

−2

0

−1 0

−1

1

−2

2

−3

3

−4

4

−5 −6 −4

5 6 −3

−2

−1

0

1 log (KH/r0)

2

3

4

5

6


 Figure 11. Contour plot of the dimensionless time DM t=r20 needed for Jm to reach SS 1.1Jm in terms of the logarithm of the dimensionless adsorption parameter
ðKH =r0 Þ,  in abscissas, and the logarithm of the dimensionless internalisation
parameter kr20 =DM , in  ordinates. The number on each curve indicates the value of log DM t=r20 . The diagonal (dashed line) corresponds with kKH r0 ¼ DM

curve connects systems sharing the same dimensionless time to reach the SS condition Jm ¼ 1:1Jm . Let us illustrate how Figure 11 could be used with the particular DM and r0 data of curve KH ¼ 2  105 m in Figure 10: as the logarithms of the dimensionless parameters for that curve are 0.30 (adsorption) and 5:30 (kinetics), we can roughly read log (DM t=r20 ) ¼ 2:5 in Figure 11 (the point is in between the iso-curves labelled ‘2’ and ‘3’), which implies that approximately 30 s are needed to reach the prescribed proximity to steady-state. If the individual values of k 9 1 and KH were not known, but just their product (say  10 m s ), we would not kr2

have a single point in the diagram but the line log Kr0H þ log DM0 ¼ 5, which crosses contour lines with increasing values of the dimensionless times as the individual value of KH is increased. Inspection of Figure 11 suggests that, in general, increasing KH delays the achievement of the steady-state. This can be physically understood as larger KH implying larger amounts of matter that must be slowly transported (by diffusion) towards the organism surface. The pattern of the iso-curves suggests two large regions roughly separated by the main diagonal (defined by kKH ¼ 1 and plotted as a dashed line in Figure 11): the lower left region (weak adsorption and kinetics) and upper right region (strong adsorption and kinetics), thus indicating the critical role played by the product kKH .

168 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

2.3.7 Discriminating the Individual Parameters of the Product kKH Through the Cumulative Plot SS The knowledge of the steady-state value Jm , allows one to isolate the value of the product kKH from equation (31) – if DM and r0 are known – but not the individual values of k and KH . However, these individual values do affect the transient evolution of the flux. Indeed, it is seen in Figure 10 that by keeping a fixed product for kKH ¼ 109 m s1 , the transient fluxes dramatically increase with the individual value of KH increasing from KH ¼ 2  106 m to KH ¼ 2  104 m. As the two first terms in the expansion of cM ðr0 , tÞ at short t (see ref. [35]) do not depend on k and rapidly decrease when KH increases, a larger KH produces a lower cM ðr0 , tÞ, which in turn produces a larger Jm . Using a different set of parameters, Figure 7 shows very different evolutions for cM ðr0 , tÞ, despite a common product kKH ¼ 105 m s1 : the larger the k, the faster the concentration moves closer to the steady-state value. In conclusion, the individual values of k and KH could be found by fitting the transient behaviour of fluxes (or surface concentrations). Figure 12 (which is similar to reported experimental transient curves [13,36,38,43,44]) shows the cumulative uptakes corresponding with fluxes depicted in Figure 10 with KH ¼ 2  105 m. It can be seen that for quite long times, the adsorbed amount is much larger than the internalised amount. After the building

Fm 2.00

GM

Uptake/10−5 mol m−2

1.50

1.00

0.50 Fu

0.00 0

50

100

150

200 t/s

250

300

350

400

Figure 12. Time evolution of the internalised cumulated uptake Fu (see equation (10) ), total cumulated uptake Fm (see equation (12) ) and surface concentration (G(t) ¼ KH cM ðr0 , tÞ). Same parameters as in Figure 10

J. GALCERAN AND H. P. VAN LEEUWEN

169

up of GM over some 30 s, the system practically reaches a steady-state regime, reflected by the linear nature of the evolution of Fm and Fu for longer times. This linearity suggests one procedure to find the individual values of the parameters in the product kKH , if experimental access to very short times is not feasible, and it is not possible to distinguish between adsorbed and internalised amounts. Figure 13 shows a detail of Figure 12, together with the line corresponding with: SS Fm  KH cSS M þ Jm t

(36)

which asymptotically tends to Fm (t) for not too small t. This straight line (dashdotted in Figure 13) can be interpreted as the result of an instantaneous building of the surface concentration up to the steady-state value, followed immediately by the steady-state regime flux. In the case of Figure 13, this approximation is quite reasonable, due to the fast fulfilment of the adsorption process discussed above. Thus, measured steady-state Fm values could be fitted to a straight line, SS the slope of which would yield Jm and the intercept of which would yield SS SS KH cM ¼ Jm =k, from which k (and KH ) can be isolated. This method based on equation (36) can be labelled ‘the instantaneous steady-state approximation’ (ISSA). As expected, if the system is still far from steady-state, the method will yield erroneous values for KH . With another set of parameters, the plot of the 2.01

Uptake/10−8 mol m−2

KHcMSS + JmSS t

2.00 Fm

GM

SS KHcM

1.99

1.98 0

5

10

15

20

25 t/s

30

35

40

45

50

Figure 13. Detail of Figure 12, showing the asymptotic behaviour of the line SS KH cSS M þ Jm t (dash-dotted line) with respect to the total cumulated uptake Fm (see equation (12) ). The dashed line corresponds with the steady-state surface concentration KH cSS M . The evolution of the surface concentration G(t) ¼ KH cM ðr0 , tÞ is also shown

170 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 3.00 Fm

Uptake/10−5 mol m−2

2.50

2.00

1.50 SS KHcM

1.00

0.50

0.00 0

1000

2000

3000

4000

5000 t/s

6000

7000

8000

9000 10 000

Figure 14. Plot of the cumulative flux Fm with the same parameters as Figure 9, showing that a linear fit of relatively long time values of Fm can lead to erroneous determinations of KH . The dashed line corresponds with the steady-state surface concentration KH cSS M

cumulated fluxes (see Figure 14) clearly shows that the intercept is not a measure of GM . From the slope and the intercept of the straight-line fitting of the rightmost part of Fm in Figure 14, a value of KH ¼ 4:3  103 m would be recovered, which is about 200–fold greater than the true value. The error could be easily discovered if the (theoretical) transient with this fitted parameters was plotted: steady-state would not even be reached at 20 000 s. Even simpler would be just to use Figure 11 (the coordinates can be ascribed to the flat region with dimensionless time 100=p), from which one would estimate that at least 109 =p s are needed to begin to consider steady-state as being approached. In fact with the true parameters, 109 =p s is also the estimate for achievement of near steadystate conditions. The plot of the ‘initial’ (t < 20 000 s) fluxes for such a true system (see Figure 9) again highlights that an observed constancy of the flux can hide a extremely sluggish tendency towards steady-state. 2.4 2.4.1

THE DIFFUSIONAL STEADY-STATE (dSS) APPROACH The Essence of the dSS Approach

We have seen that purely diffusion-controlled biouptake fluxes may require time spans of O(103 ) s to decay to their eventual steady-state values (see Section 2.3.6). In reality the situation of pure diffusion as the mode of mass transfer in

J. GALCERAN AND H. P. VAN LEEUWEN

171

the medium, is not generally maintained over such long timescales (see Chapter 3 in this volume). Even in unstirred systems, natural convection overrules mere diffusion after times of O(10103 ) s. In biouptake systems with flowing liquids (e.g. fish gills) or with mobile organisms, the effects of convection are obviously larger. Typically, in situations of mild movement of the medium with respect to the active uptake area, the transition from pure diffusion with a time-dependent diffusion layer thickness dM ( ¼ (pDt)1=2 for the planar case) to convective diffusion with a fixed dM of O(10102 ) mm (see Chapter 3 in this volume for details) is at times of O(101 to 100 ) s. Thus, it seems very appropriate to extend the dynamic flux analysis, as given before for semi-infinite diffusion, with two main simplifying hypotheses: (1) there is a diffusion layer thickness dM with a time-independent value, defined by the hydrodynamic conditions of the experiment, indicating the distance from the surface where bulk conditions are restored: cM (r0 þ dM , t) ¼ c
M ; and (2) the steady-state concentration profile between the biological surface and r ¼ r0 þ dM is rapidly adjusted to changes of the surface concentration c0M (t)  cM (r0 , t), i.e. the characteristic time for setting up or modifying the steady-state concentration profile is much smaller than the timescale of changes in the surface concentration. We refer to the set of both simplifications as the ‘diffusional steady-state’ approximation (dSS). Apparently, the most important consequence of the dSS approach is the simplification of the expressions for the flux Jm , as compared with the semiinfinite diffusion case. Indeed, for a given c0M , the steady-state flux in spherical geometry is [45]: dSS Jm (t) ¼ DM



  1 1

c
 c0M (t) cM  c0M (t) ¼ DM M þ r0 dM d

(37)

where an ‘effective diffusion layer shell thickness’, d, has been introduced: 1 1 1  þ d r 0 dM

(38)

which includes the planar case: r0 ! 1, d ! dM . This effective diffusion layer shell thickness can be seen as just the inverse of the mass transfer coefficient (usually denoted km or b [45]). In many instances, d can be considered as an unknown free parameter to be fitted from the data. For very small microorganisms, with radii typically below 10 mm, dM  r0 and then d  r0 ; as the time for steady-state spherical diffusion to settle can be estimated with tSS  d2M =pDM (see Chapter 3), hypothesis (2) above is so reasonable that the dSS approach suffices without the need to consider semi-infinite diffusion. The key consequence of the dSS approach is that the diffusion problem is greatly simplified. Although c0M still varies with time, the complete profile

172 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

cM (r, t) is defined if c0M is known. Thus the flux-balance equation (4) can be written as: dG1 (t) dG2 (t) c
 cM (r0 , t) þ ¼ DM M  k1 G1 (t)  k2 G2 (t) dt dt d

(39)

The relationship between G1 , G2 and c0M has to be specified via the adsorption isotherm. Let us first proceed with the simplest case of the linear Henry regime. 2.4.2

Linear Adsorption

In the range of linear adsorption behaviour, whatever the number of site types (see Section 2.3.1 for the merging of parameters of two sites), the surface concentration G is related to c0M via an effective linear coefficient, KH , while the first-order internalisation processes can also be described by an effective first-order constant, k. Thus, equation (39) can be recast, for instance, in terms of G as: dG(t) c
 G(t)=KH  kG(t) ¼ DM M d dt

(40)

This equation can be integrated straightforwardly [46]. If we take again the case of G(t ¼ 0) ¼ 0, the result is: G(t) ¼

     DM t tdSS c
M 1  exp d tdSS

(41)

where the characteristic time constant for this case of first-order biouptake kinetics coupled with steady-state diffusion (tdSS ) is defined by:  tdSS ¼

DM þk dKH

1 (42)

The concentration of M just outside the adsorbed layer, c0M (t), follows from G(t), via G(t) ¼ KH c0M (t) and then the flux Jm can be computed with equation (37). For example, the flux of M towards the interface is:   DM c
M DM tdSS  t=tdSS 1e 1 Jm (t) ¼ d dKH

(43)

Intuitively [46], the dSS approximation is more likely to hold for times greater than the time to practically reach SS (tSS  d2M =pDM ). Thus, the approximation agrees with the rigorous solution (transient diffusion with the bulk value restored at r ¼ r0 þ dM ) for most of the range seen in Figure 15, but not for

J. GALCERAN AND H. P. VAN LEEUWEN 10

173

(a)

Jm /10−4 mol m−2 s−1

8

6

4

2

0 0.0

0.2

0.4

0.6

0.8

1.0

t/s (b)

35

Ju /10−8 mol m−2 s−1

30 25 20 15 10 5 0 0

2

4

6

t/s

Figure 15. Comparison of curves Jm (a) and Ju (b) versus t predicted by different submodels for a system with linear adsorption. Continuous line: rigorous solution of transientwithboundaryconditioncM (r0 þ dM , t) ¼ c
M 8t;dashedline:rigorous(transient) solution with semi-infinite diffusion (solving integral equation (7) ); s: dSS approximation (given by equation (43) ). Parameters: c
M ¼ 1 mol m3 , DM ¼ 8  1010 m2 s1 , KH ¼ 7:24  104 m, k ¼ 5  104 s1 , r0 ¼ 1:8  106 m, r0 þ dM ¼ 105 m

that of Figure 16. As expected, the dSS approach for Jm (given by equation (43)) is less reliable for short t. Otherwise, the agreement is so good that dSS might be the simplest alternative for semi-infinite diffusion for microorganisms. Note that Ju starts at zero for t ¼ 0, and that it increases proportionally with G which increases with [1  expðt=tdSS Þ according to equation (41) (see Figure 15b). The dSS approximation is even better for Ju than for Jm . For the

174 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

Jm /10−8 mol m−2 s−1

1.5

1.0

0.5

0.0 0

2000

4000

6000

8000

10 000

t/s

Figure 16. Jm versus t predicted by the same submodels as in Figure 15, but with parameters: c
M ¼ 1 mol m3 , DM ¼ 1011 m2 s1 , KH ¼ 2  105 m, k ¼ 5  105 s1 , r0 ¼ 102 m, r0 þ dM ¼ 1:1  102 m

case where sites 1 are followed by internalisation whilst sites 2 adsorption are not, typical parameter values are [38]: DM ¼ O(109 ) m2 s1 , dM ¼ O(104 ) m, which, together with r0 ¼ 1:8  106 m, renders d  r0 ; the combined KH (see equation (28)) is O(104 ) m and the combined k is O(102 ) s1 . For this set of data we compute tdSS to be O(0.1) s, which in this particular case is mostly governed by the settling of the adsorptive steady-state (first term between square brackets in equation (42)). The steady-state flux (common for the dSS approximation and for the rigorous solution with bulk concentrations restored at r ¼ r0 þ dM ) can be written: SS Jm


 DM c
M  c0M c
M ¼ ¼ kKH c0M ¼ ð1=kKH þ d=DM Þ d

(44)

and, in the example, yields 109 mol m2 s1 for a bulk concentration of 3 108 mol dm . The numerical example given above also shows that, for certain sets of parameter values, the assumption of linear adsorption may be violated. Since the sites for adsorption plus internalisation have a higher affinity, they are preferentially filled; because they are much lower in number, the nonlinear
regime can be surpassed. For the above example, cSS M  cM , which combined with KH,2 (for the noninternalisation sites) of O(105 ) m, yields 2 O(1010 ) mol m of occupied sites. If the maximum number of such sites is

J. GALCERAN AND H. P. VAN LEEUWEN

175

2

O(109 ) mol m , one can still accept the linear regime hypothesis (10% occupancy), but an increase of the bulk concentration can overrule this assumption. For such situations, a more detailed analysis with Langmuirian adsorption is required. 2.4.3

Langmuirian Adsorption

If, on the timescale of observation, the degree of coverage of any site type becomes appreciable, the precise nature of the relationship between G1 , G2 and coM has to be taken into account. For the case of a Langmuirian isotherm (implying sufficiently fast kinetics of adsorption/desorption) this means that equations in (2) are applicable. Two particular cases are described here: 2.4.3.1 One Site Adsorbing and Internalising The balance of fluxes (39) can be written in terms of the surface concentration G as: dG(t) DM c
M KM DM G(t)   kG(t) ¼ d dt dðGmax  G(t) Þ

(45)

This equation can be easily integrated and reorganised in terms of coverages as:

e

ktðySS yII Þ




1ySS 1  y=ySS ¼
1yII 1  y=yII

(46)

where ySS and yII stand for the solutions of the steady-state equation associated with equation (45), yII being the secondary solution (in itself physically meaningless) corresponding with a negative concentration. In a plot of the fluxes versus c0M , those solutions would correspond with the two intersections of the dSS (see Figure 4). hyperbola for Ju and the straight line for Jm Figure 17 compares the internalisation fluxes Ju predicted by the linear and Langmuir isotherms using the dSS approximation. As expected, at short t, they converge as the Langmuir isotherm tends to the Henry isotherm for low surface concentrations c0M . Due to the saturation effect limiting the G value for the Langmuir isotherm, the linear isotherm can yield a larger steady-state value for Ju . Figure 17 also allows comparison of the Langmuir isotherm for two different diffusion regimes: dSS (continuous line) and semi-infinite (dotted line). At short t, dSS underestimates the fluxes because it ignores the initial transient. At intermediate times, the relationships reverse: dSS yields larger fluxes because of the slow supply of matter in the semi-infinite case. With the parameters of the Figure, for both Langmuirian curves there is a practically common steady-state Ju value (reached at relatively short t), because dM  r0 .

176 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

Ju /10−12 mol m−2 s−1

1.5

1.0

0.5

0.0 0

0.02

0.04

0.06

0.08

0.1

t/s

Figure 17. Comparison of Ju versus t plots predicted by different submodels for a system with one type of site (adsorbing and internalising): linear isotherm with dSS approximation (s) applying equation (43) with KH ¼ 5:2  106 m; Langmuirian isotherm with dSS approximation (continuous line) applying equation (46); Langmuirian isotherm with semi-infinite diffusion (dotted line) by numerically solving integral equation (7) ). Other parameters: c
M ¼ 5  104 mol m3 , DM ¼ 8  1010 m2 s1 , KH ¼ 2  105 m, k ¼ 5  104 s1 , r0 ¼ 1:8  106 m, r0 þ dM ¼ 105 m, KM ¼ 2:88 103 mol m3 , Gmax ¼ 1:5  108 mol m2

2.4.3.2 Two Sites: Site 1 = Adsorption + Internalisation, Site 2 = Adsorption Only. The balances of fluxes can be written:   Gmax,2 c0M Gmax,1 c0M d Gmax,1 c0M c
M  c0M þ  k ¼ D M 1 d dt KM,1 þ c0M KM,2 þ c0M KM,1 þ c0M

(47)

which can be integrated to [46]:

 SS
1yII1 II SS 1y1 k1 t ySS  ln 1  y1 =yII þ 1  y1 ¼ ln 1  y1 =y1 1 " 1ySS KM,2 Gmax,2
SS SS 2
1 y2 =y1 ln 1y2 =ySS 2 KM,1 Gmax,1

1yII1 II 2  yII ln 1y2 =yII þ 2 =y1 2 #

 II 2 KM,1 KM,1  KM,2 ySS 1  y1 y2

 

  KM,2 KM,2 þ KM,1  KM,2 yII KM,2 þ KM,1  KM,2 ySS 1 1 (48)

J. GALCERAN AND H. P. VAN LEEUWEN

177

II where ySS 1 and y1 stand for the solutions of the steady-state equation associated with equation (45). As expected, and already commented in section 2.1.3.2, II those steady-state solutions (ySS 1 and y1 ) do not involve any parameter associated with site 2. Coverages in equation (48) referred to site 2 (e.g. ySS 2 ) can be obtained from site 1 through the relationship:

y2 ¼

K y
M, 1 1  KM,2 þ KM,1  KM,2 y1

(49)

Equation (48) reverts to (46) if Gmax,2 ¼ 0. A similar reduction can be obtained when KM,1 ¼ KM,2 , showing that then the time to reach a certain y1 multiplies by 1 þ Gmax,2 =Gmax,1 (with respect to the case when Gmax,2 ¼ 0) [46]. The impact of changing KM,2 on Ju (using equation (48)) is seen in Figure 18. Because KM,1  c
M , no saturation effect of the internalising site 1 can be expected. When KM,2 is larger or similar to KM,1 (curves (a) and (b)) the approach of Ju to steady-state follows the usual ‘parabolic’ behaviour. For low KM,2 (curve (c)) the supplied M is mostly adsorbed on to site 2 (because Gmax,2  Gmax,1 ), with adsorption still following practically linear isotherms for both sites with the 12 (a) (b)

Ju /10−12 mol m−2 s−1

10

8 (c) 6 (d) 4

2

0 0

20

40 t/s

60

80

Figure 18. Impact of bioaffinity of the non-internalising sites (KM,2 ) on Ju versus t plots, with dSS approximation for two Langmuirian adsorption isotherms (i.e. applying equation (48) ). Other parameters: d ¼ 1:48  106 m, c
M ¼ 5  104 mol m3 , DM ¼ 8  1010 m2 s1 , Gmax,1 ¼ 1:5  107 mol m2 , Gmax,2 ¼ 8:85  106 mol m2 , KM,1 ¼ 2:88  103 mol m3 , k ¼ 5  104 s1 . Curves: (a) KM,2 ¼ 0:05 mol m3 , (b) KM,2 ¼ 0:005 mol m3 , (c) KM,2 ¼ 2:5  104 mol m3 , (d) KM,2 ¼ 5  105 mol m3

178 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

effect of just reducing the slope of Ju versus t. For much lower KM,2 (curve (d)), saturation of site 2 introduces a qualitative change in the shape of Ju versus t. 3 BIOUPTAKE WHEN MASS TRANSFER IS COUPLED WITH CHEMICAL REACTION (COMPLEX MEDIA) 3.1

MATHEMATICAL FORMULATION

Due to the usual diversity of components in the medium, there will be a need to consider that the species taken up interacts with other species while diffusing towards the organism surface (see Figure 19). In some cases (as in the aquatic prokaryotes that exudate Fe chelators called siderophores to improve the availability of Fe; see Chapter 9 in this volume), the medium is modified on purpose by the organisms [11,47–49]. A simple model for this interaction assumes the complexation of M with a ligand, with elementary interconversion kinetics between the free and complexed forms: ka M þ L Ð ML kd

(50)

where ka and kd denote the association rate constant and the dissociation rate constant, respectively. In spherical geometry, the continuity equations for the species are: ! qcM (r, t) q2 cM (r, t) 2 qcM (r, t) þ þ kd cML (r, t)  ka cM (r, t)cL (r, t) (51) ¼ DM qt qr2 r qr ! qcL (r, t) q2 cL (r, t) 2 qcL (r, t) þ þ kd cML (r, t)  ka cM (r, t)cL (r, t) (52) ¼ DL qt qr2 r qr Organism

ML

r0

Minter

DML

ML

ka kd

Mads

M + L

K DM

M + L

Figure 19. Schematic representation of the coupled diffusion of M (species taken up) and ML (bioinactive complex), with their interconversion kinetics involving the bioinactive ligand L

J. GALCERAN AND H. P. VAN LEEUWEN

179

and ! qcML (r,t) q2 cML (r,t) 2 qcML (r,t) ¼ DML þ kd cML (r,t)þka cM (r,t)cL (r,t) (53) qt qr2 r qr Under conditions of complexation equilibrium, such as those assumed in the bulk of medium, we have: K¼

ka c
¼
ML
kd cM cL

(54)

where K is the stability constant. For bioinactive complexes ML, the boundary condition at the biosurface is:   qcML ¼0 qr r¼r0

(55)

This hypothesis excludes lipophilic complexes [19,50] and complexes subject to accidental uptake via membrane permeases [51,52], for which the analysis would be basically different [5,18]. In this sense, we also disregard here any adsorption of M in the form of its complex ML. Since many environmentally relevant complexes diffuse much slower than M (see Chapter 3), the distinction between DM and DML is important. Their ratio is usually labelled: e

DML DM

(56)

It is apparent that the kinetics of the homogeneous reaction can have a dramatic impact on the overall uptake process by controlling the ratio of complexed to free M, which affects the velocity of transport towards the organism surface. Therefore, kinetics do matter and all the dynamic effects must be properly taken into account. The nonlinearity of the system of partial differential equations (51) and (52) poses a serious obstacle to finding an analytical solution. A reported analytical solution for the nonlinear problem of diffusion coupled with complexation kinetics was erroneous [12]. Thus, techniques such as the finite element method [53–55] or appropriate change of variables (applicable in some cases of planar diffusion) [56] should be used to find the numerical solution. One particular case of the nonlinear problem where an analytical solution can be given is the steady-state for fully labile complexes (see Section 3.3). However, there is a reasonable assumption for many relevant cases (e.g. for trace elements such as

180 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

Fe in marine water), known as the excess of ligand case, which allows linearisation of the problem via: cL (r, t)  c
L

(57)

The use of the excess ligand condition, equation (57), spares the need to consider the continuity equation (52) for the ligand. Then, two limiting cases of kinetic behaviour are particularly simple: the inert case and the fully labile case. As we will see, these cases can be treated with the expressions (for transient and steady-state biouptake) developed in Section 2, and they provide clear boundaries for the general kinetic case, which will be considered in Section 3.4. 3.2

TOTALLY INERT COMPLEXES

If the rate constants for interconversion between M and ML are infinitesimally small (on the effective timescale of the experimental conditions), the complex does not contribute significantly to the supply of metal to the biosurface. The equilibrium equation (50) behaves as if frozen. In a biouptake process, the complex ML then does not contribute to the supply of metal towards the biosurface, and all the expressions given in Section 2 apply, with the only noteworthy point that the value of c
M to be used differs from the total metal concentration. In this case, the complexed metal is not bioavailable on the timescale considered, as metal in the complex species is absent from any process affecting the uptake. 3.3

FULLY LABILE COMPLEXES

We now turn to the dynamic limit where the rates of association/dissociation of ML are infinitely fast. The complex system will maintain a transport situation governed by the coupled diffusion of M and ML. In the case of excess of ligand conditions, equation (57), the full lability condition implies the maintenance of equilibrium on any relevant spatial scale: cML (r, t) ¼ KcM (r, t)c
L

8r, t

(58)

Then, equations (51) and (53) can be summed to cancel out the kinetic terms and provide a simple diffusion equation for the total metal: cT, M (r, t)  cM (r, t) þ cML (r, t)

(59)

which reads: qcT, M (r, t) q2 cT, M (r, t) 2 qcT, M (r, t) ¼D þ r qt qr2 qr

! (60)

J. GALCERAN AND H. P. VAN LEEUWEN

181

where D, the average diffusion coefficient, given by: D

DM c
M þ DML c
ML DM þ Kc
L DML 1 þ eKc
L ¼ ¼ D M c
M þ c
ML 1 þ Kc
L 1 þ Kc
L

(61)

can be seen as resulting from the frequent flip-flops of the species M from its free state M to its complex state ML, and vice versa [41]. Boundary condition (55) is overruled by lability condition (58), and the usual boundary condition at the biological surface will derive from the coupling of transport with
internal isation (concentration and flux at the interphase). Using cM ¼ c
T, M = 1 þ Kc
L , the supply flux becomes: Jm (t) ¼ D

   
 qcM (r, t) qcT,M (r, t) ¼ DM þ DML Kc
L qr qr r¼r0 r¼r0

(62)

instead of equation (8), for the noncomplex case. Once the transport step is defined, it is necessary to take into account which is the adsorption isotherm preceding the internalisation (the latter is always assumed to be first order). By extending results from Section 2, analytical solutions can be written for steady-state for both linear and Langmuir isotherms, as well as for the transient case with the linear isotherm. Langmuirian isotherms require numerical approaches for the transient case. As a first example, the transient case with Henry isotherm can be considered. Expressions developed in Section 2.3 apply with D replacing DM , cT, M replacSS ing cM (including the substitution of c
T, M by c
M and cSS T, M by cM ) and KH (defined
as G=cMðr0 , tÞ in both cases, i.e. with or without the presence of L) by KH = 1 þ Kc
L . Other cases with analytical solutions arise from the steadystate situation. The supply flux under semi-infinite steady-state diffusion is [57]: SS Jm

   Dc
M
cSS
M ¼ 1 þ KcL 1 
r0 cM

(63)

If instead of semi-infinite diffusion, some distance dM acts as an effective diffusion layer thickness (Nernst layer approximation), then a modified expression of equation (63) applies where r0 is substituted by 1=ð1=r0 þ 1=dM Þ (see equation (38) above). For some hydrodynamic regimes, which for simplicity, are not dealt with here, the diffusion coefficient might need to be powered to some exponent [57,58]. Combining the flux given by equation (63) with a Michaelis–Menten-like expression for Ju , one recovers the modified Best equation (17), where the bioconversion capacity parameter b is now related to the total concentration of free and labile species of M:

182 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

b¼

Ju
J
r0 ¼ u

Jm DcT, M

(64)

The bioaffinity parameter a basically reflects the free metal ion concentration, whereas the limiting flux ratio b reflects the total labile metal species concentration. Due to the complexation, the ratio a/b thus changes by a factor q
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
 

1 þ eKcL in spherical geometry, while the factor 1 þ eKc
L 1 þ Kc
L is required for planar geometry [26]. As mentioned in Section 3.1, an analytical solution can be provided for the steady-state of fully labile complexes, without needing to resort to the excess of ligand approximation: SS ¼ DM Jm

c
M  cSS c
 cSS M ML þ DML ML r0 r0

(65)

which, as expected, reverts to equation (63) under an excess of ligand. For any relationship between DL and DML , assuming no complex adsorption, the steady-state complex concentration at the microorganism surface needed in equation (65) is based on the equality (except for sign) of the fluxes of L and ML, leading to: cSS ML


 K DL c
L þ DML c
ML cSS M ¼ DL þ DML KcSS M

(66)

In the particular case dealt with now (fully labile complexation), due to the linearity of a combined diffusion equation for DM cM þ DML cML , the flux in equation (65) can still be seen as the sum of the independent diffusional fluxes of metal and complex, each contribution depending on the difference between the surface and bulk concentration value of each species. But equation (66) warns against using just a rescaling factor for the total metal or for the free metal alone. In general, if the diffusion is coupled with some nonlinear process, the resulting flux is not proportional to bulk-to-surface differences, and this complicates the use of mass transfer coefficients (see ref. [11] or Chapter 3 in this volume). 3.4

PARTIALLY LABILE COMPLEXES

3.4.1 The Limiting Supply Flux in the Steady-State Uptake Considering Homogeneous Kinetics The linear steady-state equations associated with (51) and (53), under excess ligand conditions, can be solved analytically [59] in terms of the concentration of M at the surface cSS M . The resulting supply flux is:

J. GALCERAN AND H. P. VAN LEEUWEN

SS Jm ¼




DM c
M

 r0

cSS M



183

1 pffiffiffi ka C B A @1 þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
 p ffiffiffi eKc
L 1 þ eKc
L þ ka 0

eKc
L

(67)

where: ka 

ka c
L r20 DM

(68)

can be seen as a dimensionless complex formation rate constant, sometimes denoted as the Damko¨hler number [60,61] (see Chapter 3 in this volume). ka compares the diffusional timescale (r20 =DM ) with the reaction timescale (1=ka c
L ) 1=2 or, alternatively, ka compares r0 with the reaction layer thickness pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
m ¼ DM =ka cL . Equation (67) can be written [26]: SS Jm

¼


, kin Jm

  cSS M 1
cM

(69)

where the (homogeneous) kinetic characteristics of the system are included in
, kin the limiting supply flux Jm , which is a normalised mass transfer coefficient (see Chapter 3): 1 pffiffiffi ka C B A @1 þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
 p ffiffiffi eKc
L 1 þ eKc
L þ ka 0
, kin ¼ Jm

DM c
M r0

eKc
L

(70)

An extension to any number of ligands under any geometry is discussed in ref. [62]. 3.4.2

The Degree of Lability and Lability Criteria

In order to assess the impact of the homogeneous kinetics on the supply flux, the degree of lability can be defined – when only one complex is formed – as: pffiffiffi
, kin
, inert Jm  Jm ka ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x 
, labile
 pffiffiffi
, inert Jm  Jm eKc
L 1 þ eKc
L þ ka

(71)

Then, equation (67) can be rewritten as: SS Jm ¼

   cSS DM c
M
1 M 1 þ eKc
L x
cM r0

(72)

184 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

which clearly shows that an increase in the degree of lability (with other parameters in the expression kept constant) implies an increase in the supply flux. As physically expected, it can be shown [55,59] that the higher the degree of lability, the stronger the depletion of ML at the microorganism surface: x¼

1  cML ðr ¼ r0 Þ=c
ML
1  cSS M =cM

(73)

A condition for the complex having a predominantly labile behaviour could follow from x  1=2, given that x ranges between 0 (for totally inert) and 1 (for fully labile):
 ka  eKc
L 1 þ eKc
L

(74)

This expression could be regarded as a general lability criterion for the steadystate supply of M in spherical geometry. For the particular case that eKc
L  1, one can recover the condition [57]: sffiffiffiffiffiffiffiffiffiffi DM
DML c
ML c  kd ka c
L ML r0

(75)

which can be seen as the comparison between the contribution of the kinetic pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi flux (dissociation of ML within the reaction layer m ¼ DM =ka c
L , also called reacto-diffusive length [11,61]) and the limiting diffusive flux of ML. Similar lability criteria have also been derived for planar geometry and transient regimes [26]. 3.4.3

Combining Supply and Internalisation

Supply and internalisation are coupled through the value of cSS M and the flux of M crossing the interface. For the linear adsorption regime: cSS M ¼

c
M


1 þ kKH r0 = DM 1 þ eKc
L x

(76)

Similarly, for the steady-state situation with one Michaelis–Menten type of uptake site, the Best equation (17) still applies, now with a bioconversion capacity given by: b¼

Ju
J
r
u 0  ¼

Jm DM cM 1 þ eKc
L x

(77)

J. GALCERAN AND H. P. VAN LEEUWEN

185

which also encompasses the totally inert (x ¼ 0, see equation (16)) and fully labile (x ¼ 1, see equation (64)) limits. Let us consider now the influence of the radius of the microorganism. On one hand, it is well known that with decreasing radius, there is an enhancement of the diffusive flux due to the convergent nature of the spherical geometry. This can be seen, for instance, in equation (16) for the case without complexation or in equation (63) for fully labile complexes. For the case of a complexing medium with kinetics, there is also an impact of the radius on the lability: the smaller the radius, the lower the degree of lability [59], because when r0 ! 0, the dimensionless kinetic parameter ka ! 0 (see equation (68)), and the degree of lability x tends to 0 (see equation (71)). Thus, from a physical point of view, a change in r0 has two opposite effects on the supply flux, as can be seen in equation (70). However, by combining the expression for ka (equation (68))
, kin given by equation (70), it can be seen that the convergence enhancewith Jm ment dominates over the lability loss. It has been argued that the search for an improved diffusion efficiency has facilitated the evolution of some small organisms [63–65].
, kin due to changing r0 is bound to affect the This change in the supply flux Jm
, kin uptake flux. A decrease in r0 implies an increase in Jm and a decrease in b (see equation (77)) which results in an increase of the normalised flux J~ (see equation (17)). However, it must be pointed out that the internalisation step can become rate determining, and then the flux will not change any more below some r0 value. As an illustration, we analyse the concrete situation for Pb2þ , which has a ka of 107 mol1 m3 s1 [66]. This ka value is a high one, so labile behaviour is expected over a relatively large range of parameters. From Figure 20 we can see that, for the chosen values of the parameters, the degree of lability x is quite high for radii larger than 10 mm. Thus the normalised uptake flux J~ for r0 > 10 mm is much closer to that obtained assuming fully labile rather than inert behaviour. For intermediate radii around 1 mm, the system experiences a dramatic loss in lability, and the uptake is also affected. In this case, ignoring the kinetic effects (e.g. assuming fully labile behaviour) in the interpretation of the measured flux would lead to the determination of quite incorrect parameters. However, if the bioconversion capacity (due to changes in Ju
and c
L ) is low, the free M by itself is able to sustain the uptake flux. This can be seen in Figure 21, where J~ (computed whilst taking into account ka ) coincides with the fully labile case. When lability is lost (r0 below 10 mm), J~ has already reached the unity value for the inert case (mass transport is no longer a limiting step). Thus, in this latter case, ignoring the kinetics is not relevant. See ref. [57] or [11] for a more detailed discussion and practical cases. For a single microorganism with a given r0 , different metals may have remarkably different behaviour, due to the metal-specific association and dissociation kinetics of the complexes involved. Take, for example, an organism of

186 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 1.0 0.9

~ Jlabile

Normalised flux or x

0.8

x

0.7 0.6

~ J

0.5 0.4 0.3 0.2

~ Jinert

0.1 0.0 −7.0

− 6.5

−6.0

−5.5 log (r0 /m)

−5.0

− 4.5

− 4.0

Figure 20. Normalised flux J~ (equation (17) ) versus log r0 for Pb2þ taking ka ¼ 107 mol1 m3 s1 (solid curve) compared with the labile (x ¼ 1, u) and inert (x ¼ 0, ) limits in equation (77) for parameters: KM ¼ 109 mol m3 , Ju
¼ 5  108 mol m2 s1 , DM ¼ 109 m2 s1 , DML ¼ 1010 m2 s1 , K ¼ 104 mol1 m3 , c
L ¼ 101 mol m3 , c
T, M ¼ 103 mol m3 . Markers  correspond with the degree of lability x of this complexation of Pb2þ at different radii (see equation (71))

2þ

r0 ¼ 105 m which is simultaneously taking up Pb2þ and Ni (the latter metal having relatively slow complex association/dissociation kinetics [14]), and which has a similar affinity a towards both metals. The Pb(II) species are labile and their flux is controlled by their coupled diffusion, whereas the Ni(II) complexes are inert and the flux is determined by diffusion of free Ni(II). However, for similar organisms with decreasing r0 , the Pb-complexes are losing lability, resulting in a strong dimensional dependence of the relative uptake characteristics for the two metals. Again, the main conclusion is that radial transport influences the biouptake in two different ways: it not only generates changes in the magnitude of the diffusional fluxes towards the surface, but it also affects the labilities and hence the bioavailabilities of complex species. 3.5

RELATIONSHIP WITH THE FIAM

The most widely used model in environmental studies is the free ion activity model (FIAM or FIM) which postulates that the uptake is dependent on the bulk activity of free M (i.e. c
M as a practical simplification) [2,67], rather than to the total metal concentration [2,5,66,68,69]. This has led to recognition of the

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187

1.0

Normalised flux or x

0.9 0.8

~ Jlabile

0.7

~ J

0.6 0.5 0.4 0.3 x

~ Jinert

0.2 0.1 0.0 −7.0

−6.0

−5.0

−4.0 log (r0 /m)

−3.0

−2.0

−1.0

Figure 21. Figure analogous to Figure 20, showing a case where there is no kinetic impact on the normalised flux J~ . Same parameters as in Figure 20, except Ju
¼ 5  1010 mol m2 s1 and c
L ¼ 102 mol m3

importance of the speciation of M in the medium on the biological effects (see [2,9,70] and references therein). The FIAM can be physically interpreted as a model in which mass transport is not the limiting step, so that the surface and bulk concentrations are practically identical. Due to this identification between bulk and surface concentrations, the FIAM has been classified as an equilibrium or thermodynamic model [11]. If Michaelis–Menten internalisation kinetics hold (this is not necessary for the FIAM to apply), the equivalence between the FIAM and no diffusion transport can be shown mathematically [22]. Therefore, strictly speaking, the FIAM could only apply when diffusion (coupled with dissociation of complexes) is able to maintain the surface concentration of the free ion equal to its bulk value [13], although, in practice, small differences between the concentrations might be negligible. It is worth noticing that transport limitation (and failure of the FIAM) is more likely to happen when M is alone in the solution (i.e. ‘unsupported flux of M’) than when non-inert complexes are supporting the flux via dissociation. Figures 22 and 23 illustrate that the FIAM can apply due to dissociative support of M, but can fail when this support disappears. For a fixed amount of free metal ion, at large concentrations of ligand c0M ! c
M SS (Figure 22), whilst Jm ! Ju
(Figure 23). Moving towards lower concentra0 tions, cM starts to diverge from c
M indicating the increasing significance of the concentration gradient. If dissociation of complexes does not counterbalance

188 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 1.00

SS/c * cM M

0.80

0.60

0.40

0.20

0.00 0

0.05

0.1 c L*/mol m−3

0.15

0.2

Figure 22. Plot of normalised surface concentration versus c
L to illustrate that the lack of supporting dissociation by complexes can limit the application of the FIAM. Parameters as in Figure 20, but the total metal concentration c
T, M is varied to keep a constant free-metal concentration c
M ¼ 106 mol m3

1.00

0.80

~ J

0.60

0.40

0.20

0.00

0

0.005

0.01

0.015

0.02

c L*/mol m−3 SS Figure 23. Plot of normalised flux Jm =Ju
versus c
L to illustrate one limit of application of the FIAM. Parameters as in Figure 22

J. GALCERAN AND H. P. VAN LEEUWEN

189

SS the development of the gradient of cM , then Jm will decrease against the FIAM
predictions based on cM . See Chapter 10 of this volume for a detailed discussion on the FIAM and BLM (biotic ligand model, [7,71]). The FIAM has been shown to apply to a large number of cases [2,69,72]. This indicates that the mass transfer step can likely be ignored in many cases [60], probably due to a sufficiently small radius (see equation (77)) and/or relatively low bioaffinity. In any case, whatever the microorganism size, the diffusion step needs to be considered for the interpretation of transient data as they become increasingly available [4,11,19,36,38,39,43,44,47,50,73–77]. If the FIAM apSS plies, i.e. transport is not limiting, Jm does not change with time (as long as there is no medium depletion, see Section 4.1.1 below). For instance, in the case of two sites, of which only one internalises M following the Langmuir adsorption, equation (14) boils down to: SS ¼ k1 Gmax,1 Jm

c
M KM þ c
M

(78)

which implies that the internalised amount will just increase linearly with time. Notice that lability effects are irrelevant as long as the FIAM applies, because diffusion is not flux-determining. In this context, it is also clear that any increase in the parameters enhancing the actual biouptake rate increases the possibility of kinetic control of the flux [9]. In any case, exceptions to the FIAM have been pointed out [2,11,38,44,74,76,78]. For example, the uptake has been shown to depend on the c
T, M or c
ML (e.g. in the case of siderophores [11] or hydrophobic complexes [43,50]), rather than on the free c
M . Several authors [11,12,15] showed that a scheme taking into account the kinetics of parallel transfer of M from several solution complexes to the internalisation transporter (‘ligand exchange’) can lead to exceptions to the FIAM, even if there is no diffusion limitation. Adsorption equilibrium has been assumed in all the models discussed so far in this chapter, and the consideration of adsorption kinetics is kept for Section 4. Within the framework of the usual hypotheses in this Section 3, we would expect that the FIAM is less likely to apply for larger radii and smaller diffusion
due to the labile complexation of M with a coefficients (perhaps arising from D large macromolecule or a colloid particle, see Section 3.3). Against simplistic views of the FIAM, it is necessary to stress that the model does not imply that the free metal ion is the only species available to the microorganism [2,14]. Indeed, the internalisation flux (i.e. the rate of acquisition) depends on the free metal ion concentration at the biological interphase (which in the FIAM is practically c
M ), but metal bound to a ligand in the solution can dissociate, can diffuse (under a negligible gradient according to the FIAM), and can eventually be taken up.

190 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES SS In principle, the FIAM does not imply that the measured flux Jm should be linear with the metal ion concentration. The linear relationship holds under submodels assuming a linear (Henry) isotherm and first-order internalisation kinetics [2,5,66], but other nonlinear functional dependencies with c
M for adsorption (e.g. Langmuir isotherm [11,52,79]) and internalisation (e.g. secondorder kinetics) are compatible with the fact that the resulting uptake is a function (not necessarily linear) of the bulk free ion concentration c
M , as long as these functional dependencies do not include parameters corresponding with the speciation of the medium (such as c
L or K [11]).

4 KEY FACTORS AND CHALLENGES FOR FUTURE RESEARCH IN BIOUPTAKE MODELLING The preceding sections have demonstrated the considerable quantitative understanding of biouptake that can be attained by models with a sound theoretical basis. We have shown solutions for a range of conditions, ranging from relatively simple limiting cases to more involved situations involving kinetically limited metal complex dissociation fluxes. In this section, we highlight key points that should be considered in future refinements of biouptake models. 4.1 4.1.1

REFINEMENTS BASED ON MASS TRANSPORT FACTORS Finite Media

In many practical situations, the picture of an isolated microorganism in an infinitely large medium is rather too crude. The combined action of a collection of similar organisms can have a strong impact on the surrounding medium. For instance, the depletion of essential trace elements in the photic zones of lakes and oceans is well known [14]. A simple model for the depletion of the medium can be obtained by combining previous results in this chapter, for the case of excess of ligand and any degree of lability [80]. We assume that each microorganism takes up M from a finite spherical volume of radius rf (at least five times larger than r0 ). In order to obtain an analytical expression, it is convenient to consider two very different timescales [81]: the diffusive steady-state
is reached much faster
than the depletion process, so that c
M (t)  cM rf , t and c
ML (t)  cML rf , t are taken as bulk values for the semi-infinite steady-state diffusion, while they are time dependent for the depletion process. The total amount of M (free or complexed) in the volume of the medium per microorganism at a given time, O(t), can be computed by integrating the steady-state profiles associated with equation (67):
O(t) ¼ f1 cSS M (t) þ f2 cM (t)

(79)

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191

where f1 and f2 are known functions of the medium parameters (i.e. not including KH or k; see reference [80]). If a linear adsorption isotherm (instead of the Langmuirian case considered in Section 3.4.3) holds, then equation (76)
can be used to write cSS M in terms of cM . Equation (67), expression for the flux SS Jm , can also be reformulated as: SS Jm (t) ¼

c
M (t) 1 r
0  þ kKH DM 1 þ eKc
L x

(80)

Assuming that the time to re-adjust to steady-state is negligible in comparison with the depletion timescale, we can write: SS (t)dt dO(t) ¼ 4pr20 Jm

(81)

SS which, due to the linear relationships of O and Jm with c
M , integrates to:

c
M (t) ¼ c
M (0)exp(  t=tdepl )

(82)

thus predicting an exponential decay for the concentrations, with a time decay constant tdepl which is defined by the physicochemical parameters of the model
(i.e. also on the kinetics of the complexation if cSS M 6¼ cM , see Section 3.5). For the particular case of no coupled reactions, the approximate expression (82) has been shown to agree reasonably well with the exact solution of the rigorous case of no flux across r ¼ rf . We also note that the total amount of metal taken up, Fm , can be measured from the difference between the original amount in the medium and that at a given time (associated with c
M (t)). KH could then be found – following the line of the ISSA described in Section 2.3.7 – by approximating: Fm (t)  KH cSS M ðr0 , tÞ þ

ðt 0

SS 0 Jm (t )dt0

(83)

SS
where cSS M and Jm (t) can be written as functions of time through cM (t) (see equations (80) and (82)) with known medium parameters ( f1 and f2 ), and the unknown product kKH (or measured tdepl ). Thus, this allows for discrimination between KH and k values. In principle, any kind of limitation of the medium (e.g. due to some kind of clustering in a zone) tends to diminish the individual uptake rate [31]. From the point of view of modelling, the breaking of the symmetry rapidly complicates the problem (see Chapter 3 in this volume). As an exception to the general rule of decreased uptake due to inter-cell competition, it has been shown [49] that biouptake through siderophore excretion is only viable for nonisolated cells.

192 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

Thus, the community effect can have a positive impact on the biouptake of certain trace nutrients. The high degree of packing of the organisms within a volume can lead to the formation of flocs (suspended aggregates), where millions of cells cluster to form particles with dimensions in the order of millimetres [29]. Models for uptake by such ecosystems also assume sphericity, and start from a continuity equation accounting for the consumption of the species throughout the floc: qcM (r, t) q2 cM (r, t) 2 qcM (r, t) þ ¼ DM qt qr2 r qr

!  kfloc cM (r, t)

(84)

where r is now measured from the centre of the floc, and kfloc represents the first-order kinetic constant for the uptake of M by the organisms that are considered to be smeared out within the floc. Equation (84) (and similar equations) are usually solved for the steady-state case with boundary conditions of no flux of M at r ¼ 0 and cM fixed at the surface of the floc [29]. Of course, many other refinements can also be considered [82–84]. 4.1.2

Nonstagnant Media

In many natural environments, the assumption of a stagnant medium for the organism is too crude [85]. Either the organism will move in the medium or the solution will present some flow or turbulence that disturbs the stagnant regime. In both situations, there is a need to take into account not only diffusion (which is always the final step in the mass transport towards the biological surface [86– 88]), but also convection. The basic concepts of the convective diffusion problem, which is often simplified by introducing an effective diffusion layer thickness, d, are given in Chapter 3 of this volume or refs. [58,81]. Whitfield and Turner [9] estimated such a diffusion layer thickness d for gravitational sinking, convective water movements and swimming of motile phytoplankton cells and concluded that a lower boundary would be of the order of 10 mm. Mass transfer, taking into account a number of the nonstagnant regimes, has been combined with internalisation processes – under steady-state conditions – [10,16,21,30,31,49,89–92] to produce what can be seen as variants of the Best equation (17). The influence of the shape of the organism (or particle) has also been analysed [10,90,91]. 4.1.3

Complex Media

As commented on above, in general, if the complexation process of M is not linear (i.e. an excess of ligand cannot be assumed) only numerical approaches

J. GALCERAN AND H. P. VAN LEEUWEN

193

will be possible for the transient evolution. In some cases, the medium is far more complex and requires consideration of more than just a single ML species [61]. Then, we need to take into account the competition between several ligands for the same M, or various mixtures of different M and different L. The case of iron is paradigmatic: specific chelators exuded by the microorganisms to enhance iron uptake (siderophores) [49], colloidal suspension of iron oxides [93], etc. Obviously, in such cases, development of numerical approaches is then really almost the only way to obtain quantitative information, especially from a transient model.

4.2 4.2.1

REFINEMENTS BASED ON ADSORPTION PROCESSES Adsorption Isotherm and Kinetics

More complex isotherms than the Henry and Langmuir ones used here could be necessary to take into account interaction between adsorbed species, blocking effects, etc. The finite kinetics of the adsorption/desorption steps at the interface have been extensively studied by Hudson and Morel [13,15]. A wealth of literature is available on dealing with such interfacial processes [94–96] and its inclusion in the biouptake model should be implemented when experimental evidence of its necessity arises. 4.2.2

Competition

If other ions affect the internalisation process via competition for the transport sites [3,5,14,15,37,52,69,93,97–99], then a reasonable starting point is to modify the Langmuir isotherms (3) to: JuM, j (t) ¼ kM j Gmax , j

1 KM c (0, t) P M1 1 þ Ka ca (0, t)

j ¼ 1, 2 . . . a ¼ M, . . .

(85)

a

where now the superscript M is added to distinguish the uptake of this species from the others, and a is the general index that runs over the whole set of species ( j is the general index that runs over the types of internalisation sites). For the sake of simplicity, a common Gmax , j for all the species being taken up has been used. Obviously, analytical solutions become cumbersome or impossible, but the numerical approaches remain essentially the same (provided that the simultaneous fitting of a large number of parameters is not attempted). In many instances, the influence of pH has been dealt with as another competition process [3].

194 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

4.3

REFINEMENTS BASED ON INTERNALISATION FACTORS

4.3.1

Internalisation Kinetics

For simplicity, up to now, first-order kinetics have been assumed, but obviously other rate laws may apply. Further complications can be generated by the presence of multiple paths for M on a variety of sites exhibiting different kinetics [5,11] or sequential enzymatic processes [100]. Some complexes, labelled as ‘lipophilics’, have been shown to cross the membrane without the need for specific pre-adsorption sites [5,11,18,19,50]; see also Chapters 5, 6 and 10 in this volume. Fortin and Campbell [76] have recently reported the ‘accidental’ uptake of Agþ induced by thiosulfate ligand. Maintenance requirements can be included in the uptake flux expressions by the addition of a constant term [30]. This term expresses the minimum flux necessary for the organism to survive. 4.3.2

Efflux

Another factor to take into account in biouptake studies is the possibility that the organism develops strategies of eliminating toxic species by means of efflux [38,52,101]. As a first approach, the efflux rate can be set proportional to the amount of species taken up that has been internalised, thus converting the boundary condition of flux balances for two sites, equation (4), into:   dG1 (t) dG2 (t) qcM (r, t) k1 G1 (t)  k2 G2 (t) þ kout Fu (t) þ ¼ DM dt dt qr r¼r0

5

(86)

CONCLUDING REMARKS

Modelling biouptake requires the judicious consideration and selection of the underlying physical phenomena responsible for the experimental observations. We have seen that three fundamental phenomena may play a key role in biouptake: mass transfer, adsorption, and internalisation. The inclusion of additional phenomena or refinements (such as nonexcess ligand complexation, non-first-order kinetics, nonlinear isotherms, etc.) may be essential to describe certain cases, but they have handicaps, such as: . analytical solutions are rarely available; . it is difficult to obtain reliable parameters that can adequately describe such additional phenomena;

J. GALCERAN AND H. P. VAN LEEUWEN

195

. any improvements provided by a more refined theoretical model may be so small that they are indistinguishable from experimental error. Furthermore, there is presently a paucity of experimental data under appropriate conditions to provide both the driving force and the supporting evidence for development of more sophisticated models. On the other hand, if the really relevant phenomena are overlooked, then this could lead to incorrect interpretation of the fitted parameters, and, consequently, invalid predictions, e.g. if they form the basis of a risk assessment. As illustrative examples, consider two cases that highlight the range of convenience of a refinement: (1) most transient effects cannot be seen for microorganisms with very small radii, but the influence of the transient regime can be relevant in the description of accumulation data; and (2) if there is transport limitation (i.e. the FIAM assumption does not hold), the lability of the complexation becomes very relevant for both the flux and the depletion of the medium. A decision about which phenomena to keep and which to neglect – for the specific biological system under consideration and the specific measured quantity – can only be made on the basis of a close interaction between theoretical and experimental studies.

ACKNOWLEDGEMENTS The authors are most grateful to Jacques Buffle and Kevin Wilkinson (University of Geneva), Jaume Puy and Josep Monne´ (University of Lleida), and Raewyn M. Town (Queen’s University of Belfast) for their suggestions and assistance. Part of the preparation of this chapter was performed within the framework of the BIOSPEC project funded by the European Commission (contract EVK1-CT-2001-00086). This chapter is developed from [35], copyright Elsevier, 2003.

GLOSSARY BLM dSS FIAM SS * kin ISSA

Biotic ligand model Diffusive steady-state Free ion activity model Steady-state Bulk (superindex) Kinetic (superindex) Instantaneous steady-state approximation

196 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

APPENDIX A: NOTATION LATIN SYMBOLS Symbol

Name

a

Normalised bioaffinity parameter Ratio of limiting fluxes Concentration of species i (M: taken up; L: ligand; ML: complex) Steady-state concentration of species i at the surface (r ¼ r0 ) Bulk concentration of the species taken up (M). Concentration at the surface organism cM (r0 , t) Total concentration of M (free plus complexed) Average diffusion coefficient Diffusion coefficient of species i Functions of the depleted medium Diffusive flux Steady-state flux Diffusive steady-state flux Uptake (internalisation) flux due to sites of type j. Maximum uptake flux (due to sites j) Total uptake flux Normalised steady-state flux Linearised internalisation kinetic constant. Internalisation kinetic constant for sites of type j Association and dissociation rate constant for complexation Kinetic constant within a homogeneous floc Efflux kinetic constant

b ci cSS i c
M c0M c T, M D Di f1 , f2 Jm SS Jm dSS Jm J u, j  Ju
Ju
, j Ju J~ k kj ka kd kfloc kout

Units

Equations

None None

(19) (20),(64),(77)

mol m3

(1),(52),(53)

mol m3

(30), (66)

mol m3

(5)

mol m3

(37)

mol m3 m2 s1

(59) (61)

m2 s1

(1),(52),(53)

m3 mol m2 s1 mol m2 s1 mol m2 s1

(79) (8) (15) (24)

mol m2 s1

(3)

mol m2 s1 mol m2 s1 None

(13), (18), (25) (14) (18)

s1

(29)

s1 mol1 m3 s1 and s1

(3), (4)

s1 s1

(84) (86)

(54)

J. GALCERAN AND H. P. VAN LEEUWEN

K KH K M, j r r0 rf t

Equilibrium constant for complexation Linear adsorption coefficient Bioaffinity parameter for sites of type j. Radial coordinate Radius of the organism Radius of the region depleted by one organism Time

197

mol1 m3 m

(54) (28)

mol m3 m m

(2) (1),(52),(53) (7), Figure 1

m s

Section 4.1.1 (1)

Units

Equations

s1=2

(32), (33)

mol m2

(2)

mol m2 m

(2) (37)

m

(38)

None

(56)

None

(2)

None

(46) (48)

None

(46) (48)

None None s s

(68) (71), (73) (7) (41), (42)

s

(82)

GREEK SYMBOLS Symbol

Name

a, b

Auxiliary parameters for the transient solution Surface concentration of M at sites of type j Maximum surface concentration of M at sites of type j Diffusion layer thickness Effective diffusion layer shell thickness Normalised diffusion coefficient Fraction of coverage of species i Primary solution of coverage under steady-state (for site j, if subindex) Secondary solution of coverage under steady-state (for site j, if subindex) Dimensionless complex formation rate constant Degree of lability Dummy integration time Characteristic time constant Characteristic time for depletion of the medium

Gj Gmax , j

dM d e yi  ySS ySS j  yII yII j ka x t tdSS tdepl

198 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

Fu Fm O

Bioaccumulated amount Total supply from the mass transport Overall amount of M in the depletion region

mol m2

(10)

mol m2

(11)

mol

(79)

REFERENCES 1. 2.

3. 4. 5.

6. 7. 8. 9.

10. 11. 12.

Hudson, R. J. M. (1998). Modeling the fate of metals in aquatic systems: the mechanistic basis of particle–water partitioning models, Crit. Rev. Anal. Chem., 28, 19–26. Campbell, P. G. C. (1995). Interactions between trace metal and aquatic organisms: a critique of the free-ion activity model. In Metal Speciation and Bioavailability in Aquatic Systems. eds. Tessier, A. and Turner, D. R., Vol. 3, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Ltd, Chichester, pp. 45–102. Brown, P. L. and Markich, S. J. (2000). Evaluation of the free ion activity model of metal–organism interaction: extension of the conceptual model, Aquat. Toxicol., 51, 177–194. Slaveykova, V. I. and Wilkinson, K. J. (2002). Physicochemical aspects of lead bioaccumulation by Chlorella vulgaris, Environ. Sci. Technol., 36, 969–975. Tessier, A., Buffle, J. and Campbell, P. G. C. (1994). Uptake of trace metals by aquatic organisms. In Chemical and Biological Regulation of Aquatic Systems. eds. Buffle, J. and DeVitre, R. R., Lewis Publishers, Boca Raton, FL, pp. 197–230. Stumm, W. and Morgan, J. J. (1996). Trace metals: cycling, regulation, and biological role. In Aquatic Chemistry. 3rd edn, John Wiley & Sons, Ltd, New York, pp. 614–671. Campbell, P. G. C., Erre´calde, O., Fortin, C., Hiriart-Baer, W. R. and Vigneault, B. (2002). Metal bioavailability to phytoplankton – applicability of the biotic ligand model, Comp. Biochem. Physiol. C, 133, 189–206. Reinfelder, J. R., Fisher, N. S., Luoma, S. N., Nichols, J. W. and Wang, W. X. (1998). Trace element trophic transfer in aquatic organisms: a critique of the kinetic model approach, Sci. Total Environ., 219, 117–135. Whitfield, M. and Turner, D. R. (1979). Critical assessment of the relationship between biological thermodynamic and electrochemical availability. In Chemical Modeling in Aqueous Systems. ed. Jenne, E. A., American Chemical Society, Washington DC, pp. 657–680. Pahlow, M., Riebesell, U. and Wolf-Gladrow, D. A. (1997). Impact of cell shape and chain formation on nutrient acquisition by marine diatoms, Limnol. Oceanogr., 42, 1660–1672. Hudson, R. J. M. (1998). Which aqueous species control the rates of trace metal uptake, by aquatic biota? Observations and predictions of non-equilibrium effects, Sci. Total Environ. 219, 95–115. Jackson, G. A. and Morgan, J. J. (1978). Trace metal–chelator interactions and phytoplankton growth in seawater media: theoretical analysis and comparison with reported observations, Limnol. Oceanogr., 23, 268–282.

J. GALCERAN AND H. P. VAN LEEUWEN 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32.

199

Hudson, R. J. M. and Morel, F. M. M. (1990). Iron transport in marinephytoplankton – kinetics of cellular and medium coordination reactions, Limnol. Oceanogr., 35, 1002–1020. Morel, F. M. M. and Hering, J. G. (1993). Complexation. In Principles and Applications of Aquatic Chemistry. John Wiley & Sons, Ltd, New York, pp. 319–420. Hudson, R. J. M. and Morel, F. M. M. (1993). Trace-metal transport by marine microorganisms – implications of metal coordination kinetics, Deep-Sea Res. Part I, 40, 129–150. Pasciak, W. J. and Gavis, J. (1974). Transport limitation of nutrient uptake in phytoplankton, Limnol. Oceanogr., 19, 881–888. Harms, H. and Zehnder, A. J. B. (1994). Influence of substrate diffusion on degradation of dibenzofuran and 3-chlorodibenzofuran by attached and suspended bacteria, Appl. Environ. Microbiol., 60, 2736–2745. van Leeuwen, H. P. and Pinheiro, J. P. (2001). Speciation dynamics and bioavailability of metals. Exploration of the case of two uptake routes, Pure Appl. Chem., 73, 39–44. Phinney, J. T. and Bruland, K. W. (1994). Uptake of lipophilic organic Cu, Cd, and Pb complexes in the coastal diatom, Thalassiosira weissflogii, Environ. Sci. Technol., 28, 1781–1790. Button, D. K. (1985). Kinetics of nutrient-limited transport and microbial-growth, Microbiol. Rev., 49, 270–297. Sanford, L. P. and Crawford, S. M. (2000). Mass transfer versus kinetic control of uptake across solid–water boundaries, Limnol. Oceanogr., 45, 1180–1186. Galceran, J., Monne´, J., Puy, J. and van Leeuwen, H. P. (2003). Langmuir adsorption impact on the transient biouptake and accumulation. Unpublished work. Mason, R. P., Reinfelder, J. R. and Morel, F. M. M. (1996). Uptake, toxicity, and trophic transfer of mercury in a coastal diatom, Environ. Sci. Technol., 30, 1835–1845. van Leeuwen, H. P. (2000). Speciation dynamics and bioavailability of metals, J. Radioanal. Nucl. Chem., 246, 487–492. Jansen, S., Blust, R. and van Leeuwen, H. P. (2002). Metal speciation dynamics and bioavailability: Zn(II) and Cd(II) uptake by mussel (Mytilus edulis) and carp (Cyprinus carpio), Environ. Sci. Technol. 36, 2164–2170. van Leeuwen, H. P. (1999). Metal speciation dynamics and bioavailability: inert and labile complexes, Environ. Sci. Technol., 33, 3743–3748. Best, J. B. (1955). The inference of intracellular enzymatic properties from kinetic data obtained on living cells, J. Cell Comp. Physiol., 46, 1–27. Koch, A. L. (1990), Diffusion–the crucial process in many aspects of the biology of bacteria, Advances in Microbial Ecology, 11, 37–70. Brezonik, P. L. (1994). Kinetics of biochemical reactions and microbial processes in natural waters. In Chemical Kinetics and Process Dynamics in Aquatic Systems. Lewis Publishers, Boca Raton, FL, pp. 419–552. Bosma, T. N. P., Middeldorp, P. J. M., Schraa, G. and Zehnder, A. J. B. (1997). Mass transfer limitation of biotransformation: quantifying bioavailability, Environ. Sci. Technol., 31, 248–252. Ploug, H., Stolte, W. and Jørgensen, B. B. (1999). Diffusive boundary layers of the colony-forming plankton alga Phaeocystis sp – implications for nutrient uptake and cellular growth, Limnol. Oceanogr., 44, 1959–1967. Oldham, K. B. and Myland, J. C. (1994). Steady-state voltammetry. In Fundamentals of Electrochemical Science. Academic Press, San Diego, pp. 263–308.

200 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 33. 34. 35. 36. 37. 38. 39. 40. 41.

42. 43.

44. 45. 46.

47. 48. 49.

Holub, K. (1966). Surface reaction of an adsorbed substance transported by diffusion to a spherical electrode, Collect. Czech. Chem. Commun., 31, 1655–1665. Holub, K. and van Leeuwen, H. P. (1984). Influence of reactant adsorption on limiting currents in normal pulse polarography. 2. Theory for the stationary, spherical electrode, J. Electroanal. Chem., 162, 55–65. Galceran, J., Monne´, J., Puy, J. and van Leeuwen, H. P. (2003). The impact of the transient uptake flux on bioaccumulation. Linear adsorption and first-order internalisation coupled with spherical semi-infinite mass transport, Mar. Chem., in press. Knauer, K., Behra, R. and Sigg, L. (1997). Adsorption and uptake of copper by the green alga Scenedesmus subspicatus (Chlorophyta), J. Phycol., 33, 596–601. Sunda, W. G. and Huntsman, S. A. (1998). Control of Cd concentrations in a coastal diatom by interactions among free ionic Cd, Zn, and Mn in seawater, Environ. Sci. Technol., 32, 2961–2968. Mirimanoff, N. and Wilkinson, K. J. (2000). Regulation of Zn accumulation by a freshwater gram-positive bacterium (Rhodococcus opacus), Environ. Sci. Technol., 34, 616–622. Campbell, P. G. C. (2001). Predicting Metal Bioavailability in Aquatic Environments. ICOBTE (Int. Conf. on Biogeochemistry of Trace Elements), Guelph, Ontario, Canada, p. 24. Holub, K. and Koryta, J. (1965). Surface reaction of adsorbed substance transported by diffusion to a plane electrode, Collect. Czech. Chem. Commun., 30, 3785–3796. De Jong, H. G. and van Leeuwen, H. P. (1987). Voltammetry of metal-complex systems with different diffusion-coefficients of the species involved. 2. Behaviour of the limiting current and its dependence on association/dissociation kinetics and lability, J. Electroanal. Chem., 234, 17–29. Zoski, C. G., Bond, A. M., Allinson, E. T. and Oldham, K. B. (1990). How long does it take a microelectrode to reach a voltammetric steady-state? Anal. Chem. 62, 37–45. Phinney, J. T. and Bruland, K. W. (1997). Trace metal exchange in solution by the fungicides Ziram and Maneb (dithiocarbamates) and subsequent uptake of lipophilic organic zinc, copper and lead complexes into phytoplankton cells, Environ. Toxicol. Chem., 16, 2046–2053. Fortin, C. and Campbell, P. G. C. (2000). Silver uptake by the green alga Chlamydomonas reinhardtii in relation to chemical speciation: influence of chloride, Environ. Toxicol. Chem., 19, 2769–2778. Bard, A. J. and Faulkner, L. R. (1980) Electrochemical Methods, Fundamentals and Applications. John Wiley & Sons, Ltd, New York. van Leeuwen, H. P. and Galceran, J. (2004). Biointerfaces and mass transfer. In Physicochemical Kinetics and Transport at Biointerfaces. eds. van Leeuwen, H.P. and Ko¨ster, W., Vol. 9, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Chichester, pp. 113–146. Vasconcelos, M. T. S. D. and Leal, M. F. C. (2001). Adsorption and uptake of Cu by Emiliania huxleyi in natural seawater, Environ. Sci. Technol., 35, 508–515. Wilhelm, S. W. and Trick, C. G. (1994). Iron-limited growth of cyanobacteria – multiple siderophore production is a common response, Limnol. Oceanogr., 39, 1979–1984. Volker, C. and Wolf-Gladrow, D. A. (1999). Physical limits on iron uptake mediated by siderophores or surface reductases, Mar. Chem., 65, 227–244.

J. GALCERAN AND H. P. VAN LEEUWEN 50. 51.

52.

53.

54.

55. 56.

57. 58. 59. 60. 61. 62. 63. 64. 65. 66.

201

Croot, P. L., Karlson, B., van Elteren, J. T. and Kroon, J. J. (1999). Uptake of 64Cu oxine by marine phytoplankton, Environ. Sci. Technol., 33, 3615–3621. Erre´calde, O., Seidl, M. and Campbell, P. G. C. (1998). Influence of a low molecular weight metabolite (citrate) on the toxicity of cadmium and zinc to the unicellular green alga Selenastrum capricornutum: an exception to the free-ion model, Water Res., 32, 419–429. van Ginneken, L., Chowdhury, M. J. and Blust, R. (1999). Bioavailability of cadmium and zinc to the common carp, Cyprinus carpio, in complexing environments: a test for the validity of the free ion activity model, Environ. Toxicol. Chem., 18, 2295–2304. Puy, J., Galceran, J., Salvador, J., Cecı´lia, J., Dı´az-Cruz, J. M., Esteban, M. and Mas, F. (1994). Voltammetry of labile metal macromolecular systems for any ligand-to-metal ratio, including adsorption phenomena – the role of the stability constant, J. Electroanal. Chem., 374, 223–234. Puy, J., Torrent, M., Monne´, J., Cecı´lia, J., Galceran, J., Salvador, J., Garce´s, J. L., Mas, F. and Berbel, F. (1998). Influence of the adsorption phenomena on the NPP and RPP limiting currents for labile metal–macromolecular systems, J. Electroanal. Chem., 457, 229–246. van Leeuwen, H. P., Puy, J., Galceran, J. and Cecı´lia, J. (2002). Evaluation of the Koutecky´–Koryta approximation for voltammetric currents generated by metal complex systems with various labilities, J. Electroanal. Chem., 526, 10–18. Galceran, J., Cecı´lia, J., Salvador, J., Monne´, J., Torrent, M., Companys, E., Puy, J., Garce´s, J. L. and Mas, F. (1999). Voltammetric currents for any ligandto-metal concentration ratio in fully labile metal–macromolecular complexation. Easy computations, analytical properties of the currents and a graphical method to estimate the stability constant, J. Electroanal. Chem., 472, 42–52. Pinheiro, J. P. and van Leeuwen, H. P. (2001). Metal speciation dynamics and bioavailability. 2. Radial diffusion effects in the microorganism range, Environ. Sci. Technol., 35, 894–900. Levich, V. G. (1962). Physicochemical Hydrodynamics. Prentice-Hall, Englewood Cliffs, NJ. Galceran, J., Puy, J., Salvador, J., Cecı´lia, J. and van Leeuwen, H. P. (2001). Voltammetric lability of metal complexes at spherical microelectrodes with various radii, J. Electroanal. Chem., 505, 85–94. Jannasch, H. W., Honeyman, B. D. and Murray, J. W. (1996). Marine scavenging: the relative importance of mass transfer and reaction rates, Limnol. Oceanogr., 41, 82–88. Wolf-Gladrow, D. and Riebesell, U. (1997). Diffusion and reactions in the vicinity of plankton: a refined model for inorganic carbon transport, Mar. Chem., 59, 17–34. Galceran, J., Puy, J., Salvador, J., Cecı´lia, J., Mas, F. and Garce´s, J. L. (2003). Lability and mobility effects on mixtures of ligands under steady-state conditions, Phys. Chem. Chem. Phys., 5, 5091–5100. Sunda, W. G. and Huntsman, S. A. (1995). Iron uptake and growth limitation in oceanic and coastal phytoplankton, Mar. Chem., 50, 189–206. Koch, A. L. (1996). What size should a bacterium be? A question of scale, Ann. Rev. Microbiol., 50, 317–348. Sunda, W. G. and Huntsman, S. A. (1997). Interrelated influence of iron, light and cell size on marine phytoplankton growth, Nature, 390, 389–392. Morel, F. M. M. (1983). Principles of Aquatic Chemistry. John Wiley & Sons, Ltd, New York.

202 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 67. 68. 69. 70.

71. 72. 73. 74.

75. 76. 77. 78. 79.

80. 81. 82. 83. 84. 85.

Parker, D. R. and Pedler, J. F. (1997). Reevaluating the free-ion activity model of trace metal availability to higher plants, Plant and Soil, 196, 223–228. Anderson, M. A., Morel, F. M. M. and Guillard, R. R. L. (1978). Growth limitation of a coastal diatom by low zinc ion activity, Nature, 276, 70–71. Hare, L. and Tessier, A. (1996). Predicting animal cadmium concentrations in lakes, Nature, 380, 430–432. Tessier, A. and Turner, D. R., eds. (1995). Metal Speciation and Bioavailability in Aquatic Systems. Vol. 3, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Ltd, Chichester. Playle, R. C. (1998). Modelling metal interactions at fish gills, Sci. Total Environ. 219, 147–163. Hare, L. and Tessier, A. (1998). The aquatic insect Chaoborus as a biomonitor of trace metals in lakes, Limnol. Oceanogr., 43, 1850–1859. Hudson, R. J. M. and Morel, F. M. M. (1989). Distinguishing between extracellular and intracellular iron in marine-phytoplankton, Limnol. Oceanogr., 34, 1113–1120. Parent, L., Twiss, M. R. and Campbell, P. G. C. (1996). Influences of natural dissolved organic matter on the interaction of aluminum with the microalga Chlorella: a test of the free-ion model of trace metal toxicity, Environ. Sci. Technol., 30, 1713–1720. Fisher, M., Zamir, A. and Pick, U. (1998). Iron uptake by the halotolerant alga Dunaliella is mediated by a plasma membrane transferrin, J. Biol. Chem., 273, 17 553–17 558. Fortin, C. and Campbell, P. G. C. (2001). Thiosulfate enhances silver uptake by a green alga: role of anion transporters in metal uptake, Environ. Sci. Technol., 35, 2214–2218. Kujawinski, E. B., Farrington, J. W. and Moffett, J. W. (2002). Evidence for grazing-mediated production of dissolved surface-active material by marine protists, Mar. Chem., 77, 133–142. Wilkinson, K. J., Campbell, P. G. C. and Couture, P. (1990). Effect of fluoride complexation on aluminum toxicity towards juvenile atlantic salmon (Salmo salar), Can. J. Fish. Aquat. Sci., 47, 1446–1452. Blust, R., van Ginneken, L. and Comhaire, S. (1997). Bioavailability of radiocobalt to the common carp, Cyprinus carpio, in complexing environments. In Freshwater and Estuarine Radioecology. Vol. 68, eds. Desmet, G., Blust, R., Comans, R. N. J., Fernandez, J. A., Hilton, J. and de Bettencourt, A., Elsevier, Amsterdam, pp. 311–317. Pinheiro, J. P., Galceran, J. and van Leeuwen, H. P. (2003). Metal speciation dynamics and bioavailability. Effects of bulk depletion in biouptake, Environ. Sci. Technol., submitted. Csanady, G. T. (1986). Mass-transfer to and from small particles in the sea, Limnol. Oceanogr., 31, 237–248. Priesack, E. (1991). Analytical solution of solute diffusion and biodegradation in spherical aggregates, Soil Sci. Soc. Am. J., 55, 1227–1230. Chung, G. Y., McCoy, B. J. and Scow, K. M. (1993). Criteria to assess when biodegradation is kinetically limited by intraparticle diffusion and sorption, Biotechnol Bioeng., 41, 625–632. Traytak, S. D. (1996). Competition effects in steady-state diffusion-limited reactions: renormalization group approach, J. Chem. Phys., 105, 10 860–10 867. Vogel, S. (1994). Life in Moving Fluids: the Physical Biology of Flow. Princeton University Press, Princeton, NJ.

J. GALCERAN AND H. P. VAN LEEUWEN 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99.

100. 101.

203

Berg, H. C. and Purcell, E. M. (1977). Physics of chemoreception, Biophys. J., 20, 193–219. Lazier, J. R. N. and Mann, K. H. (1989). Turbulence and the diffusive layers around small organisms, Deep-Sea Res., 36, 1721–1733. Reynolds, C. S. (1994). The long, the short and the stalled – on the attributes of phytoplankton selected by physical mixing in lakes and rivers, Hydrobiologia, 289, 9–21. Kronig, R. and Bruijsten, J. (1951). On the theory of heat and mass transfer from a sphere in a flowing medium at low values of Reynolds number, Appl. Sci. Res. A, 2, 439–446. Munk, W. H. and Riley, G. A. (1952). Absorption of nutrients by aquatic plants, J. Mar. Res., 11, 215–240. Karp-Boss, L., Boss, E. and Jumars, P. A. (1996). Nutrient fluxes to planktonic osmotrophs in the presence of fluid motion, Oceanogr. Mar. Biol., 34, 71–107. Simoni, S. F., Schafer, A., Harms, H. and Zehnder, A. J. B. (2001). Factors affecting mass transfer limited biodegradation in saturated porous media, J. Contam. Hydrol., 50, 99–120. Santana-Casiano, J. M., Gonza´lez-Da´vila, M., Laglera, L. M., Pe´rez-Pen˜a, J., Brand, L. and Millero, F. J. (1997). The influence of zinc, aluminum and cadmium on the uptake kinetics of iron by algae, Mar. Chem., 59, 95–111. Kleijn, J. M. and van Leeuwen, H. P. (2000). Electrostatic and electrodynamic properties of biological interphases. In Physical Chemistry of Biological Interfaces. eds. Baszkin, A. and Norde, W., Marcel Dekker, New York, pp. 49–83. Kankare, J. and Vinokurov, I. A. (1999). Kinetics of Langmuirian adsorption onto planar, spherical, and cylindrical surfaces, Langmuir, 15, 5591–5599. Bhugun, I. and Anson, F. C. (1997). A generalized treatment of the dynamics of the adsorption of Langmuirian systems at stationary or rotating disk electrodes, J. Electroanal. Chem., 439, 1–6. Pagenkopf, G. K. (1983). Gill surface interaction model for trace-metal toxicity to fishes: role of complexation, pH, and water hardness, Environ. Sci. Technol., 17, 342–347. Sunda, W. G. and Huntsman, S. A. (1998). Processes regulating cellular metal accumulation and physiological effects: phytoplankton as model systems, Sci. Total Environ., 219, 165–181. Meyer, J. S., Santore, R. C., Bobbitt, J. P., DeBrey, L. D., Boese, C. J., Paquin, P. R., Allen, H. E., Bergman, H. L. and DiToro, D. M. (1999). Binding of nickel and copper to fish gills predicts toxicity when water hardness varies, but free-ion activity does not, Environ. Sci. Technol., 33, 913–916. Button, D. K. (1998). Nutrient uptake by microorganisms according to kinetic parameters from theory as related to cytoarchitecture, Microbiol. Mol. Biol. Rev., 62, 636–644. Lee, J. G., Ahner, B. A. and Morel, F. M. M. (1996). Export of cadmium and phytochelatin by the marine diatom Thalassiosira weissflogii, Environ. Sci. Technol., 30, 1814–1821.

5 Chemical Speciation of Organics and of Metals at Biological Interphases BEATE I. ESCHER AND LAURA SIGG Environmental Microbiology and Molecular Ecotoxicology, and Analytical Chemistry of the Aquatic Environment (EAWAG), Swiss Federal Institute for Environmental ¨ berlandstrasse 133, CH-8600 Du¨bendorf, Switzerland Science and Technology U

1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Chemical Speciation of Organic Chemicals . . . . . . . . . . . . . . 1.2 Metal Speciation and Biological Interactions. . . . . . . . . . . . . 2 Speciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Speciation of Organic Compounds . . . . . . . . . . . . . . . . . . . . . 2.1.1 Hydrophobic Ionogenic Organic Compounds (HIOCs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Examples of Environmentally Relevant HIOCs . . . . 2.1.3 Redox Speciation of Organic Compounds . . . . . . . . . 2.2 Metal Speciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Inorganic Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Organic Complexes: Hydrophilic Complexes . . . . . . . 2.2.3 Organic Complexes: Hydrophobic Complexes. . . . . . 2.2.4 Organometallic Species . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.5 Redox Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.6 Solubility of Solid Phases and Binding to Colloids and Particles . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.7 Kinetics of Complexation Reactions . . . . . . . . . . . . . . 3 Membranes and Surrogates or Membrane Models. . . . . . . . . . . . . 3.1 Octanol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Other Solvent–Water Systems . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Liposomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Biological Membranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Interactions of HIOCs with Biological Interphases . . . . . . . . . . . . 4.1 Partitioning and Sorption Models . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Octanol–Water Partitioning . . . . . . . . . . . . . . . . . . . . .

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4.1.2

Membrane–Water Partitioning: General Derivation of Membrane–Water Partition Coefficients of a Charged or Neutral Compound or Species . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Thermodynamics of Membrane–Water Partitioning . . . . . . 4.3 pH-Dependence of Membrane–Water Partitioning . . . . . . . 4.4 Ion Pair Formation at the Membrane Interphase . . . . . . . . . 4.5 Speciation in the Membrane: Interfacial Acidity Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Sorption of HIOCs to Charged Membranes Vesicles and Biological Membranes. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Site of Interaction of HIOCs with Membranes . . . . . . . . . . . 4.8 Effects of Speciation of HIOCs at Biological Interphases . . 4.8.1 Ion Trapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.2 Bioaccumulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.3 Toxicity: Uncoupling Effect . . . . . . . . . . . . . . . . . . . . . 5 Interaction of Metal Species with Biological Interphases . . . . . . . 5.1 Binding to Biological Ligands and Free Ion Activity Model (FIAM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Uptake of Specific Complexes . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Interactions of FA and HA with Biological Interphases . . . 6 Interaction of Hydrophobic Metal Complexes and Organometallic Compounds with Biological Interphases . . . . . . . 6.1 Hydrophobic Metal Complexes . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Organometallic compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Mercury . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Organolead Compounds. . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 Organotin Compounds . . . . . . . . . . . . . . . . . . . . . . . . . 7 Conclusions and Recommendations for Further Research . . . . . . List of Symbols and Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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INTRODUCTION

The objective of this chapter is to discuss the role of speciation for interactions and uptake at biological interphases. Both organic chemicals and metals will be considered in order to emphasise common mechanisms, as well as fundamental differences. Acid–base reactions, redox reactions and complexation between metallic ions and various types of ligands have to be considered in regard to speciation. Particular attention will be paid to the role of interactions between metals and organic chemicals. The role of speciation regarding the various types of possible interactions at biological interphases (partitioning into the lipid

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bilayer, specific binding to carrier ligands and unspecific binding to functional groups, polar and electrostatic interactions) will be discussed. A related topic, the role of speciation for interaction with organic matter, is beyond the scope of this chapter. 1.1

CHEMICAL SPECIATION OF ORGANIC CHEMICALS

Historically, organic environmental pollutants were hydrophobic, often persistent, neutral compounds. As a consequence, these substances were readily sorbed by particles and soluble in lipids. In modern times, efforts have been made to make xenobiotics more hydrophilic – often by including ionisable substituents. Presumably, these functional groups would render the compound less bioaccumulative. In particular, many pesticides and pharmaceuticals contain acidic or basic functions. However, studies on the fate and effect of organic environmental pollutants focus mainly on the neutral species [1]. In the past, uptake into cells and sorption to biological membranes were often assumed to be only dependent on the neutral species. More recent studies that are reviewed in this chapter show that the ionic organic species play a role both for toxic effects and sorption of compounds to membranes. Speciation of hydrophobic ionogenic organic compounds (HIOCs) may influence their bioavailability and bioaccumulation, as well as sorption to organic matter and particles. For the charged species, specific sorption processes may play a role, while neutral organic compounds only undergo hydrophobic partitioning via van der Waals plus hydrogen donor/acceptor interactions. Finally, the toxic effect of HIOCs, in particular their specific toxic effect of uncoupling the electron transport from the ATP synthesis, is strongly influenced by their speciation [2]. To date, there have been only very few studies on the sorption of environmentally relevant HIOCs to membranes. In contrast, there exists a large body of literature on ionogenic drug partitioning (see, e.g. [3–5]), and the partitioning of hydrophobic ions [6], and the use of fluorescent membrane probes [7]. This literature review attempts to relate the findings from these related scientific fields to environmental chemistry. 1.2

METAL SPECIATION AND BIOLOGICAL INTERACTIONS

The role of metal speciation in the uptake of metals by biological systems has long been recognised, in particular with respect to aquatic organisms [8], and also in soil systems [9,10]. It is clear that metal ions cannot simply diffuse through the hydrophobic core of membranes. Various biological mechanisms of metal transport across biological membranes are known [11]. These mechanisms include permeation through ion channels, transport by carrier ligands (proteins), binding of metals to various components of the membrane,

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partitioning of hydrophobic metal complexes, and in some cases transport of specific complexes [11,12]. In the case of ion channels and carrier ligands, interactions of metal ions with specific membrane components have to occur. The chemical species, in which the metal ions occur outside the cells and in which they are transported to the biological interphase, are thus of key significance for subsequent specific interactions at the membrane. For any mechanism involving binding of metal ions to biological components, ligand-exchange reactions of metals between the external ligands and the biological ligands have to occur. In the simplest case, such reactions involve the exchange of coordinated water molecules of a hydrated metal ion with a biological ligand. Other complexes may exchange by dissociation of the complexes to the hydrated metal ion, or by other mechanisms. The stability of the metal species outside the membranes, as well as their dissociation kinetics, are thus of significance with regard to binding to biological ligands ([13,14], and Chapter 3 in this volume). On the other hand, the presence of hydrophobic complexes is a prerequisite for partitioning and diffusion of metals into the lipid bilayer. In the following paragraphs, various types of metal complexes will be discussed, which are relevant to the interactions of metals in aquatic systems. The role of these various types of metal complexes with respect to interactions at the biological interphases will be systematically examined.

2

SPECIATION

2.1 2.1.1

SPECIATION OF ORGANIC COMPOUNDS Hydrophobic Ionogenic Organic Compounds (HIOCs)

HIOC is a term that refers to organic compounds that can be ionised in the environment and thus are present in two or more species. Basically, the group of HIOCs includes weak organic acids and bases and organometallic compounds, e.g. organotins. This latter group will be treated separately (see Section 2.2.4). Organic acids dissociate according to:
HAw Ð Hþ w þ Aw

(1)

where HAw and A
w are the acid and the conjugate base in the aqueous phase, and Hþ represents the proton. The corresponding equilibrium constant, i.e. the w acidity constant Kaw , is defined by: K aw ¼

aAw aHw aHAw

(2)

B. I. ESCHER AND L. SIGG

209

where aHAw and aAw are the activities of species HA and A
in the aqueous phase and aHw is the hydrogen ion activity ðpH ¼
log aHw Þ. The basicity constant can be defined in an analogous way to the acidity constant. To simplify matters, one can also speak of the acidity constant of the conjugate acid of a base, HBþ . Compounds with an acidity constant, pKaw , in the range of 4 to 10, i.e. weak organic acids or bases, are present in two species forms at ambient pH. This pKaw range includes aromatic alcohols and thiols, carboxylic acids, aromatic amines and heterocyclic amines [15]. Conversely, alkyl-H and saturated alcohols do not undergo protonation/deprotonation in water ðpKaw  14Þ. 2.1.2

Examples of Environmentally Relevant HIOCs

Many pesticides are moderate to weak acids. Strong acid pollutants are fully ionised at ambient pH. Examples include trifluoroacetic and chloroacetic acids, whose use as herbicides has been banned but which still occur as solvent degradation products [16], or the pesticide 2,4,5-trichlorophenoxyacetic acid ðpKaw 2:83Þ. Then there are a number of pesticides, e.g. the phenolic herbicide dinoseb and the fungicide pentachlorophenol, whose speciation varies strongly in the environmental pH-range. For this reason, one has to consider the pKaw when estimating their environmental fate. Structures of the compounds discussed in this section are depicted in Table 1, together with a listing of their pKaw and octanol–water partition coefficients, Kow , of the neutral species (unless otherwise indicated). Typical basic pollutants include the industrial chemicals aniline and N,N-dimethylaniline. Recently, attention has turned to drugs and personal care products, many of which are acids and bases. More than 30 000 ionisable compounds are listed in the 1999 world drug index, which corresponds with 63 % of all drugs [17]. Interestingly, some of the pharmaceuticals are structurally very similar to known environmental pollutants: e.g. the pesticide mecoprop and the hydrolysis product of the lipid regulator clofibrate, clofibric acid, are isomeric molecules that exhibit similar behaviour in the environment [18]. Drugs and personal care products are increasingly detected in the effluents of wastewater treatment plants, rivers, lakes, and the marine environment [19–23]. Prominent examples are the anti-inflammatory drug ibuprofen [24] and disinfectant agents such as triclosan or tetrabromocresol [19]. Ciprofloxazin, a zwitterionic antibiotic (at pH 7) was identified to be the agent responsible for mutagenicity in hospital wastewater [25]. Another example is oxalinic acid, a frequently used antibiotic in fish farming [26]. Since the membrane–water partition coefficient is a relevant parameter for the pharmacokinetic behaviour, i.e. drug uptake, many more studies on the speciation of drugs at membrane interphases can be found in the

210 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES Table 1. Examples of environmentally relevant HIOCs Compound name

Structure

Aniline

NH2

Pentachlorophenol

Cl

Cl

Cl

Application

pKaw

log Kow

Industrial intermediate

4.63a

2.35a

Fungicide

4.75b

5.24b

Pesticide

4.62b

3.56b

Herbicide

3.78c

1.26c at pH 7

Metabolite of pharmaceutical compound (blood lipid regulator)

4.46d

2.57

anti-inflammatory drug

4.45/ 5.7e

3.5e

Antiseptic used in 8.05 f personal care products

5.4 f

OH Cl

Cl

Dinoseb

O2N

OH NO2

Mecoprop

CH3 Cl

O H3C

COOH H

Clofibric acid Cl

O H3 C

Ibuprofen

H3 C

Triclosan

Cl

COOH

OH O Cl Cl

COOH CH3

B. I. ESCHER AND L. SIGG Ciprofloxacin

211

O OOC

F

N

Antibiotic in human medicine

6.08 and 8.58g

0.074 at pH 7.4h

Veterinary antibiotic

6.9i

0.68i

N N H H

Oxalinic acid

CH3 O

N

O

COOH O

a

[15]. b [116]. c [245]. d,e [22]. f Own measurements (unpublished). g [246]. h [247]. i [26].

literature than reported for environmental pollutants. Since most of the conclusions are generally valid and since drugs have been identified as emerging environmental pollutants, this review also covers work from the pharmaceutical sector. 2.1.3

Redox Speciation of Organic Compounds

Redox conditions have a minor impact on organic compounds as compared with metals. Most organic chemicals that pose a toxicological hazard due to their chemical reactivity are not hydrophobic enough to create a toxicological problem in a hydrophobic membrane environment. Exceptions include quinones, some of which can be reduced to hydroquinones through enzymatic and nonenzymatic redox cycling with their corresponding semiquinone radicals [27]. Redox cycling may also produce reactive oxygen species that – apart from reaction with other biomolecules – may damage the membrane lipids and membrane-bound proteins. Protection against cell damage due to oxidative stress is provided, amongst others, by glutathione (GSH), a cellular tripeptide with a thiol function in a cysteine residue. GSH is deprotonated to GS
, which is a scavenger for electrophilic compounds and is reduced to GS–SG in defense of reactive oxygen species [28]. 2.2

METAL SPECIATION

Metal speciation is discussed here from the perspective of the speciation occurring in natural freshwater environments. This speciation is relevant for interactions of metals with aquatic organisms.

212 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

2.2.1

Inorganic Complexes

Inorganic ligands in aqueous solutions, and in particular in natural freshwaters, include, in addition to H2 O and OH
, the major ions carbonate and bicarbonate, chloride, sulfate and also phosphate [29]. The distribution of metal ions between these ligands depends on pH and on the relative concentrations of the ligands. The pH is a master variable with regard to the occurrence of hydrolysed species and to the formation of carbonate and bicarbonate complexes. Stability constants of metal complexes with inorganic ligands are generally well known [30]. Inorganic speciation of metals can therefore easily be evaluated by thermodynamic calculations if the composition of the solution is known [29,31]. Under typical freshwater conditions, at pH 7–9 and in presence of millimolar concentrations of carbonate, most transition metals in solution (Cu(II), Zn(II), Ni(II), Co(II), Cd(II), Fe(III), etc.) occur predominantly as hydroxo or carbonato complexes. For a few metals, chloro complexes may be predominant (Ag(I), Hg(II) ), if chloride is in the range 10
4
10
3 mol dm
3 or higher. Alkali and alkali-earth cations occur predominantly as free aquo metal ions [29]. At lower pH values, the fraction of free aquo metal ions generally increases. Strong sulfide complexes of several transition metals have recently been shown to occur even under oxic conditions [32,33].

2.2.2

Organic Complexes: Hydrophilic Complexes

Organic ligands that may significantly influence the speciation of metals in natural waters (and in other aquatic media) comprise a large range of compounds. Complexation of metal ions by organic ligands cannot be modelled as simply as the inorganic speciation, because the composition of natural organic matter is not known in detail and the binding characteristics of the macromolecular ligands require sophisticated models. Simple organic molecules such as small carboxylic acids (oxalate, acetate, malonate, citrate, etc.), amino acids and phenols are all ligands for metals. Such compounds may all occur as degradation products of organic matter in natural waters. The complexes formed are typically charged hydrophilic complexes. The stability of the metal complexes with these ligands is, however, moderate in most cases. Model calculations including such compounds at realistic concentrations indicate that their effects on speciation are relatively small [29]. A further category of ligands includes the synthetic chelating polycarboxylate ligands such as EDTA (ethylenediaminetetraacetate) and NTA (nitrilotriacetate). These ligands form very stable complexes with a number of metals. They occur at low concentrations in natural waters, due to inputs from sewage treatment plants [34]. They have also been widely used as complexing ligands in culture media for investigation of interactions between metals and organ-

B. I. ESCHER AND L. SIGG

213

isms, especially for algae, in order to control the free aquo metal ion concentrations [35,36]. If present in excess of the trace metals, as it is the case in culture media, EDTA and NTA dominate the speciation of trace metals. These charged hydrophilic complexes are very soluble and increase the overall solubility of trace metals. Fulvic acids (FA) and humic acids (HA) play a very important role in the complexation of metals in natural waters [37–39]. FA and HA are polymeric ligands with molecular weights typically in the range 500–2000 g mol
1 for FA and 2000–5000 g mol
1 for HA. Recent spectroscopic work has started to reveal more clearly the structures of these polymeric molecules [40–43]. FA and HA comprise both hydrophobic and hydrophilic domains. Phenolic and carboxylic groups bound to various aromatic and aliphatic structures are the most important complexing functional groups in FA and HA. To describe the complexation properties of FA and HA, the heterogeneity of the various binding sites and the polyelectrolyte nature of metal ion binding have to be taken into account [37]. The various models for complexation of metals with FA and HA cannot be discussed here; for details see, for example, [37–39, 44–47]. It is clear that the stability of metal complexes with FA and HA depends on the ratio of metal to ligand, because the strongest binding sites are occupied at low metal concentrations. Increasing evidence for the presence of unknown strong organic ligands for trace metals has been shown by a number of studies in seawater [48–57,58,59] and in freshwater [60–64]. This evidence is based on indirect methods, which indicate strong complexation of the metals, but do not identify the structure of the ligands involved. A controversial discussion is ongoing in the literature on the question whether specific strong ligands can be distinguished from strong binding by humic and fulvic acids [65–67]. Specific strong chelators may be produced biologically and either excreted during growth of the organisms (algae, cyanobacteria, bacteria) or released upon partial decomposition of the biomass [68–71]. They may include biological ligands such as glutathione, phytochelatins and siderophores [59,71,72]. Very stable complexes may be due to the occurrence of N- or S-functional groups in chelating ligands [5,72,73]. In a complex solution the total metal concentration in solution cM, t can be represented by the following general equation: cM, t ¼ cM þ

X i

cMLi inorg þ

X

cMLi org

(3)

i

P  where cM represents the free metal ion concentration, cMLi inorg the sum of P  i cMLi org the sum of organic complexes. inorganic complexes, and i

The relationship between free metal ion activity (or concentration, depending on the conventions used for the stability constants) and cM, t is given by:

214 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

cM ¼ cM, t

1þ

X

bi cLi inorg

i

þ

X

!
1 bi cLi org

(4)

i

where bi represents the overall thermodynamic stability constant of the complex MLi , cLi inorg the concentration of inorganic ligand Linorg and cLi org the concentration of organic ligand Lorg . If all stability constants and ligand concentrations are known, the free metal ion concentration at equilibrium can be calculated by equation (4). Complexation by natural organic matter cannot be reliably represented in terms of simple discrete ligands and requires sophisticated models. Figure 1 illustrates the speciation of Cu in the presence of various inorg

oxal

cit

FA/HA

L1/L2

EDTA

CuCO03

CuCO03

CuOHcit

CuFA

CuL1

CuEDTA

−4

−6

log[Cu-species]

−8 Cu2+

CuOx Cu2+

−10

−12

−14

Cu(OH)02

Cu(OH)02

CuCO03

CuHA CuL2 CuCO03

Cucit Cu2+

Cu2+

Cu(OH)02

Cu(OH)02

CuCO03

CuCO03

Cu2+

Cu2+

Cu(OH)02

Cu(OH)02

−16

Figure 1. Calculated speciation of Cu in presence of inorganic and organic ligands. In all cases, C Cu, t is 2  10
8 mol dm
3 (dashed line), pH 8, total carbonate species 2  10
3 mol dm
3 . Stability constants are from [30], unless otherwise indicated. Inorg: speciation in the presence of the inorganic ligands carbonate and hydroxide only; oxal: 1  10
6 mol dm
3 oxalate; cit: 1  10
6 mol dm
3 citrate; FA/HA: 3 mg dm
3 FA and 0:3 mg dm
3 HA, according to the WHAM model [44]; L1/L2: lakewater ligands as determined in [60], 8  10
8 mol dm
3 L1 (log K ¼ 14:0, conditional for pH 8) and 5  10
7 mol dm
3 L2 (log K ¼ 12:0, conditional for pH 8); EDTA: 2  10
5 mol dm
3 EDTA in a culture medium also containing Ca and other trace elements. Only the most abundant Cu species are shown

B. I. ESCHER AND L. SIGG

215

ligands, namely of inorganic ligands (carbonate and hydroxide), of oxalate, of citrate, of FA and HA according to the WHAM model [44], of strong lakewater ligands (L1/L2) [60], and of EDTA in a culture medium. This figure illustrates how the concentration of the free aquo ion Cu2þ decreases in the presence of strong ligands. Copper is over 90% organically complexed in the presence of citrate, FA and HA, EDTA and lakewater ligands under the conditions considered in Figure 1. 2.2.3

Organic Complexes: Hydrophobic Complexes

A number of organic ligands forming hydrophobic complexes are known in analytical chemistry, in which they have been used as carriers for metal extraction in organic solvents (e.g. dithiocarbamates, oxine [74]) and as ligands in carrier-based ion-selective electrodes (e.g. macrocyclic compounds [75,76]). The occurrence of ligands forming organic hydrophobic complexes in natural waters has not been clearly demonstrated, but is likely. Dithiocarbamate metal complexes are used in fungicides and may therefore occur in natural waters [77]. The significance of other organic pollutants in forming hydrophobic metal complexes has not yet been investigated in detail. Some natural compounds may also form uncharged hydrophobic complexes, such as e.g. catechol. Chlorocatechols form complexes with different hydrophobic character [78]. Furthermore, some uncharged inorganic species (e.g. HgCl02 , HgS0 , AgCl0 ) also behave as hydrophobic complexes [79–81]. The same relationships between free metal ions and total metal concentrations hold as above. Equation (4) may include the concentration of hydrophobic ligands. However, the occurrence of hydrophobic complexes is particularly relevant to the interactions with membranes. 2.2.4

Organometallic Species

The occurrence of organometallic species (compounds with at least one carbon– metal bond) is a key factor for the biological effects of a number of metallic elements. Of particular environmental concern are methylmercury and other organomercury compounds, organotin compounds (e.g. tributyltin) and alkylated lead compounds [82]. Methylmercury has been observed in many aquatic systems in varying proportions to total mercury [83,84–86]. Methylmercury is formed in natural environments by bacterial methylation [81,87]. Methylmercury forms inorganic complexes, which may be uncharged, in particular CH3 HgCl0 with hydrophobic properties [79]. Methylmercury may also strongly bind to humic acids [88]. Triorganotin compounds, in particular tributyltin (TBT) and triphenyltin (TPT) have been introduced directly into the environment as pesticides and

216 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

antifouling agents in boat paint. The organotin compounds form uncharged hydroxo and chloro complexes (R3 SnOH0 , R3 SnCl0 ), which also exhibit hydrophobic properties [89]. At higher pH, triorganotins are present as hydroxides R3 SnOH0 . At low pH, they become protonated to the cation R3 Snþ with a pKaw of 6.25 for TBT and 5.2 for TPT. The cation forms strong complexes with
Cl
, Br
, and NO
3 , and more labile complexes with ClO4 . 2.2.5

Redox Reactions

A number of trace metals may occur in different redox states (Mn(II/IV), Fe(II/III), Cu(I/II), Cr(III/VI), Hg(0/II) etc.). The various oxidation states of an element differ in their coordination properties, and thus in their speciation. For example, Cr(VI) occurs as an anionic species (CrO2
4 ), whereas Cr(III) forms hydrolysed species and has limited solubility as an (hydr)oxide. In oxygenated water, the oxidised species of these elements predominate at equilibrium, but the reduced species may be present at low concentrations as reactive intermediates (e.g. Fe(II), Mn(II)). Low concentrations of Fe(II) have been observed in oxygenated seawater and fresh water under the influence of light [90–93]. Reduction or oxidation reactions may also occur at the biological interphases [94,95]. Binding to biological ligands is also strongly dependent on the redox states of a metal. 2.2.6

Solubility of Solid Phases and Binding to Colloids and Particles

Under relevant conditions (neutral pH, presence of carbonate) the concentrations of dissolved trace metals are limited by the solubility of their solid hydroxides or carbonates. A prominent example is the solubility of Fe(III), which is very low (around 10
10 mol dm
3 ) under relevant conditions of fresh water or seawater at neutral pH [96]. Iron(III) occurs primarily as solid or colloidal iron hydroxide at neutral pH. Even if the solubility limit of relevant solid phases is not exceeded, a large fraction of trace metals in natural waters often occurs bound to particles of various size ranges (nanometres to millimetres). An important process for binding of metals to particles is adsorption to mineral surfaces (often oxides or hydroxides) [29]. The colloidal size range is generally defined as the range of a few nanometres to less than 1 mm, respectively the range of molar mass larger than 1000
10 000 g mol
1 [97]. This size range comprises small mineral particles, as well as organic macromolecules such as large HA. Recent studies have indicated the significance of the colloidal fraction for the speciation of trace metals in natural waters [98–101]. Metals in this size range may be either organically complexed to macromolecules, adsorbed to mineral surfaces, or (co)-precipitated as solid phases.

B. I. ESCHER AND L. SIGG

2.2.7

217

Kinetics of Complexation Reactions

The kinetics of ligand-exchange reactions must be considered to evaluate exchange of metals between external ligands and biological ligands. The kinetics of complex formation of a metal with a ligand depend on the water exchange rates of metal ions [102,103]. For most metal ions, the water-exchange rates are fast, and complex formation reactions are generally fast (on timescales of less than seconds). Noteworthy exceptions are complex formation reactions of Ni(II), Cr(III), Fe(III), and Al(III), which are much slower than reactions of other cations and may occur on time scales of hours to days. If the metals bound in complexes exchange with biological ligands, the dissociation kinetics of these complexes, the ligand-exchange kinetics and the association kinetics with the biological ligands must be considered. Simple dissociation kinetics of complexes are related to their thermodynamic stability constants by the relationship: M þ L Ð ML

(5)

K ¼ kf =kd

(6)

where K is the thermodynamic equilibrium constant of reaction (5), kf is the rate constant for formation of the complex ML, and kd is the rate constant for dissociation of the complex ML. Dissociation kinetics of strong complexes are thus typically slow. The role of complexation kinetics for the biouptake processes is discussed in Chapters 3 and 10 in this volume and in ref. [14].

3 3.1

MEMBRANES AND SURROGATES OR MEMBRANE MODELS OCTANOL

The octanol–water partition coefficient, Kow , is the most widely used descriptor of hydrophobicity in quantitative structure–activity relationships (QSAR), which are used to describe sorption to organic matter, soil, and sediments [15], bioaccumulation [104], and toxicity [105–107]. Octanol is an amphiphilic
1 bulk solvent with a molar volume of 0:12 dm3 mol when saturated with water. In the octanol–water system, octanol contains 2:3 mol dm
3 of water (one molecule of water per four molecules of octanol) and water is saturated with 4:5  10
3 mol dm
3 octanol. Octanol is more suitable than any other solvent system (for) mimicking biological membranes and organic matter properties, because it contains an aliphatic alkyl chain for pure van der Waals interactions plus the alcohol group, which can act as a hydrogen donor and acceptor.

218 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

3.2

OTHER SOLVENT–WATER SYSTEMS

The octanol–water partition coefficient appears to correlate better with biological activity than partition coefficients in other solvent–water mixtures as, for example, hexane–water, because the amphiphilic nature of octanol can accommodate a greater variety of more or less hydrophobic molecules. In pharmaceutical science, the notion was taken up that no single solvent– water system is able to mimic the complex properties of a biological membrane. Leahy et al. proposed the so-called ‘critical quartet’ of organic solvent–water systems [108]. The original quartet was composed of an alkane, representing a solvent, which can merely interact via van der Waals forces, octanol as amphiprotic solvent, chloroform as a hydrogen donor, and dibutylether or propylene glycol dipelargonate as a hydrogen acceptor. The idea behind this choice was that uptake in biological membranes is a composite process influenced by the different types of interactions listed above. Chiou chose glyceryl trioleate (triolein) as model lipid because of its similarity to triglycerides which are abundant in organisms [109]. Triolein is also a bulk lipid and the good correlation with the bioconcentration factor is restricted to neutral compounds of moderate hydrophobicity. No attempts were made to measure partitioning of ionogenic compounds with the glyceryl trioleate–water partition system.

3.3

LIPOSOMES

All model systems mentioned in Sections 3.1 and 3.2 have the disadvantage of being bulk phases. The simplest model system that mimicks the anisotropic properties and ordered structure of biological membranes are liposomes. Liposomes are artificial lipid bilayer vesicles of known lipid composition and of controlled size [110,111]. They can be prepared either in the gel state or in the liquid crystalline state (as in biological membranes), depending on temperature and the phospholipid composition. Alternatively, planar black lipid bilayers have been used for partition studies. A black lipid film is usually formed across a small hole in a Teflon sheet. Due to its high solvent content (mostly decane), it is not the best system for partitioning studies, but it offers the advantage of allowing direct measurement of the permeability of the membrane [112]. Principal differences between bulk media–water and membrane–water partition coefficients are listed in Table 2. These differences are essentially based on the several orders of magnitude difference in surface-to-volume ratio. In the liposomal system, charges built up due to sorption of charged species can be electrically ‘neutralised’ by counter-ions from the electrolyte (diffuse double

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219

Table 2. Comparison of general properties of membrane model systems Bulk media

Membrane

Small equilibrium surface-to-volume ratios Bulk media have to maintain electrical neutrality

Very high surface-to-volume ratios because membranes are only 5–10 nm thick Sorbed charged species build up surface potential shielded by the electrolyte

layer). Hence, the properties of the membrane–water interphase, as opposed to those of the membrane core, become important. There are a variety of experimental methods available to determine liposome–water partition constants [113]. The best established one is equilibrium dialysis [114–116]. Alternatively, ultracentrifugation or ultrafiltration can be used to separate the liposomes from the aqueous phase. The pH-metric method is specifically designed to measure partition constants of ionogenic compounds [117]. Other methods initially developed for neutral compounds, e.g. lipid bilayers immobilised covalently [118] or noncovalently [119] to a solid support material have been evaluated recently for their applicability for HIOCs [120]. Liposomes can also be immobilised in agarose–dextran gel beads and packed in chromatography columns [121]. This method has already been applied to investigate the partitioning behaviour of lipophilic cations [122]. Methods specific for charged molecules include electrophoretic measurements of the x-potential [123] and conductance measurements [7]. 3.4

BIOLOGICAL MEMBRANES

While most model lipid membranes are composed of only one or a limited number of components, biological membranes contain a wide variety of phospholipids and other lipids. In addition, integral membrane proteins can make up the majority of components in a membrane. Biological membranes are extensively reviewed in Chapters 1 and 2 of this volume. At this point, it is only important to mention that for organic compounds and HIOCs, pure phospholipid bilayers appear to be a good surrogate for biological membranes, because organic compounds are mainly localised in the lipid domain of the membranes, although they can still interact and interfere with functional proteins. A comparison of membrane–water distribution ratios of various substituted phenols at pH 7, some of which were neutral, others partially or fully ionised, measured with phosphatidyl choline liposomes and chromatophores (photosynthetically active membranes that contain up to 85% proteins) revealed equal distribution ratios if the values were normalised to lipid content [116]. Hence, sorption to proteins was negligible in this case.

220 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

4

INTERACTIONS OF HIOCS WITH BIOLOGICAL INTERPHASES

4.1 4.1.1

PARTITIONING AND SORPTION MODELS Octanol–Water Partitioning

Kow is the most successful descriptor for hydrophobicity of neutral organic compounds [17,124]. Early attempts to extend the simple concept of Kow from neutral organic compounds to HIOCs have either neglected the partitioning of the charged species [125] or have determined apparent octanol–water distribution ratios Dow (pH,I) at a given pH and with a given ionic strength [126,127]. Dow (pH,I) is defined as the ratio of the sum of all organic species i in the octanol phase, cio , to the sum of all organic species in the aqueous phase, ciw . P  cio i P (7) Dow (pH, I) ¼ ciw i

The distribution ratio is strongly dependent on pH and the ionic strength, as is depicted in Figure 2 for the organic acid dinitro-o-cresol (DNOC) and for the organic base 3,4-dimethylaniline (DMA). Despite a large decrease of the Dow at pH values where the charged species predominates, partitioning of the charged species cannot fully be neglected. Depending on the ionic strength, the partitioning of the neutral species is three or more orders of magnitude higher than that of the ionic species. Westall and co-workers [128–130] proposed a detailed model of octanol–water partitioning of HIOCs whose essential equations are depicted in Figure 3a for acids and 3b for bases. For simplicity, all equations for electrolyte partitioning of monovalent and divalent salts [131] have been omitted. Nevertheless, in most cases, in particular in experiments with monovalent salts, pure electrolyte partitioning accounted for less than 10% of the overall partitioning. The lines in Figure 2, which show lipophilicity profiles in the octanol–water system, have been calculated with the full model and the equilibrium constants given in Jafvert et al., and Johnson and Westall [129,130]. Ion pair formation is the dominant process for controlling the partitioning of charged species. Typically, ion pair partitioning is about 10 000 times higher as compared to ion partitioning. Ion pair formation in octanol is also dependent upon the type of counter-ion present. The ion pair of pentachlorophenoxide (PCP
) with Liþ partitions about half a log-unit preferentially into octanol than þ the ion pair with Naþ or K , both of which form about equally strong ion pairs [129]. Moreover, the acidic drug proxicromil exhibited ion pair partitioning that was threefold higher with Liþ than with Naþ [132]. Experiments of ion pair 2þ formation of PCP
with divalent counter-ions Mg2þ and Ca suggest that a 2:1
2þ complex of PCP and M is formed, most likely in the form of MPCPþ with PCP
as a counter-ion [129]. For bases, so far only chloride has been used as

B. I. ESCHER AND L. SIGG

221

3

0.1 mol dm−3 K+

(a)

0.01 mol dm−3 K

2

logD

logDmw

logDow

1

+

0 0.1 mol dm−3 K+ −1 0.01 mol dm−3 K+

−2

0.001 mol dm−3 K+

−3 −4

0.0001 mol dm−3 K 2

4

6

8

+

10

12

pH

3 0.1 mol dm−3 Cl−

(b) logDmw

2

logD

1

0

−1 logDow

−2

2

4

6

8

10

pH

Figure 2. Lipophilicity profiles of (a) dinitro-o-cresol and (b) 3,4-dimethylaniline. Dow values were calculated with the data and model described by Jafvert et al. [129], and Johnson and Westall [130]. Dmw values were calculated with the data and model described by Escher et al. [140]

counter-ion [130]. Again, a difference between the partitioning of the neutral and charged species greater than two orders of magnitude was observed with the ion pair as the dominant complex for all charged species. Only the unsubstituted aniline does not appear to form an ion pair with chloride [130].

222 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES (a)

Ao− /Mo+

HAo KHAow HAw

(b)

K

Ka

+ Hw

KAMow

+

− Aw

BHo+ /Xo−

Bo KBow Bw

AMo

+ A−Mow

K

− BH+X ow

+ Hw+

Kb

BHw+

+

+

Mw

BHXo KBHXow + Xw−

Figure 3. Model for octanol–water partitioning of organic acids (a) and organic bases (b). The figure has been prepared according to the model described by Jafvert et al. [129]; the electrolyte partitioning is omitted for brevity Zwitterion

logDow

10 000

Cation

Anion

1000

Zwitterion

100 0

2

4

6 pH

8

10

12

Figure 4. Scheme of lipophilicity profile of zwitterionic compounds. The line drawn represents the case where the neutral tautomer predominates or the zwitterion is rather hydrophobic, resulting in a bell-shaped profile. The dashed line represents the case where the zwitterion predominates and intramolecular interactions are not possible, resulting in a U-shaped profile. Adapted with permission from [133]: Pagliara, A. et al. (1997). ‘Lipophilicity profiles of ampholytes’, Chem. Rev., 97, 3385–3400; copyright (1997) American Chemical Society

Particularly interesting examples are also the lipophilicity profiles of ampholytes. Depending on the ratio between the neutral tautomer and the zwitterionic tautomer, the log Dow versus pH profile may be bell-shaped or U-shaped [133] (Figure 4). For zwitterions, the shape of the lipophilicity profile depends upon the structure and conformation of the molecule. If the charged groups are situated in proximity and can interact with each other, the zwitterion might be more hydrophobic than the anionic and the cationic species, resulting in a bell-shaped lipophilicity profile. If, however, intramolecular interactions are not possible for steric reasons, the lipophilicity profile is U-shaped [133].

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4.1.2 Membrane–Water Partitioning: General Derivation of Membrane–Water Partition Coefficients of a Charged or Neutral Compound or Species The chemical potential, miw , of a compound i in the aqueous phase, indicated by subscript w, is defined according to: miw ¼ m0iw þ RT ln aiw

(8)

where m0iw is the standard chemical potential and aiw is the activity of compound i in the aqueous phase. If charged lipids are incorporated in the membrane phase (indicated by subscript m) or if charged species are sorbed to the membrane surface, an ~ im will build up according to: electrochemical potential m ~im ¼ m0im þ RT ln aim þ zi F C m

(9)

where zi F C corresponds with the electrostatic contribution to the electrochemical potential in the charged membrane bilayer. At equilibrium, the electrochemical potentials in the two phases are equal (m~im ¼ miw ), and equations (8) and (9) can be combined to give: Dmw G0i ¼ m0im
m0iw ¼
RT ln


 aim
zi F C aiw

(10)

where the standard free-energy change for the phase-transfer reaction, Dmw G0i , is related to the dimensionless partition coefficient, K0i , by a Boltzmann-type expression: Ki0 ¼

aim
zRTi F C e aiw

(11)

The activity ai of a given compound or species i is a function of its activity coefficient gi and the mole fraction xi : ai ¼ gi xi

(12)

Activity coefficients in the aqueous phase, giw , of neutral molecules are set equal to one because of the zero charge, and under the assumption that the activity coefficient of the infinitely diluted solution equals the actual activity coefficient. The activity coefficients of the charged species can be approximated with the Davies equation: log giw


pffiffiffi  I pffiffiffi
BI ¼ zi A 1þ I

(13)

224 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

where zi is the charge, I is the ionic strength (mol dm
3 ), A ¼ 0:509, and B ¼ 0:3 at 298 K. The activity coefficients in the membrane phase are set to one. This assumption is justified at low concentrations of ions in the membrane, especially when considering their location at the interface of the hydrophobic and hydrophilic domains [134], but might be inappropriate at concentrations near saturation. The dimensionless partition coefficient Ki0 is based on mole fractions xi or number of moles ni . In the literature, partition coefficients are more often defined as concentration ratios. At low solute concentration and when the adsorbed amounts become very small, the activity coefficients approach zero and the surface potential also becomes insignificant (zi F c ! 0): Ki0 

xim nim ¼ xiw niw

(14)

Under these conditions, Ki0 can be converted to the concentration-based dimen sionless partition coefficient, Kimw , with the following equation:  ¼ Kimw

cim ¼ fKi0 ciw

(15)

where f is the phase ratio, i.e. the ratio of the molar volume of the aqueous phase, Vw , and the molar volume of the membrane lipids, Vm : f¼

Vm Vw

(16)

Often, the concentration of compound or species i in the membrane is given in molality (mol kg
1 ), which yields the membrane–water partition coefficient, Kimw (in units of dm3w kg
1 m ): Kimw ¼

mim ¼ frm Ki0 ciw

(17)

where rm is the mass concentration or density of the membrane lipids. The  and Kimw are approximately equal because the density of phosvalues of Kimw pholipids, rPL (1:015 kgPL dm
3 PL [135]) is close to the density of water. The description of the sorption of charged molecules at a charged interface includes an electrostatic term, which is dependent upon the interfacial potential difference, Dc (V). This term is in turn related to the surface charge density, s (C m
2 ), through an electric double layer model. The surface charge density is calculated from the concentrations of charged molecules at the interface under the assumption that the membrane itself has a net zero charge, as is the case, for example, for membranes constructed from the zwitterionic lecithin. Moreover,

B. I. ESCHER AND L. SIGG

225

one can assume that the sorption of i does not lead to an expansion of the membrane surface. P zi mim (18) s¼F SPL NA where NA is the Avogadro constant, SPL is the surface area occupied by a single
1 membrane lipid molecule (SPL  0:7 nm2 molecule for phospholipids [136]). The Gouy–Chapman diffuse layer model has been shown to describe adequately the electrostatic potential produced by charges at the surface of the membrane [137]. For a symmetrical background electrolyte, s and c are related by:
 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fc (19) s ¼ 8er e0 RTI sin h 2RT where I refers to the ionic strength in units of mol cm
3 , er is the relative permittivity or dielectric constant, and e0 is the permittivity of the free space. Alternatively, in the literature, the constant capacitance model and the Stern model were used to describe the dependence of the surface charge density on the surface potential. In the constant capacitance model, the surface charge is defined as: s ¼ Cc

(20)

where C is the specific capacitance, which varies typically between 0.2 and 1 Fm
2 in biological membranes [138]. The Stern model is effectively a serial combination of the constant capacitance and Gouy–Chapman model. All three models yielded similar quality of fits to the experimental liposome–water partitioning data [120]. There are several underlying assumptions for using the combination of the Boltzmann equation and the Gouy–Chapman theory of diffuse double layer or other electrostatic models used to describe the partitioning of charged species into membranes. First, the charged species must not be uniformly distributed throughout the membrane, but rather be sorbed close to the surface of the membrane. This is a realistic assumption as will be demonstrated in detail in Section 4.7. This suggests that in the case of membranes we consider an adsorption mechanism rather than absorption or partitioning. Second, it has to be assumed that the charges are distributed uniformly across the surface, and that neither the standard chemical potential nor the activity coefficient varies with distance from the membrane. This assumption is more difficult to justify even if lateral diffusion of bilayer components is quite fast. The good agreement of experimental data with model predictions, however, demonstrates that this assumption is reasonable.

226 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

Several investigators [7,123] suggested the use of a Langmuir-type saturation model in addition to the electrostatic model to account for saturation effects. The Langmuir model implies that there are a finite number of localised sorption sites [15]: mim ¼

 mmax mim im KL ciw or KL ciw ¼ max  1 þ KL ciw mim
mim

(21)

where mmax im is the maximum mass concentration of molecules adsorbed and KL is the Langmuir sorption constant, which is equivalent to Kimw . If the adsorption sites are not localised in space (as is the case for sorption to a fluid lipid membrane), then the Langmuir equation could be transformed to the Volmer isotherm [7], mim

KV ciw ¼

mim max ðmim
mim Þ max mim
mim

(22)

where KV is the Volmer association coefficient. If mim  mmax im then the Volmer equation reduces to the Langmuir equation. The combined Langmuir–Stern equation was quite insensitive to changes in the number of molecules maximally adsorbed to the surface [7]. McLaughlin and Harary found saturation at one molecule of negatively charged 2,6-toluidinyl naphthalenesulfonate (TNS) per one to three phosphatidyl choline (PC) molecules [7]. A study on the sorption of pentachlorophenoxide to PC vesicles based on electrophoretic mobility measurements found sorption sites in the size of 4.3 PC molecules [123]. A later study considered both neutral and charged PCP and found sorption sites in the size of one and seven PC molecules, respectively [139]. Such high membrane coverage would lead, however, to a significant membrane expansion (PCP, 50 % saturated, 25 % membrane expansion, PCP
, 50 % saturated, 3.6% membrane expansion [140]). Thus, later studies proposed that Langmuir-type sorption cannot be reasonably obtained without membrane expansion, and that experimentally data should be fitted with an electrostatic model alone [120,140]. Neutral compounds show saturation only at membrane burdens, which begin to affect membrane structures. Very hydrophobic and well-shielded anions and cations such as tetraphenylborate or tetraphenylphosphonium already show saturation at a binding density of 1 per 100 lipids [6]. Anyway, these disputes over number of sorption sites are purely academic. Such high concentrations are not likely to be encountered in the environment and are likely to be lethal for all biological organisms. 4.2

THERMODYNAMICS OF MEMBRANE–WATER PARTITIONING

The partition coefficient Kmw is directly related to the free energy of transfer between the aqueous and the membrane phase. The enthalpy and entropy contri-

B. I. ESCHER AND L. SIGG

227

butions to the partitioning process can be deduced from a van’t Hoff plot of lnKmw versus the inverse temperature [1]. Although the thermodynamic behaviour depends not only on the nature of the solvent but also of the solute, some general findings can be summarised. The Kow and Kmw usually increase with increasing temperature [141,142]. The thermodynamics of Kow and Kmw are similar in those cases where nonpolar interactions are dominant [143] but the partitioning process is more complex for Kmw than for Kow , because it is influenced by structural changes in the lipid bilayer. Sulfonamides had positive enthalpies, DH, for Kmw and varying sign for Kow , whereas entropies, DS, were positive in both systems [144]. For a series of linear aliphatic alcohols, the enthalpy is positive for shorter alcohols (chain length ¼ 6) but becomes large and more negative for the longer alcohols (chain length ¼ 7) [145]. In addition, if cholesterol is incorporated in the membrane, making the membrane more rigid, then the enthalpy becomes large and positive but decreases linearly with increasing chain length [145]. The strong effect of the lipid type indicates that lipid–lipid interactions play a significant role for the thermodynamics in addition to lipid–solute interactions. The large difference in the hydrophobic binding of the cationic tetraphenylphosphonium and anionic tetraphenylborate is caused by the large changes in the enthalpy of the phase transfer. While the entropic contribution is similar for both ions, the DH is slightly positive ( þ 14:6 kJ mol
1 ) for tetraphenylphosphonium (TPPþ ), whereas it is negative (up to
15:1 kJ mol
1 ) for tetraphenylborate (TPB
) [6]. It is also interesting to note that variations in the structure of TPB
by the introduction of F, Cl, or CF3 on the phenyl rings or replacement of a phenyl group by a cyano-group do not have a large influence on the thermodynamics of sorption, but strongly influence the movement across the membrane. The central energy barrier in the membrane is the lower the better the charge is delocalised over the entire molecule [146]. The thermodynamics of partitioning strongly depend on the physical state of the membrane. Usually more energy is required to insert organic chemicals in bilayers of the gel state as compared with the fluid state. DH and DS of substituted phenols were negative above, and positive below, the transition temperature from gel to liquid crystalline state [143]. For neutral phenols and chlorobenzenes, as well as for sulfonamides at their isoelectric pH, liposome– water partitioning is entropy dominated below, and enthalpy dominated above, the transition temperature [143,144,147,148], but under both conditions large entropy changes were observed, similar to what was observed in fish–water partitioning of chlorobenzenes [149]. 4.3

pH-DEPENDENCE OF MEMBRANE–WATER PARTITIONING

The membrane–water distribution ratio Dmw is defined by the ratio between the sum of the molalities of all species of the considered compound in the

228 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

membrane phase and the sum of concentrations of all species in the aqueous phase. P mim X i Dmw (pH) ¼ P  ¼ aiw K imw (23) ciw i i

Dmw can be derived from the partition coefficients of the single species (equation 23) if the fractions of the species, aiw , under given conditions are known (Henderson–Hasselbalch equation). The model for the membrane–water partitioning is depicted in Figure 5a. The pH-profiles of the liposome–water distribution ratios of a representative acid, DNOC (Figure 2a) and a base, DMA (Figure 2b) reveal a much smaller dependence of Dmw on the pH than it is the case for octanol–water partitioning. The Kow of the neutral species and the apparent Dow of the charged species at an ionic strength of 0:01
0:1 mol dm
3 differ by more than three orders of magnitude, while the difference is only one order of magnitude or smaller for the membrane–water system. In addition, there is very little ionic strength dependence on the partitioning of the charged species, due to the lack of ion pair formation in the membrane. Conversely, in octanol, where ion pairing or copartitioning of the counter-ion is a prerequisite for partitioning of a charged species, the concentration of the counter-ion strongly influences the apparent distribution ratio of the charged species. This general trend is important with (a) HAm

HAm

Am−

Am−

HAm

Am−HAm Am−

Am− Am−

K A−

KHA

mw

HAw

(b)

mw

Ka

− w

A

+ H+w

(c)

HBXm

AMm

DAM A−w

DHBX mw

+ Mw+

BH

+ w

mw

+ X−w

Figure 5. (a) Model for membrane–water partitioning of organic acids (equations from [140]). (b) Ion pair formation of the conjugate base of organic acids with alkali ions or metal ions, and (c) of the conjugate acid of organic bases with anionic counterions. Inclusion of ion pair formation in the partitioning model is only necessary under the specific conditions described in the text

B. I. ESCHER AND L. SIGG

229

respect to bioaccumulation and toxicity of ionogenic compounds, which will be discussed in Section 4.8. In principle, hydrophobic anions bind more strongly to membranes than structurally similar cations. Tetraphenylphosphonium (TPPþ ) and tetraphenylborate (TPB
) have approximately the same molecular volume and geometry, but TPB
binds 5000 times more strongly to lipid bilayers than TPPþ [6]. The difference is caused by the internal dipole moment of a lipid bilayer, which is caused primarily by the ester groups in the phospholipids that link the fatty acids to the glycerol backbone [150]. The resulting dipole is oriented with its positive pole inside the lipid layer, and this favours both absorption and translocation of negatively charged ions [6]. However, this general finding for hydrophobic anions and cations does not necessarily apply for ionogenic pollutants. Many environmentally relevant HIOCs are amphiphilic or form hydrophobic ions that are amphiphilic. Such compounds intercalate into the membrane with their hydrophobic part in the bilayer core and the hydrophilic or ionic domain interacting with the polar and charged head groups of the membrane-building lipids (see Section 3.4). Therefore the better the charge of a compound is accommodated in the polar head groups, the smaller will be the difference between the log Kmw of the neutral and the corresponding charged species, Dmw: Dmw ¼ log Kamw
log Kbmw

(24)

where a and b are the acid and conjugate base. Values of Dmw are typically larger for the anion-forming acids than for the cation-forming bases (Table 3) [4,117,120,151,152]. The conjugate base of the phenols can better delocalise the charge over the entire ring system, in particular, when there are electron-withdrawing substituents like nitro-groups. Hence, Dmw is smaller for the phenols than for the carboxy acids, whose charge cannot be delocalised and lacks any direct conjugation with the aromatic ring system. Furthermore, the Dmw values increase in absolute magnitude from primary to tertiary amines (Table 3). This finding can be rationalised in terms of a more pronounced amphiphilicity and better direct interaction of the charged amino group of primary amines with, for example, phosphate groups of the phospholipid molecules of lipid bilayers. Conversely, higher substituted amines have a more shielded charged group that may intercalate deeper into the membrane, but that may have overall less favourable interactions with the membrane. In addition, the steric bulk of several substituents on an amino group appears to disturb the structure of the membrane more than a single substituent. Dmw for a series of (p-methylbenzyl)alkylamines increase with increasing alkyl chain length [153]. This trend was not observed for the corresponding octanol–water partition data, which is additional evidence that the increase in Dmw is caused by an unfavourable steric constraint. The positively charged

230 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES Table 3. Examples of membrane–water partitioning of HIOCs and the difference in partitioning between neutral and charged species Compound

Lipid

Vesicle type

pKaw log Kimw (neutral species)

Phenols 2,4,6-Trichlorophenol 2,3,4,6-Tetrachlorophenol Pentachlorophenol Pentachlorophenol 2,4-Dinitrophenol 2-Methyl-4,6-dinitrophenol 2-s-Butyl-4,6-dinitrophenol

DOPC DOPC DOPC PC DOPC DOPC DOPC

Sonicated SUVa Sonicated SUV Sonicated SUV MLV Sonicated SUV Sonicated SUV Sonicated SUV

6.15 5.4 4.75 4.75 3.94 4.31 4.62

3.99 4.46 5.10

Carboxy acids 5-Phenylvaleric acid Salicylic acid Diclofenac Diclofenac Ibuprofen

DMPC PC Soy-PC DOPC DOPC

Sonicated SUV Extruded LUV Sonicated SUV LUV LUV

Other acids Warfarin

PC

Dmw Ref.

2.64 2.76 3.96

1.49 1.00 0.74 0.70 0.74 0.42 0.61

[120] [120] [120] [123] [120] [120] [120]

4.88 2.98 3.99 3.99 4.45

2.94 2.50 4.50 4.50 3.80

1.44 1.46 1.50 1.90 1.99

[4] [4] [152] [152] [117]

Extruded LUVb

5.00

3.39

1.99 [4]

Amino acids FCCP CCCP

Egg-yolk PC Sonicated SUV Egg-yolk PC Sonicated SUV

6.2 5.95

4.12 3.79

0.00 [154] 0.00 [155]

Anilines 3,4-Dimethylaniline 2,4,6-Trimethylaniline

Egg-yolk PC Extruded LUV Egg-yolk PC Extruded LUV

5.23 4.38

2.11 2.38


0.12 [120]
0.26 [120]

Aliphatic primary amines 4-Phenylbutylamine Amlodipine

DMPC DMPC

Sonicated SUV Sonicated SUV

10.54 9.02

2.41 3.75


0.29 [151] 0.00 [151]

Aliphatic secondary amines Propranolol (p-Methylbenzyl)methylamine (p-Methylbenzyl)propylamine (p-Methylbenzyl)pentylamine (p-Methylbenzyl)heptylamine

PC PC PC PC PC

Extruded LUV Extruded LUV Extruded LUV Extruded LUV Extruded LUV

9.24 9.93 9.98 10.08 10.02

3.24 3.09 3.07 3.50 4.40


0.48 0.55 0.96 1.66 1.69

Aliphatic tertiary amines Lidocaine Tetracaine

PC DOPC

Extruded LUV LUV

7.86 8.49

2.06 3.23


1.15 [4]
1.12 [117]

a

[4] [153] [153] [153] [153]

SUV ¼ small unilamellar liposomes, b LUV ¼ large unilamellar liposomes.

amino groups interact with the phosphate structures of the lipids, and both substituents have to intercalate between the fatty acid chains. This becomes increasingly more difficult the longer or bulkier the two substituents. Dmw of stronger uncouplers, e.g. carbonylcyanide-p-trifluoromethoxyphenylhydrazone (FCCP) [154], carbonylcyanide-m-chlorophenylhydrazone (CCCP)

B. I. ESCHER AND L. SIGG

231

[155], and 5-chloro-3-t-butyl-20 -chloro-40 -nitrosalicylanilide (S-13) [156], are not significant, i.e. both neutral and charged species partition equally well into the lipid bilayer because the charge is well delocalised over the entire molecule. 4.4

ION PAIR FORMATION AT THE MEMBRANE INTERPHASE

Ion pairs are outer-sphere association complexes, which have to be clearly distinguished from the organometallic complexes discussed in Section 6. Ion pair formation appears to be much less important in biological membranes as compared with octanol, because the charge of the ions at the membrane interphase can be balanced by counter charge in the electrolyte in the adjacent aqueous phase. The reactions involved in ion pair formation are depicted in Figures 5b for acids and 5c for bases, and the equilibrium constant Kix0 is defined as follows: Kix0 ¼

aixm aiw axw

(25)

The subscripts i and x label the ionic constituents of the ion pair and aixm refers to the activity of the ion pair in the membrane phase. At a constant counter-ion activity, axw , and for the ideal case that giw and gix ¼ 1, equation (25) can be converted to the commonly defined distribution ratio Dixmw : Dixmw ¼

mixm ¼ Kix0 axw fr ciw

(26)

Note that no ion pair is assumed in the aqueous phase. The overall distribution ratio of the charged species is then a combination of the partition coefficient of the charged species and the distribution ratio of the ion pair. Dmw values of the drugs amlodipine and 4-phenylbutylamine were not significantly different in de-ionised water and a 0:02 mol dm
3 phosphate/citrate buffer (pH around 7) [151]. The dependence of the overall Dmw of phenols at high pH on the Kþ concentration was rather small [116]. Earlier models of membrane–water partitioning of substituted phenols directly applied the model set-up for octanol–water partitioning [129] but ion pair formation appeared to be not very prominent [116]. A similar set of experimental data was later successfully evaluated with the model described in Section 4.1.2, accounting for the ionic strength effect fully through its effect on the activity coefficients and the membrane electrostatics [120,140]. Austin et al. [132] measured the ionic strength dependence of the liposome– water distribution of several acidic and basic drugs and modelled the data with a combination of electrostatic and ion pair models. They concluded that the increased apparent Dmw values at higher ionic strength were due primarily to the reduction in surface potential and not to ion pairing. Ion pairing was also excluded because the apparent Dmw varied at fixed ionic strength with the

232 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

concentration of drug. The ion pair formation accounted for no more than 5 % of the overall partitioning of the anionic drug proxicromil [132]. In addition, z-potential measurements on PCP
showed no significant effect of ionic strength on adsorption characteristics [123]. This finding suggests that no ion pair is formed, but also indicates that screening of the membrane surface by ions has little effect on the energetics of adsorption, i.e. PCP
is buried at some depth below the membrane surface. The reason for the insignificance of ion pair formation at the membrane interphase lies in the relative permittivity (dielectric constant) er at the sorption sites of HIOCs in the membrane (see also Section 4.7). Ion pair formation is generally high in solvents of low er (e.g. octanol er ¼ 10), and decreases rapidly until it becomes insignificant when er > 40, e.g. in water [157]. In membranes, er varies from five at the hydrophobic core to about 70 at the membrane surface. Consequently, the insignificance of ion pair formation is a further indication that HIOCs are not deeply intercalated into the membrane but sorb to the region of the polar head groups. Ion pair formation appears to become relevant only for stronger complexing agents. The partitioning of the protonated form of DMA increases significantly in the presence of formic acid/formate buffer at pH 3, and is most likely due to complex formation between the anilinium ion and formate [120]. In addition, hydrophilic substances can be taken up into the membrane when complexes with hydrophobic counter-ions are formed. This property has been exploited for increasing the uptake of peptidic drugs by, for example, salicylate [157]. 4.5 SPECIATION IN THE MEMBRANE: INTERFACIAL ACIDITY CONSTANT The interfacial acidity constant or apparent acidity constant in the membrane phase K am refers to the relative ratio of acidic and corresponding basic species in the membrane at a given (aqueous) pH-value: K am ¼

mAm aHw mHAm

(27)

K am is therefore directly related to the aqueous acidity constant: K am ¼

K Amw Ka K HAmw w

(28)

The pK am is consequently equal to the pK aw shifted by Dmw and can be directly deduced from the lipophilicity profile (Figure 6). Since Dmw is generally smaller in the membrane–water system as compared to the octanol–water

B. I. ESCHER AND L. SIGG

233

log Dmw

log Kamw pKa w

log Kbmw pKa

m

Figure 6.

pH

Derivation of the pK am from a lipophilicity profile, a refers to acid, b to a base

system (see Section 4.3), the pK am of an acid is shifted by about one log unit to higher values and that of a base is shifted by about one unit to lower values. The better the charge of a molecule can be delocalised and accommodated in the lipid bilayer, the smaller is the pKa shift. Molecules like CCCP or FCCP do not have a pKa shift at all [154,155]. The pKa shift can be directly measured by the solvatochromic shift of the ultraviolet absorption spectra. For PCP, the pK am is 5.97 in phosphatidyl choline membranes, and increases up to 6.78 in the negatively charged phosphatidyl glycerol membranes [123]. The addition of cholesterol decreases the pK am again slightly in both types of membranes. There exists an inverse relationship between the pKa and the dielectric constant of the medium [123]. This relationship gives an indication that the dielectric constant at the sorption site in the membrane is smaller than in the aqueous phase. 4.6 SORPTION OF HIOCS TO CHARGED MEMBRANES VESICLES AND BIOLOGICAL MEMBRANES Most studies investigating the role of speciation in membrane–water partitioning have been performed with liposomes made up of phosphatidyl choline with varying types and lengths of acyl chains, because PC is a zwitterion over most of the typical pH range of the partitioning experiments. Biological membranes, however, contain a variety of charged or ionisable lipids, e.g. phosphatidyl ethanolamine, phosphatidyl inositol, phosphatidyl serine, phosphatidyl glycerol, or phosphatidic acid (see Table 4 for a list of abbreviations and pKa values). Charged head groups have no influence on the partition behaviour of the neutral species but strongly influence sorption of the charged species. Miyoshi et al. measured the apparent Dmw values at pH 7 of 35 substituted phenols in PC liposomes with 10% cholesterol, 20% negatively charged cardiolipin, and 20% positively charged stearylamine [114]. A selection of their results is listed in Table 5. Cholesterol decreases the Dmw , because it makes the membrane more rigid. The addition of positively charged stearylamine had

234 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES Table 4. Major building blocks of lipid bilayers in biological membranes and their speciation and acidity constants Lipid

Charge at pH 7 pKa (PO4 )

Phosphatidyl choline

Zwitterionic

Phosphatidyl inositol

Negative

Phosphatidylethanolamine Zwitterionic

41 2.5 3.2 2.5–3.1 1.7

Phosphatidylglycerol Phosphatidyl serine

Negative Negative

2.9–3.5 <3.6

Phosphatidic acid Cardiolipin Oleic acid

Negative Negative Mixed

3.0–4.0 2.5

pKa (group)

Ref.

[248] [3] [3] [248] 9.5–11.5 (
NHþ 3 ) [248] 9.7 [160] [248] 9.5–11.5 (
NHþ 3 ) [248] 3.2–6.0 (
COOH) 8.0–9.0 (PO4 ) [248] [248] 7.5–7.8 [160]

Table 5. Log Dmw values determined at pH 6 in liposomes composed of different ratios of PC with other lipids (data from ref. [114]) Compound

PC

2,4-Dichlorophenol 2,4,6-Trichlorophenol 2,4-Dinitrophenol 2-Methyl-4,6-dinitrophenol 2-s-Butyl-4,6-dinitrophenol

3.54 3.61 2.7 2.66 3.5

a

Cholesterol-PC Cardiolipin-PC Stearylamine-PC (1:10, m:ma) (1:5, m:m) (1:5, m:m) 3.22 3.5 2.63 2.6 2.98

3.45 3.7 2.6 2.59 3.34

3.21 3.67 2.24 2.67 3.15

Mass ratios of phospholipids used to prepare liposomes.

no systematic influence on Dmw , but the Dmw was smaller in the negatively charged liposome for those compounds that were partly dissociated at pH 6 [114]. The interaction of the tertiary amine tetracaine is much stronger with negatively charged lipid bilayers than with neutral ones [158]. Extensive studies have been performed with the secondary amine propranolol (pK aw ¼ 9:24) [3,113,159,160]. In PC liposomes, the Dmw increases with increasing pH because the neutral form sorbs better to the zwitterionic membrane than the positively charged species (Figure 7). If the membrane is negatively charged over the entire pH range, Kmw of the neutral species is similar to the value in the PC liposomes, but the Kmw of the positively charged species with the negatively charged membrane is twice as high as compared with the Kmw of the neutral species. If the liposomes contain lipids that deprotonate in the pH range where propranolol is positively charged, a peak in the lipophilicity profile can be observed at pH values where the lipids carry negative and propranolol carries positive charge.

B. I. ESCHER AND L. SIGG

235

4000

4000

PC/OA 76/24 mol/mol

PC/PE 2/1 mol/mol

2000

2000 PC

PC

1000 0

3

4

5

6

7

8

9

10 11 3

4

5

6

7

4000

9

10 11

2000

3

4

5

6

7 pH

8

9

PC

10 11 2

3

4

5

6 7 pH

8

0

4

PI/PC (3/7 mol/mol)

PC

1000

1000

3

log Dmw

Dmw

8 PI

PC/PE/OA molar ratio 55/22/23

3000

0

3000 Dmw

Dmw

3000

9 10 11

Figure 7. Lipophilicity profile of propranolol in liposomes composed of zwitterionic and charged lipids (phosphatidyl ethanolamine (PE), oleic acid (OA), phosphatidyl inositol (PI)). Conditions of measurements are described in [113]. The dotted line indicates the partitioning profile of propranolol in the egg PC liposome system. The bars show the pH-dependent charge profile of propranolol (hatched bars: positively charged propranolol) and the lipids in the membrane (black bars: negatively charged lipids). Reprinted from [113]: Kra¨mer, S. (2001). ‘Liposome/water partitioning’, In Pharmacokinetic Optimization in Drug Research. eds. Testa, B. et al. Reproduced by permission of Verlag Helvetica Chimica Acta, Zu¨rich

It is interesting to note that the pH profiles for Dmw with membranes containing charged lipids do not show an inflection at the exact pKaw but the inflection point is somewhat higher than the pKaw . This is due to the build-up of an electrochemical double layer, i.e. negative charges on the membrane surface lead to accumulation of positively charged ions and therefore a decreased local pH in the vicinity of the membrane. It is possible to correct for this effect by calculating the local pH from the surface potential of the membrane or from the measured electrokinetic potential of the liposome [3]. The studies on phospholipid bilayers with defined amounts of charged component are helpful to explain the partition characteristics in biological membranes. Liposome–water partition data of propranolol in lipids from kidney epithelial cells (a common model system in pharmaceutical sciences for the uptake into the gastrointestinal tract) have been successfully described with partition models developed for pure bilayers or defined mixtures [159]. Since lipophilic cations and anions can be used as probes for the membrane potential, their interaction with microbial and mitochondrial membranes has been studied

236 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

extensively [161]. Only inactivated nonintact microbial cells (neither Grampositive nor negative, nor yeast) are able to bind the negatively charged phenyldicarbaundecaborane and other lipophilic anions [162]. Reasons for the observed discrepancy may lie in the cell wall, the outer membrane of the Gram-negatives, and energy-dependent active transport processes. 4.7

SITE OF INTERACTION OF HIOCS WITH MEMBRANES

The partition coefficient of a given compound – both in its neutral and its charged form – is greater for the uptake into fluid bilayers than into bilayers in the gel state. The local anesthetic tetracaine, which is an aliphatic tertiary amine present predominantly in its cationic form at pH 7, was found to be deeper incorporated into the fluid membrane than into the gel-phase membrane [163]. In addition, the presence of xenobiotics reduces the phase transition temperature from the gel to the fluid state [148,164]. Such an effect may cause the coexistence of laterally segregated fluid and gel domains with an uneven distribution of solute, i.e. a higher concentration in the fluid domains, as was shown for pentachlorophenoxide [165]. In addition it takes a higher concentration of solute in the fluid phase before sorption isotherms become saturated [163]. High lateral membrane heterogeneity induced by partitioning of xenobiotics with locally varying concentrations was also found experimentally for local anesthetics and insecticides like lindane, and was theoretically explained by computer simulation studies [166]. The location of a compound within a lipid bilayer can be studied using X-ray diffraction [167], neutron diffraction [164], fluorescence quenching techniques [163], differential scanning microcalorimetry [164], or NMR techniques [168,169]. There is not a unique binding site for all sorts of xenobiotics, but the compounds are intercalated in such a way into the membrane that they interact most favourably with the membrane components and with least perturbation. Some compounds, such as hydrophobic and neutral molecules, are actually dissolved in the membrane interior, whereas others exhibit more specific interactions in the polar region of the membrane. In general, interaction of the xenobiotics with the head groups leads to a stronger perturbation of the bilayer than intercalation in the membrane core [170]. Alkanes and short alcohols actually partition into the interior of the membrane [171]. The well-shielded tetraphenylphosphonium (TPPþ ) and tetraphenylborate (TPB
) ions are also deeply intercalated into the lipid bilayer [6,169]. The binding site of TPB
is located somewhere below the head-group region in the vicinity of the ester groups, while the cation TPPþ binds a few tenths of a nanometre further outwards [6]. One would expect that deprotonated substituted phenols interact with the positively charged choline group [172]. However, 31 P-NMR studies on the

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interaction of cholesterol with PC give clear evidence that the interaction of the hydroxy group of cholesterol with the carboxy group of the fatty acid is more favourable than that with the phosphate group [173]. Based on this finding, together with consideration of steric constraint by di-ortho substituted phenols, Miyoshi et al. concluded that phenols also interact with the carboxy groups of the fatty acids [114]. In contrast, the positively charged tetracaine appears to interact with the phosphate groups of negatively charged phospholipids in addition to the ester carbonyl groups [158]. The neutral species of a HIOC is usually deeper intercalated into the membrane than its corresponding charged species, which is also reflected in a higher Kmw value [174] Herbette et al. compared the sorption site of the structurally similar tertiary amines propranolol and timolol [164]. Propranolol has a naphthalene substituent on the aliphatic chain, which is deeply incorporated into the hydrophobic core of the membrane. In contrast, timolol carries a partially charged morphine ring at the same place. This substituent, due to its polarity and partial charge, does not interact favourably with the membrane interior. Consequently, the Dmw at pH 7.5 is 20 times higher for propranolol than for timolol, and timolol has less influence on the phase transition. If zwitterionic xenobiotics are introduced into the membrane, their magnitude of partitioning is strongly dependent on the position of the ionic groups, as was shown by self-consistent field modelling for a series of hypothetical model compounds composed of a phenyl ring substituted with propyl groups and one positively charged amino group and one corresponding negatively charged group [175] (see also Chapter 2 in this volume). The positive amino group is located at the outer side of the hydrophobic core, close to the phosphate groups. The partition coefficient is highest for the isomers with the negatively charged groups in the vicinity of the amino group and then decreases stepwise upon substitution in ortho-, meta-, and para-positions. Similar modelling exercises on DMPC bilayers with tetrahydroxy naphthalenes revealed how much the position of substituents can influence the orientation in the membrane. The 2,3,6,7-tetrahydroxy naphthalene spans the membrane, with the hydroxy group almost in contact with the carboxy group of the fatty acid. The opposite tendency can be expected for the evenly distributed 1,3,5,7-tetrahydroxy naphthalene, where the orientation is almost parallel to the plane of the membrane. Another approach to characterise the site of absorption in the lipid bilayer is to analyse the dielectric properties of this site. The permittivity e in the hydrophobic core of the membrane is very small (e of approximately 2 to 3), and rises outwards until it reaches the value in the aqueous phase (e ¼ 78) [6]. e is about 30 at the location of the carboxy groups of the fatty acid chain [150]. Other measurements averaged to e of 30 to 33 at the interface between polar head groups and the hydrocarbon core [176]. The e of the absorption site of

238 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

pentachlorophenoxide, the deprotonated species of PCP, is approximately 8.4 for PC membranes and 18 for the negatively charged PG membranes [177]. This means that pentachlorophenoxide is more deeply intercalated into the membrane than other ionogenic compounds, probably due to the very bulky and hydrophobic chloro substituents. The intercalation of charged molecules further causes an orientational change of the dipole of the head groups, which depends on the sign and the size of the surface charge. The choline group of PC and the phosphate group constitute a membrane dipole, which is approximately parallel to the membrane surface in undisturbed bilayers. Negatively charged amphiphiles move the choline group of PC bilayers towards the membrane interior, and positively charged ions move it towards the water phase [178]. This conformational change appears to be sterically more favourable for cations than for anions, which explains the small Dmw for acids as compared with bases, unless the bases are highly substituted, like the tertiary amines.

4.8 EFFECTS OF SPECIATION OF HIOCS AT BIOLOGICAL INTERPHASES 4.8.1

Ion Trapping

If a HIOC can only permeate a biological membrane in its neutral form, the relative concentration of charged species in the inner compartment would only depend on the acid–base equilibrium. Accordingly, if the inner compartment is more acidic and the permeating solute is a neutral base that is protonated in the inner compartment, the concentration of the charged species in the inner compartment is higher than in the outer compartment. This mechanism is called ‘ion trapping’ because the ions cannot diffuse or migrate directly back across the membrane. As was shown above, uptake into the membrane is significant for hydrophobic ions. Permeability is a product of the uptake of a species into the membrane and the energy required for crossing the central energy barrier. The permeability of a charged species is usually smaller than that of the corresponding neutral molecule, but cannot be fully neglected. Consequently ion trapping is not a general black-and-white paradigm, but depends very much on the type of compound investigated. The uptake of different cationic amphiphilic drugs in tissues of different organs could be explained by nonspecific binding to the membrane and ion trapping, but the contribution of the two uptake mechanisms appeared to be compound specific [179]. Trapp modelled the uptake of weak organic acids and bases from soil solutions into roots, and concluded that ion trapping was indeed the dominant uptake mechanism [180]. In addition, pH dependence of algal toxicity of substituted phenols could be explained by iontrapping mechanisms (unpublished results).

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Bioaccumulation

The major route for bioaccumulation of hydrophobic organic compounds in aquatic animals is passive diffusion over cell membranes. In fish, the gill epithelia are the predominant port of entry, with less than 40% of uptake across the skin [181]. Since permeability of the membrane is a direct function of the membrane–water partition coefficient and the diffusion coefficient across the membrane interior [182], the bioconcentration factor (log BCF) can be directly correlated with log Kow or log Kmw for compounds with intermediate hydrophobicity [183,184]. There are only very few studies concerned with the pH dependence of the bioaccumulation of HIOCs. Most of these studies deal with substituted phenols, some with other functional acids and organotin compounds. Bioaccumulation of organotin compounds will be treated in Section 6. Saarikoski et al., and Kishino and Kobayashi studied the uptake of substituted phenols in different species of fish and obtained consistent results [181,185]. In all three studies the bioconcentration factor BCF or the uptake rate was constant for the predominantly neutral speciation up to pH  pKaw . Above the pKaw the BCF started to decrease. The decrease did not follow the ionisation curve, but was somewhat shifted to higher pH values. This shift was more pronounced for the more acidic phenols than for the less acidic ones, as is depicted in Figure 8, where the BCF is plotted versus pH
pKaw [185]. Analogous results were obtained for gill uptake rates for phenols and carboxylic acids [181]. Saarikoski et al. [181] proposed three different mechanisms for the observed effect. Firstly, the pH at the gill surface is slightly lower than in the surrounding water. This effect alone cannot explain the relative difference of the shift for different chemicals, but could contribute to the effect. Secondly, the membranes could be permeable to the ionised form. It is not directly evident from the experimental data if the charged species is taken up or if the pHdependent bioaccumulation curves level off to zero. Saarikoski et al. estimated the permeability of the charged species to be at least three orders of magnitude smaller than that of the neutral species. Thirdly, in addition to actual membrane permeation, the diffusion across the diffusion layers adjacent to the membrane may become rate limiting for more hydrophobic compounds. Since diffusion in the aqueous phase is only dependent on size, not on the charge, the diffusion resistance of the diffusion layers is independent of pH. This theory is consistent with the experimental finding of a larger shift in the ionisation curve for the more hydrophobic compounds.

4.8.3

Toxicity: Uncoupling Effect

Uncoupling is a specific toxic effect that takes place in energy-transducing membranes (photosynthetically active membranes, inner mitochondrial

240 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

2,4,6 -TCP

PCP

(a)

100

Bioconcentration ratio

3,5 -DCP

2,5 -DCP

10 4 - CP

1

0.1

(b)

2,3,4,6 -TCP 100

2,4,5 -TCP

Bioconcentration ratio

2,3 -DCP 2,4 -DCP 10

3 - CP 2 - CP

1

Phenol

2,6 -DCP 0.1

−4

−2

0 pH – pKaw

2

4

6

Figure 8. The bioconcentration ratios of chlorophenols in goldfish at 1 h exposure to their media as a function of the difference between pH and pKa . 4-CP: 4-chlorophenol, 2,5-DCP: 2,5-dichlorophenol, 3,5-DCP: 3,5-dichlorophenol, 2,4,6-TCP: 2,4,6-trichlorophenol, PCP: pentachlorophenol, 2-CP: 2-chlorophenol, 3-CP: 3-chlorophenol, 2,4-DCP: 2,4-dichlorophenol, 2,3-DCP: 2,3-dichlorophenol, 2,4,5-TCP: 2,4,5-trichlorophenol, 2,3,4,6-TCP: 2,3,4,6-tetrachlorophenol, 2,6-DCP: 2,6-dichlorophenol. Reprinted from [185]: Water Res., 29, Kishino, T. and Kobayashi, K. ‘Relation between toxicity and accumulation of chlorophenols at various pH, and their absorption mechanism in fish’, pp. 431–442. Copyright (1995), with permission from Elsevier

membranes, or bacterial membranes), which is closely related to the permeability of biological membranes to the different chemical species of HIOCs. Weak organic acids can destroy the electrochemical proton gradient, which otherwise drives the ATP synthetase, by transporting protons back across the membrane

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[186]. In the protonophoric shuttle mechanism, the charged species migrates across the membrane (driven by the electrical component of the proton gradient), picks up a proton from the adjacent aqueous phase, and forms the neutral species, which diffuses back across the membrane, and releases a proton into the opposite aqueous phases in order to restore the equilibrium of uncoupler species at both sides of the membrane. The ability of a weak organic acid to uncouple is dependent on how well both neutral and charged species can permeate biological membranes. Good uncouplers contain p-orbital systems often with strong electron-withdrawing substituents that assure good delocalisation of the negative charge, thus enhancing the membrane permeability of the deprotonated species. Miyoshi et al. showed that the uncoupling activity of a large number of substituted phenols correlated well with their potency to increase the proton permeability across liposomal membranes [187]. Both proton permeability and uncoupling activity could be predicted with a combination of two descriptors: the apparent liposome–water distribution ratio at the pH of the experiment, together with the pKaw of the compound [187,188]. If Kow was used instead of the apparent liposome–water distribution ratio, a steric parameter had to be included into the QSAR equation [189]. A kinetic model was developed to describe the pH-dependent uncoupling activity of substituted phenols in bacterial photosynthetic membranes [2]. In this model, the overall uncoupling activity is quantitatively separated into the contribution of membrane concentration, which can be estimated by the Kmw , and of intrinsic activity. The intrinsic activity of an uncoupler is influenced not only by the hydrophobicity and acidity, but also by steric effects and by the charge distribution within the molecule [2].

5 INTERACTION OF METAL SPECIES WITH BIOLOGICAL INTERPHASES In the following section, the role of the various types of complexes mentioned above will be discussed with regard to various mechanisms of interactions at biological interphases. It is clear that metal ions and hydrophilic complexes cannot distribute into the membrane lipid bilayer or cross it. The role of hydrophilic ligands has thus to be discussed in relation to binding of metals by biological ligands. In contrast, hydrophobic complexes may partition into the lipid bilayer of membranes (see below, Section 6). 5.1 BINDING TO BIOLOGICAL LIGANDS AND FREE ION ACTIVITY MODEL (FIAM) The major transport route of metal ions over a biological membrane is generally assumed to occur over specific carrier ligands or ion channels that are

242 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

specific to certain metals [11]. Transport of metals by carrier ligands has been described for algae and bacteria [190,191]. Binding of metal ions to carrier ligands occurs in competition to the ligands in the medium (Figure 9a, adapted from [192]). The metal ions react with biological carrier ligands. These complexes can then be transported over the membrane. It is often assumed that the rate-limiting step for metal uptake is the active transport of the metal–carrier ligand complex over the membrane leading to internalisation of the metal. In this case the biological uptake of metal ions is related to the free metal ion activity in the medium (free ion activity model, FIAM) [13,192–194]. The conditions and limitations for the applicability of the FIAM are discussed in detail in [13] and in Chapters 3 and 10 in this volume. If equilibrium is established in the solution, the free metal ion activity is determined by the reactions with all the ligands in the medium, according to equation (4) above. The free metal ion activity thus reflects the overall complexation of the metal in a given medium, and the presence of strong or weak ligands. The cellular carrier ligands are in competition with all the ligands present in the medium. In this context, the effects of various ligands are briefly discussed, based on the previous paragraphs. Inorganic ligands generally form only moderately stable complexes. The ratio of free metal ion to total metal is rather high if a medium is dominated by the inorganic complexes; this is the case, for example, for Co(II), Ni(II), Cu(II), Zn(II), Ag(I), Cd(II), Pb(II) at pH 7–8 and typical freshwater carbonate concentrations. The ratio of Fe3þ to Fe(total), and in a similar way of Al3þ to Al(total) are, however, very low at neutral pH, due to strong hydrolysis. Small organic acids (e.g. oxalate, citrate) also form moderately stable complexes. The presence of strong organic ligands in excess of the metals in a solution maintains low concentrations of free metal ions. Synthetic ligands, such as EDTA and NTA, have been widely used to control the metal speciation in culture media (Figure 1, [36]). In a similar way, natural organic ligands (FA and HA, and more specific ligands) also buffer the free metal ions to low levels in natural waters (Figure 1). For example, Cu in seawater and in fresh water may often be strongly complexed so that the free metal ion concentration is buffered to very low values (Figure 1) [60,195]. To describe the dynamics of metals at biological interphases in the presence of various ligands, the kinetics of dissociation of the complexes have to be taken into account in relation to the diffusion and to the uptake kinetics ([14] and Chapters 3 and 10 in this volume). Based on kinetic criteria, labile and inert complexes can be distinguished as limiting cases with regard to biological uptake ([14] and Chapter 3, this volume). Colloidal and particulate metal species also contribute to maintaining low free metal ion concentrations. The behaviour of colloidal species of similar size may however be very different, depending on their chemical speciation and on their structure. Metals bound to HA of large size may exchange with the

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(a) MLint Cell

carrier ligand

M KLc

Water

kd

kf

Mn+ (n −x)+

M(OH)x

(n −2x)+

M(CO3)x

MCIx(n −x)+

k f1 kd1

K1

K F⬘

ML1

Organic complexes

M-fulvics

Inorganic complexes

(b)

ML0

MLint

Cell

ML0

Carrier ligand

M

Water

ML0 HgCl02 CH3HgCl0 Cu(DDC)02

KLc

kf

kd

Mn+

Uncharged hydrophobic complexes

Figure 9. (a) Scheme of the interactions between various metal species and biological carrier ligands at a biological membrane. This scheme is underlying the FIAM. Binding to the biological carrier ligand depends on the free metal ion activity, which is determined by the interactions with the various ligands (inorganic and organic) in solution. KLc , K1 , and KF0 denote the various thermodynamic stability constants, kf the formation rate constants of various complexes, kd the dissociation rate constants of these complexes. Lint denotes internal cellular ligands, to which the metals are bound after uptake (adapted from [192] ). (b) Partitioning of hydrophobic metal complexes into the lipid bilayer. This process represents an additional pathway of metal uptake. In this case, the concentration of the hydrophobic metal complexes determines uptake (after [222])

244 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

solution in a similar way to those complexed by smaller molecules, but may also be retained within the large structures. Exchange of metals bound in colloidal inorganic solid phases may be very limited. In a study of iron uptake, Fe(III)hydroxide colloids with a slow dissolution rate could not supply Fe fast enough to sustain growth of a diatom, whereas Fe was supplied more efficiently by an organic colloidal Fe(III) species [196]. In addition to slow dissociation or dissolution, colloidal and particulate species also diffuse only slowly to the interphase, due to their larger size range (cf. Chapters 3 and 10 in this volume). Further research is needed with regard to the behaviour of colloidal species. In addition to binding to specific carrier ligands, metal ions may bind unspecifically to functional groups of proteins and of other components of the cell walls and membranes. Carboxyl, amino and sulfhydryl groups are all complexing functional groups with different affinity for various metal ions. In the presence of a large excess of metal ions, a large fraction of these binding groups may be occupied. Binding to these functional groups on surfaces of algae and bacteria has often been treated within a framework of adsorption isotherms, and binding capacities and conditional binding constants have been evaluated [197–201]. Using spectroscopic methods, the nature of the binding functional groups has been determined in some cases, e.g. histidine for Cu in the algae Chlamydomonas reinhardtii and Cyclotella cryptica [202]. Here, the speciation in solution plays a similar role, as indicated in the previous paragraph. Metals bound to complexes in solution may exchange with the cellular functional groups, as a function of their thermodynamic stability and dissociation kinetics. The extent of unspecific binding to cellular functional groups is thus also expected to be related to the free metal ions in solution. In an extension of the FIAM model, the biotic ligand model of the acute toxicity of metals assumes that a given toxic effect occurs when the concentration of metal bound to biotic ligands exceeds a certain threshold concentration [203–205]. This model has been successfully applied to rationalise toxicity data from fish and Daphnia. Although the identity and abundance of biotic ligands is not known, modelling has revealed that the critical biotic ligand concentrations are much lower in crustacea than in fish [203,204]. 5.2

UPTAKE OF SPECIFIC COMPLEXES

Uptake of specific metal complexes by microorganisms requires specialised transport systems which respond to the specific ligands. The best known examples concern the uptake of iron by bacteria using siderophores ([206], cf. Chapter 9, this volume). Siderophores are strong chelating ligands for Fe(III), which are produced by bacteria in the terrestrial and aquatic environment [206,207]. Their structures include specific binding sites for iron(III), usually with hydroxamate, catecholate or a-hydroxycarboxylate functional groups. Siderophores produced by marine bacteria possess amphiphilic structures

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with distinctive properties for iron acquisition in the marine environment [208–211]. Uptake of the siderophores takes place over specialised transport systems involving outer membrane receptor proteins ([191,206] cf. Chapter 9, this volume). Uptake of small organic metal complexes over transport systems of organic metabolites may be possible, for example, of small organic acids like citrate or amino acids. However, only few examples of such processes have been studied so far. Increased uptake of cadmium by an alga has been observed in the presence of citrate and has been attributed to accidental transport of the metal–citrate complex over a citrate transporter [212]. Transport systems of inorganic anions may also play a role in metal transport. Silver uptake by algae was enhanced in the presence of thiosulfate. In this case, the silver thiosulfate complex was transported over a sulfate uptake system [213]. It remains to be demonstrated how widespread these processes may be for metal uptake in the aquatic environment [12]. 5.3 INTERACTIONS OF FA AND HA WITH BIOLOGICAL INTERPHASES The structures of FA and HA comprise both hydrophilic and hydrophobic parts. They may thus interact in various ways with biological membranes and cell surfaces [214,215]. Their role at biological interphases may involve other processes (sorption, accumulation at cell surfaces) in addition to complexation of metals. Adsorption of FA and HA to phytoplankton cells has been interpreted in terms of hydrogen bonding to the cell surfaces [214]. The accumulation of FA and HA at cell surfaces may affect the interactions of metal ions with cellular ligands and the characteristics of cell membranes (permeability) [215]. The permeability of the membrane of a green alga was increased in the presence of FA and HA, in agreement with adsorption measurements of the FA and HA [216]. Adsorption of FA and HA to cell membranes may also affect the uptake of organic compounds. This aspect has so far not been elucidated.

6 INTERACTION OF HYDROPHOBIC METAL COMPLEXES AND ORGANOMETALLIC COMPOUNDS WITH BIOLOGICAL INTERPHASES 6.1

HYDROPHOBIC METAL COMPLEXES

Partitioning of metal complexes into the lipid bilayer of membranes is only significant for hydrophobic species. FA and HA, and their metal complexes, are not expected to enter to a significant extent into the lipid bilayer, due to their large molecular size. Uptake of hydrophobic metal species by diffusion across

246 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

the membranes may be faster than uptake via an active transport system, if the speciation of a metal is dominated by hydrophobic species (Figure 9b). Some inorganic species behave as hydrophobic complexes, in particular some mercury species such as the neutral chloro complex of Hg(II), HgCl02 , and the uncharged sulfide complex HgS0 as well as the uncharged silver chloro complex AgCl0 [79–81,217]. The mercury species have been shown to diffuse rapidly through lipid membranes [79,217–219]. Dithiocarbamates and xanthates form particularly stable, neutral complexes with Cu(II), Cd(II) (and also Ni, Hg, Pb), which are membrane permeable and increase the apparent bioaccumulation of these metals [13]. In the series of sulfoxine, oxine, and chloroxine, the hydrophobicity of the neutral and the charged form, as well as of the Cu complex, increases. While the sulfoxine is not hydrophobic and does not modulate copper toxicity [220], the Cu–oxine complex is hydrophobic with an octanol–water partition constant, log Kow , of 1.7 [221] or 2.6 [222]. Chloroxine can be assumed to be even more hydrophobic, but so far its influence on uptake and toxicity has not been investigated. Uptake of Cu2þ into unilamellar liposomes was increased in the presence of 8-hydroxychinoline, and decreased again after adding HA [223]. Rapid uptake by diffusion of the lipophilic Cu complexes with diethyldithiocarbamate (DDC) and with oxine (Cu(DDC)02 and Cu(Ox)02 ) has been shown for the diatom Thalassiosira weissflogii and for several other marine phytoplankton species [222,224]. Subsequently to rapid diffusion over the membranes, these complexes are assumed to exchange with internal cellular ligands. Cadmium transfer through perfused gill tissue was increased in the presence of the complexing agents DDC, ethyl-and isopropyl-xanthate [225]. In contrast, the retention of Cd in gill tissue was not altered by DDC, but was tenfold increased by the xanthates [225]. Dithiocarbamates form particularly stable complexes with Cu2þ . They are able to abstract the Cu2þ cofactor from enzymes, leading to inhibition of enzymatic activity as was shown for the superoxide dismutase [226]. The dithiocarbamate–Cu complexes are membrane-permeable without causing leakages of the lipid bilayer, as was shown by stability experiments with liposomes [226]. Copper complexes of substituted malonic acids had no influence on the acute toxicity towards adult zebra fish [227], possibly due to stronger chelating groups at the gill epithelia. In contrast, hatching of zebra fish, which is already very sensitive to Cu2þ alone, was delayed in the presence of hydrophobic n-hexadecyl malonate, and was not influenced by the less hydrophobic benzyl malonate [227]. Overall, it appeared that the toxicity of free Cu2þ and the Cu–hexadecyl malonate complex was additive [227]. Copper complexes with organic acids from landfill leachates were contributing to the toxicity towards zebra fish embryos only if the molar mass of the complexes was sufficiently small to allow penetration of biological membranes [228]. Fractions of landfill leachate with M > 5000 g mol
1 had a

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[Image not available in this electronic edition.]

Figure 10. Median zebra fish embryo hatching rates as a function of calculated Cu2þ concentrations. Reprinted with permission from [228]: Fraser, J. K. et al. (2000). ‘Formation of copper complexes in landfill leachate and their toxicity to zebrafish embryos’, Environ. Toxic. Chem., 19, 1397–1402. Copyright SETAC, Pensacola, Florida, USA

similar toxic effect to Cu2þ alone, while the toxicity was increased significantly in the raw leachate and the fraction with M < 700 g mol
1 , as is depicted in Figure 10. A lipophilic copper complex with neocuproine has been found to increase the toxicity of a trichlorophenol in bacteria, probably due to increased transport of Cu over the membrane [229]. In most of the above-cited studies, it was assumed that the increase of toxicity was due to enhanced uptake of the metal, and that overall toxicity is only due to metal toxicity. However, stable complexes may exhibit specific toxicity by themselves. The Cu2þ complex of 2,9-dimethyl-1,10-phenanthroline has been shown to react with H2 O2 in the cell, thereby producing radicals [221]. Cu(Ox)02 exhibits a specific toxic effect on photosynthesis [230]. Cu-ethylxanthogenate enhances respiration and ATP production [230]. Indirect evidence of hydrophobic complex formation in biological membranes is also given by the modulation of the toxicity of catechol and chlorocatechol by Cu2þ [78]. Whereas toxicity of higher chlorocatechols was decreased by the addition of Cu2þ , it was increased in the case of catechol and monochlorocatechol. Tentative models to explain these findings include complex formation between mono-and di-deprotonated catechols and Cu2þ , both in the aqueous and in the membrane phase.

248 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

6.2 6.2.1

ORGANOMETALLIC COMPOUNDS Mercury

Accumulation of methylmercury in fish is a critical problem in many aquatic systems. A detailed investigation of the octanol–water distribution ratios of neutral mercury complexes has shown that HgCl02 and CH3 HgCl0 exhibit the most hydrophobic character, in comparison in particular with Hg(OH)02 and CH3 HgOH0 [79]. The concentrations of these species depend on pH and on the chloride concentration. The uptake rates of both inorganic Hg and of methylmercury in the marine diatom Thalassiosira weissflogii were dependent on the octanol–water distribution ratios, under various conditions of pH and chloride (Figure 11, [79]). This dependence indicated that Hg was taken up by passive diffusion of the uncharged chloro complexes over the membranes. For methylmercury, bioavailability in fish is not controlled by transfer across gill, skin or intestinal membranes, but rather by digestive processes, among them complexation with amino acids [231]. 6.2.2

Organolead Compounds

Tetraethyllead was used in the past as an antiknock agent in gasoline, but it has been phased out in most countries. Alkyllead compounds have a detergent-like activity on liposomes and black lipid membranes [232]. Tributyllead destroys planar lipid membranes at lower concentrations than tripropyllead, which is again more effective than triethyl- and trimethyllead [232]. Inorganic lead compounds like lead acetate and lead nitrate were effective only at twice as high concentrations [232]. 6.2.3

Organotin Compounds

The octanol–water partitioning of organotin compounds is strongly dependent on the speciation and the counter-ion type and concentration [89]. Consequently, a strong pH dependence of Dow can be observed, as is shown in Figure 12 for TBT and TPT, in the presence of 10 mmol dm
3 perchlorate. While for the bromide and chloride complex, partitioning is little more than one order of magnitude smaller than that of the hydroxide species, the nitrite and perchlorate complex differ by more than two orders of magnitude. In contrast, the liposome–water partitioning shows a very weak pH dependence (Figure 12) [233]. The log Dlipw is even slightly larger at low pH than at high pH. While in the octanol–water system, partitioning at low pH is only due to partitioning of the perchlorate complex, the triorganotin cation can directly interact with the lipid bilayer, resulting presumably in a direct complex formation with the phosphate group in the phospholipids [234]. This effect is more pronounced for TPT than for TBT, which is consistent with TPT’s higher

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Uptake rate/ amol cell−1 hr −1 nmol−1 dm−3

20

pCl

8.1 8.1 7.3 6.7 6.7 6.7 6.0 5.6 5.5 5.5 5.3 4.8 4.3 4.2 4.0

0.5 0.5 3.3 3.3 4.3 5.3 3.3 2.2 3.8 3.3 3.7 3.3 2.9 2.4 2.9

(b) Symb. pH

pCl

8.1 5.8 4.5 6.6 6.2 5.8 4.9 4.3 6.6 6.6 5.6 4.2 3.1

0.5 2.3 2.8 3.3 3.3 3.3 3.3 3.3 4.3 5.3 3.9 4.3 4.3

15

10

5

0

0

1

2

20

Uptake rate/ amol cell−1 hr −1 nmol−1 dm−3

(a) Symb. pH

3

15

10

5

0

0

1 log D ow

I 0.7 0.7 1.5⫻10−3 0.08 0.08 0.08 0.01 0.1 0.1 1.5⫻10−3 0.1 0.1 0.1 0.1 0.1

I 0.7 0.1 0.1 0.12 1.2⫻10−3 0.04 1.2⫻10−3 0.2 0.12 0.12 0.1 0.1 0.1

2

Figure 11. Uptake rates of inorganic Hg (a) and of methylmercury (b) by a marine alga as a function of the octanol–water distribution ratio of the Hg-species under various conditions of pH and chloride concentrations. The neutral species HgCl02 and CH3 HgCl0 diffuse through the membranes. Reprinted with permission from [79]: Mason, R. P. et al. (1996). ‘Uptake, toxicity, and trophic transfer in a coastal diatom’, Environ. Sci Technol., 30, 1835–1845; copyright (1996) American Chemical Society

affinity to oxygen ligands, which is also reflected in its lower acidity constant [89]. Partitioning into biomembrane vesicles was even higher at low pH than at high pH [233], indicating additional complex formation of the cationic species with ligands of the intercalated proteins.

250 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

log Dow or log Dlipw (dm3 kglip−1)

5 (a) TBT

4.5 4 3.5

log D lipw

3 2.5 2 log Dow 1.5 1

2

3

4

5

6

7

8

9 pH

pKa

log Dow or log Dlipw (dm3 kglip−1)

5 (b) TPT

4.5 4

log D lipw

3.5 3 2.5 2 1.5 1

log Dow

2

3

4

5 6 pKa

7

8

9 pH

Figure 12. pH-dependence of the octanol–water and liposome–water distribution ratio. (a) TBT, (b) TPT. Reprinted in part from [233], with permission from: Hunziker, R. W., Escher, B. I. and Schwarzenbach, R. P. (1997). ‘pH-dependence of the partitioning of triphenyltin between phosphatidylcholine liposomes and water’, Environ. Sci. Technol., 35, 3899–3904; copyright (2001) American Chemical Society

The number of organic substituents also influences interaction with lipid bilayers. Diphenyltin chloride causes disturbances of the hydrophobic region of the lipid bilayer, triphenyltin chloride adsorbs to the head-group region, and tetraphenyltin does not partition into the lipid bilayer [235–237]. Similar results were found for the butylated tins [238]. In addition, the mono-butyltin was homogeneously distributed within the lipid bilayer [238]. The difference in partitioning behaviour of triorganotin compounds has implications for their toxic effects [239,240]. The surface-active triphenyltin

B. I. ESCHER AND L. SIGG

251

Table 6. Bioaccumulation of organotin compounds

TBT TPT a

pKaw

log Kow (R3 SnOH)

6.25a 5.20a

4.10a 3.53a

log BCFss (Apparent) pH 5 2.15b 3.34b

pH 8 2.95b 3.42b

log BCFss (Without metabolism) pH 5 2.32b 3.35b

pH 8 4.40b 3.43b

[89]; b [244]; ss ¼ steady-state

has a stronger hemolytic activity than diphenyltin [241]. The almost equal hydrophobicity of TBT-OH and TBTþ favours membrane permeation of both species and consequently uncoupling of oxidative phosphorylation as mode of toxic action. In contrast, the higher affinity of TPTþ to organic ligands favours binding to sensitive sites in enzymes. Consistent with the physicochemical properties, TBT is a better uncoupler than TPT, and the dominant acute toxic mechanism of TPT is inhibition of the ATP synthetase [239]. Only very few studies have considered the role of speciation of organotin compounds in biological uptake and bioconcentration [242]. Bioconcentration factors of TBT in the midge larvae Chironomus riparius were slightly higher at pH 8 than at pH 5 [243]. The BCF values of TPT are not significantly different at pH 5 and 8, and are twice as high as compared with TBT, whose apparent BCF is decreased due to metabolism [243]. If the BCF-values are corrected for metabolic breakdown of TBT (Table 6), the ratio of the BCF-values of the hydroxides is in agreement with the hydrophobicity. However, the difference between pH 5 and 8 becomes very pronounced for TBT, while still being negligible for TPT [244].

7 CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER RESEARCH There is an abundant research on the interactions of HIOCs and metals with biological interphases, in which organic chemicals and metals are treated independently. However, few studies have considered the role of combinations of HIOCs with metals. There is a particular lack of mechanistic approaches. With regard to the metals, the FIAM has been very successful, but it remains to be shown under which conditions additional interactions, such as partitioning of hydrophobic complexes and uptake of specific complexes, are important for metal uptake and toxic effects. In particular, the role of hydrophobic complexes with both natural and pollutant compounds in natural waters has not yet been fully elucidated, since neither their abundance nor their behaviour at biological interphases are known in detail.

252 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

Considering additionally that the risk assessment of mixtures is presently an urgent issue, and that usually mixtures of exclusively organic chemicals or exclusively metals are investigated, in future more emphasis should be placed on the interactions of xenobiotic HIOCs with metals. Major research questions will include how these interactions influence bioavailability of both metals and HIOCs, interactions with biological membranes, uptake, and common toxic effects.

LIST OF SYMBOLS AND ABBREVIATIONS ABBREVIATIONS CCCP BCF DDC DMA DMPC DNOC DOPC EDTA FA FCCP FIAM GSH HA HAw HIOC Lc Li inorg Li org MLi inorg MLi org NA NTA OA PC PCP PE PG PI QSAR

Carbonylcyanide-m-chlorophenylhydrazone Bioconcentration factor Diethyldithiocarbamate 3,4-Dimethylaniline Dimyristoylphosphatidyl choline Dinitro-o-cresol Dioleylphosphatidyl choline Ethylenediaminetetraacetate Fulvic acid Carbonylcyanide-p-trifluoromethoxyphenylhydrazone Free ion activity model Glutathione Humic acid Acid in the aqueous phase Hydrophobic ionogenic organic compounds Biological carrier ligand Inorganic ligand Organic ligand Inorganic complexes Organic complexes Avogadro constant Nitrilotriacetate Oleic acid Phosphatidyl choline Pentachlorophenol Phosphatidyl ethanolamine Phosphatidyl glycerol Phosphatidyl inositol Quantitative structure–activity relationship

B. I. ESCHER AND L. SIGG

S-13 TBT TNS TPB
TPPþ TPT WHAM

253

5-chloro-3-t-butyl-20 -chloro-40 -nitrosalicylanilide Tributyltin 2,6-Toluidinyl naphthalenesulfonate Tetraphenylborate Tetraphenylphosphonium Triphenyltin Windermere humic aqueous model [44]

SYMBOLS aiw aim aiw bi cLi inorg cLi org cM, t cM C DH DC Dmw Dmw G0i DS Dixmw Dmw (pH,I) Dow (pH, I) er e0 gi I kf

Fraction of compound or species i in the aqueous phase Activity of compound i in the membrane phase Activity of compound i in the aqueous phase Overall thermodynamic stability constant of the complex MLi Concentration of inorganic ligand Linorg Concentration of organic ligand Lorg Total metal concentration in solution Free metal ion concentration Specific capacitance Enthalpy Potential difference between two phases Difference between the log Kmw of the neutral and the corresponding charged species Standard free-energy change for the phase-transfer reaction between membrane and aqueous phase Entropy Membrane–water distribution ratio of the ion pair ix Apparent membrane–water distribution ratio at a given pH with given ionic strength Apparent octanol–water distribution ratio at a given pH and with a given ionic strength Relative permittivity or dielectric constant The permittivity of the free space Activity coefficient of compound or species i Ionic strength Rate constant for formation of the complex ML

(
) (
) (
) (
) (mol dm
3 ) (mol dm
3 ) (mol dm
3 ) (mol dm
3 ) (F m
2 ) (kJ mol
1 ) (V)
1

(dm3 kg ) (kJ mol
1 ) (kJ mol
1 ) (dm3w kg
1 m ) (dm3w kg
1 m ) (dm3w dm
3 o ) (
) (
) (
) (
)
1

(dm3 mol
1 s )

254 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

kd Ka w K am Ki0  Kimw

Kimw

KL KV KLc Kiow mmax im miw m0iw m~im m~iw f rm SPL

s Vm Vw xi zi

Rate constant for dissociation of the complex ML Acidity constant in the aqueous phase Interfacial acidity constant or apparent acidity constant in the membrane phase Dimensionless membrane–water partition coefficient of species or compound i (mole fraction) Concentration-based membrane–water partition coefficient of species or compound i Membrane–water partition coefficient of species or compound i with the concentration given in molality Langmuir sorption constant Volmer sorption constant Equilibrium constant for binding of metal to biological carrier ligand Octanol–water partition coefficient of species or compound i Maximum mass concentration of molecules adsorbed to the membrane bilayer Chemical potential of a compound i in the aqueous phase w Standard chemical potential of a compound i in the aqueous phase Electrochemical potential of a compound i in the membrane phase m Electrochemical potential of a compound i in the aqueous phase w Phase ratio Mass concentration or density of the membrane lipids Surface area occupied by a single lipid molecule in the membrane Surface charge density Molar volume of the membrane lipids Molar volume of the aqueous phase Mole fraction of a compound or species i Charge of a compound or species i

(s
1 ) (
) (
)

(
) (dm3w dm
3 m ) (dm3w kg
1 m ) (dm3w kg
1 m ) (dm3w kg
1 m ) (
) (
) (mol kg
1 m ) (
) (
) (
) (
) (dm3m dm
3 w ) (kgm dm
3 m ) (SPL  0:7 nm2 molecule
1 for phospholipids) (C m
2 )
1 (dm3m mol )
1 3 (dmw mol ) (
) (
)

B. I. ESCHER AND L. SIGG

255

REFERENCES 1. 2. 3.

4. 5. 6. 7. 8.

9. 10. 11.

12. 13.

14. 15.

Schwarzenbach, R. P., Gschwend, P. M. and Imboden, D. M. (2003). Environmental Organic Chemistry. 2nd edn, John Wiley & Sons, New York. Escher, B. I., Hunziker, R., Schwarzenbach, R. P. and Westall, J. C. (1999). Kinetic model to describe the intrinsic uncoupling activity of substituted phenols in energy transducing membranes, Environ. Sci. Technol., 33, 560–570. Kra¨mer, S. D., Braun, A., Jakits-Deiser, C. and Wunderli-Allenspach, H. (1998). Towards the predictability of drug–lipid membrane interactions: the pH-dependent affinity of propranolol to phosphatidylinositol containing liposomes, Pharmaceut. Res., 15, 739–744. Ottiger, C. and Wunderli-Allenspach, H. (1997). Partition behaviour of acids and bases in a phosphatidylcholine liposome–buffer equilibrium dialysis system, Eur. J. Pharmaceut. Sci., 5, 223–231. Testa, B., van Waterbeemd, H., Folkers, G. and Guy, R. eds. (2001) Pharmacokinetic Optimization in Drug Research: Biological, Physicochemical, and Computational Strategies. Series, Verlag Helvetica Chimica Acta, Zu¨rich. Flewelling, R. F. and Hubbell, W. L. (1986). Hydrophobic ion interactions with membranes. Thermodynamic analysis of tetraphenylphosphonium binding to vesicles, Biophys. J., 49, 531–540. McLaughlin, S. and Harary, H. (1976). The hydrophobic adsorption of charged molecules to bilayer membranes: a test of the applicability of the Stern equation, Biochem., 15, 1941–1948. Tessier, A. and Turner, D. R. eds. (1995) Metal Speciation and Bioavailability in Aquatic Systems. Vol. 3, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Chichester. Peijnenburg, W. J. G. M., Posthuma, L., Eijsackers, H. J. P. and Allen, H. E. (1997). A conceptual framework for implementation of bioavailability of metals for environmental management purposes, Ecotoxicol. Environ. Saf., 37, 163–172. Sauve´, S., Dumestre, A., McBride, M. and Hendershot, W. (1998). Derivation of soil quality criteria using predicted chemical speciation of Pb2þ and Cu2þ , Environ. Toxicol. Chem., 17, 1481–1489. Simkiss, K. and Taylor, M. G. (1995). Transport of metals across membranes. In Metal Speciation and Bioavailability in Aquatic Systems. eds. Tessier, A. and Turner, D. R., Vol. 3, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Chichester, pp. 2–44. Campbell, P. G. C., Erre´calde, O., Fortin, C., Hiriart-Baer, W. R. and Vigneault, B. (2002). Metal bioavailability to phytoplankton – applicability of the biotic ligand model, Toxicol. Pharmacol., 133, 189–206. Campbell, P. G. C. (1995). Interactions between trace metals and aquatic organisms: a critique of the free-ion activity model. In Metal Speciation and Bioavailability in Aquatic Systems. eds. Tessier, A. and Turner, D. R., Vol. 3, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Chichester, pp. 45–102. van Leeuwen, H. P. (1999). Metal speciation dynamics and bioavailability: inert and labile complexes, Environ. Sci. Technol., 33, 3743–3748. Schwarzenbach, R. P., Gschwend, P. M. and Imboden, D. M. (1993). Environmental Organic Chemistry. John Wiley & Sons, New York.

256 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 16.

17.

18. 19. 20. 21. 22. 23. 24. 25. 26.

27. 28. 29. 30. 31.

32.

Berg, M., Mu¨ller, S. R., Mu¨hlemann, J., Wiedmer, A. and Schwarzenbach, R. P. (2000). Concentrations and mass fluxes of chloroacetic acids and trifluoroacetic acid in rain and natural waters in Switzerland, Environ. Sci. Technol., 34, 2675–2683. Comer, J. and Tam, K. (2001). Lipophilicity profiles: theory and measurement. In Pharmacokinetic Optimization in Drug Research: Biological, Physicochemical, and Computational Strategies. eds. Testa, B., van Waterbeemd, H., Folkers, G. and Guy, R., Series, Verlag Helvetica Chimica Acta, Zu¨rich, pp. 275–304. Buser, H.-R., Mu¨ller, M. D. and Theobald, N. (1998). Occurrence of the pharmaceutical drug clofibric acid and the herbicide mecoprop in various Swiss lakes and in the North Sea, Environ. Sci. Technol., 32, 188–192. Daughton, C. G. and Ternes, T. A. (1999). Pharmaceuticals and personal care products in the environment: agents of subtle change? Environ. Health Perspect., 107, Suppl. 6, 907–938. Halling-Sørensen, B., Nors Nielsen, S., Lanzky, P. F., Ingerslev, F., Holten Lu¨tzhøft, H.-C. and Jørgensen, S. E. (1998). Occurrence, fate and effects of pharmaceutical substances in the environment – a review, Chemosphere, 36, 357–393. Ternes, T. A. (1998). Occurrence of drugs in German sewage treatment plants and rivers, Water Res., 32, 3245–3260. Stuer-Lauridsen, F., Birkved, M., Hansen, L. P., Hølten Lu¨tzhoft, H.-C. and Halling-Sørensen, B. (2000). Environmental risk assessment of human pharmaceuticals in Denmark after normal therapeutic use, Chemosphere, 40, 783–793. ¨ llers, S., Singer, H. P., Fa¨ssler, P. and Mu¨ller, S. R. (2001). Simultaneous O quantification of neutral and acidic pesticides and pharmaceuticals at the low ng/ l level in surface and waste water, J. Chromatogr. A, 911, 225–234. Buser, H.-R., Poiger, T. and Mu¨ller, M. D. (1999). Occurrence and environmental behaviour of the chiral pharmaceutical ibuprofen in surface waters and in wastewater, Environ. Sci. Technol., 33, 2529–2535. Hartmann, A., Alder, A. C., Koller, T. and Widmer, R. (1998). Identification of fluoroquinolone antibiotics as the main source of umuC genotoxicity in native hospital wastewater, Environ. Toxicol. Chem., 17, 377–382. Holten Lu¨tzhøft, H.-C., Vaes, W. H. J., Freidig, A. P., Halling-Sørensen, B. and Hermens, J. L. M. (2000). 1-Octanol/water distribution coefficient of oxolinic acid: influence of pH and its relation to the interaction with dissolved organic carbon, Chemosphere, 40, 711–714. Bolton, J. L., Trush, M. A., Penning, T. M., Dryhurst, G. and Monks, T. J. (2000). Role of quinones in toxicology, Chem. Res. Toxicol., 13, 135–160. Josephy, P. D. (1997). Glutathione and detoxification. In Molecular Toxicology. ed. Josephy, P. D., Series, Oxford University Press, New York and Oxford. Stumm, W. and Morgan, J. J. (1996). Aquatic Chemistry. Wiley-Interscience, New York. Martell, A. E. and Smith, R. M. (1989). Critical Stability Constants. Plenum Press, New York and London. Turner, D. R. (1995). Problems in trace metal speciation modelling. In Metal Speciation and Bioavailability in Aquatic Systems. eds. Tessier, A. and Turner, D. R., Vol. 3, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons Ltd, Chichester. Rozan, T. F., Benoit, G. and Luther, G. W. (1999). Measuring metal sulfide complexes in oxic river waters with square wave voltammetry, Environ. Sci. Technol., 33, 3021–3026.

B. I. ESCHER AND L. SIGG 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47.

48. 49. 50.

257

Rozan, T. F., Lassman, M. E., Ridge, D. P. and Luther, G. W. (2000). Evidence for iron, copper and zinc complexation as multinuclear sulphide clusters in oxic rivers, Nature, 406, 879–882. Kari, F. G. and Giger, W. (1995). Modeling the photochemical degradation of ethylenediaminetetraacetate in the River Glatt, Environ. Sci. Technol., 29, 2814–2827. Morel, F. M. M., Rueter, J. G., Anderson, D. M. and Guillard, R. R. L. (1979). Aquil: a chemically defined phytoplankton culture medium for trace metal studies, J. Phycol., 15, 135–141. Price, N. M., Harrison, G. I., Hering, J. G., Hudson, R. J. M., Nirel, P. M. V., Palenik, B. and Morel, F. M. M. (1988/89). Preparation and chemistry of the artificial culture medium aquil, Biol. Oceanogr., 6, 443–461. Buffle, J. (1988). Complexation Reactions in Aquatic Systems: an Analytical Approach. Ellis Horwood, Chichester. Tipping, E. and Hurley, M. A. (1992). A unifying model of cation binding by humic substances, Geochim. Cosmochim. Acta, 56, 3627–3641. Tipping, E. (1998). Humic ion-binding model VI: an improved description of the interactions of protons and metal ions with humic substances, Aquat. Geochem., 4, 3–48. Cook, R. L. and Langford, C. H. (1998). Structural characterization of a fulvic acid and a humic acid using solid-state ramp-CP-MAS 13 C nuclear magnetic resonance, Environ. Sci. Technol., 32, 719–725. Leenheer, J. A., Wershaw, R. L. and Reddy, M. M. (1995). Strong-acid, carboxyl groups in fulvic acid from the Suwannee River, Georgia. 1. Minor structures, Environ. Sci. Technol., 29, 393–398. Leenheer, J. A., Wershaw, R. L. and Reddy, M. M. (1995). Strong-acid, carboxyl groups in fulvic acid from the Suwannee River, Georgia. 2. Major structures, Environ. Sci. Technol., 29, 399–405. Leenheer, J. A., Brown, G. K., MacCarthy, P. and Cabaniss, S. E. (1998). Models of metal binding structures in fulvic acid from the Suwannee River, Georgia, Environ. Sci. Technol., 32, 2410–2416. Tipping, E. (1994). WHAM-a chemical equilibrium model and computer code for waters, sediments, and soils incorporating a discrete site/electrostatic model of ionbinding by humic substances, Comput. Geosci., 20, 973–1023. Bartschat, B. M., Cabaniss, S. E. and Morel, F. M. M. (1992). Oligoelectrolyte model for cation binding by humic substances, Environ. Sci. Technol., 26, 284–294. Benedetti, M. F., Milne, C. J., Kinniburgh, D. G., van Riemsdijk, W. H. and Koopal, L. K. (1995). Metal ion binding to humic substances: application of the non-ideal competitive adsorption model, Environ. Sci. Technol., 29, 446–457. Kinniburgh, D. G., van Riemsdijk, W. H., Koopal, L. K., Borkovec, M., Benedetti, M. F. and Avena, M. J. (1999). Ion binding to natural organic matter: competition, heterogeneity, stoichiometry and thermodynamic consistency, Colloids Surf. A, 151, 147–166. Bruland, K. W. (1989). Oceanic zinc speciation: complexation of zinc by natural organic ligands in the central North Pacific, Limnol. Oceanogr., 34, 267–283. Bruland, K. W. (1992). Complexation of cadmium by natural organic ligands in the central North Pacific, Limnol. Oceanogr., 37, 1008–1017. Bruland, K. W., Donat, J. R. and Hutchins, D. A. (1991). Interactive influence of bioactive trace metals on biological production in oceanic waters, Limnol. Oceanogr., 36, 1555–1577.

258 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 51. 52. 53. 54.

55. 56. 57. 58. 59. 60. 61. 62. 63. 64.

65. 66. 67. 68. 69.

Coale, K. H. and Bruland, K. W. (1988). Copper complexation in the Northeast Pacific, Limnol. Oceanogr., 33, 1084–1101. Donat, J. R., Lao, K. A. and Bruland, K. W. (1994). Speciation of dissolved copper and nickel in South San Francisco Bay: a multi-method approach, Anal. Chim. Acta, 284, 547–571. Kozelka, P. B. and Bruland, K. W. (1998). Chemical speciation of dissolved Cu, Zn, Cd, Pb in Narragansett Bay, Rhode Island, Mar. Chem., 60, 267–282. Rue, E. L. and Bruland, K. W. (1995). Complexation of iron (III) by natural organic ligands in the Central North Pacific as determined by a new competitive ligand equilibration/adsorptive cathodic stripping voltammetric method, Mar. Chem., 50, 117–138. Buckley, P. J. M. and van den Berg, C. M. G. (1986). Copper complexation profiles in the Atlantic Ocean, Mar. Chem., 19, 281–296. Gledhill, M. and van den Berg, C. M. G. (1994). Determination of complexation of iron(III) with natural organic complexing ligands in seawater using cathodic stripping voltammetry, Mar. Chem., 47, 41–54. van den Berg, C. M. G., Buckley, P. J. M., Huang, Z. Q. and Nimmo, M. (1986). An electrochemical study of the speciation of copper, zinc and iron in two estuaries in England, Estuar. Coastal Shelf Sci., 22, 479–486. van den Berg, C. M. G. (1995). Evidence for organic complexation of iron in seawater, Mar. Chem., 50, 139–157. Macrellis, H. M., Trick, C. G., Rue, E. L., Smith, G. and Bruland, K. W. (2001). Collection and detection of natural iron-binding ligands from seawater, Mar. Chem., 76, 175–187. Xue, H.-B. and Sigg, L. (1993). Free cupric ion concentration and Cu(II) speciation in a eutrophic lake, Limnol. Oceanogr., 38, 1200–1213. Xue, H.-B. and Sigg, L. (1994). Zinc speciation in lake waters and its determination by ligand exchange with EDTA and differential pulse anodic stripping voltammetry, Anal. Chim. Acta, 284, 505–515. Xue, H.-B., Kistler, D. and Sigg, L. (1995). Competition of copper and zinc for strong ligands in a eutrophic lake, Limnol. Oceanogr., 40, 1142–1152. Xue, H.-B. and Sigg, L. (1998). Cd speciation and complexation by natural organic ligands in freshwater, Anal. Chim. Acta, 363, 249–259. Achterberg, E. P., van den Berg, C. M. G., Boussemart, M. and Davison, W. (1997). Speciation and cycling of trace metals in Esthwaite Water: a productive English lake with seasonal deep-water anoxia, Geochim. Cosmochim. Acta, 61, 5233–5253. Xue, H.-B. and Sigg, L. (1999). Comparison of the complexation of Cu and Cd by humic or fulvic acids or by ligands observed in lake waters, Aquat. Geochem., 5, 313–335. Kogut, M. B. and Voelker, B. M. (2001). Strong copper-binding behaviour of terrestrial humic substances in seawater, Environ. Sci. Technol., 35, 1149–1156. Town, R. M. and Filella, M. (2000). Dispelling the myths: is the existence of L1 and L2 ligands necessary to explain metal ion speciation in natural waters? Limnol. Oceanogr., 45, 1341–1357. Moffett, J. W. and Brand, L. E. (1996). Production of strong, extracellular Cu chelators by marine cyanobacteria in response to Cu stress, Limnol. Oceanogr., 41, 388–395. Moffett, J. W., Brand, L. E., Croot, P. L. and Barbeau, K. A. (1997). Cu speciation and cyanobacterial distribution in harbors subject to anthropogenic Cu inputs, Limnol. Oceanogr., 42, 789–799.

B. I. ESCHER AND L. SIGG 70. 71. 72. 73. 74. 75. 76. 77.

78.

79. 80. 81. 82.

83. 84. 85.

86.

259

Croot, P. L., Moffett, J. W. and Brand, L. E. (2000). Production of extracellular Cu complexing ligands by eucaryotic phytoplankton in response to Cu stress, Limnol. Oceanogr., 45, 619–627. Lee, J. G., Ahner, B. A. and Morel, F. M. M. (1996). Export of cadmium and phytochelatin by the marine diatom Thalassiosira weissflogii, Environ. Sci. Technol., 30, 1814–1821. Leal, M. F. C. and van den Berg, C. M. G. (1998). Evidence for strong copper(I) complexation by organic ligands in seawater, Aquat. Geochem., 4, 49–75. Le Gall, A. C. and van den Berg, C. M. G. (1998). Folic acid and glutathione in the water column of the North East Atlantic, Deep-Sea Res., 45, 1903–1918. Bruland, K. W., Franks, R. P., Knauer, G. A. and Martin, J. H. (1979). Sampling and analytical methods for the determination of copper, cadmium, zinc and nickel at the nanogram per liter level in sea water, Anal. Chim. Acta, 105, 233–245. Bakker, E., Bu¨hlmann, P. and Pretsch, E. (1997). Carrier-based ion-selective electrodes and bulk optodes. 1. General characteristics, Chem. Rev., 97, 3083–3132. Bu¨hlmann, P., Pretsch, E. and Bakker, E. (1998). Carrier-based ion-selective electrodes and bulk optodes. 2. Ionophores for potentiometric and optical sensors, Chem. Rev., 98, 1593–1687. Phinney, J. T. and Bruland, K. W. (1997). Trace metal exchange in solution by the fungicides Ziram and Maneb (dithiocarbamates) and subsequent uptake of lipophilic organic zinc, copper and lead complexes into phytoplankton cells, Environ. Toxicol. Chem., 16, 2046–2053. Schweigert, N., Hunziker, R. W., Escher, B. I. and Eggen, R. I. L. (2001). The acute toxicity of (chloro-)catechols and (chloro-)catechol–copper combinations in Escherichia coli corresponds to their membrane toxicity in vitro, Environ. Toxicol. Chem., 2, 239–247. Mason, R. P., Reinfelder, J. R. and Morel, F. M. M. (1996). Uptake, toxicity, and trophic transfer of mercury in a coastal diatom, Environ. Sci. Technol., 30, 1835–1845. Reinfelder, J. R. and Chang, S. I. (1999). Speciation and microalgal bioavailability of inorganic silver, Environ. Sci. Technol., 33, 1860–1863. Benoit, J. M., Gilmour, C. C., Mason, R. P. and Heyes, A. (1999). Sulfide controls on mercury speciation and bioavailability to methylating bacteria in sediment pore waters, Environ. Sci. Technol., 33, 951–957. Pelletier, E. (1995). Environmental organometallic chemistry of mercury, tin and lead: present status and perspectives. In Metal Speciation and Bioavailability in Aquatic Systems. eds. Tessier, A. and Turner, D. R., Vol. 3, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Chichester, pp. 103–148. Krabbenhoft, D. P., Benoit, J. M., Babiarz, C. L., Hurley, J. P. and Andren, A. W. (1995). Mercury cycling in the Allequash Creek watershed, Northern Wisconsin, Water, Air, Soil Poll., 80, 425–433. Babiarz, C. L., Hurley, J. P., Hoffmann, S. R., Andren, A. W., Shafer, M. M. and Armstrong, D. E. (2001). Partitioning of total mercury and methylmercury to the colloidal phase in freshwaters, Environ. Sci. Technol., 35, 4773–4782. Hurley, J. P., Benoit, J. M., Babiarz, C. L., Shafer, M. M., Andren, A. W., Sullivan, J. R., Hammond, R. and Webb, D. A. (1995). Influences of watershed characteristics on mercury levels in Wisconsin rivers, Environ. Sci. Technol., 29, 1867–1875. Lindqvist, O., Johansson, K., Aastrup, M., Andersson, A., Bringmark, L., Hovse˚ ., Meili, M. and Timm, B. (1991). Mercury in the nius, G., Ha˚kanson, L., Iverfeldt, A

260 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

87. 88. 89.

90. 91. 92. 93. 94.

95. 96. 97. 98.

99. 100. 101. 102.

103.

Swedish environment – recent research on causes, consequences and corrective methods, Water, Air, Soil Poll., 55, 1–261. Gilmour, C. C., Henry, E. A. and Mitchell, R. (1992). Sulfate stimulation of mercury methylation in freshwater sediments, Environ. Sci. Technol., 26, 2281–2287. Amirbahman, A., Reid, A. L., Haines, T. A., Kahl, J. S. and Arnold, C. (2002). Association of methylmercury with dissolved humic acids, Environ. Sci. Technol., 36, 690–695. Arnold, C. G., Weidenhaupt, A., David, M. M., Mu¨ller, S. R., Haderlein, S. B. and Schwarzenbach, R. P. (1997). Aqueous speciation and 1-octanol–water partitioning of tributyl- and triphenyltin: effect of pH and ion composition, Environ. Sci. Technol., 31, 2596–2602. Waite, T. D., Szymczak, R., Espey, Q. I. and Furnas, M. J. (1995). Diel variations in iron speciation in northern Australian shelf waters, Mar. Chem., 50, 79–91. O’Sullivan, D. W., Hanson, A. K., Miller, W. L. and Kester, D. R. (1991). Measurement of Fe(II) in surface-water of the equatorial Pacific, Limnol. Oceanogr., 36, 1727–1741. Emmenegger, L., Scho¨nenberger, R., Sigg, L. and Sulzberger, B. (2001). Lightinduced redox cycling of iron in circumneutral lakes, Limnol. Oceanogr., 46, 49–61. Shaked, Y., Erel, Y. and Sukenik, A. (2002). Phytoplankton-mediated redox cycle of iron in the epilimnion of Lake Kinneret, Environ. Sci. Technol., 36, 460–467. Price, N. M. and Morel, F. M. M. (1990). Role of extracellular enzymatic reactions in natural waters. In Aquatic Chemical Kinetics. Reaction Rates of Processes in Natural Waters. ed. Stumm, W., Wiley Interscience Series on Environmental Science and Technology, New York, pp. 235–257. Eide, D. and Guerinot, M. L. (1997). Metal ion uptake in eukaryotes, ASM News, 63, 199–205. Johnson, K. S., Gordon, R. M. and Coale, K. H. (1997). What controls dissolved iron concentrations in the world ocean? Mar. Chem., 57, 137–161. Buffle, J. and Leppard, G. G. (1995). Characterization of aquatic colloids and macromolecules. 1. Structure and behaviour of colloidal material, Environ. Sci. Technol., 29, 2169–2175. Benoit, G., Oktay-Marshall, S. D., Cantu, A. I., Hood, E. M., Coleman, C. H., Corapcioglu, M. O. and Santschi, P. H. (1994). Partitioning of Cu, Pb, Ag, Zn, Fe, Al and Mn between filter-retained particles, colloids and solution in six Texas estuaries, Mar. Chem., 45, 307–336. Baskaran, M. and Santschi, P. H. (1993). The role of particles and colloids in the transport of radionuclides in coastal environments of Texas, Mar. Chem., 43, 95–114. Wen, L.-S., Santschi, P., Gill, G. and Paternostro, C. (1999). Estuarine trace metal distributions in Galveston Bay: importance of colloidal forms in the speciation of the dissolved phase, Mar. Chem., 63, 185–212. Ross, J. M. and Sherrell, R. M. (1999). The role of colloids in trace metal transport and adsorption behaviour in New Jersey Pinelands streams, Limnol. Oceanogr., 44, 1019–1034. Hering, J. G. and Morel, F. M. M. (1990). The kinetics of trace metal complexation: implications for metal reactivity in natural waters. In Aquatic Chemical Kinetics – Reaction Rates of Processes in Natural Waters. ed. Stumm, W., Wiley Interscience Series on Environmental Science and Technology, New York, pp. 145–171. Margerum, D. W., Cayley, G. R., Weatherburn, D. C. and Pagenkopf, G. K. (1978). Kinetics and mechanisms of complex formation and ligand exchange. In

B. I. ESCHER AND L. SIGG

104. 105. 106. 107. 108. 109. 110. 111. 112. 113.

114. 115. 116. 117. 118. 119.

120. 121.

261

Coordination Chemistry. ed. Martell, A. E., Vol. 2, Series, Am. Chem. Soc., Monogr. Nendza, M. (1991). QSARs of bioconcentration: validity assessment of logPow/ logBCF correlations. In Bioaccumulation in Aquatic Systems. eds. Nagel, R. and Loskill, R., Series, VCH, Weinheim, Germany, pp. 43–66. Hansch, C. (1969). A quantitative approach to biochemical structure-activity relationships, Acc. Chem. Res., 2, 232–239. Hermens, J. L. M. (1989). Quantitative structure–activity relationships of environmental pollutants. In The Handbook of Environmental Chemistry, Reaction and Processes. ed. Hutzinger, J., Series, Springer, Berlin, pp. 111–162. Hermens, J. L. M. and Verhaar, H. J. M. (1996). QSARs in predictive environmental toxicology. Preface: from mechanistic studies to applications in risk assessment, Environ. Sci. Pollut. Res., 3, 96–98. Leahy, D. E., Morris, J. J., Taylor, P. J. and Wait, A. R. (1992). Model solvent systems for QSAR. 2. Fragment values (F-values) for the ‘critical quartet’, J. Chem. Soc. Perkin Trans., 2, 723–731. Chiou, C. T. (1985). Partition coefficients of organic compounds in lipid–water systems and correlations with fish bioconcentration factors, Environ. Sci. Technol., 19, 57–62. New, R. R. C. ed. (1990). Liposomes. Series, Oxford University Press, Oxford. Ostro, M. ed. (1983). Liposomes. Series, Marcel Dekker, New York. Kansy, M., Senner, F. and Gubernator, F. (1998). Physicochemical high throughput screening: parallel artificial membrane permeation assay in the description of passive absorption processes, J. Med. Chem., 41, 1007–1010. Kra¨mer, S. (2001). Liposome/water partitioning: theory, techniques, and applications. In Pharmacokinetic Optimization in Drug Research: Biological, Physicochemical, and Computational Strategies. eds. Testa, B., van Waterbeemd, H., Folkers, G. and Guy, R., Series, Verlag Helvetica Chimica Acta, Zu¨rich. Miyoshi, H., Maeda, N., Tokutake, N. and Fujita, T. (1987). Quantitative analysis of partition behaviour of substituted phenols from aqueous phase into liposomes made of lecithin and various lipids, Bull. Chem. Soc. Jpn, 60, 4357–4362. Pauletti, G. M. and Wunderli-Allenspach, H. (1994). Partition coefficients in vitro: artificial membranes as a standardized distribution model, Eur. J. Pharm. Sci., 1, 273–282. Escher, B. I. and Schwarzenbach, R. P. (1996). Partitioning of substituted phenols in liposome–water, biomembrane–water, and octanol–water systems, Environ. Sci. Technol., 30, 260–270. Avdeef, A., Box, K. J., Comer, J. E. A., Hibbert, C. and Tam, K. Y. (1998). pH-metric log P 10. Determination of liposomal membrane–water partition coefficients of ionisable drugs, Pharmaceut. Res., 15, 209–215. Pidgeon, C. and Ong, S. W. (1995). Predicting drug–membrane interactions, Chemtech, 25, 38–48. Loidl-Stahlhofen, A., Eckert, A., Hartmann, T. and Scho¨ttner, M. (2001). Solidsupported lipid membranes as a tool for determination of membrane affinity: high-throughput-screening of a physicochemical parameter, J. Pharmaceut. Sci., 90, 599–606. Escher, B. I., Schwarzenbach, R. P. and Westall, J. C. (2000). Evaluation of liposome–water partitioning of organic acids and bases: 2. Comparison of experimental determination methods, Environ. Sci. Technol., 34, 3962–3698. Beigi, F., Gottschalk, I., Lagerquist Ha¨gglund, C., Haneskog, L., Brekkan, E., ¨ sterberg, T. and Lundahl, P. (1998). Immobilized liposomes and Zhang, Y. X., O

262 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

122.

123. 124. 125. 126. 127.

128. 129. 130. 131. 132. 133. 134. 135. 136.

137. 138.

biomembrane partitioning chromatography of drugs for prediction of drug transport, Int. J. Pharmaceut., 164, 129–137. Yang, Q., Liu, X. Y., Umetani, K., Kamo, N. and Miyake, J. (1999). Partitioning of triphenylalkylphosphonium homologues in gel bead-immobilized liposomes: chromatographic measurement of their membrane partition coefficients, Biochim. Biophys. Acta-Biomem., 1417, 122–130. Smejtek, P., Wang, S. and Barstad, A. W. (1987). Adsorption of ionised and neutral pentachlorophenol to phosphatidylcholine membranes, Biochim. Biophys. Acta, 905, 213–221. Hansch, C. and Leo, A. (1995). Exploring QSAR. Fundamentals and Applications in Chemistry and Biology. American Chemical Society, Washington, DC. Fujita, T. (1966). The analysis of physiological activity of substituted phenols with substituent constants, J. Med. Chem., 9, 797–803. Manners, C. N., Payling, D. W. and Smith, D. A. (1988). Distribution coefficient, a convenient term for the relation of predictable physico-chemical properties to metabolic processes, Xenobiotica, 18, 331–350. Scherrer, R. A. (1984). The treatment of ionisable compounds in quantitative structure–activity studies with special consideration to ion partitioning. In Pesticide Synthesis Through Rational Approaches. eds. Magee, P. S., Kohn, G. K. and Menn, J. J., Vol. 255, Series, ACS Symposium Series, Washington, D. C. Westall, J. C., Leuenberger, C. and Schwarzenbach, R. P. (1985). Influence of pH and ionic strength on the aqueous–nonaqueous distribution of chlorinated phenols, Environ. Sci. Technol., 19, 193–198. Jafvert, C. T., Westall, J. C., Grieder, E. and Schwarzenbach, R. P. (1990). Distribution of hydrophobic ionogenic compounds between octanol and water: organic acids, Environ. Sci. Technol., 24, 1795–1803. Johnson, C. A. and Westall, J. C. (1990). Effect of pH and KCl concentration on the octanol–water distribution of methylanilines, Environ. Sci. Technol., 24, 1869–1875. Westall, J. C., Johnson, C. A. and Zhang, W. (1990). Distribution of LiCl, NaCl, KCl, HCl, MgCl2 , and CaCl2 between octanol and water, Environ. Sci. Technol., 24, 1803–1810. Austin, R. P., Barton, P., Davis, A. M., Manners, C. N. and Stansfield, M. C. (1998). The effect of ionic strength on liposome-buffer and 1-octanol-buffer distribution coefficients, J. Pharmaceut. Sci., 87, 599–607. Pagliara, A., Carrupt, P. A., Caron, G., Gaillard, P. and Testa, B. (1997). Lipophilicity profiles of ampholytes, Chem. Rev., 97, 3385–3400. Ba¨uerle, H. D. and Seelig, J. (1991). Interaction of charged and uncharged calcium channel antagonists with phospholipid membranes. Binding equilibrium, binding enthalpy, and membrane location, Biochem., 30, 7203–7211. Huang, C.-H. (1969). Phosphatidylcholine vesicles. Formation and physical characteristics, Biochem., 8, 344–352. Casadio, R., Venturoli, G. and Melandri, B. A. (1988). Evaluation of the electrical capacitance in biological membranes at different phospholipid to protein ratios – a study in photosynthetic bacterial chromatophores based on electrochromic effects, Eur. Biophys. J., 16, 243–253. McLaughlin, S. (1989). The electrostatic properties of membranes, Ann. Rev. Biophys. Biophys. Chem., 18, 113–136. Packham, N. K., Berriman, J. A. and Jackson, J. B. (1978). The charging capacitance of the chromatophore membrane, FEBS Lett., 89, 205–210.

B. I. ESCHER AND L. SIGG

263

139. Smejtek, P. and Wang, S. R. (1993). Distribution of hydrophobic ionisable xenobiotics between water and lipid membranes: pentachlorophenol and pentachlorophenate. A comparison with octanol–water partition, Arch. Environ. Contam. Toxicol., 25, 394–404. 140. Escher, B. I., Schwarzenbach, R. P. and Westall, J. C. (2000). Evaluation of liposome-water partitioning of organic acids and bases: 1. Development of a sorption model, Environ. Sci. Technol., 34, 3954–3961. 141. Betageri, G. V. and Rogers, J. A. (1988). The liposome as a distribution model in QSAR studies, Int. J. Pharmaceut., 46, 95–102. 142. Katz, Y. and Diamond, J. M. (1974). Thermodynamic constants for nonelectrolyte partition between dimyristoyl lecithin and water, J. Membr. Biol., 17, 101–120. 143. Rogers, J. A. and Davis, S. S. (1980). Functional group contributions to the partitioning of phenols between liposomes and water, Biochim. Biophys. ActaBiomem., 598, 392–404. 144. Martinez, F. and Gomez, A. (2002). Thermodynamics of partitioning of some sulfonamides in 1-octanol-buffer and liposome systems, J. Phys. Org. Chem., 15, 874–880. 145. Rowe, E. S., Zhang, F. L., Leung, T. W., Parr, J. S. and Guy, P. T. (1998). Thermodynamics of membrane partitioning for a series of n-alcohols determined by titration calorimetry: role of hydrophobic effects, Biochem., 37, 2430–2440. 146. Benz, R. (1988). Structural requirement for the rapid movement of charged molecules across membranes. Experiments with tetraphenylborate analogues, Biophys. J., 54, 25–33. 147. Anderson, N. H., Davis, S. S., James, M. and Kojima, I. (1983). Thermodynamics of distribution of p-substituted phenols between aqueous solution and organic solvents and phospholipid vesicles, J. Pharmaceut. Sci., 72, 443–448. 148. van Wezel, A. P., Cornelissen, G., van Miltenburg, J. K. and Opperhuizen, A. (1996). Membrane burdens of chlorinated benzenes lower the main phase transition temperature in dipalmitoyl-phosphatidylcholine vesicles: implications for toxicity by narcotic chemicals, Environ. Toxicol. Chem., 15, 203–212. 149. Opperhuizen, A., Serne´, P. and van den Steen, J. M. D. (1988). Thermodynamics of fish/water and octan-1-ol/water partitioning of some chlorinated benzenes, Environ. Sci. Technol., 22, 286–292. 150. Flewelling, R. F. and Hubbell, W. L. (1986). The membrane dipole potential in a total membrane potential model: applications to hydrophobic ion interactions with membranes, Biophys. J., 49, 541–552. 151. Austin, R. P., Davis, A. M. and Manners, C. N. (1995). Partitioning of ionizing molecules between aqueous buffers and phospholipid vesicles, J. Pharmaceut. Sci., 84, 1180–1183. 152. Balon, K., Riebesehl, B. U. and Muller, B. W. (1999). Determination of liposome partitioning of ionisable drugs by titration, J. Pharmaceut. Sci., 88, 802–806. 153. Fruttero, R., Caron, G., Fornatto, E., Boschi, D., Ermondi, G., Gasco, A., Carrupt, P. A. and Testa, B. (1998). Mechanisms of liposomes/water partitioning of (p-methylbenzyl)alkylamines, Pharmaceut. Res., 15, 1407–1413. 154. Benz, R. and McLaughlin, S. (1983). The molecular mechanism of action of the proton ionophore FCCP (carbonyl cyanide p-trifluoromethoxyphenylhydrazone), Biophys. J., 41, 381–398. 155. Kasianowicz, J., Benz, R. and McLaughlin, S. (1984). The kinetic mechanism by which CCCP (carbonyl cyanide m-chloro-phenyl-hydrazone) transports protons across membranes, J. Membrane Biol., 82, 179–190.

264 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 156. Kasianowicz, J., Benz, R. and McLaughlin, S. (1987). How do protons cross the membrane solution interface? Kinetic studies on bilayer membranes exposed to the protonophore S-13 (5-chloro-3-tert-butyl-20 -chloro-40 -nitrosalicylanilide), J. Membr. Biol., 95, 73–89. 157. Quintanar-Guerrero, D., Alle´mann, E., Fessi, H. and Doelker, E. (1997). Applications of the ion pair concept to hydrophilic substances with special emphasis on peptides, Pharmaceut. Res., 14, 119–127. 158. Shibata, A., Ikawa, K. and Terada, H. (1995). Site of action of the local anaesthetic tetracaine in a phosphatidylcholine bilayer with incorporated cardiolipin, Biophys. J., 69, 470–477. 159. Kra¨mer, S. D. and Wunderli-Allenspach, H. (1996). The pH-dependence in the partitioning behaviour of (RS)-[H-3]propranolol between MDCK cell lipid vesicles and buffer, Pharmaceut. Res., 13, 1851–1855. 160. Kra¨mer, S. D., Jakits-Deiser, C. and Wunderli-Allenspach, H. (1997). Free fatty acids cause pH-dependent changes in drug–lipid membrane interactions around physiological pH, Pharmaceut. Res., 14, 827–832. 161. Rottenberg, H. (1979). The measurement of membrane potential and DpH in cells, organelles and vesicles, Methods Enzym., 55, 547–569. 162. Daugelavicius, R., Bakiene, E., Berzinskiene, J. and Bamford, D. H. (1997). Binding of lipophilic anions to microbial cells, Bioelectrochem. Bioenerg., 42, 263–274. 163. Hutterer, R., Kra¨mer, K., Schneider, F. W. and Hof, M. (1997). The localization of the local anesthetic tetracaine in phospholipid vesicles: a fluorescence quenching and resonance energy transfer study, Chem. Phys. Lipids, 90, 11–23. 164. Herbette, L., Katz, A. M. and Sturtevant, J. M. (1983). Comparisons of the interaction of propranolol and timolol with model and biological membrane systems, Mol. Pharmacol., 24, 259–269. 165. Smejtek, P. and Wang, S. (1991). Domains and anomalous adsorption isotherms of dipalmitoylphosphatidylcholine membranes and lipophilic ions: pentachlorophenolate, tetraphenylborate, and dipicrylamine, Biophys. J., 59, 1064–1073. 166. Jorgensen, K., Ipsen, J. H., Mouritsen, O. G., Bennett, D. and Zuckermann, M. J. (1991). The effects of density fluctuations on the partitioning of foreign molecules into lipid bilayers: application to anaesthetics and insecticides, Biochim. Biophys. Acta, 1067, 241–253. 167. Mavromoustakos, T., Yang, D. P., Charalambous, A., Herbette, L. G. and Makriyannis, A. (1990). Study of the topography of cannabinoids in model membranes using X-ray diffraction, Biochim. Biophys. Acta, 1024, 336–344. 168. Seelig, A., Allegrini, P. R. and Seelig, J. (1988). Partitioning of local anesthetics into membranes: surface charge effects monitored by the phospholipid headgroup, Biochim. Biophys. Acta, 939, 267–276. 169. Ellena, J. F., Dominey, R. N., Archer, S. J., Xu, Z. C. and Cafiso, D. S. (1987). Localization of hydrophobic ions in phospholipid bilayers using 1 H nuclear Overhauser effect spectroscopy, Biochem., 26, 4584–4592. 170. Shimooka, T., Shibata, A. and Terada, H. (1992). The local anesthetic tetracaine destabilizes membrane structure by interaction with polar headgroups of phospholipids, Biochim. Biophys. Acta, 1104, 261–268. 171. Dubey, A. K., Eryomin, V. A., Taraschi, T. F. and Janes, N. (1996). Alcohol binding to liposomes by 2 H NMR and radiolabel binding assays: does partitioning describe binding? Biophys. J., 70, 2307–2315.

B. I. ESCHER AND L. SIGG

265

172. Miyoshi, H., Nishioka, T. and Fujita, T. (1986). Quantitative analysis of effects of substituted phenols on membrane characteristics of lecithin liposomes, Bull. Chem. Soc. Jpn., 59, 1099–1107. 173. Yeagle, P. L., Hutton, W. C., Huang, C. and Martin, R. B. (1975). Headgroup conformation and lipid–cholesterol association in phosphatidylcholine vesicles: A 31 P{1 H} nuclear Overhauser effect study, Proc. Natl. Acad. Sci. USA, 72, 3477–3481. 174. Eftink, M. R., Puri, R. K. and Ghahramani, M. D. (1985). Local anesthetic– phospholipid interactions. The pH-dependence of the binding of dibucaine to dimyristoylphosphatidylcholine vesicles, Biochim. Biophys. Acta, 813, 137–140. 175. Meijer, L. A., Leermakers, F. A. M. and Lyklema, J. (1999). Self-consistent-field modelling of complex molecules with united atom detail in inhomogeneous systems. Cyclic and banched foreign molecules in dimyristoylphosphatidylcholine membranes, J. Chem. Phys., 110, 6560–6579. 176. Lessard, J. G. and Fragata, M. (1986). Micropolarities of lipid bilayers and micelles. 3. Effect of monovalent ions on the dielectric constant of the water– membrane interface of unilamellar phosphatidylcholine vesicles, J. Phys. Chem., 90, 811–817. 177. Smejtek, P., Barstad, A. W. and Hsu, K. (1987). Dielectric properties of adsorption/ionization site of pentachlorophenol in lipid membranes, Biochim. Biophys. Acta, 902, 109–127. 178. Scherer, P. G. and Seelig, J. (1989). Electric charge effects on phospholipid headgroups. Phosphatidylcholine in mixtures with cationic and anionic amphiphiles, Biochem., 28, 7720–7728. 179. Daniel, W. A., Bickel, M. H. and Honegger, U. E. (1995). The contribution of lysosomal trapping in the uptake of desipramine and chloroquine by different tissues, Pharmacol. Toxicol., 77, 402–406. 180. Trapp, S. (2000). Modelling uptake into roots and subsequent translocation of neutral and ionisable organic compounds, Pest Manag. Sci., 56, 767–778. 181. Saarikoski, J., Lindstro¨m, R., Tyynela¨, M. and Viluksela, M. (1986). Factors affecting the absorption of phenolics and carboxylic acids in the guppy (Poecilia reticulata), Ecotoxicol. Environ. Saf., 11, 158–173. 182. Stein, W. D. (1986). Transport and Diffusion Across Cell Membranes. Academic Press, Orlando, FL. 183. Connell, D. (1990). Bioaccumulation of Xenobiotic Compounds. CRC Press, Boca Raton, FL. 184. Nagel, R. and Loskill, R. eds. (1991) Bioaccumulation in Aquatic Systems. Contributions to the Assessment. Proceedings of an International Workshop, Berlin. Series, VCH, Weinheim, Germany. 185. Kishino, T. and Kobayashi, K. (1995). Relation between toxicity and accumulation of chlorophenols at various pH, and their absorption mechanism in fish, Water Res., 29, 431–442. 186. Terada, H. (1990). Uncouplers of oxidative phosphorylation, Environ. Health Perspect., 87, 213–218. 187. Miyoshi, H., Nishioka, T. and Fujita, T. (1987). Quantitative relationship between protonophoric and uncoupling activities of substituted phenols, Biochim. Biophys. Acta, 891, 194–204. 188. Miyoshi, H. and Fujita, T. (1988). Quantitative analysis of the uncoupling activity of substituted phenols with mitochondria from flight muscles of house flies, Biochim. Biophys. Acta, 935, 312–321.

266 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 189. Miyoshi, H., Nishioka, T., Tokutake, N. and Fujita, T. (1990). Quantitative analysis of uncoupling activity of substituted phenols with a physicochemical substituent and molecular parameters, Biochim. Biophys. Acta, 1016, 99–106. 190. Sunda, W. G. and Huntsman, S. A. (1998). Processes regulating metal accumulation and physiological effects: phytoplankton as model systems, Sci. Tot. Environ., 219, 165–181. 191. Silver, S. and Walderhaug, M. (1992). Gene regulation of plasmid-determined and chromosome-determined inorganic ion transport in bacteria, Microbiol. Rev., 56, 195–228. 192. Sunda, W. G. (1988/89). Trace metal interactions with marine phytoplankton, Biol. Oceanogr., 6, 411–442. 193. Morel, F. M. M., Hudson, R. J. M. and Price, N. M. (1991). Limitation of productivity by trace metals in the sea, Limnol. Oceanogr., 36, 1742–1755. 194. Morel, F. M. M. and Hering, J. G. (1993). Principles and Applications of Aquatic Chemistry. John Wiley & Sons, Ltd, New York. 195. Sunda, W. G. and Huntsman, S. A. (1995). Regulation of copper concentration in the oceanic nutricline by phytoplankton uptake and regeneration cycles, Limnol. Oceanogr., 40, 132–137. 196. Rich, H. W. and Morel, F. M. M. (1990). Availability of well-defined iron colloids to the marine diatom Thalassiosira weissflogii, Limnol. Oceanogr., 35, 652–662. 197. Crist, R. H., Oberholser, K., Schwartz, D., Marzoff, J., Ryder, D. and Crist, D. R. (1988). Interactions of metals and protons with algae, Environ. Sci. Technol., 22, 755–760. 198. Crist, R. H., Martin, J. R., Guptill, P. W., Eslinger, J. M. and Crist, D. R. (1990). Interaction of metals and protons with algae. 2. Ion exchange in adsorption and metal displacement by protons, Environ. Sci. Technol., 24, 337–342. 199. Plette, A. C. C., Benedetti, M. F. and van Riemsdijk, W. H. (1996). Competitive binding of protons, calcium, cadmium, and zinc to isolated cell walls of a grampositive soil bacterium, Environ. Sci. Technol., 30, 1902–1910. 200. Daughney, C. J. and Fein, J. B. (1998). The effect of ionic strength on the 2þ adsorption of Hþ , Cd2þ , Pb and Cu2þ by Bacillus subtilis and Bacillus licheniformis: a surface complexation model, J. Colloid Interf. Sci., 198, 53–77. 201. Knauer, K., Behra, R. and Sigg, L. (1997). Adsorption and uptake of copper by the green alga Scenedesmus subspicatus (Chlorophyta), J. Phycol., 33, 596–601. 202. Kiefer, E., Sigg, L. and Schosseler, P. (1997). Chemical and spectroscopic characterization of algae surfaces, Environ. Sci. Technol., 31, 759 – 764. 203. Di Toro, D. M., Allen, H. E., Bergman, H. L., Meyer, J. S. and Paquin, P. R. (2001). Biotic ligand model of the acute toxicity of metals. 1. Technical basis, Environ. Toxicol. Chem., 20, 2383–2396. 204. Santore, R. C., Di Toro, D. M., Paquin, P. R., Allen, H. E. and Meyer, J. S. (2001). Biotic ligand model of the acute toxicity of metals. 2. Application to acute copper toxicity in freshwater fish and Daphnia, Environ. Toxicol. Chem., 20, 2397–2402. 205. McGeer, J. C., Szebedinszky, C., McDonald, D. G. and Wood, C. M. (2002). The role of dissolved organic carbon in moderating the bioavailability and toxicity of Cu to rainbow trout during chronic waterborne exposure, Comp. Biochem. Physiol. Part C: Toxicol. Pharmacol., 133, 147–160. 206. Winkelmann, G., van der Helm, D. and Neilands, J. B. (1987). Iron Transport in Microbes, Plants and Animals. VCH, Weinheim. 207. Butler, A. (1998). Acquisition and utilization of transition metal ions by marine organisms, Science, 281, 207–210.

B. I. ESCHER AND L. SIGG

267

208. Martinez, J. S., Zhang, G. P., Holt, P. D., Jung, H.-T., Carrano, C. J., Haygood, M. G. and Butler, A. (2000). Self-assembling amphiphilic siderophores from marine bacteria, Science, 287, 1245–1247. 209. Reid, R. T., Live, D. H., Faulkner, D. J. and Butler, A. (1993). A siderophore from a marine bacterium with an exceptional ferric ion affinity constant, Nature, 366, 455–458. 210. Xu, G. F., Martinez, J. S., Groves, J. T. and Butler, A. (2002). Membrane affinity of the amphiphilic marinobactin siderophores, J. Am. Chem. Soc., 124, 13 408–13 415. 211. Wilhelm, S. W., Maxwell, D. P. and Trick, C. G. (1996). Growth, iron requirements, and siderophore production in iron-limited Synechococcus PCC 7002, Limnol. Oceanogr., 41, 89–97. 212. Errecalde, O., Seidl, M. and Campbell, P. G. C. (1998). Influence of a low molecular weight metabolite (citrate) on the toxicity of cadmium and zinc to the unicellular green alga Selenastrum capricornutum: an exception to the free-ion model, Water Res., 32, 419–429. 213. Fortin, C. and Campbell, P. G. C. (2001). Thiosulfate enhances silver uptake by a green alga: role of anion transporters in metal uptake, Environ. Sci. Technol., 35, 2214–2218. 214. Campbell, P. G. C., Twiss, M. R. and Wilkinson, K. J. (1997). Accumulation of natural organic matter on the surfaces of living cells: implications for the interaction of toxic solutes with aquatic biota, Can. J. Fish. Aquat. Sci., 54, 2543–2554. 215. Parent, L., Twiss, M. R. and Campbell, P. G. C. (1996). Influences of natural dissolved organic matter on the interaction of aluminum with the microalga Chlorella: a test of the free-ion model of trace metal toxicity, Environ. Sci. Technol., 30, 1713–1720. 216. Vigneault, B., Percot, A., Lafleur, M. and Campbell, P. G. C. (2000). Permeability changes in model and phytoplankton membranes in the presence of aquatic humic substances, Environ. Sci. Technol., 34, 3907–3913. 217. Boudou, A., Delnomdedieu, M., Georgescauld, D., Ribeyre, F. and Saouter, E. (1991). Fundamental roles of biological barriers in mercury accumulation and transfer in freshwater ecosystems (analysis at organism, organ, cell and molecular levels), Wat. Air, Soil Poll., 56, 807–822. 218. Gutknecht, J. (1981). Inorganic mercury (Hg2þ ) transport through lipid bilayer membranes, J. Membrane Biol., 61, 61–66. 219. Bienvenue, E., Boudou, A., Desmazes, J. P., Gavach, C., Georgescauld, D., Sandeaux, J., Sandeaux, R. and Seta, P. (1984). Transport of mercury compounds across bimolecular lipid membranes: effect of lipid composition, pH and chloride concentration, Chem.–Biol. Interact., 48, 91–101. 220. Ahsanullah, M. and Florence, T. M. (1984). Toxicity of copper to the marine amphiphod Allorchestes compressa in the presence of water- and lipid-soluble ligands, Marine Biol., 84, 41–45. 221. Florence, T. M., Powell, H. K. J., Stauber, J. L. and Town, R. M. (1992). Toxicity of lipid-soluble copper(II) complexes to the marine diatom Nitzschia Closterium – amelioration by humic substances, Water Res., 26, 1187–1193. 222. Phinney, J. T. and Bruland, K. W. (1994). Uptake of lipophilic organic Cu, Cd, and Pb complexes in the coastal diatom Thalassiosira weissflogii, Environ. Sci. Technol., 28, 1781–1790. 223. Higuchi, K., Saitoh, T. and Hiraide, M. (2002). Selective uptake of copper (II) ions in water by chelating agent-impregnated liposomes, Bunseki Kagaku, 51, 745–749.

268 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 224. Croot, P. L., Karlson, B., van Elteren, J. T. and Kroon, J. J. (1999). Uptake of 64 Cu-oxine by marine phytoplankton, Environ. Sci. Technol., 33, 3615–3621. 225. Block, M. and Pa¨rt, P. (1986). Increased availability of cadmium to perfused rainbow trout (Salmo gairdneri, Rich) gills in the presence of the complexing agents diethyl dithiocarbamate, ethyl xanthate and isopropyl xanthate, Aquat. Toxicol., 8, 295–302. 226. Warshawsky, A., Rogachev, I., Patil, Y., Baszkin, A., Weiner, L. and Gressel, J. (2001). Copper-specific chelators as synergists to herbicides: 1. Amphiphilic dithiocarbamates, synthesis, transport through lipid bilayers, and inhibition of Cu/Zn superoxide dismutase activity, Langmuir, 17, 5621–5635. 227. Palmer, F. B., Butler, C. A., Timperley, M. H. and Evans, C. W. (1998). Toxicity to embryo and adult zebrafish of copper complexes with two malonic acids as models for dissolved organic matter, Environ. Toxicol. Chem., 17, 1538–1545. 228. Fraser, J. K., Butler, C. A., Timperley, M. H. and Evans, C. W. (2000). Formation of copper complexes in landfill leachate and their toxicity to zebrafish embryos, Environ. Toxicol. Chem., 19, 1397–1402. 229. Zhu, B.-Z. and Chevion, M. (2000). Copper-mediated toxicity of 2,4,5-trichlorophenol: biphasic effect of the copper(I)-specific chelator neocuproine, Arch. Biochem. Biophys., 380, 267–273. 230. Stauber, J. L. and Florence, T. M. (1987). Mechanism of toxicity of ionic copper and copper complexes to algae, Marine Biol., 94, 511–519. 231. Leaner, J. J. and Mason, R. P. (2002). Factors controlling the bioavailability of ingested methylmercury to channel catfish and atlantic sturgeon, Environ. Sci. Technol., 36, 5124–5129. 232. Gabrielska, J., Sarapuk, J. and Przestalski, S. (1997). Role of hydrophobic and hydrophilic interactions of organotin and organolead compounds with model lipid membranes, Z. Naturforsch. C., 52, 209–216. 233. Hunziker, R. W., Escher, B. I. and Schwarzenbach, R. P. (2001). pH-dependence of the partitioning of triphenyltin and tributyltin between phosphatidylcholine liposomes and water, Environ. Sci. Technol., 35, 3899–3904. 234. Grigoriev, E. V., Pellerito, L., Yashina, N. S., Pellerito, C. and Petrosyan, V. S. (2000). Organotin(IV) chloride complexes with phosphocholine and dimyristoyll -a-phosphatidylcholine, Appl. Organomet. Chem., 14, 443–448. 235. Langner, M., Gabrielska, J., Kleszcynska, H. and Pruchnik, H. (1998). Effect of phenyltin compounds on lipid bilayer organization, Appl. Organomet. Chem., 12, 99–107. 236. Langner, M., Gabrielska, J. and Przestalski, S. A. (2000). Adsorption of phenyltin compounds onto phosphatidylcholine/cholesterol bilayers, Appl. Organomet. Chem., 14, 25–33. 237. Rozycka-Roszak, B., Pruchnik, H. and Kaminski, E. (2000). The effect of some phenyltin compounds on the thermotropic phase behaviour and the structure of model membranes, Appl. Organomet. Chem., 14, 465–472. 238. Ambrosini, A., Bertoli, E. and Zolese, G. (1996). Effect of organotin compounds on membrane lipids: fluorescence spectroscopy studies, Appl. Organomet. Chem., 10, 53–59. 239. Hunziker, R. W., Escher, B. I. and Schwarzenbach, R. P. (2002). Acute toxicity of triorganotin compounds: different specific effects on the energy metabolism and role of pH, Environ. Toxicol. Chem., 21, 1191–1197. 240. Langner, M., Gabrielska, J. and Przestalski, S. (2000). The effect of the dipalmitolylphosphatidylcholine lipid bilayer state on the adsorption of phenyltins, Appl. Organomet. Chem., 14, 152–159.

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241. Sarapuk, J., Kleszczynska, H. and Przestalski, S. (2000). Stability of model membranes in the presence of organotin compounds, Appl. Organomet. Chem., 14, 40–47. 242. Langston, W. J. (1996). Recent developments in TBT ecotoxicology, TEN, 3, 179–187. 243. Looser, P. W., Bertschi, S. and Fent, K. (1998). Bioconcentration and bioavailability of organotin compounds: influence of pH and humic substances, Appl. Organomet. Chem., 12, 601–611. 244. Looser, P. W., Fent, K., Berg, M., Goudsmit, G.-H. and Schwarzenbach, R. P. (2000). Uptake and elimination of triorganotin compounds by larval midge Chironomus riparius in the absence and presence of Aldrich humic acid, Environ. Sci. Technol., 34, 5165–5171. 245. Tomlin, C. D. S. ed. (1997) Pesticide Manual. Series, Bracknell, Berkshire: British Crop Protection Council. 246. Vazquez, J. L., Merino, S., Domenech, O., Berlanga, M., Vinas, M., Montero, M. T. and Hernandez-Borrell, J. (2001). Determination of the partition coefficients of a homologous series of ciprofloxacin: influence of the N-4 piperazinyl alkylation on the antimicrobial activity, Int. J. Pharmaceut., 220, 53–62. 247. Montero, M. T., Freixas, J. and Hernandez Borrell, J. (1997). Expression of the partition coefficients of a homologous series of 6-fluoroquinolones, Int. J. Pharmaceut., 149, 161–170. 248. March, D. (1990). Handbook of Lipid Bilayers. CRC Press, Baton Rouge, Fl.

6 Transport of Solutes Across Biological Membranes: Prokaryotes ¨ STER WOLFGANG KO Microbiology, Swiss Federal Institute for Environmental Science and Technology ¨ berlandstrasse 133, CH-8600 Du¨bendorf, Switzerland (EAWAG), U

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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Membranes of Bacteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Properties and Functions of the Cytoplasmic Membrane . . . 2.2 Intracytoplasmic Membranes . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 The Outer Membrane of Gram-negative Bacteria . . . . . . . . . 2.4 Cell Walls of Gram-positive Bacteria . . . . . . . . . . . . . . . . . . . 2.5 The Envelope of Mycobacteria . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Bacteria Devoid of Cell Wall Peptidoglycans. . . . . . . . . . . . . 3 Substrate Translocation Across Membranes: Various Approaches to Solve the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Folding, Membrane Insertion and Assembly of Transport Proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Different Driving Forces and Modes of Energy Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Classification of Transport Systems . . . . . . . . . . . . . . . . . . . . 3.4 Various Options for Transporting a Substrate. . . . . . . . . . . . 3.5 Controlling the Number of Active Transporter Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Transport Across the Outer Membrane of Gram-negative Bacteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 General Porins as Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Porins with Selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 TonB Dependent Receptors . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Transport Through the Cell Walls of Mycobacteria . . . . . . . . . . . 6 Transport Across the Cytoplasmic Membranes of Bacteria . . . . . 6.1 Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 MIP Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.2 Mechanosensitive Channels . . . . . . . . . . . . . . . . . . . . . 6.1.3 Gas Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Physicochemical Kinetics and Transport at Biointerfaces Edited by H. P. van Leeuwen and W. Ko¨ster. ß 2004 John Wiley & Sons, Ltd

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Secondary Active Transporters . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Uniport Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Symport Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 Antiport Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.4 Binding Protein-Dependent Secondary Transporters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Primary Active Transporters . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 ATPases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 ABC Transporters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2.1 Binding Protein-Dependent Uptake Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2.2 Systems Without Autonomous Binding Protein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.3 Other Primary Active Transporters (not Diphosphate-Bond-Hydrolysis Driven) . . . . . . . 6.4 Group Translocators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Uptake of Iron: a Combination of Different Strategies . . . . . . . . 7.1 Iron – a ‘Precious Metal’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Iron Transport Across the Outer Membranes of Gram-negative Bacteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Iron Transport Across the Cell Walls of Gram-positive Bacteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Iron Translocation Across the Cytoplasmic Membrane: Various Pathways . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1 feo Type Transport Systems for Ferrous Iron. . . . . . 7.4.2 Metal Transport Systems of the Nramp Type. . . . . . 7.4.3 ABC Transporters for Siderophores/Haem/ Vitamin B12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.4 ABC Transporters of the Ferric Iron Type . . . . . . . . 7.4.5 ABC Transporters for Iron and Other Metals . . . . . 7.5 Other Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6 Phylogenetic Aspects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.7 Iron Transport in Bacteria: Conclusion and Outlook . . . . . 8 Challenges for Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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INTRODUCTION

Many functions and vital processes are linked to biological membranes. To be surrounded by one or more lipid bilayers might be favourable for a micro-

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organism in order to be protected against harsh conditions and environmental stresses. Nonetheless, communication with the environment can be highly important for the survival of a cellular organism in a certain habitat. Information about temperature, osmolarity, pressure, pH, nutrients, antimicrobial agents, etc. will help a microorganism to find the most favourable terms and to adjust its metabolism to the environmental conditions. Moreover, the ability to communicate with members of the same species (e.g. by quorum sensing) is a prerequisite for organisation in populations. Thus, in the processes of sensing and signal transduction, membranes play an important role [1,2]. Membranes also constitute permeability barriers that prevent the passage of many molecules, including essential nutrients. Therefore, it is evident that all organisms have a need for specific transporters. In general, transport of solutes into and out of cells is catalysed by proteins that are embedded in or associated with membranes. This chapter cannot give a comprehensive description and encyclopaedic listing of all existing transport systems in prokaryotes. Mainly, import systems transporting low-molecular-mass substrates will be presented. The uptake of macromolecules like bacteriocins (e.g. colicins) or DNA is an interesting topic in its own right, and will not be discussed in detail. Another major topic, transport out of the cell, is only touched upon. Prokaryotes possess a variety of both more general and highly specific systems that are involved in export of molecules across the cytoplasmic membrane, which can mediate further secretion into the environment. Substrates of these export pathways include proteins (proteases, lipases, various enzymes, cytotoxins, cytolysins, colicins, hemophores) siderophores, amino acids, antibiotics, antimicrobial agents, heavy metals, and many more. Although many of the secretion systems have been studied in detail (e.g. the ‘channel-tunnel’ protein TolC [3,4] the bacterial multidrug efflux transporter AcrB [5], or the arsenate/arsenite export ATPase [6,7]), important questions remain unsolved. For mycobacteria that secrete proteins, which are likely to play an important role in their pathogenicity, there is a lack of knowledge as to how these proteins, and the polysaccharides of the capsule, cross the outer lipid barrier. In summary, the aim of this chapter is to give insights into the nature and composition of membranes serving as biological interphases or interfaces, and to provide an overview on the important types of translocators, thereby demonstrating the diversity of bacterial uptake systems and the different mechanisms of transport and energy coupling. Selected representative examples will be discussed in more detail. In order to illustrate the different strategies of substrate translocation across membranes, and to highlight some unique features of transport, a special focus will be on the iron sequestering systems. In this context, the import of siderophores and haemophores, which are exported, then reshuffled and taken up in a receptor-mediated manner, will be described.

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MEMBRANES OF BACTERIA

Different types of membranes are found in bacteria: . the cytoplasmic membrane (CM) is common for all groups of bacteria. This plasma membrane in prokaryotes performs many of the functions carried out by membranous organelles in eukaryotes. Invagination of the cytoplasmic membrane results in various morphologically different intracytoplasmic membrane structures. . the outer membrane (OM) is characteristic of Gram-negative bacteria. . a special type of membrane forms the envelope of mycobacteria. 2.1 PROPERTIES AND FUNCTIONS OF THE CYTOPLASMIC MEMBRANE The architecture of the CM bilayer is symmetrical, with an equal distribution of the lipids (exclusively phospholipids, mainly phosphatidylethanolamine, phosphatidylglycerol and cardiolipin) among the inner and the outer leaflet. In principle, this holds true for most bacteria, except for those living at extremely high temperatures. For further information, see also Chapter 1 of this volume. A number of vital functions are associated with or linked to the CM: . osmotic and permeability barrier; . coordination of DNA replication and segregation with septum formation and cell division; . energy-generating functions, involving respiratory and photosynthetic electron transport systems, establishment of proton motive force, and transmembrane ATP-synthesising ATPase; . synthesis of membrane lipids (including lipopolysaccharide in Gram-negative cells); . synthesis of the cell wall peptidoglycan murein (see below); . sensing functions (e.g. quorum sensing, chemotaxis, including motility); . assembly and secretion of extracytoplasmic proteins; . location of transport systems (import and export) for specific solutes (nutrients and ions). In Gram-negative bacteria which are characterised by a rather complex cell envelope, the CM is also referred to as ‘inner membrane’ to distinguish it from a second lipid bilayer, termed ‘outer membrane’ (OM). The space between these two layers is called the periplasm (PP). In the periplasmic space, many proteins are found with a variety of functions. Some are involved in biosynthesis and/or export of cell wall components and surface structures (e.g. pili, flagellae,

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fimbriae), some mediate degradation, utilisation and transport of substrates, while others assist in protein folding and targeting. Also in the PP, associated with the CM, one can find the ‘murein sacculus’ (for a review see [8]). This network is formed by the macromolecule peptidoglycan, which confers the characteristic cell shape and provides the cell with mechanical protection. Peptidoglycans are unique to prokaryotic organisms and consist of a glycan backbone of N-acetylated muramic acid and N-acetylated glucosamine and cross-linked peptide chains [9–13]. 2.2

INTRACYTOPLASMIC MEMBRANES

A broad variety of intracellular membrane systems, often organised as distinct organelles, is characteristic for eukaryotic cells (see Chapter 1 of this volume). In prokaryotic organisms, intracellular membranes are restricted to only a few groups of bacteria. In particular, the intracellular membranes of phototrophic bacteria, bearing the photosynthetic apparatus, appear in various morphologies. Vesicles, tubuli and structures resembling the thylakoid stacks of chloroplasts, originate from invagination of the plasma membrane. They have evolved in order to increase the membrane area that harbours the light harvesting complexes. A special type of membrane vesicles, called chromatophores, is found in purple phototrophic bacteria such as Rhodobacter capsulatus. Chromatophores, which can be easily isolated, have been used to study the photosynthetic reaction centre that mediates the conversion of light into chemical energy. Several species belonging to the group of nonphototrophic nitrifying methane utilising bacteria also form extensive intracytoplasmic membrane systems. A similar situation is found in nitrifying and nitrogen-fixing bacteria. In the organisms mentioned above, intracytoplasmic and cytoplasmic membrane are almost identical with respect to composition and respiratory activities. Most recently, a highly unusual membrane composition was reported from anaerobic ammonium-oxidising (anammox) bacteria. In these bacteria, nitrite is reduced, nitrogen gas generated, and carbon dioxide is converted into organic carbon, as the consequence of ammonia reduction. This central energygenerating process can be described as:
NHþ 4 þ NO2 ! N2 þ 2H2 O:

The anammox catabolism, an exceptionally slow process generating toxic intermediates (hydroxylamine and hydrazin), takes place in an intracytoplasmic compartment called the anammoxosome. A surrounding impermeable membrane protects the cytoplasm from the toxic molecules produced inside this organelle-like structure. Such a tight barrier against diffusion seems to be realised by four-membered aliphatic cyclobutane rings that have been found

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as dominant molecules in the anammoxosome membrane. This highly unusual feature was never before observed in nature (although three-, five-, six- and even seven-membered aliphatic rings had been reported previously in microbial membrane lipids). The lipids contain up to five linearly fused cyclobutane moieties with cis-ring junctions building a staircase-like formation. These socalled ‘ladderane’ molecules give rise to an exceptionally dense membrane. These results further illustrate that microbial membrane lipid structures can be far more diverse than previously thought [14]. 2.3

THE OUTER MEMBRANE OF GRAM-NEGATIVE BACTERIA

The outer membrane (OM) of Gram-negative bacteria constitutes to a certain extent an osmolarity and a permeability barrier. The OM is highly asymmetrical, with the inner leaflet, oriented to the periplasm, showing a lipid composition that is similar to that of the CM. In contrast, the outer leaflet, facing the external medium, contains a number of additional components, including the lipopolysaccharides (LPSs). LPS molecules consist of three parts: lipid A serving as anchor, the core oligosaccharide functioning as spacer element, and the O-specific polysaccharide consisting of oligosaccharide repeating units. The O-specific polysaccharide moiety is highly specific for the different bacterial (sub)species. LPSs are the major antigenic determinants, preventing the entry of cell-damaging components (like bile salts in the intestine) and they serve as receptors for a number of bacteriophages. The OM serves as an anchor for flagellae, fimbriae, and pili. Such complex extracellular structures are important for locomotion, cell–cell interaction, adhesion to surfaces (binding of pathogens to tissues, and attachment of environmental strains to abiotic surfaces), and formation of biofilms (e.g. dental plaque, Legionella pneumophila in water distribution systems). Proteins can be found as integral components or associated with the OM. Some of them are thought to play an important structural role, and they may contribute to the membrane integrity. They can reach relatively high levels, as with the Escherichia coli major outer membrane protein OmpA, or the major lipoprotein [15]. Last but not least, numerous proteins that are directly or indirectly involved in many transport mechanisms (import, export) are associated with the OM. 2.4

CELL WALLS OF GRAM-POSITIVE BACTERIA

Gram-positive bacteria are devoid of an outer membrane but possess a thick murein layer consisting of up to 40 layers making up to 90% of the cell wall. In some Gram-positive bacteria, teichoic acids are covalently linked to the peptidoglycan. Teichoic acids are polyol phosphate polymers with a strong negative charge. These are strongly antigenic, and are generally absent in Gram-negative

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bacteria. In some species, teichuronic acids are found as well as lipoteichonic acids, which are composed of a glycerol teichoic acid linked to a glycolipid. Additional wall compounds can be polysaccharides, lipids and proteins. Surface components are critical determinants of the interaction of pathogenic Grampositive bacteria with their host [16–18]. 2.5

THE ENVELOPE OF MYCOBACTERIA

Certain species of mycobacteria are the causative agents of tuberculosis and leprosy. The cell walls of mycobacteria are characterised by their unusually low permeability, which contributes to the mentionable resistance of the microbes to therapeutic agents. Two special features seem to be important: an outer lipid barrier based on a monolayer of characteristic mycolic acids, and a capsule-like coat of polysaccharide and protein. The cell walls contain large amounts of C60–C90 fatty acids, mycolic acids, that are covalently linked to arabinogalactan. The unusual structures of arabinogalactan and extractable cell wall lipids, such as trehalose-based lipo-oligosaccharides, phenolic glycolipids, and glycopeptidolipids were described in recent studies [19–21]. An asymmetrical bilayer of exceptional thickness is assembled by incorporating most of the hydrocarbon chains of these lipids. Structural considerations suggest that the fluidity is exceptionally low in the innermost part of the bilayer, gradually increasing toward the outer surface. Differences in mycolic acid structure may affect the fluidity and permeability of the bilayer, and may explain the different sensitivity levels of various mycobacterial species to lipophilic inhibitors. Hydrophilic nutrients and inhibitors are believed to cross the cell wall through channels of recently discovered porins [22]. According to a new concept, the solid and elastic matrix that makes the mycobacterial cell wall a formidably impermeable barrier is the direct consequence of cross-linked glycan strands which all run in a direction perpendicular to the cytoplasmic membrane [23]. The capsule probably impedes access by macromolecules. The structure of the outer lipid barrier seems common to all mycobacteria, fast- and slow-growing, but the capsule is more abundant in slow-growing species, a group which includes all the important mycobacterial pathogens [24]. 2.6

BACTERIA DEVOID OF CELL WALL PEPTIDOGLYCANS

Two groups of eubacteria devoid of cell wall peptidoglycans have been found so far: the Mycoplasma species, which possess a surface membrane structure, and the L-forms that arise from either Gram-positive or Gram-negative bacterial cells that have lost their ability to produce the peptidoglycan structures [25], also absent in the group of Archaea. Some Archaea contain cell walls composed of pseudopeptidoglycan that differs from the ‘normal’ murein, in that one of the backbone components (N-acetylmuraminic acid) is replaced by

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N-acetyltalosaminnuronic acid. Other archaeal species contain cell walls made from thick polysaccharide layers containing acetate, glucuronic acid, galactosamine, and glucose.

3 SUBSTRATE TRANSLOCATION ACROSS MEMBRANES: VARIOUS APPROACHES TO SOLVE THE PROBLEM 3.1 FOLDING, MEMBRANE INSERTION AND ASSEMBLY OF TRANSPORT PROTEINS Evolutionary processes driven by environmental changes and varying conditions have an impact on all components in a living cell. Thus, the primary, secondary and tertiary structure of proteins determines their function and location, giving different properties in different compartments, such as outer membrane, periplasmic space, cytoplasmic membrane or cytoplasm. Proteins can function as monomers or oligomers and can occur in a soluble form, as integral constituents embedded within the membrane, or can be found associated with the lipid bilayer itself or components therein. All proteins that are localised in the periplasm or in the outer membrane, as well as proteins that are secreted into the surrounding medium, have to cross the cytoplasmic membrane at least. A number of more general as well as specific secretion pathways have evolved in all types of bacteria to assist the proteins on their way out. Most of the systems are composed of a number of different components. For all types of export machinery, it is necessary that the polypetides to be transported meet certain criteria. Depending on the type of system, a specific region (signal sequence, export signal) that can be localised at the N- or C-terminal end of the polypeptide, is essential in order to enter a particular secretion pathway. Most polypeptides have to be exported in an unfolded state. Certain proteins, called chaperones, were identified, which help to maintain the correct folded state or at least prevent incorrect premature folding. In addition, it is evident that secreted proteins cannot contain long hydrophobic stretches or domains, because their existence would block the passage through a biological lipid bilayer [26–28]. The OM is a second barrier for proteins to be secreted outside the cell. Specialised integral outer membrane proteins belonging to the usher and secretin families function to allow the secretion of folded proteins in Gram-negative bacteria [29]. Outer membrane proteins face several problems. They have to cross the inner membrane thus implying that they are not allowed to contain hydrophobic ‘membrane anchor’ or ‘stop transfer’ sequences. Moreover, correct targeting to and stable insertion into the outer membrane is important for proper functioning. A number of OM proteins assemble into oligomers even prior to insertion.

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The structural solution for the vast majority of OM proteins is provided in the form of the b-strand, a secondary fold, which allows portions of the polypeptide chain to organise as a b-barrel. In this cylindrical structure, hydrophobic residues point outwards and hydrophilic residues are located inside, which can allow the formation of a water-filled channel [30–33]. The two-dimensional topology of the proteins embedded in the cytoplasmic membrane largely depends on a-helical transmembrane regions with exceptionally high hydrophobicity. Hydrophilic as well as charged amino acids are mainly localised in the connecting loops or at the N- or C-terminus. The orientation of the polypeptide chain in the lipid bilayer is largely dictated by the number and distribution of the positively charged amino acids. The ‘positive inside rule’ of von Heijne [34–36] is based on the observation that the net positive charge of integral membrane proteins (resulting from arginine and lysine residues near the membrane surface) is significantly higher on the cytoplasmic side. Small peptides and simple proteins with only a few membranespanning regions can insert spontaneously into the bilayer. In contrast, the majority of polytopic integral membrane proteins appears to depend on the assistance of components of the general secretion machinery (e.g. SecY protein) [37,38] or specialised chaperones (e.g. YidC protein) [39,40] in order to insert correctly. Interactions with the membrane lipids, as well as intramolecular interactions, determine the three-dimensional arrangement. The first evidence that the composition of phospholipids in membranes may contribute to the topological organisation of polytopic membrane proteins was provided from the group of Dowhan [41]. It was shown that phosphatidylethanolamine (PE) in E. coli membranes assists as a molecular chaperone in the assembly of the lactose permease. This transport protein adopts a partly inverted topology when inserted into membranes devoid of PE. The correct topology and activity of lactose permease could be re-established when PE synthesis was induced after assembly of the polypeptide chain in the membrane [42], demonstrating that alterations in phospholipid composition may have a general influence on membrane proteins, indicating that the topology is not fixed, since it can respond to those changes. Recent results indicate that not only topogenic signals and membrane composition contribute to the proper topology of a membrane protein. The antimicrobial peptide nisin, produced by Lactococcus lactis, kills Gram-positive bacteria via pore formation, thus leading to the permeabilisation of the membrane. Nisin depends on the cell-wall precursor Lipid II, which functions as a docking molecule to support a perpendicular stable transmembrane orientation [43]. To date, very limited information on the atomic structure is available, since crystallisation of hydrophobic membrane proteins remains a challenging problem.

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3.2 DIFFERENT DRIVING FORCES AND MODES OF ENERGY COUPLING With respect to the driving forces and the modes of energy coupling, transport processes can be divided in four major classes: (1) some solutes are able to pass the permeability barrier of a lipid bilayer by passive diffusion (the random movement of molecules from an area of high concentration to an area of lower concentration). This is true for small apolar (lipid-soluble) molecules and small slightly polar, but uncharged molecules like water and dissolved gases (O2 , CO2 , NH2 , H2 S). Other molecules are transported via channels or channel-type proteins (e.g. porins, see Section 4.1) to overcome in a diffusion-controlled movement an otherwise impermeable membrane. The translocation of substrates in this way cannot be against a concentration gradient. (2) in secondary active transport, the translocation step across the membrane is coupled to the electrochemical potential of a given solute. The ion or other solute (electro)chemical potential (e.g. the proton gradient over the cytoplasmic membrane) created by primary active transport systems is the actual driving force, which allows an ‘uphill’ transport of another solute, even against its own concentration gradient. The uptake of a given substrate following this mechanism can be mediated as uniport (also called ‘facilitated diffusion’), as symport (also termed ‘substrate cotransport’), or as antiport in exchange with another solute. (3) primary active transport systems are characterised by coupling translocation of a solute directly to a chemical or photochemical reaction. Primary sources of chemical energy include pyrophosphate bond hydrolysis (e.g. in ATP), methyl transfer and decarboxylation. Other systems are driven by oxidoreduction, light absorption or mechanical mechanisms. (4) a translocation process exclusive to bacterial species involves the phosphoenolpyruvate:sugar phosphotransferase system (PTS), which phosphorylates its carbohydrate substrates during transport.

3.3

CLASSIFICATION OF TRANSPORT SYSTEMS

Various criteria can be applied in order to arrive at a useful classification scheme for the different mechanisms of solute transport through biological membranes. Some authors concentrate mainly on phylogenetic aspects based on sequence data. The amino acid sequences of a considerable number of well-studied transporters from many bacteria are published, and an immense set of primary sequence data will become available within the next few years (primarily from numerous genome projects). Phylogenetic trees of transport proteins are

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compiled on the basis of multiple sequence alignments; consequently, one arrives at different clusters and subclusters. Alternatively, transport systems can be classified according to their mode of energisation (see Section 3.2.) or by focusing on the biochemical characterisation of the translocation process. Looking at the kinetic properties of solute uptake often gives a first clue, since the different modes of substrate import are distinguishable with respect to their transport rates: saturation is typical of carrier-mediated transport, whereas this phenomenon is not observed in simple diffusion (see Figure 1). In many organisms, the situation becomes more complex, since mechanistically different transport may operate simultaneously. In all classification systems, transporters are divided into families and further segregated into subfamilies. Saier and co-workers established a universal classification system called the ‘transport commission’ (TC) system, which is based on both function and phylogeny [44] (see Figure 2). The main types of transporters are presented in Figure 3. 3.4

VARIOUS OPTIONS FOR TRANSPORTING A SUBSTRATE

The expression of a solute transport system depends on the metabolic features and physiological state of an organism, the environmental conditions, the bioavailability of the substrate, and the substrate requirements of the cell. A common observation in bacteria is that a given substrate (or group of similar substrates) can be sequestered by several different uptake routes, including high-affinity, low-capacity systems and at least one low-affinity, high-capacity system. Primary active transporters are generally characterised by their high substrate affinity (low Km ), and low transport capacity (high Vmax ). Many

Transport rate (V )

Carrier-mediated transport + diffusion

Carrier-mediated transport

Diffusion

Substrate concentration (S)

Figure 1.

Kinetic properties of transport processes. For details see text

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Transporterindependent diffusion

α−helical protein channels β-barrel proteins Channels

Toxin channels

Porins Gated active channels

Peptide channels

Passage of solutes through membranes via:

Pyrophosphate bond hydrolysis driven Decarboxylation driven

Transporters Primary active Transporters

Oxidoreduction driven Methyl transfer driven Light absorption driven

Carriers Mechanically driven

Uniporters

Secondary active transporters

Cation symporters Cation antiporters Obligatory solute: solute antiporters

Group translocators

Figure 2. Classification of the major types of transport mechanisms across biological membranes based on function and phylogeny (modified after M. H. Saier, 2000; [44])

primary uptake systems operate practically unidirectionally, which is favourable since nutrients can be accumulated several orders of magnitude inside the cytoplasm, even when they are available in extremely small amounts in the external medium. Such systems are typically induced (and/or de-repressed) under low environmental substrate concentrations. In contrast, most of the

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Figure 3. Examples of major types of uptake mechanisms realised in prokaryotic outer membranes (a to c) and cytoplasmic membranes (a, and d to l). The solutes to be transported are shown by filled circles; ‘x’ symbolises another solute which is transported in the same or in the opposite direction. In systems h–k, uptake is driven by the cleavage of ATP to ADP and phosphate. One type of uptake system, l, depends on the energy-rich molecule phosphoenolpyruvate shown as ‘PEP’. (a) simple diffusion; (b) diffusion pores; (c) gated channels; (d) uniporter; (e) antiporter; (f) symporter; (g) binding protein-dependent secondary active symporter; (h) binding protein-dependent ABC transporter; (i) ABC transporter with binding protein fused to integral membrane protein; (k) P-type ATPase; (l) phosphoenolpyruvate-dependent group translocator. For details see the text

secondary systems are known to exhibit low substrate affinity (high Km ), and high transport capacity (low Vmax ). Since transport is coupled to an ion or proton gradient over the membrane, substrate accumulation inside the cytoplasm is normally below 100- to 1000-fold. Under certain conditions, transport may function in the opposite direction. Members of this class of translocators are typically found to be constitutively expressed. Some systems recognise and translocate a broad variety of solutes, whereas others are restricted to a narrow spectrum or exclusively one substrate species. The diversity of prokaryotic nutrient acquisition will be illustrated by a few examples: . glucose, almost ubiquitous in nature and a favourite nutrient for many organisms, can enter living cells by multiple routes. A variety of different uptake systems is also realised in bacteria. The options include the broad

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spectrum of facilitator-type uniport systems, proton- or cation-linked permeases (symport and antiport), ABC-type transporters, as well as phosphoenolpyruvate-dependent phosphotransferase systems. It is not unusual that several parallel systems, all translocating glucose and structurally related carbohydrates, are established in a given microorganism. . in hyperthermophilic Archaea, only transporters of the ABC-type seem to exist so far for the uptake of carbohydrates (e.g. glucose, cellobiose, maltotriose, arabinose, trehalose) [45]. This probably reflects an adaptation to the extreme habitat, enabling the organisms to acquire all available sugars very effectively. . the Gram-negative bacterium E. coli is able to transport proline via two different secondary systems, one of which is Naþ -coupled (putP), while the other is Hþ -coupled (proP). In addition, a high-affinity binding proteindependent uptake system encoded by the proUVW genes exists. Moreover, at least five independent uptake systems exist for the amino acids glutamate and aspartate [46,47]. . many bacteria, ranging from environmental strains to human pathogens, have developed various strategies and specific scavenging systems for iron. This esential element, often being the growth-limiting factor, can be transported as ferrous ion, as ferric ion, or in complexed form (for details, see Section 7). 3.5 CONTROLLING THE NUMBER OF ACTIVE TRANSPORTER MOLECULES It should be envisaged that in an individual bacterial cell more than a hundred different transport systems can be encoded by the chromosome or by suitable plasmids. After sequencing whole genomes, information on genes encoding putative importers and exporters is now available for a growing number of species. It is evident that not all these transporters can be expressed and present at maximum levels at any time. That would be a tremendous waste of energy, and could be a great disadvantage for the physiology of the cell. Moreover, the membranes would be ‘overcrowded’, not leaving enough space for all the different components and functions associated with the cell envelopes (see above). Cells have to express their transport systems in a regulated manner according to their needs, depending on the metabolic state and on environmental conditions. A few major parameters, such as osmolarity of the external medium, extracellular and intracellular pH, energetic status of the cell, internal metabolites, and regulatory proteins affecting the expression of transporters give an idea of the complexity. Only a limited number of transporters are constitutively expressed. Many uptake systems are induced by the substrates that they translocate. The expression of a number of importers is de-repressed when essential nutrients reach a critically low intracellular concentration, whilst

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other systems are repressed when toxic compounds or catabolites exceed critical levels. Despite its importance, regulation cannot be discussed in great detail in this chapter, but regulation is, in principle, possible on different levels: (1) in bacteria, regulation on the transcriptional level seems to be the most important. This often involves proteins that bind to specific DNA regions. Depending on the system, such proteins can act as, for example, repressors, activators, or alternative sigma factors (in combination with the DNAdependent RNA core polymerase) thereby allowing the transcription initiation by de-repression, activation or induction. In some cases, regulatory networks are reported that include cascades of regulatory processes involving sensing and signal transduction from the outer surface to the nucleic acids. Regulation on the transcriptional level can also be achieved by expressing so-called ‘antisense’ RNA molecules that interact with messenger RNA (m-RNA), or by m-RNA stability. (2) regulation on the translational level can take advantage of m-RNA secondary structure, optimal or weak ribosome binding sites, the choice of the start codon, codon usage, and translational coupling (overlapping start and stop codons). (3) regulation can also occur at the level of protein stability, which can be influenced by a number of factors and components inside the cells or in the environment. In addition, the activity of transport proteins can be influenced by modifications such as phosphorylation–dephosphorylation or methylation–demethylation.

4 TRANSPORT ACROSS THE OUTER MEMBRANE OF GRAMNEGATIVE BACTERIA 4.1

GENERAL PORINS AS CHANNELS

Typically, functional porins are homotrimers, which assemble from monomers and then integrate into the outer membrane. The general porins, water-filled diffusion pores, allow the passage of hydrophilic molecules up to a size of approximately 600 Daltons. They do not show particular substrate specificity, but display some selectivity for either anions or cations, and some discrimination with respect to the size of the solutes. The first published crystal structure of a bacterial porin was that of R. capsulatus [48]. Together with the atomic structures of two proteins from E. coli, the phosphate limitation-induced anionselective PhoE porin and the osmotically regulated cation-selective OmpF porin, a common scheme was found [49]. Each monomer consists of 16 b-strands spanning the outer membrane and forming a barrel-like structure.

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The b-strands are connected by loops on the outside, and short turns facing the periplasm. The third loop, L3, has a unique feature, in that it is not exposed at the cell surface but folds back into the barrel. The resulting constriction zone gives the channel an hourglass-like shape. L3 contributes significantly to the permeability properties of the pore (e.g. ion selectivity and exclusion limit) [50]. Experimental data demonstrate that lysine and arginine residues contribute to the selectivity filter in the anion-selective porin PhoE of E. coli [51,52]. The exceptionally high stability of some porins is not only generated by the hydrophobic interface of the monomers. Studies with OmpF showed that loop L2 of each monomer extends into the adjacent monomer [53], leading to an interlocked arrangement of the components. The molecular mechanism of voltage gating, a phenomenon not observed with substrate-specific channels, still has to be solved. 4.2

PORINS WITH SELECTIVITY

The outer membrane of Gram-negative bacteria contains, in addition to the general pores, a number of channels, which facilitate the specific diffusion of certain substrates. Well-studied representatives are the sucrose-specific porin ScrY from Salmonella typhimurium and the maltooligosaccharide-specific maltoporin LamB from E. coli. When purified ScrY porin was reconstituted into vesicles, a high permeation rate for sucrose was observed [54]. Purified LamB reconstituted into lipid bilayers formed ion-conducting channels transporting maltose and maltodextrins (up to maltoheptaose) with a high permeation rate [55,56]. Although similar sugar binding affinities are found for for maltose (10 mmol dm
3 ) and sucrose (15 mmol dm
3 ) it has been shown previously that sucrose uptake via LamB is negligible [57]. Despite little similarity in the primary structures of LamB and ScrY, superimposition of the threedimensional structures arrives at a similar picture [58,59] (Figure 4). Both sugar-specific porins represent homotrimers with monomers formed out of 18 antiparallel b-strands. The resulting b-barrel, resembling the arrangement of the general porins, contains a constriction formed by loop L3. Characteristic for the sugar-specific porins is a substrate translocation pathway extending from the vestibule (open to the extracellular medium) to the exit (at the periplasmic side). This so-called ‘greasy slide’, built by aromatic residues, is lined by a stretch of polar amino acids termed the ‘ionic track’. The ‘greasy slide’, presumably, interacts with the hydrophobic face of the transported sugars (via van der Waals interactions), whereas the ‘ionic track’ forms hydrogen bonds with their hydroxyl groups [60,61]. It has been suggested that the sugars move down the channel via continuous formation and disruption of these hydrogen bonds [62]. Only a few residues modulating the lumen of the channel define the sugar specificity of LamB and ScrY.

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Figure 4 (Plate 5). Atomic structure of the sucrose specific selective porin ScrY isolated from the outer membrane. Longer loops are directed to the outside, shorter turns are facing the periplasm. Monomer and assembled homotrimer in side view (left and middle); top view of assembled trimer (right). (Reproduced by permission of W. Welte and A. Brosig)

4.3

TONB DEPENDENT RECEPTORS

Most Gram-negative bacteria express outer membrane receptors for the uptake of haem, iron–siderophore complexes, and vitamin B12 into the periplasm [63]. These receptors are larger than the known diffusion-controlled porins, and differ from the latter by their high substrate affinity and specificity. They are characterised by their energy requirement for active ligand transport against a concentration gradient. Energy supply is provided by an inner membraneassociated protein complex composed of the proteins TonB–ExbB–ExbD, which couples substrate translocation across the OM to the membrane potential of CM [63–65]. The molecular mechanism of energy transfer is still unknown. The enterobactin receptor FepA and the ferrichrome receptor FhuA from E. coli were the first TonB-dependent OM proteins to have their threedimensional structures solved [30,66,67]. The crystal structures of both FhuA and FepA revealed an unexpected arrangement with a globular N-terminal portion forming a ‘plug’ or ‘cork’ like domain folding into a 22-stranded b-barrel that spans the entire OM. The structure of FepA is shown in Figure 5. For more details, see Section 7.2. Based on sequence similarity, it appears that transporters of this type may also assist in the uptake and acquisition of solutes unrelated to iron chelating compounds and vitamin B12 [68]. Examples of prospective candidates are outer membrane proteins that are involved in sulfate ester utilisation in Pseudomonas putida [69], or polypeptides playing a role in starch binding at the surface of Bacteriodes thetaiotaomicron [70].

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Figure 5 (Plate 6). Crystal structure of FepA, the TonB-dependent receptor for ferricenterochelin. (Reproduced by permission of D. van der Helm and L. Esser)

5

TRANSPORT THROUGH THE CELL WALLS OF MYCOBACTERIA

The very low permeability is one of the most prominent functional features of the mycobacterial cell wall which protects the bacterial cell from noxious substances. Nonetheless, hydrophilic molecules can diffuse through the mycolic acid layer. However, the permeability of the mycobacterial cell wall is 100- to 1000-fold lower than that of most Gram-negative bacteria. It has been shown that special porins localised in the cell wall represent the main hydrophilic pathway [71,72]. Recently, such a porin, MspA of Mycobacterium smegmatis, has been characterised. In vitro studies demonstrate that MspA is an extremely stable oligomeric porin (composed of 20 kDa subunits) that forms waterfilled channels with a conductance of 4.6 nS in 1 mol dm
3 potassium chloride. Mycobacteria lacking the MspA porin displayed a nine-fold decreased

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permeability for the zwitterionic b-lactam antibiotic cephaloridine, and the transport of glucose was impaired [73]. Three other porins with properties similar to MspA were identified in the genome of M. smegmatis.

6 TRANSPORT ACROSS THE CYTOPLASMIC MEMBRANES OF BACTERIA 6.1

CHANNELS

Bacteria can survive dramatic osmotic shifts. Osmoregulatory responses mitigate the passive adjustments in cell structure and the growth inhibition that may ensue. The levels of certain cytoplasmic solutes rise and fall in response to extracellular osmolality. Responses to environmental changes necessitate the presence of components that allow sensing and regulated transport of ions and other solutes across membranes. However, the CM of all microorganisms does not tolerate proteins that form pores or pore-like structures that resemble the porins such as those (e.g. OmpF, OmpC, PhoE) found in the OM of Gramnegative bacteria or in the cell wall of mycobacteria. Such permanently open channels would immediately lead to the depolarisation of the membrane, thus resulting in a loss of function of many transporters and energy-generating systems, and so causing cell death. A similar effect can be observed when pore-forming colicins insert into (reviewed in [74–77]) or antimicrobial peptides assemble within the CM [43] in order to form open channels. Nonetheless, in microorganisms, certain types of pore-like proteins with unique features have been reported such as MIP channels, mechanosensitive channels, and gas channels.

6.1.1

MIP Channels

The family of MIP channels is named after the first discovered aquaporin from red blood cells which displays similarity to MIP (major intrinsic protein of mamalian lens fibre) [78]. The discovery of an aquaporin for the first time explained observations which were already made many years ago. Biophysical data provided the hypothesis of pore-mediated water flux. Specialised biological membranes are significantly more permeable to water than artificial lipid bilayers. Movement of water across erythrocyte membranes depends on an activation energy of about 17
25 kJ mol
1 . This is definitely below the activation energy of 46
59 kJ mol
1 needed to allow water flow through synthetic bilayers [79]. Members of the MIP family proteins occur in all classes of organism, ranging from bacteria to humans. All MIP channels share highly conserved amino acid residues and are predicted to have six hydrophobic membrane-spanning domains. They are subdivided into three major categories:

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(1) aquaporins sensu stricto, are highly specific for water [80]; (2) glycerol facilitators transport glycerol and possibly other solutes in addition to, or even in preference to, water [81]; and (3) aquaglycerolporins with a mixed function are permeable for glycerol and water. The molecular determinants underlying this specificity are not well understood. Since they are most likely to be involved in osmoregulation and metabolism, MIP channels are thought to affect a wide range of biological processes. Aquaporins are characterised by their extremely high selectivity for water; a simultaneous transport of other molecules or ions does not occur. In particular, protons can cause a special problem, since they are able to move along chains composed of H2 O molecules that are connected via hydrogen bonds (Grotthus mechanism). The mechanism preventing channel passage of protons has been proposed by using the structural model of the aquaporin AQP1 from human erythrocytes, where two asparagine residues are located in the middle of each H2 O channel of the AQP1 homotetramer. The formation of hydrogen bonds between the amido groups of these asparagine residues interrupts the chain composed of H2 O molecules, thus blocking the transfer of protons [82]. Aquaporins seem to be essential for eukaryotes, because of the large size of the multicellular organisms and their need for rapid water movement. In contrast, aquaporins are found only sporadically in bacteria, and it is a current debate as to whether small prokaryotic cells lacking internal organelles require aquaporins, or whether unmediated diffusion of water across their cytoplasmic membranes is sufficient [83]. For example, aquaporin Z exists in strains of E. coli, but homologues were not detected in most other bacteria whose genomes have been sequenced so far. Recent studies indicated that the E. coli AqpZ expression was not affected by up- or downshifts in osmolality, and no evidence was found that AqpZ mediates water permeativity under the conditions tested. Moreover, disruption of the aqpZ gene had no detectable adverse effects on growth and cell viability [83]. The GlpF protein from E. coli is the best-known glycerol facilitator to date. GlpF does not transport water, but is capable of transporting small polyalcohols (e.g. erythritol) in addition to glycerol [81]. A high-resolution structure at the molecular basis of channel selectivity was obtained by Stroud’s laboratory (University of California, Los Angeles) on the glycerol channel GlpF [84]. With ˚ resolution structure available (including three glycerol molecules the 2.2 A captured in the channel) it is possible to address the question as to how the high selectivity of this channel for glycerol can be achieved: the channel is lined with hydrophobic and amphiphatic residues on one side and polar residues on the other. Thus a so-called ‘tripathic’ channel is formed, which is so narrow ˚ ) that the glycerol molecules must pass through in single file. At the (ca. 3.8 A selectivity filter, the second glycerol molecule is tightly packed against a hydrophobic wall. This leaves no space for any substitutions to the glycerol C–H hydrogen position. In addition, both the second and third glycerol molecules

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are pinned by successive H-bonds that have been formed with a pair of donor and acceptor molecules. Due to these constraints only glycerol and water can pass through the pore [85]. L. lactis is the first Gram-positive bacterium in which a MIP channel has been functionally characterised. The lactococcal MIP protein is shown to be permeable to glycerol, like E. coli GlpF, and to water, like E. coli AQPZ. That was the first description of a microbial MIP that has a mixed function. This result provided important insights for reconstructing the evolutionary history of the MIP family and elucidating the molecular pathway of water and other solutes in these channels [86]. 6.1.2

Mechanosensitive Channels

Mechanosensitive ion channels can be looked at as membrane-embedded mechano-electrical switches. They play a critical role in transducing physical stresses at the cell membrane (e.g. lipid bilayer deformations) into an electrochemical response. Two types of stretch-activated channels have been reported: the mechanosensitive channels of large conductance (MscL) and mechanosensitive channels of small conductance (MscS). The MscL family of channels is widely distributed among prokaryotes, including several species of Archaea (e.g. Methanoccoccus jannashii, Thermoplasma acidophilum) and may participate in the regulation of osmotic pressure changes within the cell. MscL from E. coli is the first isolated molecule shown to convert the mechanical stress of the membrane into a simple response, the opening of a large water-filled pore [87]. The crystal structure of MscL from Mycobacterium tuberculosis now allows the analysis of tension-dependent channel-gating mechanisms at the molecular level. The MscL channel is a homopentamer. Each subunit consists of two a-helical transmembrane domains (TM1 and TM2), and a helical region located at the carboxy terminal end that is protruding into the cytoplasm [88]. Sukharev et al. [89] developed structural models in which a cytoplasmic gate is formed by a bundle of five amino-terminal helices (S1), the structure of which was not resolved in the crystal. Cross-linking experiments demonstrated that S1 segments form a bundle when the channel is closed. In contrast, S1 segments interact with another portion of the channel, TM2, when the channel is open. Gating was proposed to be affected by the length of the S1–TM1 linker, in a manner consistent with the model, revealing critical spatial relationships between the domains that transmit force from the lipid bilayer to the channel gate. In this model, helical tilting and expansion of TM1 was also necessary in order to open the channel [89]. Recently, electron paramagnetic resonance spectroscopy and site-directed spin labelling were used to determine the structural rearrangements that underlie the opening of such a large mechanosensitive channel. MscL was trapped in both the open, and in an intermediate closed state, by

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modulating bilayer morphology. Small movements in the first transmembrane helix (TM1) characterise the transition to the intermediate state. Subsequent massive rearrangements in both TM1 and TM2 support the highly dynamic ˚ , lined mostly by TM1, can open state. A water-filled pore of at least 25 A be formed. Members of the MscS family of small-conductance mechanosensitive channels have been identified in Eubacteria, Archaea, and several eukaryotes. McsS from E. coli has been studied in detail by applying the patch-clamp electrical ˚ resolution is availrecording technique [90], and the atomic structure at 3.9 A able [91]. MscS also responds to the tension of the membrane, but it differs from MscL in that it is voltage-modulated. The active channel in the membrane appears as a symmetrical homoheptamer, with each subunit being composed of a membrane-embedded domain and an extramembrane domain extending into the cytoplasm. The membrane domain consists of three transmembrane helices (TM1, TM2, and TM3). In the current model TM3 is lining the pore while TM1 and TM2 display an orientation which is more perpendicular to the membrane, thus playing a role as tension and voltage sensors. Pore opening might be induced by increasing the tension or by depolarisation; pore closing by tension release or hyperpolarisation. The pore extends into the extramembrane region, which forms a large water-filled chamber. This chamber connects to the cytoplasm through eight openings (seven to the side and one central), thereby functioning as a kind of molecular filter [91,92]. 6.1.3

Gas Channels

The ammonium/methylammonium transport (Amt) proteins of enteric bacteria are required for fast growth at very low concentrations of the uncharged NH3 . Homologues exist in all three domains of life. They are essential at low ammonium (NHþ 4 þ NH3 ) concentrations under acidic conditions. The Amt protein of S. typhimurium (AmtB) participates in acquisition of NHþ 4 =NH3 , but cannot concentrate either NH3 or NHþ . In general, Amt proteins appear to be bidirec4 tional channels for NH3 . They are examples of protein facilitators for a gas [93]. The majority of Amt proteins contain 11 transmembrane helices with the C-terminus facing the cytoplasm [94]. 6.2

SECONDARY ACTIVE TRANSPORTERS

The Major Facilitator Superfamily (MFS) [95–97] is the largest secondary transporter family known in the genomes sequenced to date [98]. These polytopic integral membrane proteins enable the transport of a wide range of solutes, including amino acids, sugars, ions, and toxins. Medically relevant members of the family include the bacterial efflux pumps associated with

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antibiotic resistance [99,100]. Although ubiquitous in nature, there are still no high-resolution structures published of secondary transporters (electrochemical-potential-driven porters). The low-resolution structures of a few transporters provide the first evidence that these 12 transmembrane (TM) helix proteins have more than one arrangement of their helices. Different families of 12 TM transporters might well have evolved independently of each other to arrive at the common 12 helical structures that are seen in nature. The existing data already suggest that the 12 helices can be arranged in several ways, thus pointing to the diversity of structures of membrane-transport proteins in nature. 6.2.1

Uniport Systems

Secondary active uniport systems facilitating the permeation of a single solute, dependent on the electrochemical potentials of the solute molecules, are rare in bacteria. Only a glucose uptake system of Zymomonas mobilis has been studied in more detail [101]. 6.2.2

Symport Systems

Lactose permease is a prominent example of the bacterial solute/Hþ cotransport systems. At the same time, the product of the lacY gene from E. coli is one of the best-studied bacterial transporters. LacY is a polytopic membrane protein containing 12 transmembrane helices. By catalysing the coupled stoichiometric translocation of galactosides and Hþ (lactose/Hþ symport) this transporter transduces free energy, which is stored in an electrochemical Hþ gradient, into a sugar concentration gradient. Uptake and accumulation of b-galactosides like lactose works against a concentration gradient. The primary trigger for turnover is binding and dissociation of substrate on opposite sides of the membrane. The permease has been solubilised from the membrane, purified, and reconstituted in membrane vesicles. A large collection of genetic, biochemical and physicochemical methods has been applied. The data lead to a mechanistic model describing the arrangement of the membranespanning elements, unravelling the mode of energy coupling, and defining the passage of molecules through the transporter. Experimental data from the laboratory of Kaback [102] indicate that only six side chains of the 417 residues in lac permease are irreplaceable for active transport. Glutamine 126 (helix 6) and arginine 144 (helix 5) seem to be directly involved in substrate binding and specificity. Glutamine 269 (helix 8), arginine 302 (helix 9), histidine 322 (helix 10), and glutamine 325 (helix 10) are most likely to be involved in Hþ translocation and/or coupling between Hþ and substrate translocation. The permease is protonated in the ground state (histidine 322 and glutamine 269

294 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

share a common Hþ , and glutamine 325 is charge paired with arginine 302). In this conformation, the permease binds the ligand at the interface between helix 4 (glutamine 126) and helix 5 (arginine 144, cysteine 148) at the outer surface of the membrane. A conformational change is induced by substrate binding, thus resulting in a transfer of the Hþ from histidine 322 and glutamine 269 to glutamine 325. Consequently, reorientation of the binding site to the inner surface takes place, accompanied by release of sugar. As the conformation relaxes, glutamine 325 is deprotonated on the inside, due to rejuxtaposition with arginine 302. Then the histidine 322/glutamine 269 complex is reprotonated from the outside surface, to allow reinitiation of the cycle. Recent studies with lactose permease mutant containing a cysteine in place of alanine 122 (helix 4) indicate that alkylation of Cys-122 selectively inhibits binding and transport of disaccharides. By contrast, transport of the monosaccharide galactose remained largely unaffected. The data indicate that Ala-122 is a component of the ligand-binding site and support the idea that the side chain at position 122 abuts on the non-galactosyl moiety of d-galactopyranosides [103]. For further details see [102–105]. A variety of sodium–substrate symport systems are found in bacteria. Sodium cotransport carriers are known to be involved in the acquisition of nutrients like melibiose, proline, glutamate, serine–threonine, branched-chain amino acids and citrate. Some of these also play a role in osmoadaptation. Sodium enters the cell down an electrochemical gradient. There is obligatory coupling between the entry of the ion and the entry of substrate with a stoichiometry of 1:1, leading to the accumulation of substrate within the cell. A combination of spectroscopic, biochemical and genetic methods has been applied to gain new insights into the structure and molecular mode of action of the transport proteins [106]. The melibiose carrier MelB of E. coli is a well-studied sodium symport system. This carrier is of special interest, because it can also use protons or lithium ions for cotransport. The projection structure of MelB has been ˚ resolution [107]. The 12 TM helices are arranged in an asymmetsolved at 8 A rical pattern similar to the previously solved structure of NhaA, which, however, follows an antiport mechanism (Naþ ions out of the cell and Hþ into the cell). Studies with the Naþ /proline transporter (PutP) of E. coli, suggest a 13-helix arrangement in the membrane. In this model, the N-terminus is located in the periplasm and the C-terminus is directed into the cytoplasm. Mutational analysis has identified regions of particular functional importance. For example, amino acids of transmembrane domain 2 of PutP are critical for high-affinity binding of Naþ and proline. It was shown that ligand binding induces widespread conformational changes in the transport protein. In summary, the Naþ /solute symport is the result of a series of ligand-induced structural changes [46].

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Antiport Systems

This section will mainly concentrate on a few subfamilies of the major facilitator family, namely the sugar–phosphate/anion antiporters, the Naþ =Hþ antiporters, and one example of the oxalate/formate antiporters. Structurally dissimilar anions, such as hexose phosphates, hexuronates and glycerol-3-phosphate are the substrates for an anion-exchange mechanism across the membrane [108]. In prokaryotes, the inorganic phosphate (P)-linked systems are the best characterised [109]. Representatives are the E. coli glycerol3-phosphate transporter (GlpT) and the structurally and functionally related E. coli hexose-6-phosphate transport protein, UhpT [110,111]. GlpT mediates glycerol-3-phosphate (G3P) and inorganic phosphate exchange across the cytoplasmic membrane. It possesses 12 transmembrane a-helices. Purified GlpT protein binds substrates in detergent solution, as measured by tryptophan fluorescence quenching, and its dissociation constants for G3P, glycerol-2phosphate, and inorganic phosphate at neutral pH were determined as 3.64, 0.34 and 9:18 mmol dm
3 , respectively. GlpT also displayed transport activity upon reconstitution into proteoliposomes. The phosphate efflux rate of the transporter in the presence of G3P was measured to be 29 mmol min
1 mg
1 at pH 7.0 and 37 8C, corresponding with 24 mol of phosphate s
1 (mol of protein)
1 [112]. The hexose-6-phosphate transporter UhpT protein also contains 12 transmembrane (TM) regions. Based on experimental data, Hall and Maloney [113] conclude that TM11 spans the membrane as an a-helix with approximately two-thirds of its surface lining a substrate translocation pathway. It is suggested that this feature is a general property of carrier proteins in the Major Facilitator Superfamily, and that, for this reason, residues in TM11 will serve to carry determinants of substrate selectivity [113]. Naþ =Hþ antiporters are ubiquitously found in the cytoplasmic membranes of cells and organelle membranes throughout the prokaryotic and eukaryotic kingdom. They are primarily involved in pH and Naþ homeostasis, since Naþ and Hþ are the most common ions. They play primary roles in cell physiology (e.g. in bioenergetics), and the concentration of protons in the cytoplasm is critical to the functioning of the cell and its proteins. The Naþ =Hþ antiporters cluster in several families, as concluded from the emerging genomic sequence projects (e.g. Helicobacter pylori [114], Vibrio cholerae [115], and Vibrio parahaemolyticus [116]). Two genes encoding Naþ - and Liþ -specific Naþ =Hþ antiporters were detected in E. coli: nhaA [117] and nhaB [118–120]. NhaA is the main antiporter, that has to withstand the upper limit concentration of Naþ for growth (0:9 mol dm
3 , pH 7.0) and to tolerate the upper pH limit for growth in the presence of Naþ (0:7 mol dm
3 , pH 8.5). NhaB is encoded by a housekeeping gene, which becomes essential only in the absence of nhaA. Structure and function studies have been conducted with purified NhaA.

296 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

NhaA is shown to exist in two-dimensional crystals as a dimer of monomers each composed of 12 transmembrane segments with an asymmetrical helix packing. These studies provide the first insight into the structure of a polytopic membrane protein. A number of Naþ =Hþ antiporters display dramatic sensitivity to pH, a property that confirms their role in pH homeostasis. Amino acid residues involved in the pH response have been identified in the sequence of NhaA, thus pointing to the molecular mechanism underlying this pH sensitivity. Conformational changes transducing the pH change into a change in activity were found in certain loops and at the N-terminus of the protein [121]. The NhaA (Naþ =Hþ antiporter) homologue of V. cholerae seems to contribute to the Naþ =Hþ homeostasis in this pathogenic bacterium, and is therefore presumably involved in the survival and persistence of free-living bacteria in their natural environment [115]. Another subfamily of Naþ =Hþ antiporters appears to predominantly contribute to the alkalinity of many extremophile bacteria. In Bacillus halodurans, a gene was identified which is responsible for electrogenic Naþ =Hþ antiport activity driven by DC (membrane potential, interior negative). The corresponding protein allowed the cells to maintain an intracellular pH lower than that of the external milieu (above pH 9.5). Sequence analyses indicated a significant similarity to the shaA gene product of Bacillus subtilis. Thus the shaA gene most likely encodes a Naþ =Hþ antiporter, which plays an important role in extrusion of cytotoxic Naþ [122]. In addition, results obtained from B. subtilis suggest that shaA plays a significant role at an early stage of sporulation, as well as during vegetative growth. Fine control of cytoplasmic ion levels, including control of the internal Naþ concentration, may be important for the progression of the sporulation process [123]. The three-dimensional structure of OxlT, an oxalate/formate antiporter from Oxalobacter formigenes, most recently solved [124], is explicitly different from that of both antiporter NhaA and symporter MelB (see above). There is an obvious twofold symmetry in the organisation of the 12 transmembrane helices. This supports the previous idea that the MFS proteins evolved from a duplication of a 6-TM protein to form a 12-TM protein. Moreover, it is possible that the 6-TM predecessor was created from a duplication of an ancestral 3-TM protein. 6.2.4

Binding Protein-Dependent Secondary Transporters

As demonstrated above, the typical secondary transporters work as single units, and do not depend on further transport components. One of the first examples of a secondary transport system that requires a periplasmic binding protein is the Naþ -dependent glutamate transporter of Rhodobacter sphaeroides with both transport and binding being highly specific for glutamate. Jacobs et al. [125] reported that growth of a glutamate transport-deficient mutant of

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R. sphaeroides on glutamate as sole carbon and nitrogen source was restored by the addition of millimolar amounts of Naþ . Uptake of glutamate (Km of 0:2 mmol dm
3 ) by that mutant was dependent on the proton motive force (pmf) and strictly required Naþ (Km of 25 mmol dm
3 ). Transport of glutamate was also observed in membrane vesicles when Naþ , a proton-motive force and purified glutamate binding protein, were present. A similar high-affinity transport system for the C4-dicarboxylates malate, succinate and fumarate was found in R. capsulatus [126]. Again, transport experiments indicated that the proton motive force, rather than ATP hydrolysis, drives uptake. The system is composed of DctP (periplasmic C4-dicarboxylate-binding protein), DctQ, and DctM, the latter two being characterised as integral membrane proteins. DctP, DctQ, and DctM are distinct from known transport proteins in the ABC (ATPbinding cassette) superfamily (see Section 6.3.2). The name TRAP (for tripartite ATP-independent periplasmic) transporters was proposed for this group of uptake systems [126]. Homologous systems were identified in the genomes of a number of Gram-negative bacteria, including Bordetella pertussis, E. coli, S. typhimurium and Haemophilus influenzae. 6.3

PRIMARY ACTIVE TRANSPORTERS

These transport systems use a primary source of energy to drive active transport of a solute against a concentration gradient. Primary energy sources can be chemical, electrical and solar. In this section, systems will be described mainly that hydrolyse the diphosphate bond of inorganic pyrophosphate, ATP, or another nucleoside triphosphate, in order to drive the active uptake of solutes. Transporters using another primary source of energy will be briefly mentioned. 6.3.1

ATPases

F-ATPases (including the Hþ - or Naþ -translocating subfamilies F-type, V-type and A-type ATPase) are found in eukaryotic mitochondria and chloroplasts, in bacteria and in Archaea. As multi-subunit complexes with three to 13 dissimilar subunits, they are embedded in the membrane and involved in primary energy conversion. Although extensively studied at the molecular level, the F-ATPases will not be discussed here in detail, since their main function is not the uptake of nutrients but the synthesis of ATP (‘ATP synthase’) [127–130]. For example, synthesis of ATP is mediated by bacterial F-type ATPases when protons flow through the complex down the proton electrochemical gradient. Operating in the opposite direction, the ATPases pump 3–4 Hþ and/or 3Naþ out of the cell per ATP hydrolysed. P-type ATPases from eukaryotes, bacteria, and Archaea catalyse cation uptake and/or efflux driven by ATP hydrolysis. Bacterial P-type ATPases

298 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

consisting of one, two, or three components are found in the CM. There exists only a single catalytic subunit, the special feature of which is the formation of a phosphorylated intermediate during the reaction cycle [131]. Phosphorylation of the enzyme takes place at an aspartate residue in a highly conserved sequence. The phosphorylation forces the protein into an altered conformation, and the following dephosphorylation allows its return to the original state, so mediating the ion translocation. Distinct systems have been found for uptake of þ 2þ Kþ or Mg , uptake or efflux of Cu2þ or Cu and efflux of Ca2þ , Ag2þ , 2þ 2þ 2þ Zn2þ , Co2þ , Pb , Ni , and/or Cd [132–135]. 6.3.2

ABC Transporters

ABC transporters are multidomain systems that translocate substrates across membranes. A common characteristic is the well-conserved ATP binding cassette (ABC) domain that couples ATP hydrolysis to transport. Members of this group of proteins constitute the largest superfamily of transport components, and they are found in all organisms from Archaea to humans. According to the work of Dassa, who developed a classification based on the ATPase components, the ABC systems can be divided into a number of subfamilies (for details see http://www.pasteur.fr/recherche/unites/pmtg/abc/) [136]. ABC transporters are involved in both uptake and excretion of a variety of substrates from ions to macromolecules. Whereas export systems of this type are present in all kingdoms of life, import systems are exclusively found in prokaryotes. ABC transporters are minimally composed of two hydrophobic membrane embedded components and two ATPase units. 6.3.2.1 Binding Protein-Dependent Uptake Systems Binding protein-dependent uptake systems represent a subfamily of ABC transporters. They are composed of: (1) one or several extracellular (periplasmic) binding proteins; (2) one or two different (homodimer, heterodimer, or pseudo-heterodimer) polytopic integral membrane proteins (IMP); (3) two copies of an ATP-hydrolase (or two different ATPase units) facing the cytoplasm and supplying the system with energy. The best-studied systems to date are those for the uptake of maltose, histidine, siderophores and vitamin B12 . Typical of all the ABC-type importers are the soluble binding proteins, which bind the substrate with high affinity. Early studies revealed that many binding proteins could be extracted from Gramnegative bacteria by an osmotic shock procedure, giving rise to the term ‘osmotic-shock-sensitive’ transport systems. It still holds true that the majority

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of binding proteins of Gram-negative bacteria can more or less freely diffuse in the periplasm. However, in a few cases solute binding proteins are tethered to the cytoplasmic membrane via a hydrophobic a-helical transmembrane domain, or anchored via a lipid tail attached to an N-terminal cysteine residue. Such lipoproteins are also the commonly found primary substrate receptor of ABC transporters from Gram-positive bacteria. An unusual feature was observed in binding proteins (BPs) of Archaea. They can also be tethered to the membrane by means of a hydrophobic transmembrane span that is located at the C-terminus [45]. The structures of a considerable number of BPs have been solved. In general, BPs display very limited sequence homology, since they recognise a wide variety of different ligands. Nonetheless, all these proteins possess bilobate structures. In the majority of cases the two domains are linked by a hinge region formed by two or three flexible b-strands at the bottom of the ligand binding cleft – resembling a ‘Venus flytrap’ mechanism. For this scenario, substrate binding is generally assumed to induce a substantial conformational change from the ‘open’ to the ‘closed’ formation or to stabilise the latter [137]. A few BPs described recently (see Sections 7.3.3 and 7.3.5) differed from the ‘classical’ arrangement, in that the two lobes of the polypeptide chain were combined by a single a-helix. This rather rigid connecting structure does not allow the same degree of flexibility, thus indicating that the mode of BP/ligand interaction might be different in this subclass of BPs. The hydrophobic units are embedded within the CM. Depending on the system they are active as homo dimers, hetero dimers or pseudo-hetero dimers. Based on topological analyses, they contain five to 10 transmembrane regions (for the vast majority, six membrane spanning domains are predicted). As the central part of the translocation complex, the IMPs interact with BP and ATPase. No common motif has been reported concerning the contact sites with the BPs, and the mode of interaction remains unclear. In contrast, a common motif, also known as ‘EAA motif’ was identified in the IMPs of all bacterial permeases belonging to the ABC import systems [138,139]. The EAA motif is part of a structurally conserved region forming a helix-turn helix motif and functioning as the main contact area with the ATPase units. A detailed view suggesting possible mechanisms of ATPase-IMP interaction at the molecular level was obtained in the maltose system [140,141]. For a review see [142,143]. The characteristic Walker A and Walker B motifs that are involved in ATP binding [144] are always found in the ATPase or ABC domains. In addition, a signature motif, also called the LSGGQ motif, is typical of all bacterial ABC domains involved in binding-protein-dependent import. The signature motif is absent in other types of ATPases. A more detailed view also highlighting the special features of ABC transporters involved in iron uptake is provided in Sections 7.3.3. to 7.3.5.

300 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

6.3.2.2 Systems Without Autonomous Binding Protein Bacterial ABC importers possess at least one BP that is essential for the uptake of substrates. In the ‘classical’ arrangement, this BP acts as a separate autonomous entity which is either anchored to the cytoplasmic membrane (typical of Archaea and Gram-positives, rare in the case of Gram-negatives) and/or can diffuse in the periplasmic space of Gram-negative bacteria. Systems with an unusual architecture were found in one family of Gram-negative bacteria and in some families of Gram-positive bacteria (best studied in L. lactis). ABC transporters involved in osmoregulation and osmoprotection, in particular, uptake systems for glycine/betaine and glutamate/glutamine, are characterised by ‘normal’ ATPase subunits but ‘chimeric proteins’ consisting of a hydrophilic portion fused to a hydrophobic integral membrane domain. The hydrophilic portion, localised at either the N- or the C-terminal end or both, displays characteristics typical of the classical BPs. In analogy with systems with known stoichiometry, the functional transport complex contains two or even four substrate binding domains (see Figure 3i) [145,146]. 6.3.3 Other Primary Active Transporters (not Diphosphate-Bond-Hydrolysis Driven) Decarboxylation-driven transporters catalyse decarboxylation of a substrate carboxylic acid, and use the energy released to drive extrusion of one or two ions (e.g. Naþ ) from the cytoplasm. Special enzymes mediate the decarboxylation of oxaloacetate, methylmalonyl-CoA, glutaconyl-CoA, and malonate [147]. Light absorption-driven transporters (e.g. bacterio- and halorhodopsins) pump 1 Hþ and 1 Cl
per photon absorbed. Specific transport mechanisms have been proposed [148]. A single methyltransfer-driven transporter representing a multi-subunit protein complex has been isolated from the archaebacterium Methanobacterium thermoautotrophicum [149]. The porter has been characterised as Naþ -transporting methyltetrahydromethanopterin coenzyme M methyltransferase. Oxidoreduction-driven transporters drive transport of a solute (e.g. an ion) energised by the exothermic flow of electrons from a reduced substrate to an oxidised substrate. This subclass of porters includes the NADH:ubiquinone oxidoreductases type I, which couples electron transfer to the electrogenic transport of protons or sodium ions. These multi-subunit complexes consist of 13 or 14 protein subunits [150]. 6.4

GROUP TRANSLOCATORS

The bacterial phosphoenolpyruvate (PEP)-dependent carbohydrate phosphotransferase systems (PTS) are characterised by their unique mechanism of group translocation. The transported solute is chemically modified (i.e. phosphorylated) during the process (for comprehensive reviews see [151,152] and

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Cytoplasm

Periplasm

Mannitol 1-P P

P

Mannitol IIC IIA IIB HPr

EI

Glucose 6-P

P

PEP

P

P

Glucose IIC IIB

IIA Pyruvate P

Mannose 6-P EI

HPr P

P

IIC IIA IIB

Mannose

IID

Figure 6. Uptake of various sugars via the phosphoenolpyruvate group translocator (PTS) mechanism. Please note that all systems shown share the common components E1 and HPr. For details see the text

references therein) (see Figure 6). The first step in a cascade of subsequent phosphorylation and de-phosphorylation events occurs at the expense of PEP. In contrast to ATP, which is the driving force in many biochemical processes, PEP exclusively serves as the primary energy source in carbohydrate uptake. At the same time PEP is an important precursor for the biosynthesis of cell-wall components and aromatic amino acids. In a biochemical cycle linking PTS to glycolysis, two PEP molecules are generated from one sugar. One of these PEP molecules is used for the transport of the next sugar. The transport components at the end of the cascade couple translocation with phosphorylation of the substrates [153]. Uptake systems of the PTS type are widely distributed among bacteria, but they do not occur in archaea, animals and plants. A variety of sugars and sugar derivatives can be transported (e.g. glucose, sucrose, b-glucoside, mannose, mannitol, fructose, lactose and chitobiose). Regarding their composition, PTS systems follow a modular concept (see Figure 6). PTS proteins are phosphoproteins in which the phosphate group is attached to either a histidine residue

302 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

or, in a number of cases, a cysteine residue. The typical PTS is composed of two general cytoplasmic proteins, the protein kinase enzyme I (EI) and the phospho-acceptor histidine protein (HPr). After phosphorylation of EI by PEP, the phosphate group is transferred to HPr. Enzymes II are then required for the transport of the carbohydrates across the membrane and the transfer of the phospho group from phospho-HPr to the carbohydrates. In the subsequent cascade, a variable number (three to four functional units) of the enzymes II (IIA, IIB, IIC, and, in rare cases, IID) are found, which represent sugarspecific enzymes. The autonomous entities can be arranged as one large protein, with membrane-embedded and cytoplasmic domains (e.g. uptake of mannitol in E. coli). Alternatively, two domains can be combined or just one domain can exist as an independent protein. PTS-mediated substrate translocation can be descibed by the reactions: PEP þ EI $ P  HisEI þ pyruvate

(1)

P  EI þ HPr $ P  HisHPr þ EI

(2)

P  HPr þ IIA $ P  HisIIA þ HPr

(3)

P  IIA þ IIB $ P  CysIIB þ IIA or P  HisIIB þ IIA)

(4)

IIC(IID)

P  IIB þ substrateout !

substrate
Pin þ IIB

(5)

The free energy of the phosphorylated histidine (P  His) or cysteine (P  Cys) is comparable with the free energy of PEP (DG80 ¼
61:5 kJ mol
1 ). The reactions (1) to (4) are therefore fully reversible under physiological conditions, whereas reaction (5) is irreversible. The substrate when bound to the domain IIC (or IID) obtains the phosphoryl group from the unit IIB, via unit IIA, which is rephosphorylated by P  HPr. Efficient translocation of carbohydrates depends on the phosphorylated IIB domain. The release of the phosphorylated substrate terminates the uptake process.

7 UPTAKE OF IRON: A COMBINATION OF DIFFERENT STRATEGIES 7.1

IRON – A ‘PRECIOUS METAL’

For most living bacteria (lactobacilli being the only notable exception [154]) iron is an essential nutrient. Iron is not readily available under normal conditions, although it is the fourth most abundant metal on earth. In the environment it is mainly found as a component of insoluble hydroxides; in biological systems it is chelated by high-affinity iron binding proteins (e.g. transferrins,

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lactoferrins, ferritins) or exists as a component of erythrocytes (haem, haemoglobin, hemopexin). It has a vital function because it is a component of key molecules such as cytochromes, ribonucleotide reductase and other metabolically linked compounds. Since the redox potential of Fe2þ =Fe3þ spans from 1300 mV to 2500 mV, depending on the ligand and protein environment, iron is well suited to participate in a wide range of electron-transfer reactions. Moreover, it has been shown for a number of bacterial pathogens that sufficient iron is essential [155–159]. It is not therefore surprising that microorganisms have developed a number of different sequestering strategies for this ‘precious’ metal. Under anaerobic conditions, the ferric iron can be transported without any chelators involved. Likewise, at pH 3 the ferric iron is soluble enough to support growth of acid-tolerant bacteria. At higher pH values, iron is mostly found in insoluble componds. Therefore a great variety of low-molecularweight high-affinity iron(III) binding ligands, called siderophores, are produced by many bacterial species and certain fungi. Three major structural types are found: catecholates, hydroxamates, and a-hydroxycarboxylates [160]. The chelators are released in their iron-free forms and then transported as ferric– siderophore complexes. Whereas the internalisation of siderophores is rather well characterised, the mechanism of siderophore secretion to the extracellular environment remains only poorly understood. Zhu et al. [161] identified putative export components in mycobacteria, and, most recently, an important observation was published indicating that E. coli membrane protein P43, encoded by the entS gene (formerly ybdA) a critical component of the enterochelin secretion machinery, is located in the chromosomal region of genes involved in enterobactin synthesis. The EntS protein shows strong homology to the 12-transmembrane segment major facilitator superfamily of export pumps [162]. Certain bacteria (many of them pathogens) are able to use haem-bound iron from haemoglobin, haemopexin, and haptoglobin [156,159,163]. In some bacteria (e.g. Serratia marcescens) a haem-binding protein, called haemophore, is secreted in its apo-form and then taken up in a receptor-mediated fashion [163]. In addition, some species can acquire iron from transferrins or lactoferrins involving specific uptake systems in the cell envelope [24,158,164]. A summary of the most important iron-sequestering systems is given in Figure 7. 7.2 IRON TRANSPORT ACROSS THE OUTER MEMBRANES OF GRAM-NEGATIVE BACTERIA Specific receptors for siderophores and vitamin B12 have been identified in the OM of Gram-negative bacteria. The translocation of these ligands across the outer membrane follows an energy-dependent mechanism and also involves the TonB, ExbB, ExbD proteins anchored in the cytoplasmic membrane. Biochemical and genetic data indicate that these proteins form a functional unit (the Ton complex), which couples the outer membrane receptor-mediated

304 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

Metals (Fe, Zn, Mn, ...)

Ferric siderophore

Haempexin Haemoglobin Heme Haemophore

Siderophore

Transferrin Lactoferrin

Haemophore

Cytoplasmic membrane Periplasm Outer membrane Metals (Mn, Zn, Fe ...)

Ferrous iron

Figure 7. The summary of systems involved in (or related to) the uptake and assimilation of iron represents a schematic view of a typical Gram-negative bacterium. The OM receptors, as well as the proteins of the Ton complex, are not present in Gram-positive bacteria, and were not found in mycobacteria and members of the mycoplasma group

transport to the electrochemical potential across the inner membrane (reviewed in [63–65,165,166]). Certain pathogenic Gram-negative bacteria living in their hosts under conditions where the availability of free iron is strongly limited, and the iron acquisition by siderophores is not appropriate, acquire haem and iron from host haem-carrier proteins. The main mechanisms involve either direct binding (like siderophores or vitamin B12 ) to specific OM receptors, or the release of bacterial haemophores that take up haem from host haem carriers and shuttle it back to specific TonB-dependent OM receptors [159,163,167]. The S. marcescens hemophore is a monomer which binds haem with a stoichiometry of 1, and an affinity lower than 10
9 mol dm
3 . The crystal structure of the holoprotein has been solved, and found to consist of a single module with two residues interacting with haem [168]. The secretion of haemophores depends on specific export systems of the ABC-type [169,170]. TonB-dependent OM receptors also play an essential role in the utilisation of iron that is bound to transferrins and lactoferrins. At present, the mechanism by which the iron is released from these polypeptides has not been elucidated [158,164].

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In E. coli the passage across the outer membrane is the rate-limiting step for the siderophores on their way from the environment into the cytoplasm [171]. Furthermore, the siderophore receptors display higher substrate specificity than the proteins of the ABC systems mediating further transfer of siderophores into the cytoplasm. Often there exist more different TonB-dependent OM receptors in a bacterial cell than corresponding permeases. This difference can be very striking, as, for instance, in Pseudomonas aeruginosa, where 34 putative TonB-dependent receptors were identified in the genome [172], whereas only four iron-related ABC transporters seem to exist in this organism. Interestingly, Caulobacter crescentus, a Gram-negative bacterium that grows in dilute aquatic environments has no OmpF-type porins that would allow hydrophilic substrates to diffuse passively through the outer membrane. Instead, there is evidence that as many as 65 OM receptors of the high-affinity TonB-dependent type may catalyse energy-dependent transport of a number of solutes [173]. The structures of several TonB dependent outer membrane transport proteins have been investigated, thus allowing a more detailed insight into energy-coupled uptake mechanisms. The proteins FhuA, FepA, FecA and BtuB from E. coli, whose crystal structures are available, display a striking similarity with respect to their overall organisation in the lipid bilayer. A barrel-like structure anchored in the membrane forms a channel which is (partially) closed by a globular domain referred to as a ‘cork’, ‘plug’, or ‘hatch’ domain (see Figure 8). The FhuA receptor of E. coli transports the hydroxamate-type siderophore ferrichrome (see Figure 9), the structural similar antibiotic albomycin and the antibiotic rifamycin CGP 4832. Likewise, FepA is the receptor for the catecholtype siderophore enterobactin. As monomeric proteins, both receptors consist of a hollow, elliptical-shaped, channel-like 22-stranded, antiparallel b-barrel, which is formed by the large C-terminal domain. A number of strands extend far beyond the lipid bilayer into the extracellular space. The strands are connected sequentially using short turns on the periplasmic side, and long loops on the extracellular side of the barrel. The N-terminal domain of FhuA folds into the barrel, thereby forming a ‘plug’ or ‘cork’ which obstructs the free passage of solutes through the otherwise open channel. The cork domain consists of a mixed four-stranded b-sheet and a series of short a-helices, thus delineating a pair of pockets within FhuA. The extracellular pocket is larger and open to the external medium, while the periplasmic pocket is smaller and in contact with the periplasmic space. An aromatic pocket near the cell surface representing the initial binding site of ferrichrome undergoes minor changes upon association with the ligand, revealing two distinct conformations in the presence and absence of ferrichrome [66,67]. As in FhuA, the special feature of the FepA structure is also the N-terminal domain, which folds into the barrel pore (Figure 5). The core of that ‘plug’ is a four-stranded mixed b-sheet, formed by a central b-hairpin, which is flanked on one side by an antiparallel b-strand and on the other side by a parallel b-strand.

306 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

Figure 8 (Plate 7). Structure of the Escherichia coli FhuA protein serving as receptor for ferrichrome and the antibiotic albomycin. (a) side view; (b) side aspect with partly removed barrel to allow the view on the ‘cork’ domain; (c) top view. A single lipopolysaccharide molecule is tightly associated with the transmembrane region of FhuA (reproduced by permission of W. Welte and A. Brosig)

FecA, the transporter of ferric citrate, is composed of three functional domains. In addition to the barrel and the plug, the receptor contains an extra portion at its N-terminus [174]. This domain, comprising 80 residues,

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Figure 9. Structure of the siderophore ferrichrome (and derivatives) produced by certain fungal species

is typical of a subclass of TonB-dependent receptors. It resides in the periplasm and is involved in a special signal transduction process [175]. The three-dimensional structure FecA displays a number of special features. Probably due to its flexibility, the N-terminal extension could not be located in the crystal structure. However, based on the crystallographic data obtained with and without a bound ligand, a bipartite gating mechanism was described [174]. The subsequent formation of two gates allows for a rational distinction between the binding event and the transport process. A conformational change of the extracellular loops takes place upon binding of the ligand diferricdicitrate that closes the external pocket of FecA. Ligand-induced allosteric transitions are then propagated through the outer membrane by the plug domain, signalling the occupancy of the receptor in the periplasm. These data establish the structural basis of gating for receptors dependent on the cytoplasmic membrane protein TonB [174,176]. Since the proteins in the OM have no direct access to energy-producing pathways, active transport steps depend on activation of TonB by the proton electrochemical potential of the inner membrane. Activated TonB, which together with the ExbB and ExbD proteins is part of a membrane-anchored complex, can then bind to the outer membrane iron transporters, transducing energy to them. In the absence of the proton gradient or TonB, ligands are unable to cross the outer membrane, but still bind with high affinity to their ˚ resolution of the C-terminal transporters [177]. The crystal structure at 1.55 A domain of TonB from E. coli has been reported recently. The structure displays a novel architecture with no structural homology to any known polypeptides, and there is evidence that this region of TonB (residues 164–239) dimerises. The dimer of the C-terminal domain of TonB appears cylinder-shaped, and each monomer contains a single a-helix and three b-strands. The two monomers are

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intertwined with each other, thus leading to the formation of a large antiparallel b-sheet composed of all six b-strands of the dimer [178]. The stoichiometry of the TonB-ExbB-ExbD complex is not yet solved, and it remains open if TonB functions as a dimer in vivo. 7.3 IRON TRANSPORT ACROSS THE CELL WALLS OF GRAMPOSITIVE BACTERIA Whereas many aspects of receptor-mediated transport of siderophore-chelated, haem-bound and transferrin/lactoferrin-associated iron across the outer membrane of Gram-negative bacteria are fairly well understood, comparatively little information is available on suitable systems for iron acquisition in the envelope of Gram-positive bacteria. Siderophores may diffuse through the multilayered murein (¼peptidoglycan) network without major problems, but many questions remain open as to how pathogens belonging to this group of bacteria access iron from host iron sources. One group of surface proteins, associated with the cell walls of Grampositives, is characterised by a signature sequence located near the C-terminus, reading ‘LPXTG’ or ‘NPQTN’. Proteins containing one of these known cellwall-anchoring motives will be attached to the murein. This sorting step involves specific enzymes designated sortase A and sortase B, respectively, displaying a transpeptidase function [179,180]. As illustrated below, a subclass of the cell-wall-anchored proteins may act as receptors for iron-containing compounds such as haem, haemoglobin, transferrin and lactoferrin. The Gram-positive bacterium Streptococcus pneumoniae is an important cause of respiratory tract infections, bacteremia, and meningitis. In this strain, the cell wall anchored pneumococcal surface protein A (PspA) has been demonstrated to bind lactoferrin [181]. PspA and closely related proteins in a variety of pneumococcal isolates are most likely involved in the sequestration of iron from lactoferrins, and finally contribute to the virulence of these bacteria. However, the means by which the pneumococcus acquires iron at the mucosal surface during invasive infection is not well understood at the molecular level [182]. Staphylococci have evolved sophisticated iron-scavenging systems, including cell-surface receptors for transferrin. In Staphylococcus epidermidis and certain S. aureus strains, an iron-regulated transferrin receptor (Tpn) has been described as cell-surface-associated glyceraldehyde-3-phosphate dehydrogenase, which not only retains its glycolytic enzyme activity, but also possesses NADribosylating activity and binds diverse human serum proteins. Tpn was introduced as a member of a newly emerging family of multifunctional OM proteins that are putatively involved in iron acquisition and contribute to staphylococci virulence [183,184]. Conflicting results were published recently by another laboratory, providing evidence that mutants lacking Tpn were still capable of

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binding transferrin. Instead, the stbA gene was identified to encode a putative cell-wall-anchored transferrin receptor [185]. Interestingly, in a different S. aureus strain, IsdA, a protein almost identical to StbA, was characterised as a haem-binding surface protein. Moreover, the isdA gene is located in a genomic region which also encodes a haemoglobin receptor protein and other haem-binding proteins, some of which display similarity to known transport proteins related to iron uptake [186]. A novel type of haem-associated cell-surface protein was identified in Streptococcus pyogenes [187]. The Shp protein shows most of the characteristics (signal sequence at the N-terminus and a hydrophobic putative transmembrane region followed by a positively charged C-terminus) of the cell-wall-anchored proteins described above, but it is missing an obvious sorting signal. The involvement of Shp in haem acquisition is likely, since genes encoding components of ABC transporters clustering with iron uptake systems were identified in the same region of the genome. 7.4 IRON TRANSLOCATION ACROSS THE CYTOPLASMIC MEMBRANE: VARIOUS PATHWAYS Based on experimental data and analysis of sequences available from the databases, we can conclude that different routes for the translocation of iron across the cytoplasmic membrane are possible in bacteria. They can mediate the importation of ferrous iron, and of ferric iron, both in its ionic form and coupled to siderophores or haem. Three of the transport systems represent members of the binding protein-dependent type (a subfamily of ABC transporters or traffic ATPases) (see Section 6.3.2). 7.4.1

feo Type Transport Systems for Ferrous Iron

E. coli has an iron(II) transport system, feo, which may make an important contribution to the iron supply of the cell under anaerobic conditions. Kammler et al. [188] identified the iron(II) transport genes feoA and feoB. The upstream region of feoAB contained a binding site for the regulatory protein Fur, which acts with iron(II) as a corepressor in all known iron transport systems of E. coli. In addition, a Fnr binding site was identified in the promoter region. The FeoB protein (70 kDa) was localised in the cytoplasmic membrane. The sequence revealed regions of homology to ATPases, which indicates that ferrous iron uptake may be ATP driven. Genes with significant similarity to these have been found in the genomes of a great number of bacteria. Biphasic kinetics of Fe2þ transport in a wild-type strain of H. pylori suggested the presence of high- and low-affinity uptake systems. The high-affinity system (apparent Ks ¼ 0:54 mmol dm
3 ) is absent in a mutant lacking the feoB gene. Transport via FeoB is highly specific for Fe2þ , and was inhibited by FCCP,

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DCCD and vanadate. This indicates an active process energised by ATP. Ferrozine inhibition of Fe2þ and Fe3þ uptake implied the concerted involvement of both a Fe3þ reductase and FeoB in the uptake of iron supplied as Fe3þ . It is concluded that FeoB-mediated Fe2þ represents a major pathway for H. pylori iron sequestration [189]. In addition, growth experiments on the human pathogen L. pneumophila using artificial media, as well as replication studies within iron-depleted Hartmannella vermiformis amoebae and human U937 cell macrophages, provided evidence that the FeoB transporter is important for extracellular growth and intracellular infectivity [190]. 7.4.2

Metal Transport Systems of the Nramp Type

Another example of a metal transporter family is the Nramp-family. The Nramp transporters (natural resistance associated macrophage proteins) are transmembrane proteins found in many eukaryotic and prokaryotic organisms, including Archaea, bacteria, yeast, insects, mammals and higher plants. Nramp1 was the first identified gene of this family, characterised in mice as a protein involved in host resistance to certain pathogens [191–193]. Nramp2 was shown to be the major transferrin-independent iron-uptake system of the intestine in mammals. It is capable of mediating influx of transition-metal 2þ divalent cations, including Fe2þ , Mn , and probably, Cd2þ , Co2þ , Ni2þ , 2þ 2þ Cu and Zn [194]. Smfp1, Smfp2, and Smfp3, the homologous protein in yeast, are rather selective for Mn2þ but have been recently linked to the uptake of other heavy metals, including copper, cobalt and cadmium [195]. Hence, like mammalian Nramp transporters, yeast Smf proteins exhibit a broad specificity for both essential and non-essential toxic metals. The three different Smf proteins are distinguishable by their distinct cellular localisations: Smfp1 was found in the cytoplasmic membrane, Smfp2 in intracellular vesicles, and Smfp3 at the vacuolar membrane, indicating that the transporters play different roles in metal metabolism [196]. The only bacterial Nramp proteins characterised so far are highly selective for Mn2þ . This is found for the E. coli MntH, which is a proton-dependent divalent cation co-transporter with a preference for Mn2þ (Km approximately 0:1 mmol dm
3 [197,198]). In Salmonella enterica serovar Typhimurium and E. coli, the mntH gene is regulated at the transcriptional level by both substrate cation and H2 O2 . In the presence of Mn2þ , MntH expression is prevented mainly by the manganese transport repressor, MntR. MntR strongly interacts with an inverted-repeat motif on the DNA located between the
10 polymerase binding site and the ribosome binding site. In the presence of Fe2þ , the Fur repressor blocks expression of mntH, acting through a Fur-binding motif overlapping the
35 region [199,200]. In the presence of hydrogen peroxide, mntH is activated by the OxyR protein, which binds to a consensus motif just upstream of the putative promoter [200]. Biochemical and genetic studies

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demonstrate that the MntH transporter in the Gram-positive bacterium B. subtilis is selectively repressed by Mn(II). This regulation requires the MntR protein acting under high Mn(II) conditions as repressor of mntH transcription [201]. 7.4.3

ABC Transporters for Siderophores/Haem/Vitamin B12

ABC transporters involved in the uptake of siderophores, haem, and vitamin B12 are widely conserved in bacteria and Archaea (see Figure 10). Very few species lack representatives of the siderophore family transporters. These species are mainly intracellular parasites whose metabolism is closely coupled to the metabolism of their hosts (e.g. mycoplasma), or bacteria with no need for iron (e.g. lactobacilli). In many cases, several systems of this transporter family can be detected in a single species, thus allowing the use of structurally different chelators. Most systems were exclusively identified by sequence data analysis, some were biochemically characterised, and their substrate specificity was determined. However, only very few systems have been studied in detail. At present, the best-characterised ABC transporters of this type are the fhuBCD and the btuCDF systems of E. coli, which might serve as model systems of the siderophore family. Therefore, in the following sections, this report will mainly focus on the components that mediate ferric hydroxamate uptake (fhu) and vitamin B12 uptake (btu). The fhu genes of E. coli constitute an iron-regulated operon starting with the fhuA gene, which encodes the outer membrane receptor for ferrichrome and albomycin mentioned in Section 7.2. The fhuC, fhuD, and fhuB genes – organised downstream from fhuA in this order – are essential for further translocation across the inner membrane [202]. Genes contributing to iron acquisition can also be located on mobile genetic elements (e.g. pathogenic islands) inserted into the chromosome or on episomal DNA, like the fat genes of the fish pathogen Vibrio anguillarum [203,204]. As mentioned above, transport of siderophores across the cytoplasmic membrane is less specific than the translocation through the outer membrane. In E. coli three different outer membrane proteins (among them FepA the receptor for enterobactin produced by most E. coli strains) recognise siderophores of the catechol type (enterobactin and structurally related compounds), while only one ABC system is needed for the passage into the cytosol. Likewise, OM receptors FhuA, FhuE, and Iut are needed to transport a number of different ferric hydroxamates, whereas the FhuBCD proteins accept a variety of hydroxamate type ligands such as albomycin, ferrichrome, coprogen, aerobactin, shizokinen, rhodotorulic acid, and ferrioxamine B [165,171]. For the vast majority of systems, the substrate specificity has not been elucidated, but it can be assumed that many siderophore ABC permeases might be able to transport several different but structurally related substrates.

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At present, FhuD is the best-characterised siderophore binding protein. Binding of different iron(III) hydroxamates to the mature FhuD protein has been demonstrated [205,206]. Changes in the intrinsic fluorescence of purified FhuD allowed the estimation of the dissociation constants (KD ) for ferric aerobactin (0:4 mmol dm
3 ), ferrichrome (1:0 mmol dm
3 ), ferric coprogen (0:3 mmol dm
3 ), ferrioxamine A (79 mmol dm
3 ), ferrioxamine B (36 mmol dm
3 ), ferrioxamine E (42 mmol dm
3 ), and albomycin (5:4 mmol dm
3 ). FhuD contributes to a large extent to the substrate specificity of transport through the cytoplasmic membrane. Recently, the characterisation of FepB from E. coli by intrinsic fluorescent measurements revealed a significantly lower KD (30 nmol dm
3 ) for ferric enterobactin [207]. The crystal structure of FhuD complexed with gallichrome has been solved at ˚ [208] (see Figure 11). The binding of the siderophore to FhuD is mediated 1.9 A by hydrophilic and hydrophobic interactions. The ligand binding site represents a shallow groove between the N- and C-terminal domains of the kidney-beanshaped bilobate protein. Remarkably, the polypeptide chain crosses between the N-terminal and C-terminal domains only once. The linker connecting the two domains is a kinked a-helix, which spans the entire length of the protein. The N-terminal domain consists mainly of a twisted five-stranded parallel b-sheet and the C-terminal domain is composed of a five-stranded mixed b-sheet. Both sheets are sandwiched between layers of a-helices. From the extensive, predominantly hydrophobic, domain interface in FhuD it is

Ferric siderophore Ferric siderophore

OM-Receptor

OM BP

BP

Ton complex

PP

IMP

CM ADP ATP

ADP

ATPase

ATP

Gram-positive bacteria

IMP

ADP ATP

ATPase

CM

ADP ATP

Gram-negative bacteria

Figure 10. Schematic view of the uptake of ferric siderophores by Gram-positive and Gram-negative bacteria. Please note that the murein (peptidoglycan) network associated with the cytoplasmic membrane is not shown. For details see text

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concluded that binding and release of the ligands probably do not cause large scale opening and closing of the siderophore binding site. Thus, FhuD differs from the majority of BPs in that it does not adopt the ‘classic’ fold that has been observed in almost all BPs that are structurally characterised to date (see Section 6.3.2). FhuD adopts a novel fold (missing the flexible hinge region) and represents a new class of BPs [208]. FhuD forms a distinctive family, together with all BPs that transport siderophores, haem, and vitamin B12 . Members of this siderophore family are clearly distinguishable from any other component involved in the uptake of metals. Despite considerable differences in size (28 to over 40 kDa) and very limited similarity in their amino acid sequences, the BPs of the siderophore family possess characteristic signatures, also pointing to an internal homology. Moreover, the recently solved crystal structure of the vitamin B12 binding protein BtuF [209,210] demonstrated a significant structural similarity when the FhuD and BtuF structures were

Figure 11. Crystal structure of the hydroxamate binding protein FhuD from Escherichia coli complexed with gallichrome. (Reproduced by permission of H. J. Vogel and T. E. Clarke)

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superimposed. Vitamin B12 is bound in the ‘base-on’ conformation in a deep cleft formed at the interface between the two lobes of BtuF. Comparison of the ligandbound and the apo structures lead to the conclusion that the unwinding of a surface located a-helix in the C-terminal domain of BtuF may take place upon binding to BtuC. This conformational change could be important for triggering the release of B12 into the transport cavity and further passage through the BtuC2 D2 complex in the CM [210]. At present, only two structurally characterised BPs share some topological similarities with FhuD and BtuF: Mn2þ (and possibly Zn2þ ) binding PsaA from S. pneumoniae, and the zinc-binding protein TroA from Treponema pallidum [211,212] (see Section 7.3.5). It is assumed that FhuD binds and delivers ferric hydroxamates to the FhuB transport protein in the cytoplasmic membrane. Genetic and biochemical experimental approaches (e.g. protease protection and cross-linking experiments) indicate a physical interaction of FhuD with FhuB [202,206]. Likewise, the vitamin B12 binding protein is thought to transport the ligand to the transport components in the membrane. This picture is in good agreement with the observed formation in vitro of a stable complex between BtuF and BtuCD (with the stoichiometry BtuC2 D2 F). After Locher et al. [209,213] had determined a high-resolution atomic structure of BtuC2 D2 (the first structure of an ABC importer complex composed of integral membrane proteins and ATPases), modelling of the individual crystal structures suggested that two surface exposed glutamates from BtuF may interact with arginine residues on the periplasmic surface of the BtuC dimer in the CM [209]. These glutamate and arginine residues had already been reported to be conserved among BPs and IMPs related iron and B12 uptake [202]. It therefore can be assumed that they may play a more general role in protein–protein interaction and the triggering of conformational changes. FhuB is an extremely hydrophobic polytopic integral membrane protein. During substrate translocation, FhuB plays a central role in the system, interacting not only with FhuD and FhuC but also with the different ferric hydroxamates. For many years, FhuB was unique among the integral membrane proteins, in that it is about double the size (70 kDa) of comparable components from other ABC transporters and it consists of two major domains displaying significant homology to each other. Both halves (FhuB[N] and FhuB[C]) of the polypeptide are essential for transport; deletion of either domain results in loss of activity. FhuB[N] and FhuB[C] are still functional when produced as two distinct polypeptides [171]. Recently, FhuB-like IMPs have been identified in V. cholerae, Rhizobium leguminosarum, and R. capsulatus. Complementation studies with the dissected FhuB strongly suggest that each of the two FhuB halves has the potential to insert independently into the lipid bilayer, where it diffuses and associates stochastically with the complementary subunit present. The mode of recognition and interaction of the transport components is probably very similar in most ABC transporters. Little is known, however, about

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the interaction of the integral membrane proteins at the molecular level. The interaction of the other siderophore family IMPs may in principle follow the same rule as the FhuB[N]–FhuB[C] interaction. Most IMPs involved in siderophore uptake might form hetero dimers. In haeme and vitamin B12 transport systems the formation of homo dimers is most likely, since only one IMP was detected in the relevant genomic regions of e.g. E. coli, V. cholerae, P. aeruginosa, Shigella dysenteriae, Yersinia enterocolitica and Y. pestis. Several areas of striking homology are present in the primary structures of the siderophore family IMPs. One of these regions includes a glycine residue at a distance of about 100 amino acids from the C-terminus. It corresponds with the conserved Gly [139], which is part of the ‘E A A - - - G - - - - - - - - - I - L P’ motif defined by Dassa and Hofnung [138] (see Section 6.3.2). This conserved region (CR), present twice in FhuB, plays a general role in the translocation process [214]. The homologous regions, especially the conserved glycine residues, are believed to be structurally and/or functionally important for the other siderophore family uptake systems as well. The topology of FhuB differs from the equivalent components of other ABC transporters, in that each half consists of 10 membrane-spanning regions. The location of N- and C-termini is cytosolic. The CR is also oriented to the cytoplasm. However, in contrast to the ‘classical’ arrangement, this putative ATPase interaction loop is followed by four instead of two transmembrane spans [215]. A schematic topology model is presented in Figure 12. It is assumed that the hydrophilic regions may – entirely

Figure 12 (Plate 8). Transmembrane arrangement of the polytopic FhuB protein in the cytoplasmic membrane as determined by the analysis of ß-lactamase proteins C-terminally fused to various portions of FhuB. The FhuB protein is composed of two times 10 membrane-spanning regions connected by loops contacting the periplasm or the cytoplasm. These loops were predicted to entirely or partly fold back into the overall structure. The conserved regions (CR) typical of all prokaryotic importers belonging to the ABC transporter family are shown in dark gray. They are important for the interaction with the FhuC protein – the ATPase supplying energy for the siderophore translocation process

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or partially – fold back into a channel-like structure built by the transmembrane spans. At present, it cannot be decided to what extent the ‘loops’ are accessible from the periplasm or cytoplasm. Sequence analysis data suggest a similar arrangement for all IMPs of the siderophore family. Support for this idea came again from the structural data of the BtuC2 D2 complex [213]. Remarkably, each of the hydrophobic BtuC units contains 10 transmembrane regions. This arrangement is in perfect agreement with the predicted FhuB topology model, containing altogether 20 membrane-spanning segments. See also Figure 13. The analysis of the primary structure of FhuC had suggested a function as an ATP-binding component. FhuC was one of the first ATPases (of bindingprotein-dependent import systems) in which highly conserved residues in the ‘Walker A’ and ‘Walker B’ consensus motifs were altered. A total loss of function in all these FhuC derivatives indicated that FhuC indeed acts as an ATP-hydrolase, thereby energising the transport process, most likely via inducing conformational changes in the components of the permease complex [165,171,216]. Since the ATPases are the components which are the most conserved among all ABC transporters, it is highly likely that the structural features and the mechanism of energisation are very similar in all these systems. It was concluded from previous studies, in particular in the histidine and in the

Figure 13 (Plate 9). Crystal structure of the BtuC2 D2 complex involved in the uptake of vitamin B12 . Two copies of the polytopic integral membrane protein BtuC and of the ATPase subunit BtuD are shown, together with bound ATP (reproduced by permission of K. Locher). For more details see the text

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maltose uptake systems, that the active ATPase subunits function as a dimer. The crystal structures of some ATPases have been solved in absence of the integral membrane proteins (for further information see [142,217–221]. They all adopt a similar L-shaped structure with two arms, one containing the signature motif, and the other the Walker A and B motifs. Different arrangements of the ATPase proteins in a putative dimer had been proposed, but it remained unclear which orientation is realised in the active permease complex: ‘back to back’, ‘head to tail’ or ‘head to head’. In the reported structure of the BtuC2 D2 complex the ‘head to tail’ orientation is realised, with a surprisingly small interface between the two ATPase units and with the Walker A motif of one monomer facing the LSGG motif of the other. Each nucleotide-binding site contains residues from both monomers. This architecture now supports previous biochemical data obtained with the functional ABC transporters, in that it provides a sound basis for the cooperativity observed in the nucleotide-binding domains [222,223]. In addition, the participation of the highly conserved family signature motif (LSGGQ) in ATP binding and hydrolysis becomes more understandable. Interaction of ATPase FhuC with IMP FhuB was first demonstrated by dominant negative effects on transport of FhuC derivatives with single amino acid replacements in the putative ATP-binding domains. Furthermore, immunoelectron microscopy with anti-FhuC antibodies showed FhuB-mediated association of FhuC with the cytoplasmic membrane [216]. Moderate overexpression of the FhuB derivatives (point mutation in the CRs) in a fhu wild-type strain displayed a negative complementing phenotype to various extents, as shown by growth tests, and transport rates. These experimental data already indicated that the CR is mainly involved in the interaction with FhuC. Again, a detailed molecular view identifying amino acid residues as potential candidates for protein–protein interaction and suggesting possible mechanisms of ATPase-IMP interaction was feasible by analysing the structure of the BtuC2 D2 for vitamin B12 uptake (Figure 13). In this arrangement, the BtuC homo dimer resembles the two halves of FhuB, whereas the BtuD units are equivalent to the FhuC components. Since proteins trapped in a crystal structure represent only a snap shot of a dynamic process, further studies will be necessary in order to unravel the details of the actual translocation process. 7.4.4

ABC Transporters of the Ferric Iron Type

The first transporter of this type characterised as an iron-supply system that functions in the absence of any siderophore was the Sfu system of S. marcescens [224]. Later, similar systems were reported from Neisseria gonorrhoea and Neisseria meningitidis, and have been detected by analysing the genomes of a variety of bacteria, e.g. Actinobacillus pleuropneumoniae, B. halodurans, Campylobacter jejuni, Ehrlichia chaffeensis, Halobacterium sp., H. influenzae,

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Brachyspira hyodysenteriae, Pasteurella haemolytica, P. aeruginosa, V. cholerae and Y. enterocolitica [156–158,164]. The Sfu/Fbp-like systems contribute to the virulence of pathogenic bacteria. They are thought to mediate the further transport into the cytoplasm of ferric iron that is acquired from lactoferrin or transferrin and delivered into the periplasm in a receptor-mediated Ton complex-dependent fashion [157–159]. A rather uniform organisation of ferric iron transport genes seem to be the rule for most bacterial species studied so far. A putative iron-regulated operon contains genes encoding the substrate-binding protein, the IMP, and the ATPase – in this order. The ferric-binding protein (FbpA) is one of the major iron-regulated proteins, and is highly conserved in all species of pathogenic Neisseria [157]. The first crystal structure was solved for the FbpA homologue from H. influenzae (HitA), and was found to be of the ‘classical’ arrangement with a flexible hinge region. Interestingly, iron binding in HitA and transferrin appears to have developed independently by convergent evolution. From structural comparison of HitA with other prokaryotic BPs and the eukaryotic transferrins, it is concluded that these proteins are related by divergent evolution from an anion-binding common ancestor rather than from an iron-binding ancestor. The iron-binding site of HitA incorporates a water molecule and an exogenous phosphate ion as iron ligands [157]. The IMPs of the ferric iron type display an internal homology, in which each half, smaller than IMPs of most other ABC transporters, harbours a CR as putative interaction site with the ATPase. Interestingly, in the B. hyodysenteriae Bit system the hydrophobic membrane domains are expressed as two separate proteins. The ATPases from ferric iron transport systems show typical characteristics, and are supposed to follow the same mechanism of energising the translocation step of substrates into the cytosol. No detailed studies have been reported at the molecular level. 7.4.5

ABC Transporters for Iron and Other Metals

The third group of ABC type importers related to iron uptake in bacteria was discovered a few years ago. Transport systems of the metal type are present in many bacterial species. Only a small number of uptake systems are primarily involved in the acquisition of iron. Many have a higher specificity for metals like zinc or manganese. For some systems it has been clearly shown that they are essential for iron acquisition (e.g. Yfe of Y. pestis and Sit of S. typhimurium). As in the ABC transport systems mentioned above, the genes encoding components of metal-type ABC transporters are often organised in operons. The expression of the vast majority seems to be regulated by the degree of metals present in the environment, often depending on the metals to be transported. A number of repressors acting at the transcriptional level with

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different metal binding specificity and different recognition sequences on the DNA have been identified. The crystal structures of binding proteins PsaA from S. pneumoniae and TroA from T. pallidum have been solved at 2.0 ˚ solution, respectively [211,212]. Both proteins consist of an N- and and 1.8 A C-lobe, each composed of b-strand bundles surrounded by a-helices. The two domains are linked together by a single helix. Also found for the structurally similar siderophore binding protein FhuD the structural topology was fundamentally different from that of other ‘classical’ ABC-type binding proteins, in that PsaA and TroA were lacking the characteristic ‘hinge peptides’ involved in conformational change upon solute uptake and release. Experimental evidence suggests that the BPs of the metal-type systems do not completely share metal specificity, as S. typhimurium SitA binds primarily iron and Yersinia pestis YfeA iron and manganese. PsaA from S. pneumoniae is presumed to bind primarily Mn2þ , and possibly Zn2þ , T. pallidum TroA and S. pneumoniae AdcA bind primarily Zn2þ , and Synechocystis MntC binds Mn2þ . The variation in metal specificity amongst the metal-type BPs is reflected by the variation in those residues (His, Asp, Glu) that are sequence related to the metal-coordinating residues, allowing the BPs to be grouped into several subclusters. The hydrophobic components of the metal-type system display characteristics typical of IMPs from most ABC transporters. The same holds true for the corresponding ATPases.

7.5

OTHER SYSTEMS

L. pneumophila, a facultative intracellular parasite of human alveolar macrophages and protozoa, causes legionnaires’ disease. Two genes related to virulence were detected, iraA encoding a 272-amino-acid protein that shows sequence similarity to methyltransferases, and iraB coding for a 501-amino-acid protein that is highly similar to di- and tripeptide transporters from both prokaryotes and eukaryotes. Experimental data suggest that IraA is critical for the virulence of L. pneumophila, while IraB is involved in a novel mode of iron acquisition, which may utilise iron-loaded peptides [225]. Treponema denticola, which is strongly associated with the pathogenesis of human periodontal disease, does not appear to produce siderophores, so it must acquire iron from other sources. Recently, this Gram-negative bacterium has been shown to express two homologous iron-regulated outer membrane proteins with haemin binding ability. These proteins, HbpA and HbpB, both of the size of 44 kDa, do not show any similarity to TonB-dependent OM receptors, and thus may be part of a previously unrecognised iron-acquisition pathway [226].

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The Gram-negative anaerobic bacterium Porphyromonas gingivalis has been implicated as a major pathogen in the development and progression of chronic peridontitis. The iht gene locus of this organism is involved in iron haem transport. In addition to a TonB-dependent OM receptor (IhtA) and a typical ABC transport system (IhtCDE), IhtB was characterised as an OM haem-binding lipoprotein. Experimental data and sequence analysis suggest that IhtB is a peripheral outer membrane chelatase involved in iron uptake [227]. 7.6

PHYLOGENETIC ASPECTS

The almost identical design suggests a common origin of all ABC systems. However, the members of the three iron-transport families, the siderophore/ haem type, the ferric iron (Fbp/Sfu) type, and the metal (Fe, Zn, Mn) type, are clearly distinguishable with respect to the primary structure of the different components. The integral membrane proteins and the substrate binding proteins display significant similarity only within their families. In particular, BPs and IMPs of the siderophore family seem to be totally unrelated to any other known ABC transporter. By contrast, the ferric iron type proteins display a low but significant homology to the equivalent components that are involved in the utilisation of, for example, sulfate, spermidine and putrescine. The ATPases of different families show a higher degree of conservation, but still cluster in distinctive groups. All three major families can be divided in subfamilies. The formation of subfamilies is not species specific, and components of a given cluster can be found in Gram-positives, Gram-negatives and Archaeae. Some bacteria possess uptake systems of all the ABC types mentioned in this chapter. For example, the pathogenic microbe H. influenzae is able to sequester iron via siderophore-type systems, ferric iron systems, and metal-type systems. Similarly, strains of Yersinia use multiple routes to take up iron bound to siderophores (e.g. yersiniabactin) and haem, as well as unliganded iron by the ferric-iron-type Yfu system and the metal-type Yfe system. No iron-uptake systems of the ABC transporter type were identified in the genomes of Mycoplasma genitalium and Mycoplasma pneumoniae. In contrast, among the 19 ABC transporters of the related species Ureaplasma urealyticum six presumed different Fe3þ and/or haem transporters were identified [228]. 7.7 IRON TRANSPORT IN BACTERIA: CONCLUSION AND OUTLOOK Various strategies of iron acquisition are realised in a great number of microbes. Of the different uptake systems, the three different groups of ABC

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transporters (siderophore/haem/vitamin B12 type, ferric iron type, metal type) are of particular interest. They can serve as model systems to study general aspects of: . . . . . .

evolution and biodiversity; gene expression and regulation; protein structure and folding of polypeptides; topology and membrane insertion of proteins; intra- and inter-molecular interactions; and substrate binding and translocation mechanisms at the molecular level.

In addition, the unique features of iron-uptake systems make the components involved ideal candidates: . to examine their potential as targets for antimicrobial agents; . to investigate their role in virulence mechanisms of pathogens; and . to deliver siderophore–drug conjugates to microbes causing infections in humans and animals.

8

CHALLENGES FOR FUTURE RESEARCH

The most challenging aspects related to transport phenomena can be summarised as follows: . solve the three-dimensional structures of representatives from all major groups of transport proteins, particularly those of the hydrophobic components embedded in the cytoplasmic membrane; . unravel the dynamics of transfer processes; . understand transport mechanisms at the molecular level; and . create data sets in order to predict protein structure and function based on sequence information, and to identify potential interaction partners.

ACKNOWLEDGEMENTS The author apologises to those whose papers and important studies were not cited because of space limitations. The author is grateful to W. Welte and A. Brosig (Konstanz, Germany), D. van der Helm and L. Esser (Norman, USA) H. J. Vogel and T. E. Clarke (Calgary, Canada), and K. Locher (Pasadena, USA) who provided excellent material for some of the figures presented in the chapter.

322 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

GLOSSARY ACRONYMS ABC Amt AqpZ ATP BP btu CM CR DCCD FCCP feo fhu Hpr IMP LPS MFS MIP MscL MscS Nramp OM PE PEP pmf PP PTS TC TM TRAP

ATP binding cassette Ammonium/methylammonium transport Aquaporin Z Adenosine triphosphate Binding protein Vitamin B12 uptake Cytoplasmic membrane Conserved region Dicyclohexylcarbodiimide Carbonyl cyanide para-trifluoromethoxyphenylhydrazone Ferrous iron uptake Ferric hydroxamate uptake Histidine protein (from PTS system) Integral membrane protein Lipopolysaccharides Major facilitator superfamily Major intrinsic protein Mechanosensitive channels of large conductance Mechanosensitive channels of small conductance Natural resistance associated macrophage proteins Outer membrane Phosphatidylethanolamine Phosphoenolpyruvate Proton motive force Periplasm Phosphotransferase system Transport commission Transmembrane domain Tripartite ATP-independent periplasmic

SYMBOLS DGo Dc KD

0

Km Vmax Ks

Standard-free-energy difference at pH 7 Membrane potential Concentration of ligand to reach half maximum binding Concentration at which the transport rate reaches half its maximum (Vmax ) Maximum transport rate Saturation concentration

(kJ mol
1 ) (mV) (mol dm
3 ) (mol dm
3 )
1 (mol min
1 mg )
3 (mol dm )

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REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

15. 16. 17. 18. 19.

Manson, M. D., Armitage, J. P., Hoch, J. A. and Macnab, R. M. (1998). Bacterial locomotion and signal transduction, J. Bacteriol., 180, 1009–1022. Aizawa, S.-I., Harwood, C. S. and Kadner, R. K. (2000). Signalling components in bacterial locomotion and sensory transduction, J. Bacteriol., 182, 1459–1471. Koronakis, V., Sharff, A., Koronakis, E., Luisi, B. and Hughes, C. (2000). Crystal structure of the bacterial membrane protein TolC central to multidrug efflux and protein export, Nature, 405, 914–919. Koronakis, V., Andersen, C. and Hughes, C. (2001). Channel-tunnels, Curr. Opin. Struct. Biol., 11, 403–407. Murakami, S., Nakashima, R., Yamashita, E. and Yamaguchi, A. (2002). Crystal structure of bacterial multidrug efflux transporter AcrB, Nature, 419, 587–593. Bhattacharjee, H., Zhou, T., Li, J., Gatti, D. L., Walmsley, A. R. and Rosen, B. P. (2000). Structure–function relationships in an anion-translocating ATPase, Biochem. Soc. Trans., 28, 520–526. Rosen, B. P. (2002). Biochemistry of arsenic detoxification, FEBS Lett., 529, 86–92. Ho¨ltje, J. V. (1998). Growth of the stress-bearing and shape-maintaining murein sacculus of Escherichia coli, Microbiol. Mol. Biol. Rev., 62, 181–203. Weidel, W. and Pelzer, H. (1964). Bagshaped macromolecules – a new outlook on bacterial cell walls, Adv. Enzymol., 26, 193–232. Park, J. T. (1996). The convergence of murein recycling research with betalactamase research, Microb. Drug Resist. Springer, 2, 105–112. Rogers, H. J., Perkins, H. R. and Ward, J. B. (1980). The bacterial autolysins. In Microbial Cell Walls and Membranes. eds. Rogers, H. J., Perkins, H. R. and Ward, J. B., Chapman & Hall, London, pp. 437–460. Kandler, O. and Ko¨nig, H. (1985). Cell envelopes of archaebacteria. In The Bacteria. eds. Woese, C. R. and Wolfe, R. S., Academic Press, New York, pp. 413–457. Hartmann, E. and Ko¨nig, H. (1990). Comparison of the biosynthesis of the methanobacterial pseudomurein and the eubacterial murein, Naturwissenschaften, 77, 472–475. Sinninghe Damste, J. S., Strous, M., Rijpstra, W. I., Hopmans, E. C., Geenevasen, J. A., van Duin, A. C., van Niftrik, L. A. and Jetten, M. S. (2002). Linearly concatenated cyclobutane lipids form a dense bacterial membrane, Nature, 419, 708–712. Braun, V. and Rehn, K. (1969). Chemical characterization, spatial distribution and function of a lipoprotein (murein-lipoprotein) of the E. coli cell wall. The specific effect of trypsin on the membrane structure, Eur. J. Biochem., 10, 426–438. Shockman, G. D. and Barret, J. F. (1983). Structure, function, and assembly of cell walls of gram-positive bacteria, Ann. Rev. Microbiol., 37, 501–527. Baddiley, J. (1989). Bacterial cell walls and membranes. Discovery of the teichoic acids, Bioessays, 10, 207–210. Koch, A. L. (2000). The exoskeleton of bacterial cells (the sacculus): still a highly attractive target for antibacterial agents that will last for a long time, Crit. Rev. Microbiol., 26, 1–35. Escuyer, V. E., Lety, M.-A., Torrelles, J. B., Khoo, K.-H., Tang, J.-B., Rithner, C. D., Frehel, C., McNeil, M. R., Brennan, P. J. and Chatterjee, D. (2001). The role of the embA and embB gene products in the biosynthesis of the terminal hexaarabinofuranosyl motif of Mycobacterium smegmatis arabinogalactan, J. Biol. Chem., 276, 48 854–48 862.

324 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.

31. 32. 33. 34. 35. 36. 37. 38. 39. 40.

Crick, D. C., Mahapatra, S. and Brennan, P. J. (2001). Biosynthesis of the arabinogalactan–peptidoglycan complex of Mycobacterium tuberculosis, Glycobiology, 9, 107R–118R. Chatterjee, D. and Khoo, K. H. (2001). The surface glycopeptidolipids of mycobacteria: structures and biological properties, Cell. Mol. Life Sci., 58, 2018–2042. Brennan, P. J. and Nikaido, H. (1995). The envelope of mycobacteria, Ann. Rev. Biochem., 64, 29–63. Dmitriev, B. A., Ehlers, S., Rietschel, E. T. and Brennan, P. J. (2000). Molecular mechanics of the mycobacterial cell wall: from horizontal layers to vertical scaffolds, Int. J. Med. Microbiol., 290, 251–258. Draper, P. (1998). The outer parts of the mycobacterial envelope as permeability barriers, Front. Biosci., 15, 1253–1261. Nikaido, H. (1999). Microdermatology: cell surface in the interaction of microbes with the external world, J. Bacteriol., 181, 4–8. Pines, O. and Inouye, M. (1999). Expression and secretion of proteins in E. coli, Mol. Biotechnol., 12, 25–34. Economou, A. (1999). Following the leader: bacterial protein export through the Sec pathway, Trends Microbiol., 7, 315–320. Danese, P. N. and Silhavy, T. J. (1998). Targeting and assembly of periplasmic and outer-membrane proteins in Escherichia coli, Ann. Rev. Genet., 32, 59–94. Thanassi, D. G. (2002). Ushers and secretins: channels for the secretion of folded proteins across the bacterial outer membrane, J. Mol. Microbiol. Biotechnol., 4, 11–20. Buchanan, S. K., Smith, B. S., Venkatramani, L., Xia, D., Esser, L., Palnitkar, M., Chakraborty, R., van der Helm, D. and Deisenhofer, J. (1999). Crystal structure of the outer membrane active transporter FepA from Escherichia coli, Nat. Struct. Biol., 6, 56–63. Buchanan, S. K. (1999). Beta-barrel proteins from bacterial outer membranes: structure, function and refolding, Curr. Opin. Struct. Biol., 9, 455–461. Tamm, L. K., Arora, A. and Kleinschmidt, J. H. (2001). Structure and assembly of b-barrel membrane proteins, J. Biol. Chem., 276, 32 399–32 402. Schulz, G. E. (2000). b-Barrel membrane proteins, Curr. Opin. Struct. Biol., 10, 443–447. von Heijne, G. (1995). Membrane protein assembly: rules of the game, Bioessays, 17, 25–30. von Heijne, G. (1998). Structural aspects of transmembrane alpha-helices, Acta Physiol. Scand. Suppl. 643, 163, 17–19. von Heijne, G. (1999). Recent advances in the understanding of membrane protein assembly and structure, Q. Rev. Biophys., 32, 285–307. Mori, H. and Ito, K. (2001). The Sec protein-translocation pathway, Trends Microbiol., 9, 494–500. Mu¨ller, M., Koch, H. G., Beck, K. and Schafer, U. (2001). Protein traffic in bacteria: multiple routes from the ribosome to and across the membrane, Prog. Nucleic Acid Res. Mol. Biol., 66, 107–157. Chen, M., Xie, K., Jiang, F., Yi, L. and Dalbey, R. E. (2002). YidC, a newly defined evolutionarily conserved protein, mediates membrane protein assembly in bacteria, Biol. Chem., 383, 1565–1572. Froderberg, L., Houben, E., Samuelson, J. C., Chen, M., Park, S. K., Phillips, G. J., Dalbey, R., Luirink, J. and De Gier, J. W. (2003). Versatility of inner membrane protein biogenesis in Escherichia coli, Mol. Microbiol., 47, 1015–1027.

¨ STER W. KO 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54.

55. 56. 57. 58.

325

Bogdanov, M., Sun, J., Kaback, H. R. and Dowhan, W. (1996). A phospholipid acts as a chaperone in assembly of a membrane transport protein, J. Biol. Chem., 271, 11 615–11 618. Bogdanov, M., Heacock, P. N. and Dowhan, W. (2002). A polytopic membrane protein displays a reversible topology dependent on membrane lipid composition, EMBO J., 21, 2107–2116. van Heusden, H. E., De Kruijff, B. and Breukink, E. (2002). Lipid II induces a transmembrane orientation of the pore-forming peptide lantibiotic nisin, Biochemistry, 41, 12 171–12 178. Saier, M. H. Jr (2000). A functional–phylogenetic classification system for transmembrane solute transporters, Microbiol. Mol. Biol. Rev., 64, 354–411. Koning, S. M., Albers, S. V., Konings, W. N. and Driessen, A. J. (2002). Sugar transport in (hyper)thermophilic archaea, Res. Microbiol., 153, 61–67. Jung, H. (2001). Towards the molecular mechanism of Naþ /solute symport in prokaryotes, Biochim. Biophys. Acta – Bioenerg., 1505, 131–143. Haardt, M., Kempf, B., Faatz, E. and Bremer, E. (1995). The osmoprotectant proline betaine is a major substrate for the binding-protein-dependent transport system ProU of Escherichia coli K-12, Mol. Gen. Genet., 246, 783–786. Weiss, M. S., Abele, U., Weckesser, J., Welte, W., Schiltz, E. and Schulz, G. E. (1991). Molecular architecture and electrostatic properties of a bacterial porin, Science, 254, 1627–1630. Cowan, S. W., Schirmer, T., Rummel, G., Steiert, M., Ghosh, R., Pauptit, R. A., Jansonius, J. N. and Rosenbusch, J. P. (1992). Crystal structures explain functional properties of two Escherichia coli porins, Nature, 358, 727–733. Jeanteur, D., Lakey, J. H. and Pattus, F. (1991). The bacterial porin superfamily: sequence alignment and structure prediction, Mol. Microbiol., 5, 2153–2164. Bauer, K., Struyve´, M., Bosch, D., Benz, R. and Tommassen, J. (1989). One single lysine residue is responsible for the special interaction between polyphosphate and the outer membrane porin PhoE of Escherichia coli, J. Biol. Chem., 264, 16 393–16 398. Benz, R., Schmid, A., van der Ley, P. and Tommassen, J. (1989). Molecular basis of porin selectivity: membrane experiments with OmpC–PhoE and OmpF–PhoE hybrid proteins of Escherichia coli K-12, Biochim. Biophys. Acta, 981, 8–14. Phale, P. S., Philippsen, A., Kiefhaber, T., Koebnik, R., Phale, V. P., Schirmer, T. and Rosenbusch, J. P. (1998). Stability of trimeric OmpF porin: the contributions of the latching loop L2, Biochemistry, 37, 15 663–15 670. Hardesty, C., Ferran, C. and DiRienzo, J. M. (1991). Plasmid-mediated sucrose metabolism in Escherichia coli: characterization of scrY, the structural gene for a phosphoenolpyruvate-dependent sucrose phosphotransferase system outer membrane porin, J. Bacteriol., 173, 449–456. Benz, R., Schmid, A., Nakae, T. and Vos-Scheperkeuter, G. H. (1986). Pore formation by LamB of Escherichia coli in lipid bilayer membranes, J. Bacteriol., 165, 978–986. Charbit, A., Wang, J., Michel, V. and Hofnung, M. (1998). A cluster of charged and aromatic residues in the C-terminal portion of maltoporin participates in sugar binding and uptake, Mol. Gen. Genet., 260, 185–192. Luckey, M. and Nikaido, H. (1980). Specificity of diffusion channels produced by lambda phage receptor protein of Escherichia coli, Proc. Natl Acad. Sci. USA, 77, 167–171. Schirmer, T., Keller, T. A., Wang, Y. F. and Rosenbusch, J. P. (1995). Structural ˚ resolution, basis for sugar translocation through maltoporin channels at 3.1 A Science, 267, 512–514.

326 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 59. 60. 61. 62. 63.

64. 65. 66.

67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77.

Forst, D., Welte, W., Wacker, T. and Diederichs, K. (1998). Structure of the sucrose-specific porin ScrY from Salmonella typhimurium and its complex with sucrose, Nature Struct. Biol., 5, 7–46. Dutzler, R., Wang, Y.-F., Rizkallah, P. J., Rosenbusch, J. P. and Schirmer, T. (1995). Crystal structures of various maltooligosaccharides bound to maltoporin reveal a specific sugar translocation pathway, Structure, 4, 127–134. Meyer, J. E. W., Hofnung, M. and Schulz, G. E. (1997). Structure of maltoporin from Salmonella typhimurium ligated with a nitrophenyl-maltotrioside, J. Mol. Biol., 266, 761–775. Meyer, J. E. W. and Schulz, G. E. (1997). Energy profile of maltooligosaccharide permeation through maltoporin as derived from the structure and from statistical analysis of saccharide–protein interactions, Protein Sci., 6, 1084–1091. Braun, V., Hantke, K., Eick-Helmerich, K., Ko¨ster, W., Preßler, U., Sauer, M., Scha¨ffer, S. and Zimmerman, L. (1987). Iron transport systems in Escherichia coli. In Iron Transport in Microbes, Plants and Animals. eds. Winkelmann, S., van der Helm, D. and Neilands, J. B., Verlag Chemie, Weinheim, pp. 35–51. Kadner, R. J. (1990). Vitamin B12 transport in Escherichia coli: energy coupling between membranes, Mol. Microbiol., 4, 2027–2033. Postle, K. (1999). Active transport by customised beta-barrels, Nature Struct. Biol., 6, 3–6. Locher, K. P., Rees, B., Koebnik, R., Mitschler, A., Moulinier, L., Rosenbusch, J. P. and Moras, D. (1998). Transmembrane signaling across the ligand-gated FhuA receptor: crystal structures of free and ferrichrome-bound states reveal allosteric changes, Cell, 95, 771–778. Ferguson, A. D., Hofmann, E., Coulton, J. W., Diederichs, K. and Welte, W. (1998). Siderophore-mediated iron transport: crystal structure of FhuA with bound lipopolysaccharide, Science, 282, 2215–2220. Ko¨ster, W. unpublished results. Kahnert, A. and Kertesz, M. A. (2000). Characterization of a sulfur-regulated oxygenative alkylsulfatase from Pseudomonas putida S-313, J. Biol. Chem., 275, 31 661–31 667. Shipman, J. A., Berleman, J. E. and Salyers, A. A. (2000). Characterization of four outer membrane proteins involved in binding starch to the cell surface of Bacteroides thetaiotaomicron, J. Bacteriol., 182, 5365–5372. Jarlier, V. and Nikaido, H. (1990). Permeability barrier to hydrophilic solutes in Mycobacterium chelonei, J. Bacteriol., 172, 1418–1423. Trias, J., Jarlier, V. and Benz, R. (1992). Porins in the cell wall of mycobacteria, Science, 258, 1479–1481. Stahl, C., Kubetzko, S., Kaps, I., Seeber, S., Engelhardt, H. and Niederweis, M. (2001). MspA provides the main hydrophilic pathway through the cell wall of Mycobacterium smegmatis, Mol. Microbiol., 40, 451–464. Lazdunski, C. J. (1995). Colicin import and pore formation: a system for studying protein transport across membranes? Mol. Microbiol., 16, 1059–1066. Stroud, R. M., Reiling, K., Wiener, M. and Freymann, D. (1998). Ion-channelforming colicins, Curr. Opin. Struct. Biol., 8, 525–533. Riley, M. A. and Wertz, J. E. (2002). Bacteriocins: evolution, ecology, and application, Ann. Rev. Microbiol., 56, 117–137. Smarda, J. and Smajs, D. (1998). Colicins – exocellular lethal proteins of Escherichia coli, Folia Microbiol. (Praha), 43, 563–582.

¨ STER W. KO 78. 79. 80. 81. 82. 83. 84. 85. 86.

87. 88. 89. 90. 91. 92. 93. 94. 95.

327

Gorin, M. B., Yancey, S. B., Cline, J., Revel, J. P. and Horwitz, J. (1984). The major intrinsic protein (MIP) of the bovine lens fiber membrane: characterization and structure based on cDNA cloning, Cell, 39, 49–59. Fettiplace, R. and Haydon, D. A. (1980). Water permeability of lipid membranes, Physiol. Rev., 60, 510–550. Verkman, A. S. and Mitra, A. K. (2000). Structure and function of aquaporin water channels, Am. J. Physiol., 278, F13–F28. Heller, K. B., Lin, E. C. and Wilson, T. H. (1980). Substrate specificity and transport properties of the glycerol facilitator of Escherichia coli, J. Bacteriol., 144, 274–278. Murata, K., Mitsuoka, K., Hirai, T., Walz, T., Agre, P., Heymann, J. B., Engel, A. and Fujiyoshi, Y. (2000). Structural determinants of water permeation through aquaporin-1, Nature, 407, 599–605. Soupene, E., King, N., Lee, H. and Kustu, S. (2002). Aquaporin Z of Escherichia coli: reassessment of its regulation and physiological role, J. Bacteriol., 184, 4304–4307. Nollert, P., Harries, W. E., Fu, D., Miercke, L. J. and Stroud, R. M. (2001). Atomic structure of a glycerol channel and implications for substrate permeation in aqua(glycero)porins, FEBS Lett., 504, 112–117. Wilson, E. K. (2001). Membrane proteins on the move, TIBS, 26, 350–351. Froger, A., Rolland, J. P., Bron, P., Lagree, V., Caherec, F. L., Deschamps, S., Hubert, J. F., Pellerin, I., Thomas, D. and Delamarche, C. (2001). Functional characterization of a microbial aquaglyceroporin, Microbiology, 147, 1129–1135. Sukharev, S. (1999). Mechanosensitive channels in bacteria as membrane tension reporters, FASEB J., 13 (Suppl.), S55–S61. Chang, G., Spencer, R. H., Lee, A. T., Barclay, M. T. and Rees, D. C. (1998). Structure of the MscL homolog from Mycobacterium tuberculosis: a gated mechanosensitive ion channel, Science, 282, 2220–2226. Sukharev, S., Betanzos, M., Chiang, C. S. and Guy, H. R. (2001). The gating mechanism of the large mechanosensitive channel MscL, Nature, 409, 720–724. Martinac, B., Buechner, M., Delcour, A. H., Adler, J. and Kung, C. (1987). Pressure-sensitive ion channel in Escherichia coli, Proc. Natl Acad. Sci. USA, 84, 2297–2301. Bass, R. B., Strop, P., Barclay, M. and Rees, D. C. (2002). Crystal structure of Escherichia coli MscS, a voltage-modulated and mechanosensitive channel, Science, 298, 1582–1587. Bezanila, F. and Perozo, E. (2002). Force and voltage sensors in one structure, Science, 298, 1562–1563. Soupene, E., Lee, H. and Kustu, S. (2002). Ammonium/methylammonium transport (Amt) proteins facilitate diffusion of NH3 bidirectionally, Proc. Natl Acad. Sci. USA, 99, 3926–3931. Thomas, G. H., Mullins, J. G. and Merrick, M. (2000). Membrane topology of the Mep/Amt family of ammonium transporters, Mol. Microbiol., 37, 331–344. Saier, M. H. Jr, Beatty, J. T., Goffeau, A., Harley, K. T., Heijne, W. H., Huang, S. C., Jack, D. L., Jahn, P. S., Lew, K., Liu, J., Pao, S. S., Paulsen, I. T., Tseng, T. T. and Virk, P. S. (1999). The major facilitator superfamily, J. Mol. Microbiol. Biotechnol., 1, 257–279.

328 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113. 114. 115.

Henderson, P. J. F. (1993). The 12-transmembrane helix transporters, Curr. Opin. Cell Biol., 5, 708–721. Marger, M. D. and Saier, M. H., Jr (1993). A major super family of transmembrane facilitators that catalyze uniport, symport and antiport, Trends Biochem. Sci., 18, 13–20. Paulsen, I. T., Nguyen, L., Sliwinski, M. K., Rabus, R. and Saier, M. H., Jr (2000). Microbial genome analyses: comparative transport capabilities in eighteen prokaryotes, J. Mol. Biol., 301, 75–100. Cheng, J., Hicks, D. B. and Krulwich, T. A. (1996). The purified Bacillus subtilis tetracycline efflux protein TetA(L) reconstitutes both tetracycline-cobalt/Hþ and Naþ (Kþ )=Hþ exchange, Proc. Natl Acad. Sci. USA, 93, 14 446–14 451. Walsh, C. (2000). Molecular mechanisms that confer antibacterial drug resistance, Nature, 406, 775–781. Kra¨mer, R. (1994). Functional principles of solute transport systems: concepts and perspectives, Biochim. Biophys. Acta, 1185, 1–34. Kaback, H. R., Sahin-Toth, M. and Weinglass A. B. (2001). The kamikaze approach to membrane transport, Nat. Rev. Mol. Cell. Biol., 8, 610–620. Guan, L., Sahin-Toth, M. and Kaback, H. R. (2002). Changing the lactose permease of Escherichia coli into a galactose-specific symporter, Proc. Natl Acad. Sci. USA, 99, 6613–6618. Kaback H. R. (1998). Structure/function studies on the lactose permease of Escherichia coli, Acta Physiol. Scand. Suppl. 643, 163, 21–33. Sahin-Toth, M., Karlin, A. and Kaback, H. R. (2000). Unraveling the mechanism of the lactose permease of Escherichia coli, Proc. Natl Acad. Sci. USA, 97, 10 729–10 732. Wilson, T. H. and Ding, P. Z. (2001). Sodium–substrate cotransport in bacteria, Biochim. Biophys. Acta – Bioenerg., 1505, 121–130. Hacksell, I., Rigaud, J. L., Purhonen, P., Pourcher, T., Hebert, H. and Leblanc, ˚ resolution of the melibiose permease, an G. (2002). Projection structure at 8A Na–sugar co-transporter from Escherichia coli, EMBO J., 21, 3569–3574. Maloney, P. C., Ambudkar, S. V., Anatharam, V., Sonna, L. A. and Varadhachary, A. (1990). Anion exchange mechanisms in bacteria, Microbiol. Rev. 54, 1–17. Ambudkar, S. V., Larson, T. J. and Maloney, P. C. (1986). Reconstitution of sugar phosphate transport systems of Escherichia coli, J. Biol. Chem., 261, 9083–9086. Fann, M. C. and Maloney, P. C. (1998). Functional symmetry of UhpT, the sugar phosphate transporter of Escherichia coli, J. Biol. Chem., 273, 33 735–33 740. Hall, J. A., Fann, M. C. and Maloney, P. C. (1999). Altered substrate selectivity in a mutant of an intrahelical salt bridge in UhpT, the sugar phosphate carrier of Escherichia coli, J. Biol. Chem., 274, 6148–6153. Auer, M, Kim, M. J., Lemieux, M. J., Villa, A., Song, J., Li, X.-D. and Wang D.-N. (2001). High-yield expression and functional analysis of Escherichia coli glycerol-3-phosphate transporter, Biochemistry, 40, 6628–6635. Hall, J. A. and Maloney, P. C. (2001). Transmembrane segment 11 of UhpT, the sugar phosphate carrier of Escherichia coli, is an a-helix that carries determinants of substrate selectivity, J. Biol. Chem., 276, 25 107–25 113. Inoue, H., Sakurai, T., Ujike, S., Tsuchiya, T., Murakami, H. and Kanazawa, H. (1999). Expression of functional Naþ =Hþ antiporters of Helicobacter pylori in antiporter-deficient Escherichia coli mutants, FEBS Lett., 443, 11–16. Vimont, S. and Berche, P. (2000). NhaA, an Naþ =Hþ antiporter involved in environmental survival of Vibrio cholerae, J. Bacteriol. 182, 2937–2944.

¨ STER W. KO

329

116. Kuroda, T., Shimamoto, T., Inaba, K., Tsuda, M. and Tsuchiya, T. (1994). Properties and sequence of the NhaA Naþ =Hþ antiporter of Vibrio parahaemolyticus, J. Biochem. (Tokyo), 116, 1030–1038. 117. Goldberg, E. B., Arbel, T., Chen, J., Karpel, R., Mackie, G. A., Schuldiner, S. and Padan, E. (1987). Characterization of a Naþ =Hþ antiporter gene of Escherichia coli, Proc. Natl Acad. Sci. USA, 84, 2615–2619. 118. Pinner, E., Padan, E. and Schuldiner, S. (1992). Cloning, sequencing, and expression of the nhaB gene, encoding a Naþ =Hþ antiporter in Escherichia coli, J. Biol. Chem., 267, 11 064–11 068. 119. Padan, E., Maisler, N., Taglicht, D., Karpel, R. and Schuldiner, S. (1989). Deletion of ant in Escherichia coli reveals its function in adaptation to high salinity and an alternative Naþ =Hþ antiporter system(s), J. Biol. Chem., 264, 20 297– 20 302. 120. Pinner, E., Kotler, Y., Padan, E. and Schuldiner, S. (1993). Physiological role of NhaB, a specific Naþ =Hþ antiporter in Escherichia coli, J. Biol. Chem., 268, 1729–1734. 121. Padan, E., Venturi, M., Gerchman, Y. and Dover, N. (2001). Naþ =Hþ antiporters. Biochim. Biophys. Acta – Bioenerg., 1505, 144–157. 122. Kitada, M., Kosono, S. and Kudo, T. (2000). The Naþ =Hþ antiporter of alkaliphilic Bacillus sp., Extremophiles, 4, 253–258. 123. Kosono, S., Ohashi, Y., Kawamura, F., Kitada, M. and Kudo, T. (2000). Function of a principal Naþ =Hþ antiporter, ShaA, is required for initiation of sporulation in Bacillus subtilis, J. Bacteriol., 182, 898–904. 124. Hirai, T., Heymann, J. A. W., Shi, D., Sarker, R., Maloney, P. C. and Subramaniam, S. (2002). Three-dimensional structure of a bacterial oxalate transporter, Nat. Struct. Biol., 9, 597–600. 125. Jacobs, M. H., van der Heide, T., Driessen, A. J. and Konings, W. N. (1996). Glutamate transport in Rhodobacter sphaeroides is mediated by a novel binding protein-dependent secondary transport system, Proc. Natl Acad. Sci. USA, 93, 12 786–12 790. 126. Forward, J. A., Behrendt, M. C., Wyborn, N. R., Cross, R. and Kelly, D. J. (1997). TRAP transporters: a new family of periplasmic solute transport systems encoded by the dctPQM genes of Rhodobacter capsulatus and by homologs in diverse gram-negative bacteria, J. Bacteriol., 179, 5482–5493. 127. Blair, A., Ngo, L., Park, J., Paulsen, I. T. and Saier, M. H. Jr (1996). Phylogenetic analyses of the homologous transmembrane channel-forming proteins of the F0 F1 –ATPases of bacteria, chloroplasts and mitochondria, Microbiology, 142, 17–32. 128. Deckers-Hebestreit, G. and Altendorf, K. (1996). The F0 F1 -type ATP synthases of bacteria: structure and function of the F0 complex, Ann. Rev. Microbiol., 50, 791–824. 129. Dimroth, P., Wang, H., Grabe, M. and Oster, G. (1999). Energy transduction in the sodium F-ATPase of Propionigenium modestum, Proc. Natl Acad. Sci. USA, 96, 4924–4929. 130. Kakinuma, Y., Yamato, I. and Murata, T. (1999). Structure and function of vacuolar Naþ -translocating ATPase in Enterococcus hirae, J. Bioenerg. Biomemb., 31, 7–14. 131. Møller, J. V., Juul, B. and le Maire, M. (1996). Structural organization, ion transport, and energy transduction of P-type ATPases, Biochim. Biophys. Acta – Rev. Biomemb., 1286, 1–51.

330 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 132. Fagan, M. J. and Saier, M. H. Jr (1994). P-type ATPases of eukaryotes and bacteria: sequence analyses and construction of phylogenetic trees, J. Mol. Evol., 38, 57–99. 133. Ku¨hlbrandt, W., Auer, M. and Scarborough, G. A. (1998). Structure of the P-type ATPases, Curr. Opin. Struct. Biol., 8, 510–516. 134. Rensing, C., Ghosh, M. and Rosen, B. P. (1999). Families of soft-metal-ion transporting ATPase, J. Bacteriol., 181, 5891–5897. 135. Palmgren, M. G. and Axelsen, K. B. (1998). Evolution of P-type ATPases, Biochim. Biophys. Acta, 1365, 37–45. 136. Dassa, E. and Bouige, P. (2001). The ABC of ABCS: a phylogenetic and functional classification of ABC systems in living organisms, Res. Microbiol., 152, 211–229. 137. Quiocho, F. A. and Ledvina, P. S. (1996). Atomic structure and specificity of bacterial periplasmic receptors for active transport and chemotaxis: variation of common themes, Mol. Microbiol., 20, 17–25. 138. Dassa, E. and Hofnung, M. (1985). Sequence of gene malG in E. coli K12: homologies between integral membrane components from binding proteindependent transport systems, EMBO J., 9, 2287–2293. 139. Saurin, W., Ko¨ster, W. and Dassa, E. (1994). Bacterial binding protein-dependent permeases: characterization of distinctive signatures for functionally related integral cytoplasmic membrane proteins, Mol. Microbiol., 12, 993–1004. 140. Mourez, M., Jehanno, M., Schneider, E. and Dassa, E. (1998). In vitro interaction between components of the inner membrane complex of the maltose ABC transporter of Escherichia coli: modulation by ATP, Mol. Microbiol., 30, 353–363. 141. Hunke, S., Mourez, M., Jehanno, M., Dassa, E. and Schneider, E. (2000). ATP modulates subunit–subunit interactions in an ATP-binding cassette transporter (MalFGK2) determined by site-directed chemical cross-linking, J. Biol Chem., 275, 15 526–15 534. 142. Schneider, E. (2001). ABC transporters catalyzing carbohydrate uptake, Res. Microbiol., 152, 303–310. 143. Davidson, A. L. (2002). Mechanism of coupling of transport to hydrolysis in bacterial ATP-binding cassette transporters, J. Bacteriol., 184, 1225–1233. 144. Walker, J. E., Saraste, M., Runswick, M. J. and Gay, N. J. (1982). Distantly related sequences in the alpha- and beta-subunits of ATP synthase, myosin, kinases and other ATP-requiring enzymes and a common nucleotide binding fold, EMBO J., 1, 945–951. 145. Obis, D., Guillot, A., Gripon, J. C., Renault, P., Bolotin, A. and Mistou, M. Y. (1999). Genetic and biochemical characterization of a high-affinity betaine uptake system (BusA) in Lactococcus lactis reveals a new functional organization within bacterial ABC transporters, J. Bacteriol., 181, 6238–6246. 146. van der Heide, T., Stuart, M. C. A. and Poolman, B. (2001). On the osmotic signal and osmosensing mechanism of an ABC transport system for glycine betaine, EMBO J., 20, 7022–7032. 147. Buckel, W. (2001). Sodium ion-translocating decarboxylases, Biochim. Biophys. Acta – Bioenerg., 1505, 15–27. 148. Kolbe, M., Besir, H., Essen, L. and Oesterhelt, D. (2000). Structure of the light˚ resolution, Science, 288, 1390–1396. driven chloride pump halorhodopsin at 1.8 A 149. Gottschalk, G. and Thauer, R. K. (2001). The Naþ -translocating methyltransferase complex from methanogenic archaea, Biochim. Biophys. Acta – Bioenerg., 1505, 28–36.

¨ STER W. KO

331

150. Friedrich, T. (1998). The NADH:ubiquinone oxidoreductase (complex I) from Escherichia coli, Biochim. Biophys. Acta – Bioenerg., 1364, 134–146. 151. Postma, P. W., Lengeler, J. W. and Jacobson, G. R. (1993). Phosphoenolpyruvate:carbohydrate phosphotransferase systems of bacteria, Microbiol. Rev., 57, 543–594. 152. Saier, M. H. ed. (2002). The Bacterial Phosphotransferase System. Horizon Scientific Press, Norfolk. 153. Siebold, C., Flukiger, K., Beutler, R. and Erni, B. (2001). Carbohydrate transporters of the bacterial phosphoenolpyruvate: sugar phosphotransferase system (PTS), FEBS Lett. 504, 104–111. 154. Weinberg, E. D. (1997). The Lactobacillus anomaly: total iron abstinence, Perspect. Biol. Med., 40, 578–583. 155. Expert, D., Enard, C. and Masclaux C. (1996). The role of iron in plant host– pathogen interactions, Trends Microbiol., 4, 232–237. 156. Genco, C. A. and Desai, P. J. (1996). Iron acquisition in the pathogenic Neisseria, Trends Microbiol., 4, 179–184. 157. Mietzner, T. A., Tencza, S. B., Adhikari, P., Vaughan, K. G. and Nowalk, A. J. (1998). Fe(III) periplasm-to-cytosol transporters of Gram-negative pathogens, Curr. Top. Microbiol. Immunol., 225, 113–135. 158. Schryvers, A. B., Bonnah, R., Yu, R. H., Wong, H. and Retzer, M. (1998). Bacterial lactoferrin receptors, Adv. Exp. Med. Biol., 443, 123–133. 159. Vasil, M.-L. and Ochsner, U. A. (1999). The response of Pseudomonas aeruginosa to iron: genetics, biochemistry and virulence, Mol. Microbiol., 34, 399–413. 160. Ku¨hn, S., Braun, V. and Ko¨ster, W. (1996). Ferric rhizoferrin uptake into Morganella morganii; characterization of genes involved in the uptake of a polyhydroxycarboxylate siderophore, J. Bacteriol., 178, 496–504. 161. Zhu, W., Arceneaux, J. E., Beggs, M. L., Byers, B. R., Eisenach, K. D. and Lundrigan, M. D. (1998). Exochelin genes in Mycobacterium smegmatis: identification of an ABC transporter and two non-ribosomal peptide synthetase genes, Mol. Microbiol., 29, 629–639. 162. Furrer, J. L., Sanders, D. N., Hook-Barnard, I. G. and McIntosh, M. A. (2002). Export of the siderophore enterobactin in Escherichia coli: involvement of a 43 kDa membrane exporter, Mol. Microbiol., 44, 1225–1234. 163. Wandersman, C. and Stojilkovic, I. (2000). Bacterial heme sources: the role of heme, hemoprotein receptors and hemophores, Curr. Opin. Microbiol., 3, 215–220. 164. Cornelissen, C. N. and Sparling, P. F. (1994). Iron piracy: acquisition of transferrin-bound iron by bacterial pathogens, Mol. Microbiol., 14, 843–850. 165. Braun, V., Hantke, K. and Ko¨ster, W. (1998) Bacterial iron transport: mechanisms, genetics, and regulation. In Iron Transport and Storage in Microorganisms, Plants, and Animals. Vol. 35 of ‘Metal Ions in Biological Systems’, eds. Sigel, A. and Sigel, H., Marcel Dekker, New York, pp. 67–145. 166. Moeck, G. S. and Coulton J. W. (1998). TonB-dependent iron acquisition: mechanisms of siderophore-mediated active transport, Mol. Microbiol., 28, 675–681. 167. Letoffe, S., Nato, F., Goldberg, M. E. and Wandersman, C. (1999). Interactions of HasA, a bacterial haemophore, with haemoglobin and with its outer membrane receptor HasR, Mol. Microbiol., 33, 546–555. 168. Arnoux, P., Haser, R., Izadi, N., Lecroisey, A., Delepierre, M., Wandersman, C. and Czjzek, M. (1999). The crystal structure of HasA, a hemophore secreted by Serratia marcescens, Nature Struct. Biol., 6, 516–520.

332 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 169. Wandersman, C. (1998). Protein and peptide secretion by ABC exporters, Res. Microbiol., 149, 163–170. 170. Idei, A., Kawai, E., Akatsuka, H. and Omori, K. (1999). Cloning and characterization of the Pseudomonas fluorescens ATP-binding cassette exporter, HasDEF, for the heme acquisition protein HasA, J. Bacteriol., 181, 7545–7551. 171. Ko¨ster, W. (1997). Transport of iron(III) hydroxamates across the cytoplasmic membrane of Escherichia coli. In Bioinorganic Chemistry, Transition Metals in Biology and their Coordination Chemistry. ed. Trautwein, A. X., Wiley-VCH, pp. 56–68. 172. Stover, C. K., Pham, X. Q., Erwin, A. L., Mizoguchi, S. D., Warrener, P., Hickey, M. J., Brinkman, F. S. L., Hufnagle, W. O., Kowalik, D. J., Lagrou, M., Garber, R. L., Goltry, L., Tolentino, E., Westbrock-Wadman, S., Yuan, Y., Brody, L. L., Coulter, S. N., Folger, K. R., Kas, A., Larbig, K., Lim, R., Smith, K., Spencer, D., Wong, G. K. S., Wu, Z., Paulsen, I. T., Reizer, J., Saier, M. H., Hancock, R. E. W., Lory, S. and Olson, M. V. (2000). Complete genome sequence of Pseudomonas aeruginosa PA01, an opportunistic pathogen, Nature, 406, 959–964. 173. Nierman, W. C., Feldblyum, T. V., Laub, M. T., Paulsen, I. T., Nelson, K. E., Eisen, J., Heidelberg, J. F., Alley, M. R. K., Ohta, N., Maddock, J. R., Potocka, I., Nelson, W. C., Newton, A., Stephens, C., Phadke, N. D., Ely, B., DeBoy, R. T., Dodson, R. J., Durkin, A. S., Gwinn, M. L., Haft, D. H., Kolonay, J. F., Smit, J., Craven, M. B., Khouri, H., Shetty, J., Berry, K., Utterback, T., Tran, K., Wolf, A., Vamathevan, J., Ermolaeva, M., White, O., Salzberg, S. L., Venter, J. C., Shapiro, L. and Fraser, C. M. (2001). Complete genome sequence of Caulobacter cerscentus, Proc. Natl Acad. Sci., 98, 4136–4141. 174. van der Helm, D., Chakraborty, R., Ferguson, A. D., Smith, B. S., Esser, L. and Deisenhofer, J. (2002). Bipartite gating in the outer membrane protein FecA, Biochem. Soc. Trans., 30, 708–710. 175. Braun, V. and Braun, M. (2002). Iron transport and signalling in Escherichia coli, FEBS Lett., 529, 78–85. 176. Ferguson, A. D., Chakraborty, R., Smith, B. S., Esser, L., van der Helm, D. and Deisenhofer, J. (2002). Structural basis of gating by the outer membrane transporter FecA, Science, 295, 1715–1719. 177. Postle, K. (2002). Close before opening, Science, 295, 1658–1659. 178. Chang, C., Mooser, A., Plu¨ckthun, A. and Wlodawer, A. (2001). Crystal structure of the dimeric C-terminal domain of TonB reveals a novel fold, J. Biol. Chem., 276, 27 535–27 540. 179. Navarre, W. W. and Schneewind, O. (1999). Surface proteins of gram-positive bacteria and mechanisms of their targeting to the cell wall envelope, Microbiol. Mol. Biol. Rev., 63, 174–229. 180. Mazmanian, S. K., Ton-That, H., Su, K. and Schneewind, O. (2002). An ironregulated sortase anchors a class of surface protein during Staphylococcus aureus pathogenesis, Proc. Natl Acad. Sci. USA, 99, 2293–2298. 181. Hammerschmidt, S., Bethe, G., Remane, P. H. and Chhatwal, G. S. (1999). Identification of pneumococcal surface protein A as a lactoferrin-binding protein of Streptococcus pneumoniae, Infect. Immun., 67, 1683–1687. 182. Hakansson, A., Roche, H., Mirza, S., McDaniel, L. S., Brooks-Walter, A. and Briles, D. E. (2001). Characterization of binding of human lactoferrin to pneumococcal surface protein A, Infect. Immun., 69, 3372–3381. 183. Modun, B., Kendall, D. and Williams, P. (1994). Staphylococci express a receptor for human transferrin: identification of a 42 kilodalton cell wall transferrinbinding protein, Infect. Immun., 62, 3850–3858.

¨ STER W. KO

333

184. Modun, B. and Williams, P. (1999). The staphylococcal transferrin-binding protein is a cell wall glyceraldehyde-3-phosphate dehydrogenase, Infect. Immun., 67, 1086–1092. 185. Taylor, J. M. and Heinrichs, D. E. (2002). Transferrin binding in Staphylococcus aureus: involvement of a cell wall-anchored protein, Mol. Microbiol., 43, 1603–1614. 186. Mazmanian, S. K., Skaar, E. P., Gaspar, A. H., Humayun, M., Gornicki, P., Jelenska, J., Joachmiak, A., Missiakas, D. M. and Schneewind, O. (2003). Passage of heme-iron across the envelope of Staphylococcus aureus, Science, 299, 906–909. 187. Lei, B., Smoot, L. M., Menning, H. M., Voyich, J. M., Kala, S. V., Deleo, F. R., Reid, S. D. and Musser, J. M. (2002). Identification and characterization of a novel heme-associated cell surface protein made by Streptococcus pyogenes, Infect. Immun., 70, 4494–4500. 188. Kammler, M., Scho¨n, C. and Hantke, K. (1997). Characterization of the ferrous iron uptake system of Escherichia coli, J. Bacteriol., 175, 6212–6219. 189. Velayudhan, J., Hughes, N. J., McColm, A. A., Bagshaw, J., Clayton, C. L., Andrews, S. C. and Kelly, D. J. (2000). Iron acquisition and virulence in Helicobacter pylori: a major role for FeoB, a high-affinity ferrous iron transporter, Mol. Microbiol., 37, 274–286. 190. Robey, M. and Cianciotto, N. P. (2002). Legionella pneumophila feoAB promotes ferrous iron uptake and intracellular infection, Infect. Immun., 70, 5659–5669. 191. Lissner, C. R., Weinstein, D. L. and O’Brien, A. D. (1985). Mouse chromosome 1 Ity locus regulates microbicidal activity of isolated peritoneal macrophages against a diverse group of intracellular and extracellular bacteria, J. Immunol., 135, 544–547. 192. Gruenheid, S., Pinner, E., Desjardins, M. and Gros P. (1997). Natural resistance to infection with intracellular pathogens: the Nramp1 protein is recruited to the membrane of the phagosome, J. Exp. Med., 185, 717–730. 193. Cellier, M., Govoni, G., Vidal, S., Kwan, T., Groulx, N., Liu, J., Sanchez, F., Skamene, E., Schurr, E. and Gros, P. (1994). Human natural resistance-associated macrophage protein: cDNA cloning, chromosomal mapping, genomic organization, and tissue specific expression, J. Exp. Med., 180, 1741–1752. 194. Gunshin, H., Mackenzie, B., Berger, U. V., Gunshin, Y., Romero, M. F., Boron, W. F., Nussberger, S., Gollan, J. L. and Hediger, M. A. (1997). Cloning and characterization of a mammalian proton-coupled metal-ion transporter, Nature, 388, 482–488. 195. Liu, X. F., Supek, F., Nelson, N. and Culotta, V. C. (1997). Negative control of heavy metal uptake by the Saccharomyces cerevisiae BSD2 gene, J. Biol. Chem., 272, 11 763–11 769. 196. Portnoy, M. E., Liu, X. F. and Culotta, V. C. (2000). Saccharomyces cerevisiae expresses three functionally distinct homologues of the Nramp family of metal transporters, Mol. Cell Biol., 20, 7893–7902. 197. Kehres, D. G., Zaharik, M. L., Finlay, B. B. and Maguire, M. E. (2000). The NRAMP proteins of Salmonella typhimurium and Escherichia coli are selective manganese transporters involved in the response to reactive oxygen, Mol. Microbiol., 36, 1085–1100. 198. Makui, H., Roig, E., Cole, S. T., Helmann, J. D., Gros, P. and Cellier, M. F. M. (2000). Identification of the Escherichia coli K-12 Nramp orthologue (MntH) as a selective divalent metal ion transporter, Mol. Microbiol., 35, 1065–1078.

334 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 199. Patzer, S. I. and Hantke, K. (2001). Dual repression by Fe2þ -Fur and Mn2þ -MntR of the mntH gene, encoding an NRAMP-like Mn2þ transporter in Escherichia coli, J. Bacteriol., 183, 4806–4813. 200. Kehres, D. G., Janakiraman, A., Slauch, J. M. and Maguire, M. E. (2002). Regulation of Salmonella enterica serovar Typhimurium mntH transcription by H2 O2 , Fe2þ , and Mn2þ , J. Bacteriol., 184, 3151–3158. 201. Que, Q. and Helmann, J. D. (2000). Manganese homeostasis in Bacillus subtilis is regulated by MntR, a bifunctional regulator related to the diphtheria toxin repressor family of proteins, Mol. Microbiol., 35, 1454–1468. 202. Ko¨ster, W. (2001). ABC transporter-mediated uptake of iron, siderophores, heme and vitamin B12, Res. Microbiol., 152, 291–301. 203. Crosa, J. H. (1997). Signal transduction and transcriptional and post transcriptional control of iron-regulated genes in bacteria, Microbiol. Mol. Biol. Rev., 61, 319–336. 204. Ko¨ster, W. L., Actis, L. A., Waldbeser, L. S., Tolmasky, M. E. and Crosa, J. H. (1991). Molecular characterization of the iron transport system mediated by the pJM1-plasmid in Vibrio anguillarum 775, J. Biol. Chem., 266, 23 829–23 833. 205. Ko¨ster, W. and Braun, V. (1990). Iron(III)hydroxamate transport: binding of ferrichrome to the periplasmic FhuD protein, J. Biol. Chem., 265, 21 407–21 410. 206. Rohrbach, M. R., Braun, V. and Ko¨ster W. (1995). Ferrichrome transport in Escherichia coli K-12: altered substrate specificity of mutated periplasmic FhuD and interaction of FhuD with the integral membrane protein FhuB, J. Bacteriol., 177, 7186–7193. 207. Sprencel, C., Cao, Z., Qi, Z., Scott, D. C., Montague, M. A., Ivanoff, N., Xu, J., Raymond, K. M., Newton, S. M. and Klebba, P. E. (2000). Binding of ferric enterobactin by the Escherichia coli periplasmic protein FepB, J. Bacteriol., 182, 5359–5364. 208. Clarke, T. E., Ku, S. Y., Dougan, D. R., Vogel, H. J. and Tari, L. W. (2000). The structure of the ferric siderophore binding protein FhuD complexed with gallichrome, Nat. Struct. Biol., 7, 287–291. 209. Borths, E. L., Locher, K. P., Lee, A. T. and Rees, D. C. (2002). The structure of Escherichia coli BtuF and binding to its cognate ATP binding cassette transporter, Proc. Natl Acad. Sci. USA, 99, 16 642–16 647. 210. Karpowich, N. K., Huang, H. H., Smith, P. C. and Hunt, J. F. (2003). Crystal structures of the BtuF periplasmic-binding protein for vitamin B12 suggest a functionally important reduction in protein mobility upon ligand binding, J. Biol. Chem., 278, 8429–8434. 211. Lee, Y. H., Deka, R. K., Norgard, M. V., Radolf, J. D. and Hasemann, C. A. (1999). Treponema pallidum TroA is a periplasmic zinc-binding protein with a helical backbone, Nat. Struct. Biol., 6, 628–633. 212. Lawrence, M. C., Pilling, P. A., Epa, V. C., Berry, A. M., Ogunniyi, A. D. and Paton, J. C. (1998). The crystal structure of pneumococcal surface antigen PsaA reveals a metal-binding site and a novel structure for a putative ABC-type binding protein, Structure, 15, 1553–1561. 213. Locher, K. P., Lee, A. T. and Rees, D. C. (2002). The E. coli BtuCD structure: a framework for ABC transporter architecture and mechanism, Science, 296, 1091–1098. 214. Ko¨ster, W. and Bo¨hm, B. (1992). Point mutations in 2 conserved glycine residues within the integral membrane protein FhuB affect iron (III) hydroxamate transport, Mol. Gen. Genet., 232, 399–407.

¨ STER W. KO

335

215. Groeger, W. and Ko¨ster W. (1998). Transmembrane topology of the two FhuB domains representing the hydrophobic components of bacterial ABC transporters involved in the uptake of siderophores, haem and vitamin B12, Microbiology, 144, 2759–2769. 216. Schultz-Hauser, G., Ko¨ster, W., Schwarz, H. and Braun V. (1992). Iron (III) hydroxamate transport in Escherichia coli K-12: FhuB-mediated membrane association of the FhuC protein and negative complementation of fhuC mutants, J. Bacteriol., 174, 2305–2311. 217. Hung, L. W., Wang, I. X., Nikaido, K., Liu, P. Q., Ames, G. F. and Kim, S. H. (1998). Crystal structure of the ATP-binding subunit of an ABC transporter, Nature, 396, 703–707. 218. Diederichs, K., Diez, J., Greller, G., Muller, C., Breed, J., Schnell, C., Vonrhein, C., Boos, W. and Welte, W. (2000). Crystal structure of MalK, the ATPase subunit of the trehalose/maltose ABC transporter of the archaeon Thermococcus litoralis, EMBO J., 19, 5951–5961. 219. Hopfner, K. P., Karcher, A., Shin, D. S., Craig, L., Arthur, L. M., Carney, J. P. and Tainer, J. A. (2000). Structural biology of Rad50 ATPase: ATP-driven conformational control in DNA double-strand break repair and the ABC-ATPase superfamily, Cell, 101, 789–800. 220. Nikaido, H. (2002). How are the ABC transporters energized? Proc. Natl Acad. Sci. USA, 99, 9609–9610. 221. Schmitt, L. and Tampe, R. (2002). Structure and mechanism of ABC transporters, Curr. Opin. Struct. Biol., 12, 754–760. 222. Fetsch, E. E. and Davidson, A. L. (2002). Vanadate-catalyzed photocleavage of the signature motif of an ATP-binding cassette (ABC) transporter, Proc. Natl Acad. Sci. USA, 99, 9685–9690. 223. Liu, P. Q. and Ames, G. F. (1998). In vitro disassembly and reassembly of an ABC transporter, the histidine permease, Proc. Natl Acad. Sci. USA, 95, 3495–3500. 224. Angerer, A., Gaisser, S. and Braun, V. (1990). Nucleotide sequences of the sfuA, sfuB, and sfuC genes of Serratia marcescens suggest a periplasmic-bindingprotein-dependent iron transport mechanism, J. Bacteriol., 172, 572–578. 225. Viswanathan, V. K., Edelstein, P. H., Dumais Pope, C. and Ciancotto, N. P. (2000). The Legionella pneumophila iraAB locus is required for iron assimilation, intracellular infection, and virulence, Infect. Immun., 68, 1069–1079. 226. Xu, X., Holt, S. C. and Kolodrubetz, C. (2001). Cloning and expression of two novel hemin binding protein genes from Treponema denticola, Infect. Immun., 69, 4465–4472. 227. Dashper, S. G., Hendtless, A., Slakeski, N., Jackson, C., Cross, K. J., Brownfield, L., Hamilton, R., Barr, I. and Reynolds, E. C. (2000). Characterization of a novel outer membrane hemin-binding protein of Porphyromonas gingivalis, J. Bacteriol., 182, 6456–6462. 228. Glass, J. I., Lefkovitz, E. J., Glass, J. S., Helner, C. R., Chen, E. Y. and Cassell, G. H. (2000). The complete sequence of the mucosal pathogen Ureaplasma urealyticum, Nature, 407, 757–762.

7 Transport of Solutes Across Biological Membranes in Eukaryotes: an Environmental Perspective RICHARD D. HANDY School of Biological Sciences, The University of Plymouth, Drake Circus, Plymouth, PL4 8AA, UK

F. BRIAN EDDY Environmental and Applied Biology, School of Life Sciences, The University of Dundee, Nethergate, Dundee, DD1 4HN, Scotland UK

1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Fundamental Processes in Solute Transport . . . . . . . . . . . . . 2 Solute Adsorption: Example of Naþ Binding to the Gill Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Solute Import into Epithelial Cells . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Ion Channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Co-transport on Symporters. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Counter-transport on Antiporters . . . . . . . . . . . . . . . . . . . . . . 4 Intracellular Trafficking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Solute Export from Epithelial Cells . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Export from the Cell to the Blood via Ion Channels and Antiporters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Export from the Cell to the Blood by Primary Transport: ATPases . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusion and Environmental Perspectives . . . . . . . . . . . . . . . . . . Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Physicochemical Kinetics and Transport at Biointerfaces Edited by H. P. van Leeuwen and W. Ko¨ster. ß 2004 John Wiley & Sons, Ltd

338 338 341 344 345 345 346 347 348 348 349 349 350 352

338 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

1

INTRODUCTION

This chapter attempts to illustrate the principles of solute transport in eukaryote cells, and then explains the intimate relationship between cellular ion transport and environmental chemistry. The information presented herein is thus complementary to that presented in Chapter 6 of this volume, for prokaryotes. Since this book is about the interface between the environment and biological surfaces, we will draw on examples from epithelia where this is a particular concern, such as fish gills and intestine. However, the principles of solute transport that we discuss are universal, and will apply to a wide variety of epithelia, including those that do not have direct contact with the external environment (e.g. renal epithelium). The gill is also a particularly useful model to consider, because, under certain environmental conditions, the direction of solute transfer may be reversed (e.g. in freshwater versus seawateradapted fish), and, of course, the gill epithelial cells have intimate contact with the aqueous environment. The fundamental principles of solute transport are demonstrated with reference to sodium (Naþ ) transport initially, which is arguably the most characterised solute transport process of all eukaryote cells [1–8]. Sodium transport also ultimately depends on at least one solute transporting protein that is ubiquitous in eukaryotes (the Naþ pump [9–14]). We then illustrate how these principles apply to other solutes of environmental concern, particularly in relation to divalent ions and trace metals. Solute transfer across membranes has been identified in many organisms, but the details of the transport mechanisms that are involved have often been neglected, although they may be of fundamental importance in understanding environmental toxicology and chemistry. In this chapter, we use the chemical symbol to describe metals where we do not wish to imply a particular charge or oxidation state (e.g. Cu for copper generally), and only give valency where a particular chemical species is relevant (e.g. Cuþ , Cu2þ , Al3þ , Fe2þ , etc.). 1.1

FUNDAMENTAL PROCESSES IN SOLUTE TRANSPORT

All eukaryote cells are faced with differences in intracellular solute composition when compared with the external environment. Many eukaryotes live in seawater, and have cells which are either bathed in seawater directly, or have an extracellular body fluid which is broadly similar to seawater [3]. Osmoregulation and body fluid composition in animals has been extensively reviewed (e.g. [3,15–21]), and reveals that many marine invertebrates have body fluids that are iso-osmotic with seawater, but may regulate some electrolytes (e.g. SO2
4 ) at lower levels than seawater. Most vertebrates have a body fluid osmotic pressure (about 320 mOsm kg
1 ), which is about one-third of that in seawater (1000 mOsm kg
1 ), and also regulate some electrolytes in body fluids at

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much lower concentrations than seawater (e.g. Naþ , Cl
, Ca2þ , Mg2þ , SO4 ). Amongst the vertebrates, the elasmobranchs (sharks, skates and rays) are notably different, with body fluids that are iso-osmotic with seawater; although only one-third of it is attributed to salts, with the majority of it being due to urea. Importantly, most eukaryote cells ‘see’ an extracellular medium which is of relatively fixed composition, either by virtue of the huge buffering in the medium (e.g. oceanic seawater), or because specialised osmoregulatory organs (e.g. gills, gut, kidney) regulate body fluid composition. Many multicellular eukaryotes have regulatory mechanisms which maintain relatively fixed body fluid compositions that protect the intracellular compartments from change (Claude Bernard’s ‘Constancy of the internal milieu’). However, there are a number of key differences in solute concentrations between the intracellular and extracellular environment, which arise mainly from: (1) the effects of large fixed anions (e.g. cellular proteins) which tend to repel diffusible anions (e.g. Cl
), creating anion differences across the cell membrane (Donnan equilibria); (2) relative differences in the permeability of biological membranes to solutes (e.g. higher Kþ permeability compared with Naþ ). In general, solutes with a small hydrated radius and absent/low charge density will diffuse more easily [22]; (3) the source of the solute. Cells may generate intracellular solutes during metabolism, e.g. glucose from glycogen stores, or urea or ammonia from protein catabolism. The combination of these events may create both chemical and electrical gradients across the cell membrane, which must be overcome by energy expenditure if the solutes are to be moved against these electrochemical gradients. The absolute rate of flux of a solute will also depend on the surface area of the cell membrane and the particular types of lipids and proteins that constitute the cell membrane in a particular cell type. The process of solute transport through a cell may involve several steps, as shown in Figure 1: (1) (2) (3) (4)

adsorption of the solute on to the surface of the cell membrane; import of the solute across the cell membrane into the cell; intracellular trafficking and/or storage in membrane-bound compartments; export of the solute from the cell.

An idealised eukaryotic epithelium is represented in Figure 1. This might, for example, be the gut mucosa, the reabsorbing portion of a renal tubule system, or a gill epithelium. The solute must move from the bulk solution (e.g. the external environment, or a body fluid such as urine) into an unstirred layer

340 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES Unstirred layer Bulk solution

Unstirred solution Mucus A− M+

A−

M

+

M+ A−

M+

Me A+ A−

+

K1

M+ A−

X M+ K4 A− M+

1. Adsorption

M+

A−

A−

A

K2

K3

Blood

paracellular

K6

A−

M+

−

M+ M+

M+ +

M+ A−

M+

M+

A−

Epithelia

SP

4. Export ATP

K5

3. Cytosolic carriers?

AP

Kn

X+

2. Import

Intracellular stores

M+

M+

Tight junction

M+

Figure 1. Solute transfer across an idealised eukaryote epithelium. The solute must move from the bulk solution (e.g. the external environment, or a body fluid) into an unstirred layer comprising water/mucus secretions, prior to binding to membranespanning carrier proteins (and the glycocalyx) which enable solute import. Solutes may then move across the cell by diffusion, or via specific cytosolic carriers, prior to export from the cell. Thus the overall process involves: 1. Adsorption; 2. Import; 3. Solute transfer; 4. Export. Some electrolytes may move between the cells (paracellular) by diffusion. The driving force for transport is often an energy-requiring pump (primary transport) located on the basolateral or serosal membrane (blood side), such as an ATPase. Outward electrochemical gradients for other solutes (Xþ ) may drive import of the required solute (Mþ , metal ion) at the mucosal membrane by an antiporter (AP). Alternatively, the movement of Xþ down its electrochemical gradient could enable Mþ transport in the same direction across the membrane on a symporter (SP). A
, diffusive anion such as chloride. K1–6 refers to the equilibrium constants for each step in the metal transfer process, Kn indicates that there may be more than one intracellular compartment involved in storage. See the text for details

comprising water/mucous secretions (see Section 2), prior to binding to membrane-spanning carrier proteins which enable solute import. The solute may also interact with other ligands in the cell glycocalyx, not just the membranebound proteins, but these are not shown for clarity. Solutes may then move across the cell by diffusion or via specific cytosolic carriers. In the case of ‘nonreactive’ solutes like Naþ or glucose, these probably move across the cell by diffusion. However, some solutes, such as transition metals, are highly reactive with structural components in the cell (e.g. with haem centres in proteins) and must be moved around the cell by specific carriers (usually peptides). These carriers or molecular chaperones enable controlled delivery of the solute to the relevant part of the cell. The driving force for solute transfer

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is often an energy-requiring pump (primary transport) located on the basolateral or serosal membrane (blood side), such as an ATPase. Outward electrochemical gradients for other solutes (Xþ , Figure 1) may drive import of the required solute (secondary transport). These primary and/or secondary transport systems may be electrogenic (moving an unequal number of charges across the cell membrane), thus creating voltage differences that may contribute to paracellular absorption (diffusive flux between the cells of the epithelium) of solutes down the electrochemical gradient. This latter movement of solutes between the cells depends critically on the permeability of the tight junctions that hold the cells together, and this is greatly influenced by the Ca2þ content of the medium as well as the driving force for diffusion by this route [23]. Exclusion of diffusive anions (A
), such as chloride, may also contribute to voltage differences via Donnan effects in the mucus layer and within the cell (see below). Figure 1 also illustrates some of the thermodynamic considerations in solute transfer across the cell. K1–6 represent the equilibrium constants (log K is inversely related to affinity) for all the steps in solute transfer. The steps K1–4 represent those for movement of free solute into the unstirred water and mucous solution (K1 and K2), binding to the mucoproteins (K3), and from mucoprotein to importer (K4), while K5 depicts binding to cytosolic carriers, and K6 binding to an exporter. It is sometimes difficult to differentiate the thermodynamic steps in adsorption experimentally, and K1–3 may be given one overall binding constant (as in the gill models, see Section 2). It would, however, be a gross oversimplification to assume that transport is achieved simply by each step having a higher binding affinity than the previous one. This is clearly not the case, as transporters on both sides of the cell may have similar binding affinities for a given solute. After considering the reversibility of each ligandbinding event, it is also necessary to consider the local solute concentration and ligand availability at that particular position in the cell. It is the overall effect of solute and ligand availability, and binding affinity, that enables solute movement to the next step in the overall process. This of course requires the accurate measurement of free solute and ligand concentrations in different parts of the cell. We are at least some way towards measuring these with spectrofluorometric techniques that can measure free-ion movements across cells (e.g. Ca2þ sparks in excitable cells [24]). An in-depth critical evaluation of the various parameters and processes that must be considered in modelling of biouptake is given in Chapter 10 of this volume. 2 SOLUTE ADSORPTION: EXAMPLE OF Naþ BINDING TO THE GILL SURFACE The first step in the movement of any solute across a cell membrane is the provision of a readily available supply of solutes to the membrane surface. The

342 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

overall process of adsorption on to the cell membrane surface is influenced by several factors [22, 25–28] including: (1) (2) (3) (4)

the free solute concentration in the environment; the number and type of solute binding ligands on the epithelial surface; the rate of solute uptake and any associated replacement of surface ligands; unstirred layer formation on the extracellular surface of the cell membrane.

In the context of environmental biology, these processes have been mostly investigated at the surface of fish gills with respect to Naþ transport [29–33] and the uptake of toxic metals [34–38]. The general anatomy of the gills is beyond the scope of this text (see reviews [39–44]), but, as with any model system for adsorption processes, it is important to define the components that make up the surface interface. These are the bulk water (solution that freely exchanges with the external environment), unstirred layers of waters (relatively nonmobile solvent layers adjacent to the membrane surface), mucus (secreted by the epithelia), the glycocalyx on the cell surface and associated external binding sites on membrane-bound ion transporters (Figures 1 and 2). These are common components of biological interfaces, but authors often use varied terminology. For example, in fish gill research these surface layers (often including the bulk water in the opercular cavity) are collectively called the ‘gill microenvironment’ [45,46]. Authors generally may not differentiate the secreted mucus layer from the water (or other layers of body fluids) component of ‘unstirred layers’. This situation might arise from the difficulties in experimentally measuring the solute composition of the adjacent solute and mucus layers in anatomically complex epithelia such as the gills [32, 47,48]. However, differentiation of the water/mucus unstirred layer may be of functional significance, given the vast differences in the composition, rheology and ion-exchange properties of mucus solutions as compared with simple salines. Importantly, the relative permeabilities of chloride to sodium are about 10% less in mucus solutions when compared with simple salines, and the mobility of Naþ is about 50% less in mucus than in salines [49,50]. Mucus is therefore much more than a simple unstirred barrier to diffusion. Distinguishing between adsorption on to the cell surface and the actual transfer across the cell membrane into the cell may be difficult, since both processes are very fast (a few seconds or less). For fish gills, this is further complicated by the need to confirm transcellular solute transport (or its absence) by measuring the appearance of solutes in the blood over seconds or a few minutes. At such short time intervals, apparent blood solute concentrations are not at equilibrium with those in the entire extracellular space, and will need correcting for plasma volume and circulation time in relation to the time taken to collect the blood sample [30]. Nonetheless, Handy and Eddy [30] developed a series of ‘rapid solution dipping’ experiments to estimate radiolabelled Naþ

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Unstirred layer

Bulk water

Unstirred water Mucus Cl−

Cl− Na+

Cl−

Cl−

Cl− Na+ − Na+ Cl

Na+

+

Na

ATP

2K+

Cl-

Na+

H+

+

Cl Na Na+

HCO3−

HCO3−

CO2 −

3Na+

Cl−

CA

CO2

Blood

Na+

Na+

Na+

Epithelia

Cl−

Cl−

ATP

H+

CA

CO2

CO2

+

Na

Cl−

Tight junction

6−18 mV Mucous layer Donnan potential 1−3 mV Trans-epithelial potential

Figure 2. Sodium and chloride uptake across an idealised freshwater-adapted gill epithelium (chloride cell), which has the typical characteristics of ion-transporting epithelia in eukaryotes. In the example, the abundance of fixed negative charges (mucoproteins) in the unstirred layer may generate a Donnan potential (mucus positive with respect to the water) which is a major part of the net transepithelial potential (serosal positive with respect to water). Mucus also contains carbonic anhydrase (CA) which facilitates dissipation of the [Hþ ] and [HCO
3 ] to CO2 , thus maintaining the concentration gradients for these counter ions which partly contribute to Naþ import (secondary transport), whilst the main driving force is derived from the electrogenic sodium pump (see the text for details). Large arrow indicates water flow

adsorption to the gills. These experiments showed that the combined steps of Naþ adsorption to the gill surface and uptake to the blood (absorption) took <60 s, and that the adsorption step was very sensitive to micromolar changes in water pH and Ca2þ concentration, as predicted from the ion-exchange theory of mucoproteins [51,52]. Figure 3 illustrates the time course of a rapid solution dipping experiment to resolve Naþ adsorption time to the gills and body surface of rainbow trout (Oncorhynchus mykiss). This experiment showed that only 5 and 2 nmoles of Naþ appeared in the entire blood volume and whole liver respectively over 45 s, as compared with 35 nmoles associated with the fish surface/epithelial cells, an apparent adsorption of 88% of the Naþ compared with 12% transfer into the blood (Figure 3). On the basis of this first experiment, we suggested an optimum adsorption time of 30 s to study Naþ binding

344 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

60

Amount of Na+/nmol

50

40

30

20

10

0 0

10

20

30 40 50 60 Time in radiolabelled fresh water/s

70

80

90

Figure 3. Time course of Naþ binding to the exterior surface (
, gill and body combined) of 10 g rainbow trout compared with uptake into the entire plasma volume (?) or whole livers (&) of the fish. Naþ uptake into the liver is also normalised to 0.325 g of fresh liver weight (¶) to enable a direct comparison with the blood volume of the 10 g fish (0.325 ml, see Gingerich and Pityer [87]). Fish were dipped in 500 ml fresh water þ containing 0:2 mmol l
1 Na and 10 mCi of 22 Naþ (see [30] for other water-quality details), and then rinsed in 30 l of unlabelled freshwater for 15 s to remove excess radio-isotope. Data are means  S.E. (n ¼ 6 fish). Note that Naþ measurements in/on tissues are absolute amounts in nmoles, not concentration units

to fish gills [53]. This experiment illustrates some common features of absorption phenomena, namely, the rapidity of the process (a few seconds) and the consequent difficulties in measuring this against a background of solute flux across a living epithelium.

3

SOLUTE IMPORT INTO EPITHELIAL CELLS

The movement of solutes from the external environment into the cell is usually achieved using cell membrane-spanning proteins that facilitate solute transfer. These are necessary, since most solutes (e.g. sugars, amino acids, salts) will not readily diffuse through the hydrophobic cell membrane. Movement of solutes into the epithelial cell can involve a variety of protein carriers or channels including (see Figure 1):

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(1) passive diffusion through ion channels into the cell; (2) co-transport of solute into the cell on a symporter; (3) counter-transport of the solute into the cell on an antiporter. These methods of solute transfer usually rely on a relatively low intracellular concentration of the solute of interest, so that it will readily diffuse into the cell down the electrochemical gradient (as in the case of ion channels). Alternatively, the solute may be moved into the cell using chemical energy derived from another solute moved in the same direction (co-transport) or opposite direction (countertransport) on the carrier protein (symporters and antiporters respectively). The transfer of the second solute is in turn dependent on an inward electrochemical gradient. Ultimately, these gradients are established by primary, energyrequiring solute pumps (e.g. ATPases), which, on most epithelia, are located on the basolateral/serosal membrane (see Section 5.2 for discussion of ATPases). 3.1

ION CHANNELS

These are essentially membrane-spanning proteins with an aqueous pore through the middle (the channel). Each ion channel is usually constructed from several subunits, which come together to make the functional protein. The channel is usually selective for particular solutes on the basis of pore size and the chargescreening properties of the pore surface. Thus we have epithelial Naþ , Kþ , Ca2þ , Cu2þ , Cl
channels, etc. [53–56]. However, they are not just simply holes in the cell membrane, and the pore can be closed or opened by subtle movements of the protein subunits or particular amino acid groups on the inner surface of the channel. In epithelial tissue the signal for channel opening can be the binding of the right solute to the channel, or via solute-sensing systems in the cell that result in phosphorylation of the channel (e.g. via intracellular protein kinases) [61]. The intracellular signal can be simple binding of molecules to the channel (e.g. ATP binding). Some channels are also voltage sensitive in epithelial tissue [58], and are opened or closed by voltage change, although this type of channel dominates more in excitable tissue such as nerves and muscle. Each major group of ion channels can therefore have many subtypes, some of which are found in the same epithelium. For example, Kþ channels include voltage-sensitive and ATPdependent subtypes [57]. The epithelium may have a variety of ion channels þ present to achieve synchronised ion uptake or secretion e.g. Naþ , K and
Cl channels involved in net NaCl uptake or secretion in the intestine [58]. Ion channels can also be involved in solute export from cells (see below). 3.2

CO-TRANSPORT ON SYMPORTERS

Symporters are membrane-spanning proteins which translocate two or more solutes in the same direction across the cell membrane. In epithelial tissue, such

346 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

as the gill [53], intestine [58] and renal tubules [59], symporters are used to move þ NaCl, KCl, and combinations of Naþ , K , and Cl
(Na–K–2Cl co-transporter) into the cell. These co-transporters are the main members of the family of electroneutral cation–chloride transporting proteins [59] which partly facilitate NaCl and KCl absorption across epithelia into the blood. For example, the NaCl co-transporter drives Cl
into the cell using the energy from the inward Naþ gradient. These co-transporters are also vital for cell volume control in eukaryote cells, and, for example, KCl efflux from red cells is associated with regulatory volume decreases in response to cell swelling [60]. The electroneutral cation–chloride symporters are probably the most wellknown symporters [61], but there are many others. For example, Naþ -glucose and Naþ -amino acid co-transporters use the inward Naþ gradient to drive glucose or amino acid absorption in the intestine [62,63]. Sodium–inorganic phosphate co-transporters enable phosphate absorption in the intestine and excretion by the kidney [64], whilst renal a-ketoglutarate co-transport with Naþ enables absorption of an essential substrate for renal metabolism [65]. More recently, divalent cation–chloride co-transporters have been implicated in epithelia for metal absorption. For example, work in our laboratory has revealed chloride-dependent Cu absorption across the intestine, which is best explained by a basolateral Cu–Cl symport [66]. 3.3

COUNTER-TRANSPORT ON ANTIPORTERS

These transporters are similar to symporters, in that they are also secondary transport systems that rely on the electrochemical energy from one solute gradient to drive transport of another. In antiporters, the solutes are moving in opposite directions across the cell membrane, for example, Naþ in exchange for Hþ on the Naþ =Hþ exchanger [67], and Cl
in exchange for HCO
3 on the exchanger [68]. These exchangers are involved in acid–base balance Cl
=HCO
3 in animals, and the location of the antiporter can be on either the mucosal or basolateral membrane, depending on the function of the epithelia. For example in the intestine of marine fish, mucosally located Cl
=HCO
3 probably functions in base secretion by the gut [69], whilst serosally located Cl
=HCO
3 in chicken intestine probably functions to promote recovery from elevated intracellular pH in the gut epithelial cells [68]. In freshwater fish gills, the antiporter is apically located, to enable chloride uptake into the cell (Figure 2). The anion exchanger can move anions other than Cl
, for example Cl
=HCO
3 can exchange nitrite in place of chloride [69], and this is the reason for marked nitrite toxicity to aquatic organisms [70]. Developments in genomics and availability of specific-fluorescent antibodies for ion-transporting proteins have also revealed some historic misinterpretation of antiporter function. For example, Naþ uptake in exchange for acid excretion in the freshwater fish gill was originally interpreted as evidence for an apical Naþ =Hþ exchanger [4,5].

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However, recent work suggests the presence of an outwardly directed proton pump (Hþ -ATPase) in the apical membrane, with Naþ entering the electronegative cell via a specific Naþ channel [71,72]. Thus two separate transporters working in opposite directions achieve the function of Naþ uptake and acid excretion in the gill, although they are in close proximity in the cell membrane þ and might be regarded functionally as achieving Naþ =H exchange (Figure 2).

4

INTRACELLULAR TRAFFICKING

The intracellular environment of eukaryote cells can be subdivided into many regions, including the organelles, nucleus, cytoplasm and the cell periphery. Thus solutes must be delivered to the right intracellular compartment at the correct time to efficiently serve cellular biochemistry. Uncharged solutes such as glucose presumably diffuse across the cell, and the traditional view held until recently was that the major electrolytes, such as Naþ , Kþ , Cl
and Mg2þ , also move around the cell by simple diffusion to eventually arrive at the relevant subcellular compartment by chance. The view of simple diffusion across the cell may apply to uncharged solutes, but it is a gross oversimplification for the major electrolytes. The presence of mucoids and other large nondiffusible polyanions in the cell suggest that ionexchange phenomena will greatly influence ion distributions in the cytoplasm and on the surface of organelles (review [73]), so that local differences in ion content occur. The location of ion-transporting proteins will also influence ion distribution in the cell. Perhaps the best example of this phenomenon comes from Ca2þ sparks in cardiac tissue. In cardiac Purkinje cells, intracellular Ca2þ transients are initiated in the narrow space (‘fuzzy space’) between the sarcolemma (cell membrane) and the adjacent sacroplasmic reticulum, where Ca2þ transporters are also concentrated [24]. There is some circumstantial evidence of higher local Naþ concentrations in this space as well [74]. Thus, for the major electrolytes, it seems that the combination of diffusion, ion-exchange phenomena, and the exact location of ion transporters will be major factors in ion distribution across the cell, and facilitate movement of ions within the cell. The above situation is satisfactory for solutes that are not particularly reactive with proteins or membrane lipids, but this is not true for many trace metals that are also toxic. In general, metals that react with thiol groups on proteins, or can change oxidation state resulting in the generation of oxygen radicals which can subsequently damage cell membranes, are carefully regulated in the cell. Reactive metals such as Cu, Fe, Mn, etc. are carried almost exclusively by specific metal-ion chaperones [53,75,84]. These chaperones are usually small peptides, and will deliver metal ions to specific compartments within the cell (e.g. Cu [53]). This method of trace-metal trafficking is part of the normal epithelial cell function during the absorption of essential trace metals, and the

348 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

free-ion concentration of trace metals can be extremely low inside the cell (e.g. cytosolic ½Cu2þ i is nanomolar or less [75]). This mode of intracellular trafficking has some important consequences from the perspective of environmental toxicology. For example, if the supply of metal chaperone is overwhelmed by metal influx, then cytotoxicity will result. It also implies that epithelial cells require a readily available store of additional protein chaperones, or some other means of initiating metal chelation to prevent cytotoxicity. This is indeed the case with epithelial tissues such as intestine, which are able to induce metalbinding proteins such as metallothioneins during metal toxicity.

5

SOLUTE EXPORT FROM EPITHELIAL CELLS

The final step in solute transfer across the eukaryote epithelium is export of the solute from the cell across the serosal/basolateral membrane into the blood or other body fluid (Figure 1). In epithelial cells the serosal membrane is enriched with the ubiquitous Naþ Kþ -ATPase or Naþ pump, and this defines some of the electrochemical properties of the membrane, and indeed the whole cell. This enzyme has several important features [9–14]. Firstly, it is powered by the hydrolysis of ATP and therefore is a primary transport system. Secondly, it is electrogenic; that is, it imports and exports an unequal number of charges (3 Naþ outward: 2Kþ inward, see Figure 2). Thus the Naþ pump tends to create a net negative voltage in the cell, and this is in part responsible for the negative resting potential across the cell membranes of all eukaryote cells. This in turn generates the uphill gradient for cation export from the cell, since these cations must also overcome this attractive inside negative charge to escape from the cell. Conversely, the inside negative charge (or serosal positive, depending on your point of view) will drive negative solutes from the cell (e.g. Cl
). Thus exporting anions from epithelial cells to the blood is energetically easier than exporting cations. 5.1 EXPORT FROM THE CELL TO THE BLOOD VIA ION CHANNELS AND ANTIPORTERS The methods of solute transfer across the serosal/basolateral membrane can include ion channels and antiporters similar to those described earlier. In the case of serosally located cation channels, these primarily work because the intracellular electrolyte concentration is high enough to overcome the electrical gradient (e.g. some Kþ channels). For anion channels, the negative charge inside the cell compared with the blood will help drive (repel) anions from the cell (e.g. Cl
efflux on voltage-sensitive channels in the intestine [58]). In the case of antiporters, the operation is fundamentally the same as that used in the mucosal membrane, except that the driving force is derived from an ion

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gradient between the cell and the blood. This may of course mean that the function of the antiporter is different, since its role will be to extrude ions into the blood rather than from the external environment. These different functions are usually species specific. For example, the rat intestine has a mucosally
located Cl
=HCO
3 exchanger to serve Cl absorption, but the exchanger is serosally located in the chicken intestine and is involved in acid–base balance in the epithelial cells [68]. Other variants of the anion exchanger family are also implicated on the serosal membrane. For example, sulfate extrusion from the
gut cells to the blood of rabbits is partly driven by a putative SO2
4 =Cl exchanger [76]. Electrogenic antiporters may also be present in the serosal (basolateral) membrane to facilitate ion export from the cell to the blood. In the freshwater fish gill and intestine, basolateral 1Ca2þ =3Naþ exchange enables the uptake of Ca2þ into the blood from the epithelial cells [77]. 5.2 EXPORT FROM THE CELL TO THE BLOOD BY PRIMARY TRANSPORT: ATPASES The classic example of primary transport is the ATP-requiring Naþ pump discussed earlier. In all epithelia, this functions to drive Naþ uptake into the blood (or extracellular fluid) by the active export of Naþ from the epithelial cells to the blood, and is therefore basolaterally/serosally located. This is, however, only one of many ion-pumping ATPases which have been identified in eukaryote cells. This family of primary transporters are membrane spanning, usually constructed of at least two subunits, and use the energy from the hydrolysis of ATP to drive the transport process. There are other ATPases for the active transport of Ca2þ [77,78], Cu [53], Cl
[79], Hþ [71,72], and Mg2þ [80]. It is likely that many more will be discovered on the protein databases emerging from the genomic era. Of the ATPases above, at least the Ca2þ pumps are located on the serosal membrane, whilst others may be used to load cytoplasmic vesicles with ions prior to exocytosis from the cell to the blood (e.g. Cu [53]). Hþ -ATPase is involved in acid extrusion from epithelia, and tends to be mucosally/apically located, as in the fish gill (Figure 2). Clearly, ATPases provide important mechanisms for solute efflux from inside epithelial cells.

6

CONCLUSION AND ENVIRONMENTAL PERSPECTIVES

The fundamental process of transferring a solute from the environment, across a cell(s) to the blood involves the common steps of adsorption, influx, intracellular trafficking or distribution, and efflux to the blood. This process applies to physiologically important solutes like Naþ and amino acids, and applies equally to solutes of environmental concern, such as toxic metals. Animals spend a significant portion of their energy budgets on osmotic regulation; indeed, at the

350 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES þ

cellular level, energy expended via the Naþ K ATPase is preserved over other ATP expenditures [81]. It is therefore logical to assume that any environmental factor which alters solute transfer might be energetically expensive, and may ultimately influence the long-term survival of the organism. Some of these environmental aspects are obvious, such as anthropogenic sources of chemicals that disrupt the structure of delicate epithelia involved in solute transport, or directly inhibit the solute transporting proteins (e.g. Cu þ inhibition of Naþ K ATPase [82]). The general effects of environmental stress are also well known, since many of the hormones released into the blood during stressful situations will alter the activity of ion transporters (e.g. corticosteroids, catecholamine [14]). However, some effects are less intuitively obvious, and have been neglected. Unstirred layer formation can have large effects on solute transport, and, on a minute-by-minute basis, animals are constantly readjusting physiological systems (e.g. gill ventilation rate, blood flow) which will affect unstirred layer formation. Ventilation and blood flow are influenced by many environmental factors, but the interrelationship between environmentally induced cardiovascular adjustment, unstirred layer formation, and the cost of solute transport remain to be explored. Ion transport in very dilute freshwater environments can also be problematic from the perspective of electrochemical theory. For example, electrochemical theory predicts that Naþ entry through epithelial channels will stop when the external Naþ is <0:1 mmol l
1 Naþ (typical of many freshwaters), given intracellular Naþ concentrations of 10–20 mmol l
1 in gill epithelial cells [83]. Thus elevation of Naþ concentrations at the epithelial surface (adsorption) becomes critical to ion-channel function and Naþ uptake into the cells [50]. Alternatively, we might postulate other transporters coupled to the Naþ channel to drive uptake (e.g. Hþ slippage [84] on the Hþ -ATPase). Finally, environmental monitoring and prediction of toxicity are important aspects of any plan to protect the environment. Several features of solute transfer have been suggested in this regard. Most notably, the predictive value of metal binding to the gills for acute toxicity in ‘biotic ligand models’ [85] or ion influx measurements [86]. However, some features of solute transport have yet to be exploited, such as changes in the gene expression of ion transporters as biomarkers of exposure or effect.

GLOSSARY Absorption: strictly the transfer of solute from the environment to the blood, but is often used to generally describe solute uptake from the environment into an animal.

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Adsorption: the process of solute accumulation at a cell membrane surface. For cations, this usually involves electrostatic binding to anionic groups on the cell membrane. Antiporter: a secondary ion transporter that moves a solute against its electrochemical gradient by using energy derived from the movement of another solute in the opposite direction down its electrochemical gradient. Antiporters are also called exchangers, and the exchange process is sometimes referred to as counter transport. Apical membrane: the exterior facing cell membrane of a gill cell. Basolateral membrane: the cell membrane on the blood or extracellular fluid side of an epithelial cell. Bulk water: free-moving water that is readily exchanged or mixed in the environment, and is not part of an unstirred water layer. Carbonic anhydrase: an enzyme found in cells and in mucus secretions responsible for the (reversible) hydration of carbon dioxide. Donnan potential: a voltage arising from the passive uneven distribution of diffusible ions, usually across a cell membrane, or between a mucus layer and simple saline solution. Gill microenvironment: the surface layers of water/mucus adjacent to the gills, inside the opercular cavity of fishes. H þ -ATPase: an ion-pumping protein responsible for energy-dependent movement of Hþ across biological membranes. Ion flux: the movement of ions across a biological membrane, cell, or tissue layer. This flux may be into the cell or organism (influx) or out of the cell or organism (efflux). Mucosal membrane: the external environmental surface of an epithelium such as the gut. þ Naþ K -ATPase: a ubiquitous membrane-spanning protein, which uses ATP as a source of energy for moving ions, responsible for Naþ flux against the electrochemical gradient. Primary transport: the active transport of a solute against the electrochemical gradient by carrier proteins which derive energy for transport directly from the hydrolysis of ATP. Secondary transport: the transport of solutes against the electrochemical gradient using energy derived from the co- or counter-transport of another solute down its electrochemical gradient. The latter gradient ultimately being derived from other primary transporters. Serosal membrane: The cell membrane of the epithelial cell adjacent to the blood (serosal) side of the tissue. Sometimes also called the basolateral membrane in some gill and intestinal epithelia, because anatomical folds of the serosal membrane may extend laterally along the sides of the epithelial cells.

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Symporter: a secondary ion transporter that moves a solute against its electrochemical gradient by using energy derived from the movement of another solute in the same direction across the cell membrane down its electrochemical gradient. Symporters are also called co-transporters. Transepithelial potential: the voltage measured across an epithelium. Unstirred layer: a relatively nonmobile layer of water and/or mucus secretions adjacent to a biological membrane. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

Ussing, H. H. and Zerahn, K. (1951). Active transport of sodium as the source of electric current in the short-circuited isolated frog skin, Acta Physiol. Scand., 23, 110–127. Shaw, J. (1959). The absorption of sodium ions by the crayfish, Astacus pallipes Lereboullet. I. The effect of external and internal sodium concentrations, J. Exp. Biol., 36, 126–144. Potts, W. T. W. and Parry, G. (1964). Osmotic and Ionic Regulation in Animals. Pergamon Press, Oxford. Maetz, J. (1972). Branchial sodium exchange and ammonia excretion in the goldfish, Carassius auratus. Effects of ammonia loading and temperature changes, J. Exp. Biol., 56, 601–620. þ þ Maetz, J. (1973). Naþ =NH4 , Naþ =H exchanges and NH3 movements across the gill of Carassius auratus, J. Exp. Biol., 58, 255–275. Kirschner, L. B. (1983). Sodium chloride absorption across the body surface: frog skins and other epithelia, Am. J. Physiol., 244, R429–R443. Marshall, W. S. and Bryson, S. E. (1998). Transport mechanisms of seawater teleost chloride cells: an inclusive model of a multifunctional cell, Comp. Biochem. Physiol., 119A, 97–106. Ahearn, G. A., Duerr, J. M., Zhuang, Z., Brown, R. J., Aslamkhan, A. and Killebrew, D. A. (1999). Ion transport processes of crustacean epithelial cells, Physiol. Biochem. Zool., 72, 1–18. Skou, J. C. (1983). On the mechanism behind the ability of Na, K-ATPase to discriminate between Naþ and Kþ , Curr. Topics Membr. Trans., 19, 323–341. Skou, J. C. (1988). Overview: the Na,K-pump, Meth. Enzymol., 156, 1–25. Blanco, G. and Mercer, R. W. (1998). Isoenzymes of the Na-K-ATPase: heterogeneity in structure, diversity in function, Am. J. Physiol., 275, F633–F650. Blostein, R. (1999). Jeanne Mannery Fisher Memorial Lecture 1998. Structure– function studies of the sodium pump, Biochem. Cell Biol., 77, 1–10. Pavlov, K. V. and Sokolov, V. S. (2000). Electrogenic ion transport by the Naþ , Kþ -ATPase, Membr. Cell Biol., 13, 745–788. Therien, A. G. and Blostein, R. (2000). Mechanisms of sodium pump regulation, Am. J. Physiol., 279, C541–C566. Holmes, W. N. and Donaldson, E. M. (1969). The body compartments and the distribution of electrolytes. In Fish Physiology. Vol. 1, eds. Hoar, W. S. and Randall, D. J., Academic Press, London, pp. 1–89. Eddy, F. B. (1982). Osmotic and ionic regulation in captive fish with particular reference to salmonids, Comp. Biochem. Physiol., 73B, 125–141.

R. D. HANDY AND F. B. EDDY 17. 18. 19. 20. 21.

22. 23. 24. 25. 26. 27. 28. 29. 30. 31.

32. 33. 34. 35.

353

Evans, D. H. (1984). The roles of gill permeability and transport mechanisms in euryhalinity. In Fish Physiology, Vol. XB, Gills, Ion and Water Transport. eds. Hoar, W. S. and Randall, D. J., Academic Press, London, pp. 239–284. Davenport, J. (1985). Osmotic control in marine animals. In Physiological Adaptations of Marine Animals. ed. Laverack, M. S., The Company of Biologists Limited, Cambridge, pp. 207–244. Eddy, F. B. and Penrice, W. S. (1998). Osmotic and ionic regulation in fish. In Fish Diseases. Non Infectious Disorders. Vol. 2, eds. Leatherland, J. F. and Woo, P. T. K., CAB International, Oxford, pp. 225–244. Harris, R. R. and Aladin, N. V. (1997). The ecophysiology of osmoregulation in crustacea. In Ionic Regulation in Animals. eds. Hazon, N., Eddy, F. B. and Flik, G., Springer, Berlin, pp. 1–25. Hazon, N., Tierney, M. L., Anderson, W. G., Mackenzie, C., Cutler, C. and Cramb, G. (1997). Ion and water balance in elasmobranch fish. In Ionic Regulation in Animals. eds. Hazon, N., Eddy, F. B. and Flik, G., Springer, Berlin, pp. 70–86. Williams, R. J. P. (1981). Physico-chemical aspects of inorganic element transfer through membranes, Phil. Trans. R. Soc. Lond. B., 294, 57–74. McWilliams, P. G. and Potts, W. T. W. (1978). The effects of pH and calcium concentrations on gill potentials in the brown trout Salmo trutta, J. Comp. Physiol., 126, 277–286. Cordeiro, J. M., Spitzer, K. W., Giles, W. R., Ershler, P. E., Cannell, M. B. and Bridge, J. H. B. (2001). Location of the initiation site of calcium transients and sparks in rabbit heart Purkinje cells, J. Physiol., 531, 301–314. Pedley, T. J. (1983). Calculations of unstirred layer thickness in membrane transport experiments: a survey, Q. Rev. Biophys., 16, 115–150. Barry, P. H. and Diamond, J. M. (1984). Effects of unstirred layers on membrane phenomena, Physiol. Rev., 64, 763–872. Barry, P. H. (1998). Derivation of unstirred-layer transport number equations from the Nernst–Planck flux equations, Biophys. J., 74, 2903–2905. Pohl, P., Saparov, S. M. and Antonenko, Y. N. (1998). The size of the unstirred layer as a function of solute diffusion coefficient, Biophys. J., 75, 1403–1409. Kirschner, L. B. (1978). External charged layer and Naþ regulation. In Osmotic and Volume Regulation. (Alfred Benzon Symposium XI Munksgaard), Academic Press, New York, pp. 310–324. Handy, R. D. and Eddy, F. B. (1991). Effects of inorganic cations on sodium adsorption to the gill and body surface of rainbow trout, Oncorhynchus mykiss, in dilute solutions, Can. J. Fish. Aquat. Sci., 48, 1829–1837. Shephard, K. L. (1989). The effects of mucus and mucilaginous materials on ion-distributions at epithelial surfaces. In Mucus and Related Topics. eds. Chantler, E. and Ratcliffe, N. A., The Company of Biologists, Cambridge, pp. 123–130. Shephard, K. L. (1992). Studies on the fish gill microclimate: interactions between gill tissue, mucus and water quality, Environ. Biol. Fish., 34, 409–420. Shephard, K. L. (1994). Functions for fish mucus, Rev. Fish Biol. Fisher., 4, 401–429. Pagenkopf, G. K. (1983). Gill surface interaction model of trace metal toxicity to fishes: role of complexation, pH, and water hardness, Environ. Sci. Technol., 17, 342–347. Campbell, P. G. C. and Stokes, P. M. (1985). Acidification and toxicity of metals to aquatic biota, Can. J. Fish. Aquat. Sci., 42, 2034–2049.

354 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 36. 37. 38.

39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53.

Handy, R. D. and Eddy, F. B. (1990). The interactions between the surface of rainbow trout, Oncorhynchus mykiss, and waterborne metal toxicants, Funct. Ecol., 4, 385–392. Playle, R. C., Dixon, D. G. and Burnison, K. (1993). Copper and cadmium binding to fish gills: estimates of metal–gill stability constants and modelling of metal accumulation, Can. J. Fish. Aquat. Sci., 50, 2678–2687. MacRae, R. K., Smith, D. E., Swoboda-Colberg, N., Meyer, J. S. and Bergman, H. (1999). Copper binding affinity of rainbow trout (Oncorhynchus mykiss) and brook trout (Salvelinus fontinalis) gills: implications for assessing bioavailable metal, Environ. Toxicol. Chem., 6, 1180–1189. Hughes, G. M. (1984). General anatomy of the gills. In Fish Physiology, Vol. XA, Gills. eds. Hoar, W. S. and Randall, D. J., Academic Press, London, pp. 1–72. Laurent, P. (1984). Gill internal morphology. In Fish Physiology, Vol. XA, Gills. eds. Hoar, W. S. and Randall, D. J., Academic Press, London, pp. 73–184. Pisam, M., Carott, A. and Rambourg, A. (1987). Two types of chloride cells in the gill epithelium of a freshwater adapted euryhaline fish Lebistes reticularis. Their modifications during adaptation to saltwater, Am. J. Anat., 179, 40–50. Pisam, M., Prunet, P., Boeuf, G. and Rambourg, A. (1988). Ultrastructural features of chloride cells in the gill epithelium of the Atlantic salmon, Salmo salar, and their modifications during smoltification, Am. J. Anat., 183, 235–244. Pisam, M., Prunet, P. and Rambourg, A. (1989). Accessory cells in the gill epithelium of the freshwater rainbow trout Salmo gairdneri, Am. J. Anat., 184, 311–320. Laurent, P. and Perry, S. F. (1991). Environmental effects on fish gill morphology, Physiol. Zool., 64, 4–25. Wright, P. A., Randall, D. J. and Perry, S. F. (1989). Fish gill water boundary layer: a site of linkage between carbon dioxide and ammonia excretion, J. Comp. Physiol. B., 158, 627–635. Playle, R. C. and Wood, C. M. (1989). Water chemistry changes in the gill microenvironment of rainbow trout: experimental observations and theory, J. Comp. Physiol. B., 159, 527–537. Handy, R. D. and Eddy, F. B. (1991). The absence of mucus on the secondary lamellae of unstressed rainbow trout, Oncorhynchus mykiss (Walbum), J. Fish Biol., 38, 153–155. Powell, M. D., Speare, D. J. and Burka, J. F. (1992). Fixation of mucus on rainbow trout (Oncorhynchus mykiss Walbaum) gills for light and electron microscopy, J. Fish. Biol., 41, 813–824. Guth, D. and van Engelhardt, W. (1989). Is gastro-intestinal mucus an ion-selective barrier? In Mucus and Related Topics. eds. Chantler, E. and Ratcliffe, N. A., The Company of Biologists, Cambridge, pp. 117–121. Handy, R. D. (1989). The ionic composition of rainbow trout body mucus, Comp. Biochem. Physiol. A., 93, 571–575. Scott, J. E. (1968). Ion binding in solutions containing acid mucopolysaccharides. In The Chemical Physiology of Mucopolysaccharides. ed. Quintarelli, G., Little Brown, London, pp. 171–187. Scott, J. E. (1989). Ion binding: patterns of affinity depending on types of acid groups. In Mucus and Related Topics. eds. Chantler, E. and Ratcliffe, N. A., The Company of Biologists, Cambridge, pp. 111–115. Handy, R. D., Eddy, F. B. and Baines, H. (2002). Sodium-dependent copper uptake across epithelia: a review of rationale with experimental evidence from gill and intestine, Biochim. Biophys. Acta-Biomembranes, 1566, 104–115.

R. D. HANDY AND F. B. EDDY 54. 55. 56. 57. 58.

59. 60. 61. 62. 63. 64. 65. 66.

67. 68. 69. 70. 71. 72.

355

Benos, D. J. and Stanton, B. A. (1999). Functional domains within the degenerin/ epithelial sodium channel (Deg/ENaC) superfamily of ion channels, J. Physiol., 520, 631–644. Lucu, C. and Obersnel, V. (1996). Cadmium influx across isolated Carcinus gill epithelium. Interaction of lanthanum and calcium with cadmium influxes, J. Comp. Physiol. B., 166, 184–189. Niisota, N. and Marunaka, Y. (1997). Regulation of Cl
transport by IBMX in renal A6 epithelium, Pflu¨gers Arch., 434, 227–233. Anderson, P. A. V. and Greenberg, R. M. (2001). Phylogeny of ion channels: clues to structure and function, Comp. Biochem. Physiol. B., 129, 17–28. Loretz, C. A. (1995). Electrophysiology of ion transport in teleost intestinal cells. In Cellular and Molecular Approaches to Fish Ionic Regulation. eds. Wood, C. M. and Shuttleworth, T. J., Fish Physiology Series, Vol. 14, Academic Press, San Diego, pp. 25–56. Mount, D. B., Delpire, E., Gamba, G., Hall, A. E., Poch, E., Hoover, R. S. and Hebert, S. C. (1998). The electroneutral cation–chloride cotransporters, J. Exp. Biol., 201, 2091–2102. Hoffmann, E. K. (1982). Anion exchange and anion–cation co-transport systems in mammalian cells, Phil. Trans. R. Soc. Lond. B, 299, 519–535. Hoffmann, E. K. and Dunham, P. B. (1995). Membrane mechanisms and intracellular signalling in cell volume regulation, Int. Rev. Cytol., 161, 173–262. Kellett, G. L. (2001). The facilitated component of intestinal glucose absorption, J. Physiol., 531, 585–595. Sundaram, U., Wisel, S. and Fromkes, J. J. (1998). Unique mechanism of inhibition of Naþ -amino acid cotransport during chronic ileal inflammation, Am. J. Physiol., 275, G483–G489. Werner, A., Dehmelt, L. and Nalbant, P. (1998). Naþ -dependent phosphate cotransporters: the NaPi protein families, J. Exp. Biol., 201, 3135–3142. Dantzler, W. H. (1996). Comparative aspects of renal organic anion transport, Cell. Physiol. Biochem., 6, 28–38. Handy, R. D., Musonda, M. M., Phillips, C. and Falla, S. J. (2000). Mechanisms of gastro-intestinal copper absorption in the African Walking Catfish: copper dose-effects and a novel anion-dependent pathway in the intestine, J. Exp. Biol., 203, 2365–2377. Giannakou, M. E. and Dow, J. A. T. (2001). Characterisation of the Drosophila melanogaster alkalia-metal/proton exchanger (NHE) gene family, J. Exp. Biol., 204, 3703–3716. Calonge, M. L. and Ilunda´in, A. A. (1998). HCO
3 -dependent ion transport systems and intracellular pH regulation in colonocytes from the chick, Biochim. Biophys. Acta-Biomembranes, 1371, 232–240.
Grosell, M. and Jensen, F. B. (1999). NO
2 uptake and HCO3 excretion in the intestine of the European flounder (Platichthys flesus), J. Exp. Biol., 202, 2103–2110. Williams, E. M. and Eddy, F. B. (1986). Chloride uptake in fresh-water teleosts and its relationship to nitrite uptake and toxicity, J. Comp. Physiol. B, 156, 867–872. Lin, H. and Randall, D. J. (1995). Proton pumps in fish gills. In Cellular and Molecular Approaches to Fish Ionic Regulation. eds. Wood, C. M. and Shuttleworth, T. J., Academic Press, New York, pp. 1–23. Sullivan, G. V., Fryer, J. N. and Perry, S. F. (1995). Immunolocalization of proton pumps (Hþ -ATPase) in pavement cells of rainbow trout gill, J. Exp. Biol., 198, 2619–2629.

356 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 73.

74. 75. 76. 77.

78. 79. 80. 81. 82. 83. 84. 85. 86. 87.

Gupta, B. L. (1989). The relationship of mucoid substances and ion and water transport, with new data on intestinal goblet cells and a model for gastric secretion. In Mucus and Related Topics. eds. Chantler, E. and Ratcliffe, N. A., The Company of Biologists, Cambridge, pp. 81–110. Su, Z., Sugishita, K., Ritter, M., Li, F., Spitzer, K. W. and Barry, W. H. (2001). The sodium pump modulates the influence of INa on [Ca2þ ]i transients in mouse ventricular myocytes, Biophys. J., 80, 1230–1237. Lippard, S. J. (1999). Free copper ions in the cell? Science, 284, 748–749. Langridge-Smith, J. E. and Field, M. (1981). Sulfate transport in rabbit ileum: characterisation of the serosal border anion exchanger process, J. Membr. Biol., 63, 207–214. Flik, G., Verbost, P. M. and Wendelaar Bonga, S. E. (1995). Calcium transport processes in fish. In Cellular and Molecular Approaches to Fish Ionic Regulation. eds. Wood, C. M. and Shuttleworth, T. J., Fish Physiology Series, Vol. 14, Academic Press, San Diego, pp. 317–342. Carafoli, E. (1991). Calcium pump of the plasma membrane, Physiol Rev., 71, 129–153. Gerencser, G. A. (1996). The chloride pump: a Cl
-translocating P-type ATPase, Crit. Rev. Biochem. Mol. Biol., 31, 303–337. Flatman, P. W. (1984). Magnesium transport across cell membranes, J. Membr. Biol., 80, 1–14. Krumschnabel, G., Schwarzbaum, P. J., Lisch, J., Biasi, C. and Wieser, W. (2000). Oxygen-dependent energetics of anoxia-tolerant and anoxia intolerant hepatocytes, J. Exp. Biol., 203, 951–959. Li, J., Lock, R. A. C., Klaren, P. H. M., Swarts, H. G. P., Schuurmans Stekhoven, F. M. A. H., Wendelaar Bonga, S. E. and Flik, G. (1996). Kinetics of Cu2þ inhibition of Naþ =Kþ -ATPase, Toxicol. Lett., 87, 31–38. Morgan, I. J., Potts, W. T. W. and Oates, K. (1994). Intracellular ion concentrations in branchial epithelial cells of brown trout (Salmo trutta L.) determined by X-ray microanalysis, J. Exp. Biol., 194, 139–151. Nelson, N. (1999). Metal ion transporters and homeostasis, EMBO J., 18, 4361–4371. Reid, S. D. and McDonald, D. G. (1991). Metal binding activity of the gills of rainbow trout (Oncorhynchus mykiss), Can. J. Fish. Aquat. Sci., 48, 1061–1068. Handy, R. D. and Depledge, M. H. (1999). Physiological responses: their measurement and use as environmental biomarkers in ecotoxicology, Ecotoxicology, 8, 329–349. Gingerich, W. H. and Pityer, R. A. (1989). Comparison of whole body and tissue blood volumes in rainbow trout (Salmo gairdneri) with 125 I bovine serum albumin and 51 Cr-erythrocyte tracers, Fish Physiol. Biochem., 6, 39–47.

8 Transport of Colloids and Particles Across Biological Membranes MARINA G. TAYLOR AND KEN SIMKISS School of Animal and Microbial Sciences, University of Reading, Whiteknights, Reading, RG6 6AJ, UK

1 2

3

4 5

6

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Colloids and Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Organic Coatings of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Larger Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Micelles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contaminants in the Aquatic Environment . . . . . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Separation of Dissolved and Colloidal Fractions . . . . . . . . . 3.3 Bioaccumulation of Metals as Colloid Complexes and Free Ions – a Kinetic Model . . . . . . . . . . . . . . . . . . . . . . . 3.4 Bioaccumulation of Silver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Bioaccumulation of Tributyltin . . . . . . . . . . . . . . . . . . . . . . . . Membrane Transport Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . Endocytosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Endocytotic Pathways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Phagocytosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Pinocytosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Caveolae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Receptor-Mediated Endocytosis . . . . . . . . . . . . . . . . . . . . . . . Evidence for the Endocytotic Uptake of Contaminants . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Endocytosis by Aquatic Invertebrates. . . . . . . . . . . . . . . . . . . 6.2.1 Assimilation Efficiency Models . . . . . . . . . . . . . . . . . . 6.2.2 Further Bioaccumulation Studies . . . . . . . . . . . . . . . . 6.3 Endocytosis by Terrestrial Invertebrates. . . . . . . . . . . . . . . . . 6.4 Endocytosis of Airborne Particles . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6.4.2 Diesel Exhaust Particles and Fly-Ash. . . . . . . . . . . . . 6.4.3 Nickel Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.4 Lead Chromate Particles . . . . . . . . . . . . . . . . . . . . . . . 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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INTRODUCTION

Inorganic and organic compounds are often present in the environment in complex forms. Levels of contaminating metals and molecules are variable, depending on the natural conditions and anthropogenic activities. The contaminants may be airborne as vapour, droplets or dust particles, and in the soil in aqueous or particulate forms. In the case of aqueous systems, they can exist as emulsions, as dissolved ions or molecules and as suspended or sedimentary particles. Environmental particles have been reviewed in the first two volumes of this series [1,2]. Airborne particulate matter may be associated with many carcinogenic and other toxic agents. Hazardous materials include coal dust, fly-ash from power stations, metals and metal oxides from mining, extraction and refining and materials used as catalysts in industrial processes, as well as particulate matter from, for example, diesel exhausts. The use of materials such as asbestos in buildings and machinery is now largely discontinued, but poses a health hazard when the material is disturbed. Recognition of the importance of atmospheric particles is reflected in a dedicated volume in this series [3]. In this chapter we emphasise the interaction with the biosphere. The terrestrial environment suffers from the persistence of metals from industrial processes, as well as herbicides and pesticides which may also be transmitted through the food chain with deleterious effects to both individual species and ecosystems. The aquatic environment suffers from the same sources of contamination as those described for the atmosphere and the soil. However, the contaminants can be far from the original sources as they enter the water from aerial deposition, land runoff and deliberate dumping. The aquatic environment is, however, very heterogeneous. Surface waters support pelagic organisms which are exposed to pollutants that may be from soluble material and suspended solids. These materials can be inorganic or organic in origin, and frequently contain biological detritus. The suspended solids will gradually descend the water column, perhaps adsorbing contaminants and aggregating before reaching the sediment. They may also be resuspended by turbulent activity. Once in the sediment, the particles can be changed further by adsorption of pollutants, local

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Table 1. Endocytosis and environmental contaminants Occurrence (1) Endocytosis is an ubiquitous system for engulfing solid/colloidal materials by cells by encapsulating them in membrane-bound vesicles. (2) Typically, it is linked to a system for acidifying and digesting organic material (Figure 4). Properties (3) The phenomenon is easily observed in wide variety of individual and epithelial cells (Section 6). (4) However, it is experimentally difficult to separate it from extracellular processes that use similar methods of digestion and absorption (Section 6.1). Experimental Approaches (5) Compare feeding and nonfeeding Protozoa exposed to otherwise similar treatments (Section 5.3). (6) Use organisms where particulate and nonparticulate digestive processes are anatomically separated (Sections 6.1 and 6.2). (7) Study alternative interphases, as in exposure of respiratory organs to environmental particles (Section 6.4).

pH factors and anoxic conditions. Benthic organisms are then exposed to these contaminants. The importance of particulate matter as a polluting vector in sediments has only really been recognised in the past twenty years. It had been thought that the sediments in both freshwater and marine environments provided a sink for pollutants, ensuring that they were no longer bioavailable. However, it is now recognised that as many sediment-dwelling organisms are suspension or deposit feeders, the importance of this uptake route for contaminants needs to be assessed. There is consequently extensive research in this area and discussion as to whether the sediment or the interstitial pore water is the major source for the uptake of pollutants in these sediment-dwelling organisms. A number of protocols have been established to assess the toxicity and bioaccumulation of sediment-associated contaminants [4,5]. Table 1 gives a guide to the chapter, which discusses aspects of endocytosis in handling environmental contaminants.

2 2.1

COLLOIDS AND PARTICLES INTRODUCTION

Contaminants in soils and sediments can be adsorbed on to inorganic minerals such as clays and metal oxides, notably hydrated iron oxide, FeOOH and manganese dioxide, MnO2 , or adsorbed on to organic matter such as humic

360 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

acids, or associated with other colloids and particles. A colloid is a dispersion of small particles in a continuous phase. The criterion used to define these states is generally size within the range of 1 nm to 1 mm [6]. Particle size can be critical, in that the smaller particles have a relatively larger surface adsorption capacity. Measurements of particle size involve initial separations between dissolved and particulate matter. Earlier separations involved filtering through 0:45 mm membrane filters, which meant that colloids could be in either fraction. The development of the technique of Field Flow Fractionation (FFF) achieves a better resolution in size fractionation. It also allows new physicochemical studies of each fraction, and a revision of earlier assumptions regarding speciation of metals and molecules in the environment [7]. FFF is essentially a chromatography-like separation, but differs in that the separations are carried out within a flat open channel (Figure 1) rather than a packed-bed column or a capillary tube. The field, which drives the sample molecules or particles towards the accumulation wall, involves gravitational, centrifugal, fluid cross-flow, thermal gradient, electrical or magnetic forces. Recent refinements to FFF separation techniques, such as the cross-flow filtration (CFF) approach, have Inflow FIELD

Outflow (to detector)

Exploded view FIELD Parabolic flow profile

FLOW Flow vectors

Accumulation wall

Figure 1. Schematic of an FFF channel with the separation mechanism for normal FFF shown in detail. Reprinted from [7]: Beckett, R. and Hart, B. T. ‘Use of field flow fractionation techniques to characterize aquatic particles, colloids and macromolecules’. In Environmental Particles. Vol. 2, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems. Series eds. Buffle, J. and van Leeuwen, H. P., pp. 165–205. Copyright 1993 ß IUPAC. Reproduced with permission

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given new insights into those pollutants that are in solution or associated with colloids or other particles in the aquatic environment [8]. An important property of colloidal suspensions is their tendency to aggregate, and the stability of the colloidal phase will depend on the interactions between the particles and the interface. Most hydrophilic particles in contact with a polar medium such as water acquire a surface electric charge. Hydrophobic colloids will develop a weak electrical double layer due to induced dipoles, and so stabilise the colloid by hindering the close approach of other particles. However, when the ionic strength is increased by the addition of ions, especially of high charge, attractive forces become more important and allow close approach of the particles, according to the Schultze–Hardy rule, and so favour aggregation [9]. There is a critical coagulation concentration of electrolytes for hydrophobic colloids [6]. Hydrophilic particles may become charged by ionisation, ion adsorption or ion dissolution. In an aquatic environment when the particles may also be coated by organic matter, they will have a negative surface charge. This results in an electrical double layer at the interface of the suspended particle and the suspension medium. The double layer is important in considering the stability and aggregation properties of colloids. Sites at the charged particle surface can attract ions, often hydrated, as well as dipolar molecules of opposite charge, as an adsorbed layer, referred to as the Stern layer, while ions with centres beyond the Stern layer which are in the diffuse part of the double layer are described as the Gouy–Chapman layer (Figure 2). The Gouy–Chapman layer takes account of thermal motion, giving a region of dispersed ions interacting electrostatically. − Stern − layer −

−

− − − − − − − − − − −

Gouy−Chapman diffuse layer

−

−

−

Figure 2. The distribution of ions around a charged particle, showing the tightly bound Stern layer and the diffuse Gouy–Chapman region. Reprinted from [45] Simkiss, K. and Taylor, M. G. ‘Transport of metals across membranes’. In Metal Speciation and Bioavailability in Aquatic Systems. eds. Tessier, A. and Turner, D. R., Vol. 3, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle J. and van Leeuwen, H. P. Copyright 1995 ß John Wiley & Sons Limited. Reproduced with permission

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A theoretical model for the adsorption of metals on to clay particles (<0:5 mm) of sodium montmorillonite, has been proposed, and experimental data on the adsorption of nickel and zinc have been discussed in terms of fitting the model and comparison with the Gouy–Chapman theory [10]. In clays, two processes occur. The first is a pH-independent process involving cation exchange in the interlayers and electrostatic interactions. The second is a pHdependent process involving the formation of surface complexes. The data generally fitted the clay model and were seen as an extension to the Gouy– Chapman model from the surface reactivity to the interior of the hydrated clay particle. The important forces involved in the adsorption of metals on to particles are attractive electrostatic or van der Waals forces. These concepts explain many of the properties of colloids with respect to the adsorption of contaminants or ionexchange factors and the aggregation of the colloids into larger particles. These larger particulates may then descend the water column to the sediment. This occurs most notably in estuarine environments, as increases in salinity lead to estuarine silting. Binding of electrolytes to hydrophobic colloids is often used to facilitate their coagulation and precipitation. Colloids are thermodynamically unstable conglomerates that form heterogeneous dispersions in aqueous systems. They tend to coagulate and precipitate, which means that the materials of which they are composed may be present both in the water column and in sediments. The coagulation and precipitation stages are generally considered irreversible, but forces in the environment can redisperse the particles. 2.2

ORGANIC COATINGS OF PARTICLES

An additional characteristic of such particulate matter is that it is frequently coated with natural organic material, such as humic and fulvic acids and exopolymers, which may themselves be colloids. These tend to have a negatively charged surface, making them prime targets for the association of cationic contaminants. Colloids have a very large surface area and are therefore able to act as effective absorbents. The molar mass of macromolecules is of itself no handicap to solubility, since it depends on their interaction with the solvent. Macromolecules like proteins or humic acids will have hydrophilic and hydrophobic regions that not only determine their solubility but also their reactivity to other molecules present. Humic acids are poorly defined polymeric structures with carboxylic acid and hydroxyl groups (attached to both aliphatic and aromatic moieties) being the most important functional groups at the surface [11]. Thus, humic acids occur in a range of sizes [7], and the best calibration standard for determining their molar mass is the random coil polyelectrolyte sodium polystyrenesulfonate, rather than globular proteins. The reactivity of humic acids makes them very important in the regulation, speciation and

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transport of ions, nutrients and contaminants in both soils and the freshwater environment. Diffusion coefficients of cadmium–humic acid complexes and lead–fulvic acid complexes have been shown to increase with pH in voltammetric studies, demonstrating the influence of pH on the aggregation/disaggregation properties of these complexes [12]. In studies of the interactions between both hydrophilic and hydrophobic contaminants and humic acid surfaces [13], it was concluded that the rate of hydrophilic interactions depended on pH and ionic strength, but they were generally fast, whereas interactions with hydrophobic surfaces were slower, as rearrangement of the humic acid structures were required to expose their internal hydrophobic regions. It has been observed that materials diffuse into the green alga Selenastrum capriconatum faster at pH 5 than pH 7, and this has been attributed to the adsorption of humic acids on to the cell membrane under these conditions [14]. A second type of organic coating is the exopolymer or organic matter produced by bacteria. This consists largely of polysaccharides, and often coats mineral particles such as silica or FeOOH. Exopolymers and other adsorbed organic matter are considered to be an important food source for deposit- and filter-feeding organisms. The exopolymers have an affinity for dissolved metal ions, and so may provide a route for the uptake of pollutant metals and organic molecules that have either a positive charge or dipole (see also Chapter 10 of this volume). In a laboratory study by Schlekat et al. [15], it was demonstrated that coating silica particles with an exopolymer prepared from an estuarine bacterium enhanced the sorption of cadmium on to the particles. The composition of the exopolymer was glucose, galactose and glucuronic acid in the ratio 5:2:1. These investigations also compared the effects of salinity, pH and different concentrations of cadmium. Increasing salinity resulted in less cadmium associated with the particles, presumably due to competition with the chloride ion. The pH had a dramatic effect, resulting in only ca. 10% absorbed at pH 5 to more than 95% at pH 9. 2.3

LARGER PARTICLES

The role of larger particles in the aquatic environment has been studied extensively, particularly in the marine environment. The larger particles (>100 mm) have a heterogeneous composition, which includes biotic detritus, faecal pellets and amorphous aggregates referred to as ‘marine snow’, which consists of both organic and inorganic matter [16]. These particles have been found to be responsible for most of the downward mass flux in the seas, although the rate of sinking depends on the origin, composition and density of the particle. The particles can then contribute to the sediment or become resuspended by turbulent activity. They are a source of nutrients for many benthic and boundary benthic organisms, and become part of the food chain, as well as acting as

364 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

mechanisms for the cycling of contaminants. For example, benthopelagic copepods are particle feeders that can be predated by benthopelagic fish. Much of our understanding of these particles is derived from their propensity to accumulate trace metals. The particles are therefore a source of essential trace elements required for enzyme activity, but they may also contribute pollutant metals such as cadmium and lead. Studies of radionuclides have contributed to our knowledge of the dynamics of the ‘marine snow’, and concentrations in macro- and micro-zooplankton have been determined. Trace elements can also be released from the particles and recycled in the environment [17]. 2.4

MICELLES

An example of association colloids of interest to environmentalists are micelles that are often composed of amphiphilic molecules similar to those found in biomembranes. The hydrophobic regions of the molecule forming the micelle in aqueous solutions tend to be oriented towards the centre, leaving the hydrophilic regions in contact with the water. The micelles are especially important as a mode of encapsulation and transport of organic contaminants. A possible application of these properties of micelles has been proposed for remediation of contaminated sites. A cryo-transmission electron microscopy study of the ionic biosurfactant rhamnolipid, pKa 5.6 (Figure 3) which is produced by Pseudomonas aeruginosa, showed that the molecule changed its morphology with pH [18]. At pH 5.5 the surfactant was largely present as lamellar sheets, at pH 6–6.5 they were mostly vesicles, and at higher pH 7–8 the structures were largely small micelles. Exposure to cadmium at pH 6.8 resulted in a doubling in the number of vesicles that were often smaller in size, whereas exposure to the organic compound octadecane at pH 7.0 resulted in a decrease in the number of vesicles, and mostly micelles were observed. The changes in morphology were verified by dynamic laser scattering intensity. These changes were discussed in terms of the ratio of the effective diameter of the polar head groups to the nonpolar tails of the surfactants. The monomers line up as planar bilayers when the ratio is 1. As the ratio increases, the structure curves initially to form vesicles and, as it increases, further micelles are formed. The changes in the ratio depend on whether or not the carboxyl groups are protonated, since repulsions between the ionised carboxyl groups can affect the transition from the bilayer to micelle structure. Cadmium stabilises the vesicle structure presumably as cadmium

HO

O CH3 OH

Figure 3.

OCH-CH2COO-CH-CH2COOH OH

R1

R2

Ionic biosurfactant rhamnolipid, R1 , R2 ¼ C5 H11 , C7 H15 or C9 H19

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binds to the carboxyl groups. By contrast octadecane would be expected to interact hydrophobically with the nonpolar tails. The outcome of these properties leads to the dispersion of the organic molecule with a maximum at pH 6.0–7.0. This study illustrates the potential for the use of surfactants for remediation of contaminated soils, taking account of size and charge through pH effects (see also Chapter 2 in this volume).

3. 3.1

CONTAMINANTS IN THE AQUATIC ENVIRONMENT INTRODUCTION

The contaminants present in the aquatic environment consist of both inorganic and organic compounds. Their interactions with the colloidal, mineral and coated particle surfaces reflect the nature of these hydrophilic and lipophilic attractions. There is an extensive literature on the analysis of metals in the aquatic environment as a measure of environmental contamination [19–22]. The metal can be present as free ions, ion pairs, or soluble complexes with organic ligands, as well as being adsorbed on to either colloids or particles which can be present either in the water column as suspended solids or in the sediment. All of these properties can affect the bioavailability of metals, especially in estuaries [23]. In the 1980s, it was established that sediment geochemistry may be an important factor influencing bioavailability, but it was not understood sufficiently well to make predictions. Frequently, there was no clear relationship between the concentration of metals in the water and sediment and bioaccumulation, which varied between different organisms in the same environments [24]. There was therefore an impetus towards understanding the processes that control bioavailability in order to assess the environmental impact. The first consideration was the speciation and distribution of the metal in the sediment and water. Benthic organisms are exposed to surface water, pore water and sediment via the epidermis and/or the alimentary tract. Common binding sites for the metals in the sediment are iron and manganese oxides, clays, silica often with a coating of organic carbon that usually accounts for ca. 2% w/w. In a reducing environment contaminant metals will be precipitated as their sulfides. There is not necessarily a direct relationship between bioavailability and bioaccumulation, as digestion affects the availability and transport of the metals in animals, in ways that differ from those in plants. The prediction of sediment toxicity based on chemical data alone was questioned in a discussion paper by O’Connor and Paul [25]. But even with the inclusion of a bioassay there are problems. It was considered that a sediment should be classified as toxic if there was less than an 80% survival of exposed

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amphipods, although it is clear that the responses of amphipods may not reflect toxicity to other forms of life. The difficulty is illustrated in a number of studies on the distribution of metals between dissolved and particulate phases and how this may affect their bioavailability. The role of organic coatings such as humic acid and exopolymers, in the absorption of cadmium, has been studied by Selck et al. [26] in the deposit-feeding polychaete Capitella species I (previously described as Capitella capitata). They concluded that uptake of cadmium by particle ingestion was greater than uptake from the dissolved phase, which was ca. 33% of the total uptake. They compared the uptake from uncoated particles, humic acid coated particles and low and high coating with exopolymers, also relating it to the gut passage time. The efficiency of cadmium absorption was in the order: uncoated particles > humic acid coated particles
to high exopolymer coating > low exopolymer coating. Conditional stability constants have been determined for cadmium binding to humic acid in freshwater, log K
6.5 [27], which may be comparable to binding to humic acid coated particles. The experiments demonstrated the importance of cadmium uptake from particles rather than from the dissolved phase. The authors recognised that the overall conclusion was similar to previous studies [28], but there remain inconsistencies in the uptake levels which may be related to the heterogeneity of the systems. Uptake from the intestine into the mucosal cells was not investigated. It was presumed that the material was digested extracellularly by hydrolytic enzymes and the released metal was taken up by facilitated diffusion. 3.2

SEPARATION OF DISSOLVED AND COLLOIDAL FRACTIONS

In a study involving several contaminated freshwater streams in New Jersey Pinelands, Ross and Sherrell [8] have used CFF, with a 10 kDa (ca. 3 nm) cutoff, to separate the filtrate (<0:45 mm) into colloidal and truly dissolved fractions in freshwater systems. The colloidal fraction, fcoll , was calculated by difference: fcoll ¼ (ctd  ctru )=ctd

(1)

where ctd represents the total dissolved concentration and ctru the truly dissolved concentration. The dissolved and colloidal concentrations of Al, Fe, Mn, Cu, Zn, Cd and Pb were examined over a year, and it was shown that the most important factor in the association of metals (Al, Fe, Mn, Cu, Zn and Pb) with colloids of 0:45 mm or less, was their affinity for binding to humic acids. Of the metals studied, lead (82%) and iron (78%) had the highest levels associated with colloids. Only with iron was the colloidal fraction correlated with pH [8] that could be related to the pH changes in the abundance of colloidal humic materials or the dissociation of iron complexes at lower pH values. What was less

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clear were the main considerations in the distribution of the metals in colloids and the larger particulate fraction, >0:45 mm. A detailed discussion of the association of lead with particles came to no firm conclusions, but there appeared to be seasonal factors in the magnitude of the distribution coefficients, perhaps related to the total suspended matter. 3.3 BIOACCUMULATION OF METALS AS COLLOID COMPLEXES AND FREE IONS – A KINETIC MODEL In a study of the bioaccumulation of metals as colloid complexes and free ions by the marine brown shrimp, Penaeus aztecus [29] the colloids were isolated and concentrated from water obtained from Dickinson Bayou, an inlet of Galveston Bay, Texas, using various filtration and ultrafiltration systems equipped with a spiral-wound 1 kDa cutoff cartridge. The total colloidal organic carbon in the concentrate was found to be 78  1 mg dm3 . The shrimps were exposed to metals (Mn, Fe, Co, Zn, Cd, Ag, Sn, Ba and Hg) as radiolabelled colloid complexes, and free-ionic radiotracers using ultrafiltered seawater without radiotracers as controls. The experiments were designed so that the animals were exposed to environmentally realistic metal and colloid concentrations. The data were analysed using a kinetic model, proposed by Farringdon and Westall [30]. The equation for metal uptake in shrimp is as follows: dcs ¼ k1 cw  k2 cs dt

(2)

where cw is the activity (Bq ml1 ) of the radiotracer in the treatment solution, and cs is the activity in shrimp tissues, and k1 and k2 are the rate constants for the uptake and clearance of the radiotracers in the animal. Then, at equilibrium: dcs ¼ k1 (cw (o)  cs )  k2 cs dt

(3)

¼ k1 cw (o)  (k1 þ k2 )cs

(4)

The rate equation is solved to give the uptake in the shrimp at time t: cs (t) ¼ cw (1)  Ksw (1  e(k1 þk2 )t )

(5)

where Ksw is a partition coefficient k1 =k2 at equilibrium (dc=dt ¼ 0) and cw (1) is the concentration in the water phase at equilibrium. The concentration factor (CF) at equilibrium can then be expressed as: CF ¼

Ksw cs (1) ¼ cw (1)  cp cp

(6)

368 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

where cp indicates the concentration of shrimp mass in the water (g ml1 ), and cw (1) and cs (1) are the activities associated with water and shrimp at equilibrium respectively. During the uptake phase, CF can be expressed using: CF ¼

Ksw cw (1)(1  exp [  (k1 þ k2 )t]) cw (o)  cw (1)(1  exp [  (k1 þ k2 )t])

(7)

where cw (o) is the initial concentration in the water and cw (1) ¼ cw (o)  cs . The results showed that the shrimp accumulated only low levels of Ba2þ , Zn2þ and Co2þ from colloid–metal complexes, and Sn2þ accumulated less from the colloid than from the free-ion experiment. However, most free-ion metals were not accumulated at significantly higher levels than the comparable colloidal forms (in one-tailed t-test, p > 0:05 using equal or unequal variances as appropriate). Tissue analyses showed that most of the metal which had been associated with the colloid was accumulated in the hepatopancreas, whereas most free-ion metals, except Mn and Ag, were found in the stomach. It appears that the shrimp is able to discriminate between colloidal and free-ion species, but the route of uptake for the colloidal metals is uncertain. It was considered that primary uptake was at the gills, but it was not clear whether the complex dissociated or was endocytosed in the hepatopancreas. Two other examples of the behaviour of chemicals in sediments and the effects on benthic organisms will be reviewed here to illustrate the complexity of these problems. The first deals with silver and the second with tributyltin (TBT). 3.4

BIOACCUMULATION OF SILVER

Although the abundance of silver in the Earth’s crust is comparatively low (0:07 mg g1 ), it is considered an environmental contaminant and is toxic at the nanomolar level. As an environmental pollutant it is derived from mining and smelting wastes and, because of its use in the electrical and photographic industries, there are considerable discharges into the aquatic environment. Consequently, there have been studies on the geochemistry and structure of silver–sulfur compounds [31]. Silver, either bound to large molecules or adsorbed on to particles, is found in the colloidal phase in freshwater. In anoxic sediments Ag(I) can bind to amorphous FeS, but dissolved silver compounds are not uncommon. A more detailed study of silver speciation in wastewater effluent, surface and pore waters concluded that 33–35% was colloidal and ca. 15–20% was in the dissolved phases [32]. Although much of the discharged silver will remain in the soil or waste water sludge at the discharge site, some will be transported in the aquatic phase as the free ion, or as colloidal suspended material. In freshwater it is found largely

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bound to sediment, but as the water enters estuarine sites and the marine environment, the speciation will change as the chloride ion levels increase, and silver will form chloro-complexes [33]. The toxicity of silver is largely related to the free-ion activity model. Although there appears to be no evidence for biomagnification, i.e. from food chains, in aquatic organisms, Luoma [24] believes that all studies of metal uptake should always be considered in terms of the appropriate food chain. An example of such a study showed that although algae accumulate considerable concentrations of metals, mainly by adsorption on to the cell surfaces, in the case of silver particles of colloidal size, the silver was not released even at pH 2.0 in the laboratory, and trophic transfer from the algae was considered unlikely in estuarine invertebrates [34]. Accumulation from the sediment by benthic organisms appears to depend on local speciation of the silver. It has been shown that in laboratory experiments with sediments amended with silver sulfide, Ag2 S, there was practically no silver accumulation in the oligochaete, Lumbriculus variegatus, and this was attributed to the low solubility of the silver sulfide [35]. In marine organisms, the bioconcentration factors for silver ranged from 8–65 for the deposit feeder, Macoma baltica, 40–180 for the filter feeder, Mytilus edulis, to 5000 for zooplankton, 24 000 in the tissue of the crustacean, Crangon crangon, and values up to 200 000 in marine algae. Although adsorption on to the cell surface is most important, especially with algae, many of the other organisms do ingest particles. Silver assimilation efficiency from food was lower in the mussel Mytilus edulis and oysters, Crassostrea virginica and Crassostrea gigas, where uptake was considered to be largely from the dissolved phase than in the clam, Macoma baltica. However, the mechanism of absorption, i.e. whether it is by extracellular digestion followed by absorption of the digested pollutant or by endocytosis of particulate matter, can only be deduced from the general basic zoology of the feeding and digestion of these organisms [36,37]. It is clear that in natural waters, ionic silver and some silver complexes were readily adsorbed on to particles with less than 25% as dissolved ions, complexes or colloids. It was also considered that the exposure route for particulate silver had not been fully explored [33]. An earlier study [38] of the adsorption of silver on to particles from intertidal sediment collected from San Francisco Bay, showed that removing bacteria, organic matter, iron and manganese oxides did affect the rate at which the silver was removed from solution, but not the total amount of silver adsorbed over 24 hours. Similar results were found with oxic sediments collected from 17 English estuaries [39]. The bioaccumulation of silver in three sediment-dwelling organisms consisting of the deposit-feeding clams, Macoma balthica, Scrobicularia plana and the polychaete, Nereis diversicolor was greater than other elements such as copper and mercury that were also present in the system. However, in

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considering the bioavailability of silver in marine environments, it is important to consider its speciation [33]. In the marine environment, silver can be present as Agþ , but also forms neutral and anionic chloro-complexes that are present in both the aqueous phase and adsorbed on to particles in the sediment. In these studies it was shown that Macoma balthica accumulated silver preferentially, but the only conclusion that could be drawn was that the bioavailability correlated with an easily extracted fraction of silver from the particles [39]. 3.5

BIOACCUMULATION OF TRIBUTYLTIN

Tributyltin (TBT), which was used in timber treatment, was introduced as an antifouling agent in the 1960s and 1970s, but, by the mid-1970s, there were already reports of its toxicity to invertebrates. One such form of this occurred in the female dogwhelk, Nucella lapillus, which grew a penis, a phenomenon known as imposex. The occurrence of this phenomenon led to population declines. There was also a near collapse of oyster mariculture on the French Atlantic coast. In early 1982, the link with tributyltin-containing antifouling paints led France to restrict their use to vessels greater than 25 metres long. Most countries had adopted these restrictions by 1989. This had the effect of reducing contamination, but the concentrations in seawater and sediment were still high enough to cause acute and chronic toxicity to aquatic benthic organisms. There is some evidence for the transfer from the sediment back into surface waters. A total ban of TBT use in 2003 and its presence on boats by 2008 has raised doubts concerning the toxicity of a proposed copper-containing triazine replacement [40], even suggesting that any ban on TBT is postponed until the safety of new compounds is assessed for their environmental impact. Much of the work on TBTs in the 1980s was reviewed in Volume 3 of this series [41], when the relationship between TBT concentrations in the clam Scrobicularia plana and TBT levels in estuarine sediments was already well established [42]. The nature of the adsorption and desorption of TBT in estuarine sediments was investigated by Langston and Pope [43], since reported partition coefficients, Kd , (the ratio of TBT between sediments and water) varied by several orders of magnitude. Partition coefficients were determined using various concentrations of TBT, different levels of suspended solids, a range of salinities and pHs, as well as sediments with a range of organic carbon contents. The sorption on to sediment was rapid with most of the TBT adsorbed on to sediment within 10 min and equilibrated in about 2 h. Plots of Kd versus concentration of TBT in water were not linear, as Kd values decreased with increasing concentration of contaminant as the proportion of TBT bound to particulates declined from 85% at low TBT values to 63.5% at high levels. The equilibrium concentrations of TBT ranged from 6.9 and 6377 ng Sn dm3 . However, a plot of Kd versus the log of the TBT concentration in water showed a linear relationship (r ¼ 0:962):

M. G. TAYLOR AND K. SIMKISS

Kd ¼ 4:6  104  (10:2  103 ( log [TBT]))

371

(8)

Interestingly, the data for all the sediments examined from estuarine and coastal waters fitted this equation. Although the concentration of TBT was always greater in sediments rather than the overlying water, there was less desorption at pH 6–7 and at low salinities, demonstrating that freshwater sediments retained higher levels of TBT. The organic component providing attachment sites for the hydrophobic regions of TBT was also an important factor. The results reflected the properties of TBT which has characteristics of both a hydrophobic organic species as well as that of a metal. It has been suggested that the plasma membrane may be the site of toxicity of TBT as might be expected from an organometallic compound [44], but there is no doubt that many benthic invertebrates accumulate TBT from the sediment, although the precise route of uptake remains unclear.

4

MEMBRANE TRANSPORT PROCESSES

The most important and universal characteristic of the cell is its ability to manipulate the location of ions and molecules. It achieves this by exploiting their hydrophilic and hydrophobic properties so as to compartmentalise them for different functions within a variety of cell membranes. This phenomenon is clearly seen with the plasma membrane – a lipid bilayer that is virtually impermeable to hydrated molecules. The influx and efflux of ions and small metabolites across this membrane occurs through aqueous pores in protein molecules that act as selective channels, pumps or transporters. The chemical specificity of these transport systems appears to depend upon the dimensions of the narrowest region (the selectivity filter), the possibility of interactions between ions during multi-occupancy of the channel, the size of the hydrated/dehydrated ions and the relative attraction of the transported molecules to the channel walls [45]. Some pollutant ions may enter the cell through an inappropriate channel (e.g. Cd through a Ca channel), but these are infrequent and typically dealt with inside the cell by binding to specific proteins (such as metallothioneins) and subsequent detoxification. Lipophilic molecules are more difficult for the cell to regulate as they cross the plasma membrane by the relatively indiscriminate process of partitioning from the environment into the lipid bilayer. There are, however, a number of metabolic pathways that introduce hydrophilic groups into such molecules and then conjugate them to polar compounds that facilitate their excretion. There is also considerable interest in multidrug resistance transporters or P-glycoproteins that reside in the membrane itself and which actively transport lipophilic molecules out of the cell or out of the membrane itself into the extracellular fluids [46,47]. By these means, the cell is able to regulate the influx and efflux of materials from the

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extracellular environment. The mechanisms involved in membrane transport processes have been extensively studied over the past 50 years, and the theoretical basis of transport by channel proteins and lipid partitioning is well established [48,49]. Physiologists have variously attempted to distinguish between the different types of carriers and pore systems, according to the accessibility of their binding sites, their saturation kinetics or their stoichiometric coupling properties, but none of these criteria can be used to satisfy a clear distinction. There is, in addition, a third mechanism by which materials may enter the cell. This is called endocytosis.

5 5.1

ENDOCYTOSIS INTRODUCTION

Endocytosis is a process whereby portions of the external surface membrane of a cell can invaginate and pinch off to form membrane-bound vesicles that pass into the interior of the cell. Dynamin, a large GTPase, is believed to have a role in the scission of the vesicle in clathrin-mediated endocytosis, but the exact process remains unclear. However, the effects of point mutations in the GTPase and GTPase effector domains (GED) have recently been analysed [50]. The mutants were used in an in vivo assay involving COS fibroblast cells, and it was found that none of the GED mutants had a significant inhibitory effect on the endocytosis of transferrin, although it was still considered that GED may have a role in the oligomerisation of dynamin. GTPase activity was also measured, and a kinetic analysis showed that the GED mutants had similar kcat (turnover rate) and Km (binding affinity) values to the wild type 3.1  0.5 s and 7:8  2:5 mmol dm3 respectively [50]. Most of the GTPase mutants had similar or higher Km values, but these were not supported by similar activities in the hydrolysis of GTP. It was concluded that dynamin oligomerisation and GTP binding alone did not facilitate endocytosis, but GTPase hydrolysis in combination with an associated conformational change are also part of the process involved in vesicle scission. Dynamin also appears to have a role in phagocytosis in macrophages, in the formation of phagosomes at the stage of membrane extension around the particle [51]. These vesicles may enclose substances present in the external medium or molecules previously adsorbed on to the cell’s surface. The significance of this route was generally underestimated, until it became clear that it is part of an extensive system of intracellular vesicles that are involved in an elaborate signalling network associated with the recycling of membrane components. Its involvement in the uptake of xenobiotic molecules is still poorly appreciated, largely because in the human its activities are restricted to only a few cell types. In many organisms, however, it is the dominant route for the

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uptake of molecules. As with other transport systems it is often extremely difficult to distinguish experimentally between the endocytotic pathway and other cellular routes. Thus, the enhanced uptake of contaminants in the presence of particulate sources may be due to endocytosis, but it might equally well be due to the ingestion of such particles with extracellular digestive processes releasing adsorbed contaminants. There are two types of endocytosis largely distinguished by the size of the endocytosed vesicle. Phagocytosis (cellular eating), which is an actin-mediated process, involves the ingestion of large particles ranging from insoluble particles and cell debris to microorganisms. These particles are usually >250 nm diameter, and they become enclosed in vesicles termed phagosomes, which often occur in only a small number of specialised cells. In contrast, pinocytosis (cellular drinking) occurs in most eukaryotic cells, and involves the ingestion of fluids and solutes and colloids via small vesicles >150 nm in diameter. A specialised form of pinocytosis is receptor-mediated endocytosis (RME). A specific receptor on the cell surface binds to a recognised ligand, and the receptor ligand complex is endocytosed into the cell. Ligands include molecules such as low-density lipoproteins, hormones and the iron-binding protein transferrin, which is a particularly interesting example, in that it is believed to be able to bind and transport other metals and is discussed in Section 5.6. 5.2

ENDOCYTOTIC PATHWAYS

Materials that have been endocytosed are delivered to lysosomes by multiple pathways for further processing and the release of nutrients and trace metals for cellular biosyntheses or exocytosis. These pathways are illustrated schematically in Figure 4. The pathway taken by the endocytosed matter appears to be regulated in the endosomes: the organelles referred to as sorting stations [52]. There are four classes of these organelles: early endosomes, late endosomes, recycling vesicles and lysosomes. The pH of early endosomes is 6.3–5.8, only slightly acid but adequate for the initial dissociation of receptor–ligand complexes and their recycling back to the cell surface. It has been proposed that endocytosed calcium has a role in the acidification process [53]. As the pH decreases, there is a concomitant release of calcium from the endosome. It is suggested that acidification can only occur when there is an initially high Ca2þ concentration in the endosome. One suggested role for the calcium is to maintain charge balance following the influx of protons via a Hþ the influx of protons Hþ pump by the efflux of Ca2þ ions. Another possibility is that the Ca2þ enables other channels such as Kþ and Cl to remain open to allow for charge compensation. The more acidic late endosomes (pH ca. 5.5 or less) are sometimes referred to as pre-lysosomes. Digestion of the food material or other macromolecules

374 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES R C

E

P

CP

CV E

H+

L

Ex

Figure 4. A schematic of endocytotic pathways in a cell. P ¼ pinocytosis; Ex ¼ Exocytosis; R ¼ receptor; C ¼ clathrin; CP, CV ¼ coated pit and coated vesicle; E ¼ endosome; L ¼ lysosome. Open arrow indicates recycling of clathrin and receptors. Solid arrows indicate pathways. See the text for discussion

occurs in the lysosome with hydrolytic enzymes, in an acidic environment which may have a pH as low as 4.6 in many cells. The exact sequence of transport and hydrolytic activity is still the subject of research, but involves a series of progressively more hostile environments. Many of the investigations into endosomal pathways have concentrated on receptor-mediated endocytosis, as in the iron–transferrin–receptor complex, and it is not clear how the systems vary depending on whether or not the pathway is clathrin-dependent or clathrin-independent [54]. Most of the work on endosomes has involved mammalian systems, but studies on the ciliate, Paramecium multimicronucleatum [55] have shown the presence of parasomal sacs with a cytosolic coat resembling clathrin, as in the coated pits of mammalian cells. It is not clear if these structures are functionally similar, but a typical Paramecium will have up to 8500 coated pits on its surface, with a coating which was morphologically identical to the triskelions seen in the clathrin cages of higher organisms. These appeared to be lost quite quickly. As in mammalian cells the early endosomes appeared to have a sorting role, but differed from mammalian cells in some respects. A dual labelling experiment revealed two populations. One, a pre-endosomal vesicle (188  41 nm diameter) contained both the marker, horseradish peroxidase (HRP) and the goldlabelled antibody to a component of the plasma membrane, whilst the second appeared to be an early endosome-derived vesicle (90  17 nm diameter). These vesicles were formed from coated evaginations on the early endosome, and retained only the HRP marker. These vesicles were also located deeper in the

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cytoplasm. This system was quite different from the feeding phagosome/lysosome pathway. 5.3

PHAGOCYTOSIS

Phagocytosis is common in eukaryotes. It is the basic means by which many organisms obtain their food especially for single-celled organisms such as protozoa and slime moulds. In higher eukaryotes, phagocytosis is an important process in the response to foreign matter in specialised cells such as circulating monocytes and neutrophils, as well as tissue-associated macrophages and some epithelial cells. Phagocytosis is an important mechanism for the organism to rid itself of bacteria and pathogenic material, as well as cell debris and remnants of apoptosis. However, it can also provide a route for the uptake of pollutant particulate material. It is seen to be especially important in the incorporation of airborne particulate material, which often has serious health consequences (see Section 6.4). In terrestrial invertebrates, food is obtained either from particulate matter in the soil or from molecules dissolved in interstitial water. Most of these organisms have extracellular digestion, with nutrients and foreign material being absorbed by one or more of the routes available for transport across membranes, such as diffusion, channels or pinocytosis. There have been few studies to establish which route is taken. The phagocytic process is initiated by the interaction of specialised plasma membrane receptors with specific ligands, localised on the surface of the particles. Contact of a phagocyte with a suitable particle causes a local accumulation of actin-rich cortical material at that site. The ligand–receptor complex triggers the local reorganisation of the submembranous actin-based cytoskeleton that mediates the engulfment of particles. The actin filaments form part of the pseudopodia, which can then surround and engulf the particle, which is then digested in a lysosome. The scission of the particle is mediated by the dynamin family of GTPases [51]. Physical contact with the particle surface is necessary but not sufficient on its own to trigger phagocytosis, because some form of recognition is necessary, as, for example, in antibodies binding to the Fc receptors on a macrophage. Some form of chemical identification is, therefore, important as a particle approaches a cell, is recognised, adheres to the cell, is engulfed and then digested in a phagosome (see also Chapter 2 in this volume). Many of the receptors that are involved recognise the surface components of microorganisms or identify the opsonin molecules that coat foreign particles. Nonspecific coatings include polysaccharides such as lectins, while the more specific opsonins include IgA and IgG antibodies and complement fragments C3b and C3a, and, in addition, the complement receptor C3 (CR3) of the integrin superfamily. Phagocytotic-competent receptors for fibronectin and vitronectin also belong to the integrin superfamily.

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The first event following the binding of a particle to the cell surface is the clustering of the receptors, which are the trigger for the activation of several cellular proteins, including the receptors and the submembranous cytoskeleton. Actin-driven engulfment requires the progressive recruitment of receptors that work in a zipper-like manner linking the ligands on the surface of the particles. The outcome is that the actin microfilaments are polymerised, filling the pseudopods of the phagocytic cups that embrace the particle. Subsequently, the actin depolymerises and allows fusion of the phagosome with an endosome [56]. The pathways of phagocytic signal transduction remain at present unknown, due to their complexity. There have been several studies to determine which surface properties on unopsonised particles are important in their uptake by phagocytic cells. The driving force has often been related to the use of liposomes as carriers of drugs and other macromolecules, but may also be important for the removal of particles in body fluids. The two steps of the phagocytosis, binding to the surface of the phagocyte and subsequent internalisation of the particle, have been subject of binding and kinetic studies. In order to study which properties of the membrane were important in the interaction with endocytic cells, liposomes are prepared to ensure that they are of colloidal size, diameter range 80–110 nm. In particular, the lipid composition of the surrounding membrane has been investigated [57]. Studies appear to indicate that negatively charged groups, such as phosphatidyl serine (PS) and phosphatidyl glycerol, are more effective than neutral lipids, such as phosphatidyl choline (PC), in increasing the binding of the colloidal particle to the cell membrane and the subsequent endocytosis. However, the net negative charge was not the sole determinant in its binding to the cell surface, as the uptake also depended on the nature of the head group. Nevertheless, a higher overall charge density appears to promote uptake in some cells [57]. In a murine macrophagelike cell line J774, preliminary studies indicated that the rate of endocytosis after binding is faster than the actual rate of binding. It is suggested that the number of bound liposomes may be controlling the overall uptake. In a more detailed study [58] it was found that there were 6.9 times more negatively charged than neutral liposomes, associated with 106 J774 cells at 37 8C. Binding studies at 37 8C were conducted using inhibitors of endocytosis. Affinity constants defined as, K ¼ kN, where K is the product of k representing the binding affinity for a liposome and a binding site, and N the number of binding sites in a cell, were determined. Scatchard plots were linear over a 1 limited range of lipids. The affinity constant, K
1012 dm3 mol and number of binding sites, 3000 for the negatively charged PS/PC/Chol liposomes, were an order of magnitude greater than for the neutral PC/Chol liposomes. It was found that at steady state the number of liposomes on the cell surface at 37 8C was similar to the values at 4 8C or 37 8C without endocytosis. This implies that, following endocytosis, the binding sites are rapidly recycled back the cell surface, so leaving the number of binding sites relatively constant.

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A more recent study of the binding of multilamellar colloids to macrophages (J774 cells) has shown that cationic colloids bind to the cell surface more efficiently than neutral ones [59] but are not endocytosed. Biocompatible particles were synthesised with a mean size of 200–300 nm, to allow endocytosis. Particles were labelled with 2  103 mol dm3 calcein for analysis by fluorescence microscopy. After exposure of the cells to the particles, the fluorescence images indicated that the cationic colloids were strongly adsorbed on to the surface of the macrophage, and analysis of the adsorption curve suggested a Langmuir isotherm, which assumes one class of adsorption sites. Kinetic studies were attempted at 4, 15, 25 and 37 8C, but the colloids tended to aggregate at all temperatures above 4 8C. Four models were used to determine the binding mechanisms from the kinetic data. A detailed analysis of binding at 4 8C, was made. Models were set up involving one or two surface sites which also satisfied the overall kinetics but the analyses were not definitive. Although it was demonstrated that the cells were capable of endocytosis of fluorescence-conjugated transferrin, there was no evidence for the endocytosis of the cationic colloids. 5.4

PINOCYTOSIS

Pinocytosis is a process whereby external fluids can be taken into a cell. This process could, therefore, facilitate the uptake of contaminated material that had been digested extracellularly to give soluble pollutants. Pinocytosis is a constitutive process that occurs continuously. However, it is generally not a saturable process that limits the intake of material, since any membrane material that is removed by endocytosis is matched by an exocytotic process returning material to the membrane surface. There are two proposed pathways for pinocytosis. The first is a clathrin-dependent pathway producing micropinosomes, while the second is an actin-dependent process producing macropinosomes. In a review, [54] devoted largely to the clathrin-independent pathway, it was considered that pinocytosis in many mammalian cells occurred by both clathrin-dependent and clathrin-independent mechanisms. Examples of clathrin-independent pinocytosis were given for kidney intercalated cells, cultured fibroblasts and cultured hepatocytes. In many amoebae, nonselective pinocytosis appeared to be the dominant mode of endocytosis [54]. Although the process has been studied most in single-celled organisms such as Dictyostelium, there is some evidence that, for example, fibroblasts have similar mechanisms for macropinocytosis [60]. However, in a study of the uptake of 10 nm gold-labelled asialorosomucoid and 5 nm gold-labelled bovine serum albumin into rat hepatocytes, electron microscopy revealed that the uptake of asialorosomucoid was clathrin dependent (i.e. into small clathrin-coated vesicles), whilst the uptake of bovine serum albumin was a clathrin-independent process [61].

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There have been many studies designed to establish whether the endosomal pathway to lysosomes, and the recycling of receptors is the same with clathrindependent and clathrin-independent pinocytosis. The pathway appears to be determined in the endosome, with perhaps the lysosome being the default pathway [54]. During this sorting process, some endosomes are transported to the Golgi apparatus and become associated with secretory vesicles. 5.5

CAVEOLAE

An interesting feature of many cells is the permanent presence on the plasma membrane of flask-shaped regions termed caveolae. They are abundant in certain capillary endothelial cells, and appear to have a role in cholesterol binding, although many other functions have been suggested [62]. 5.6

RECEPTOR-MEDIATED ENDOCYTOSIS

Receptor-mediated endocytosis (RME) is a specialised form of pinocytosis related to the particular needs of cells. The receptor–ligand complexes form at clathrin-coated pits at the plasma membrane. These are pinched off to form clathrin-coated vesicles. The clathrin coat is lost quite rapidly and allows fusion with early endosomes. Clathrin-coated pits are on the cytosolic face of the plasma membrane and are in specialised regions occupying up to about 2% of the total plasma membrane area of cells such as hepatocytes and fibroblasts. The clathrin structure consists of triskelions which facilitate the curvature of the membrane to form the pits. Many internalised ligands have been observed in clathrin-coated pits and vesicles, and it is believed by many that these structures function as intermediates in the endocytosis of many ligands bound to cellsurface receptors. Some receptors are clustered over clathrin-coated pits even in the absence of ligands. Other receptors diffuse freely in the plane of the plasma membrane, but undergo a conformational change when binding to the ligand, so that when the receptor–ligand complex diffuses into the pit it is retained there. More than one complex can be seen in the same coated pit or vesicle. The removal of clathrin can facilitate the recycling of the membrane receptors. Some receptors can make the round trip in and out of the cell every 20 min, making several hundred journeys without being denatured. Others make only two or three before the receptor and ligand are degraded in the lysosome, thus restricting the number of receptors on the cell surface. Thus, a crucial factor in endocytosis involves the recycling of cell-surface receptors and membranes, as well as the maintenance of cell polarity. This receptor-mediated endocytotic pathway has been especially well studied in the uptake of iron from blood plasma. Iron, because of its very low-solubility product (< 1017 at pH 7.4), is transported in plasma bound to the iron-binding protein transferrin. Two Fe3þ ions bind to each transferrin molecule. Entry into

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mammalian cells occurs by receptor-mediated endocytosis, whereby the iron transferrin binds to a receptor, forming an iron–transferrin–receptor complex in a clathrin-coated pit. Fusion with a primary endosome allows the recycling of the transferrin–membrane receptor and the clathrin associated with the coated pit. This is accomplished by a reduction of pH in the endosome. The transfer of iron to the cytosol also requires the activity of a ferrireductase (not yet identified in mammalian cells) as well as a Fe2þ transporter, since the iron in the cytosol exists primarily as Fe2þ . However, the receptor-mediated endocytosis of iron–transferrin studies [63] does not explain the initial uptake of iron from nutrients in the intestinal (villus) cells, since apotransferrin is generally not available in the lumen, except in a limited amount from biliary excretion. Work on other iron transport mechanisms has mainly been reported in the last five years. One development has been the cloning and characterisation of a protoncoupled metal ion transporter in the rat DCT1 [64]. The divalent cation/metal ion transporter (DCT1) was found to transport not only Fe2þ , but also Zn2þ , Mn2þ , Cu2þ , Co2þ , Cd2þ and Pb2þ . DCT1 operates in the acidic environment found in the proximal duodenum and is similar to that found in transferrin receptor mediated endosomes. DCT1 was found to have considerable homology with the Nramp proteins. Nramp1 is a macrophage protein involved with resistance to infectious diseases. However, Nramp2 has a broader spectrum of activity, and has a key role in the metabolism of transferrin-bound iron by transporting free Fe2þ from the endosome to the cytoplasm. Nramp2 has been observed in recycling endosomes and also in the plasma membrane by immunofluorescence and confocal microscopy [65]. It appears that DCT1 is the rat homologue of Nramp2 that was determined in the mouse and human. The conclusion is that although the initial uptake of iron and other metals takes place by a transferrin-independent process (as described above), on crossing the basolateral membrane, the metals (Zn2þ , Mn2þ , Cu2þ , Cd2þ and Pb2þ ) have a similar affinity for transferrin as Fe2þ and are circulated in the serum as metal transferrin complexes. This suggests that the receptor-mediated endocytotic pathway of iron for cellular uptake may be available for other metals. For example, it has been shown that 80–90% of aluminium in blood plasma is present as the aluminium transferrin complex, which can cross the blood brain by receptor-mediated endocytosis [66]. 6 EVIDENCE FOR THE ENDOCYTOTIC UPTAKE OF CONTAMINANTS 6.1

INTRODUCTION

Most amoeboid protozoa assimilate particles by invagination of the plasma membrane in an actin-based phagocytotic process and digest them in food

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vacuoles. Freshwater ciliates are suspension feeders ingesting organic matter and bacteria, but, because of the presence of a pellicle, the plasma membrane has a fixed area. It is, therefore, a good example where the membrane materials have to be continually recycled from used food vacuoles to be incorporated into the cytopharyngeal membrane and form a new food vacuole [67]. In sponges, digestion is exclusively intracellular, and this is also the dominant system in the cnidaria (jellyfish and corals) and triclad turbellaria (flatworms). It is well developed in molluscs, especially in lamellibranchs (bivalve clams), cephalopoda and gastropods (snails), as well as echinoderms (starfish and sea urchins). Digestion is predominantly extracellular in annelids (worms), crustacea (crabs and shrimps) and chordates (vertebrates). Intracellular digestion clearly depends upon the food material being broken down into particles that are smaller than the enveloping cell. This implies that such organisms feed on small particles or possess some way of disrupting larger particles by physical attrition or extracellular digestion. In a review of the feeding and digestion in the Bivalvia, Owen [37] has described the feeding mechanisms of each lineage of bivalves. There is a formal distinction between deposit and suspension feeders, but many deposit feeders, such as some species of Macoma and Scrobicularia plana, supplement their food intake by filtering suspended matter. The contents of the guts of these animals include algal material, organic detritus and particulate mineral material. Although digestion may be largely extracellular, there is a considerable body of evidence for the role of the midgut or digestive diverticula in intracellular digestion (Figure 5). Much of the evidence for endocytosis and lysosomal digestion in these bivalves derives from Owen’s ultrastructural work [69,70]. From these studies, he was able to identify the digestive cells of the digestive tubules from experiments involving feeding iron oxide and carbon particles. Phagosomes have not been observed in cells from all species, but it is likely that ingested particulate matter in bivalves is at least partially endocytosed and digested intracellularly. Engulfing and ingesting foreign particles is clearly an important form of nutrition, but the process has the advantage of also being able to remove particulates and destroy potential pathogens. It is in this context that the process persists in the vertebrates, where macrophages in the lungs remove particulates and a variety of cells endocytose invading bacteria. Given this diversity of examples, what evidence is required to assess the significance of endocytosis in the uptake of contaminants via colloids and particles? One consequence of the uptake of some contaminants is a reduction in the ability of lysosomes to retain the dye Neutral Red. As a consequence, the Neutral Red retention time has been developed as an index of lysosomal membrane fragility and thus of toxicity. The test has been used on the digestive cells involved with intracellular digestion of endocytosed food following administration of organic contaminants, such as polycyclic aromatic hydrocarbons [71]. The phenomenon has been reported many times after exposure to

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[Image not available in this electronic edition.]

Figure 5. Digestion strategies in molluscs. Modified from [68]: Decho, A. W. and Luoma, S. N. (1996) ‘Flexible digestion strategies and trace metal assimilation in marine bivalves’ in Limnol. Oceanogr., 41, 568–572. Reproduced with permission

xenobiotics and other contaminants, and has recently been suggested as a biomarker for exposure of earthworms to zinc and copper in the soil [72,73]. The cause of the increase in lysosomal fragility is not well understood, and the link with endocytosis is not rigorously established, as the contaminants often appear to inhibit phagocytosis in haemocytes in Mytilus edulis [74]. It has been suggested that the leakage of Neutral Red may be as a result of some impairment of the membrane proton pump in haemolymph cells of the freshwater snail Viviparus contectus after exposure to copper [75]. There have been many studies on the role of haemocytes in invertebrates, but their role in ingested material is not clear. Haemocytes are the molluscan analogue of the vertebrate macrophage. They are present in the haemolymph and appear to be able to migrate through epithelia, and they are found in the mantle fluid of bivalves and appear to be involved in the uptake of particulate matter. In a study of the clam Tridacna maxima that had been injected intramuscularly with a suspension of carbon particles, it was found that within 24 h the extracted haemocytes were laden with the particles. They had cleared the haemolymph of the particles within 48 h [76]. In the tridacnidae some zooxanthellae are

382 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES Table 2.

Experimental approaches demonstrating endocytosis of contaminants

Protozoa (1) Endocytosis of particulate material by Tetrahymena increases growth rate from dissolved nutrients by seven to eight fold [78]. (2) Lead precipitates ingested by Tetrahymena [79]. (3) Lead material tracks through digestive vacuoles and enters cytoplasm of Tetrahymena [79,80]. (4) Tetrahymena mutants lacking functional phagocytosis require high levels of iron and copper supplements [81]. Table 3.

Experimental approaches demonstrating endocytosis of contaminants

Metazoa (1) Physiological studies of digestion in marine bivalves show that it progresses via two separate routes: a rapid intestinal system using extracellular processes, and a slower system involving the digestive gland and endocytosis [82]. (2) The use of pulse-chase methods identifies differences in the timing and efficiency of absorption between the two pathways, enabling the study of uptake in the endocytosis system [83]. (3) Ultrastructural and radioisotope studies on the phagocytosis of particles by gills [84] or lungs [85] demonstrate the endocytosis of particles by mobile macrophages, and their subsequent lysosomal attack.

endocytosed and digested within the lysosomes of amoebocytes that occur in the circulation or intertubular spaces of the diverticula [77]. Table 2 gives some of the experimental approaches demonstrating endocytosis of contaminants in Protozoa, and Table 3 summarises the experimental approaches for Metazoa. 6.2

ENDOCYTOSIS BY AQUATIC INVERTEBRATES

There is considerable evidence that organisms ingest colloidal and particulate material, notably in suspension and deposit feeders. However, there have been few definitive studies demonstrating that these materials might be taken into the cell by endocytotic processes, especially for benthic organisms in sediments. Frequently, the evidence presented is circumstantial, except perhaps in the case of single-celled organisms. An attempt has been made to produce a mathematical model based on the rate constants of the processes involved in the fate of endocytosed material from uptake to the fusion with the endosome and the subsequent degradation in lysosomes [86], but there are few examples of its use. In a review of feeding and digestion in the Bivalvia [37], it was proposed that the accumulation of metal-bound particulates in the digestive gland was a twophase process reflecting extracellular and intracellular digestion, and Viarengo [87] has reached similar conclusions. In a pulse chase study of the uptake of radiolabelled metals (Ag, Cd, Cr, Hg, Se) by the zebra mussel Dreissena

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polymorpha, the egestion rate was determined by counting the radioactivity in faecal pellets. After an initial egestion of Cd and Cr, a second egestion pulse was found for Ag, Se and Hg, and it was concluded that this was indicative of intracellular digestion [88]. Earlier it was shown that a two-phase digestion system operated in both the deposit-feeding Macoma balthica and the suspension-feeding clam Potamocorbula amurensis. In an experiment investigating the uptake of Cr(III), it was found that no Cr(III) was taken up during the rapid intestinal pathway involving extracellular digestion, but it was taken up in the slower digestive gland pathway requiring intracellular digestion [68]. The time courses for the retention of 51 Cr-labelled beads in bivalves are shown in Figure 6. Following Owen’s work [37] it is presumed that the uptake of the particulate material was by endocytosis. In their early work on the uptake of insoluble iron particles by Mytilus edulis, George et al. [84] suggested that the gill and mantle cells may be important sites of phagocytosis, since the material could easily be seen on electron micrographs. The role of endocytosis in the accumulation of particle-bound metals is considered to be especially important in lamellibranch molluscs, and metal deposits are frequently observed in residual bodies of these cells. X-ray micro analyses of electron micrographs of the amoebocytes, harvested from the mantle fluid of the oyster Ostrea edulis, frequently identify copper associated with sulfur, and zinc associated with phosphate, in distinct inclusion bodies [90]. This suggests that these metals may have been endocytosed, since amoebocytes are phagocytic cells. 6.2.1

Assimilation Efficiency Models

Various attempts have been made to rationalise the terminology used to define the response of aquatic invertebrates to chemical contaminants. Thus, terms Intestinal faeces

Glandular faeces

Lag period

0

Ingestion

25

50

Time/h

Figure 6. Time courses in the retention of 51 Cr beads in the bivalves, Potamocorbula amurensis and Macoma balthica. During the lag period there was no significant release. Modified from [89]

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such as concentration factors, bioaccumulation and assimilation efficiency (AE) have been used in an attempt to overcome some of the difficulties associated with the term ‘bioavailability’. These concepts have been critically reviewed by Fisher and Reinfelder [91]. AE is essentially a ratio of the element of interest retained in the organism compared with the original uptake. In demisponges, where digestion is largely by amoebocytes, it is sometimes referred to as retention efficiency when applied to the food particles, such as bacteria, diatoms or detritus: retention efficiency ¼ (ambient  exhalant)  100=ambient

(9)

where ambient represents the concentration of particles near the inhalant surfaces and exhalant refers to the concentration of particles from the oscular stream of the sponge [92]. More commonly, AE is defined as the ratio: AE ¼ (ingestion  excretion  egestion)=ingestion

(10)

Initially, it was calculated from mass-balance data measuring ingestion, excretion and egestion. Excretion data were determined by analysis of the depuration water. The inherent experimental difficulties in collecting faecal pellets for egestion measurements from aquatic organisms has led to a pulse-chase radiotracer feeding technique. Animals are fed for a time shorter than their gut passage time with radiolabelled isotopes, and so the amount ingested can be quantified. This is followed by a depuration stage, when the animal is given unlabelled food until the egestion period is past the gut evacuation time. In a study of the uptake of selenium by Macoma balthica, faecal pellets and water from the depuration stages were counted, and the data from the two methods confirmed to within 10% [93]. The bioavailability of selenium to a benthic deposit-feeding bivalve, Macoma balthica from particulate and dissolved phases was determined from AE data. The selenium concentration in the animals collected from San Francisco Bay was very close to that predicted by a model based on the laboratory AE studies of radiolabelled selenium from both particulate and solute sources. Uptake was found to be largely derived from particulate material [93]. The selenium occurs as selenite in the dissolved phase, and is taken up linearly with concentration. However, the particle-associated selenium as organoselenium and even elemental selenium is accumulated at much higher levels. The efficiency of uptake from the sediment of particulate radiolabelled selenium was 22%. This contrasts with an absorption efficiency of ca. 86% of organoselenium when this was fed as diatoms – the major food source of the clam. The experiments demonstrated the importance of particles in the uptake of pollutants and their transfer through the food web to molluscs, but the mode of assimilation was not discussed.

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The AE methods have been used to determine the effects of different algae as food sources in the bioaccumulation of radiolabelled essential (Co, Se, Zn) and nonessential trace metals (Ag, Am, Cd, Cr) in the mussel Mytilus edulis [94]. Assimilation of essential metals was correlated with carbon assimilation, but not nonessential metals. The distribution of the metal in the alga and the gut passage time in the mussel was found to be important. An interesting outcome of the observed depuration patterns was that there could be a two- or three-phase process. This were interpreted as indicative of extracellular followed by intracellular digestion [95]. A possible third phase might be due to metabolic loss of metals. Several models have been developed for a kinetic approach to bioaccumulation that would model the trophic transfer of contaminant in animals from ingested food. A first-order kinetic model has been proposed, which considers uptake from both dissolved and particulate phases [95]. A particular application of that model is to separate the pathways for metal uptake in marine suspension and deposit feeders since: dcA ¼ ðku cw Þ þ ðAE  IR  cf Þ  ðke þ gÞcA dt

(11)

where cA is the chemical concentration in the animals (mg g1 ), t is the time 3 of exposure (d), ku is the uptake rate constant from the dissolved phase
dm 1 1 3 g d Þ, cw is the chemical composition in the dissolved phase mg dm , AE is the chemical assimilation efficiency from ingested particles, IR is the ingestion
rate of the animal
mg g1 d1 , cf is the chemical concentration in ingested particles mg mg1 , ke is the efflux rate constant (per day) and g is the growth rate constant (per day). As the body size of the organism increases, the new tissue mass dilutes the toxicant. Without the growth-rate constant, the derived elimination rate overestimates the actual elimination, as it incorporates both ke and g in the growing organism [96]. By using steady-state conditions, it is possible to calculate and separate the concentration in the animal of the contaminant derived from the dissolved and particulate phase, and so estimate the fraction coming from each source: ðku cw Þ ðkew þ gÞ

(12)

ðAE  IR  cf Þ ðkef þ gÞ

(13)

cw, ss ¼ cf , ss ¼

cw, ss and cf , ss (in mg g1 ) are the chemical concentrations in organisms from the water and from food, and kew and kef are the corresponding efflux rates. A further step is to determine the assimilation efficiency from metals in particles digested extracellularly and intracellularly. This is derived from the

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metal depuration rate. For example, in studies with bivalves it was found that there were three different losses with respect to time. Firstly, a rapid loss representing passage through the gut and including extracellular digestion; secondly, a slower loss attributed to intracellular digestion following phagocytosis of fine particles; and thirdly, a loss that could be attributed to the physiological turnover of assimilated metals. The assimilation efficiencies of cadmium, chromium and zinc have been investigated in the green mussel Perna viridis and the clam Ruditapes philippinarum when fed with one of five species of phytoplankton or seston [97]. The five different phytoplankton and seston (particle size 363 mm) were kept in 0:22 mm filtered seawater enriched with nutrients, to which had been added radiolabelled 109 Cd, 51 Cr and 65 Zn for four to seven generations before being harvested, washed in filtered seawater and fed to the bivalves for 30 min in pulse-chase experiments. The bivalves were depurated for three days, during which time individual specimens were counted for radiolabel. Faeces were collected every 1 to 5 h during depuration, and the metal gut passage time calculated. An estimate of the cytoplasmic metal content of the phytoplankton was determined after removal of surface-adsorbed metal by EDTA. The AEs for each metal for each feeding strategy were calculated. They were consistently lower for the seston source. The AE was higher for the clam than the mussel for Cd and Zn. Chromium was the least assimilated metal, but the AEs were comparable for both species and seemed to be related to the gut passage time. Egestion of each metal was determined in relation to the production of faeces, and appeared to be complete within 60 h. See also Figure 6. A biphasic pattern of egestion was found, corresponding firstly with the rate of extracellular (faster) digestion, and secondly, to intracellular (slower) digestion. It was suggested that fine particles resulting from extracellular digestion were then phagocytosed by the digestive cells. Both phases were present for cadmium, but no second phase was detected for chromium and zinc. This did not necessarily imply that there was no intracellular digestion in the latter case, but that the absorption of the metal was very efficient, with little loss to the faeces. These models suggest new ways of assessing environmental impact, and they may assist our understanding of how endocytosis of particles can influence the uptake of metals. 6.2.2

Further Bioaccumulation Studies

Other examples of work that have attempted to address the role of endocytosis of particulate matter in the uptake of contaminants from the environment include the assimilation of 210 polonium. This is the final a-emitting daughter nuclide in the natural decay of 238 uranium, and marine organisms are believed to be the major source of 210 Po in 70% of the Portuguese human population [98]. In this work, Mytilus edulis were fed the alga, Isochrysis galbana, labelled

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with 210 Po, for 18 h, and were then fed unlabelled algae for up to 20 days. The mussels were sampled at intervals, and the tissues, digestive gland, mantle/gill, foot and remainder of the soft tissue counted for 210 Po. There was a triphasic loss of labelled polonium from the mussel soft tissue, with the first occurring on day 1, a second, slower loss occurring between days 5 and 7 days, and an even slower loss ultimately attaining control levels at 20 days. The experiment was interpreted as showing rapid extracellular digestion involving little absorption, followed by slower intracellular digestion with a higher rate of absorption. In a study of the importance of the sediment in the uptake of TBT, Langston and Burt [42] exposed the bivalve Scrobicularia plana for a month to 14 Clabelled TBT in water or water plus sediment. The distribution coefficient for the partitioning of the TBT between sediment and water was determined giving values of KD between 104 and 2  104 depending on the acidity of the water – the lower values occurring at pH < 6 [43]. Uptake into the bivalve in the presence of sediment accounted for more than 90% of body burden compared with water uptake of less than 10% [99]. These results demonstrate how sediment materials can enhance the bioaccumulation of pollutants into organisms. It would appear that the TBT is carried into the bivalve as particles that release the contaminant after being endocytosed. There is, however, no direct evidence for this interpretation, and an alternative explanation would be that digestion in the alimentary tract released the TBT and that a low intestinal pH facilitated its uptake. In an attempt to establish unequivocally that bivalves could endocytose particles and release adsorbed contaminants, ion-exchange resins and the mineral hydroxyapatite were used as particles that could be dosed with radioisotopes and fed to the suspension feeder, Mytilus edulis. The adsorption of cadmium and zinc ions on to the particles were fitted to a Langmuir adsorption isotherm, and parameters indicating the coverage of the particles and the adsorption constants were calculated [100]. The particles were then suspended in aerated artificial seawater and introduced to the mussel, Mytilus edulis for two hours and washed for 30 min in clean seawater [101]. In an extended experiment, some mussels were kept in the seawater for up to seven days, being sampled at intervals for subcellular fractionation and histological studies of the digestive glands. The histological studies of the digestive gland sampled after 18 h showed a large number of particles in the digestive cells, indicating that the particles had indeed been endocytosed. After 24 h, similar sections showed a total absence of particles, showing that they had then been exocytosed back into the alimentary tract. The subcellular fractionation studies showed that with time the distribution of metals shifted from the particulate fraction to the cytosol fraction, where they were presumably bound to a metallothionein type protein. A linear plot showed that the levels of the metals in the cytosol could be related to the logarithm of the binding constant to the particle [100].

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An ultrastructural study of the digestive gland of the cephalopod Sepia officinalis using ferritin as a tracer, also provided evidence for endocytosis and intracellular digestion of large proteins (and perhaps particles) inside the digestive cell [102]. The animals were fed on shrimps that had been injected with ferritin in seawater, and the tissues were examined after 4 h and 18 h. It was shown that the ferritin was captured by electron-dense endocytotic vesicles that fused to form heterophagosomes that were then digested in heterolysosomes. The presence of iron in the digestive cells was confirmed by positive staining by the Perl’s Prussian Blue method in light microscopy. 6.3

ENDOCYTOSIS BY TERRESTRIAL INVERTEBRATES

Most terrestrial invertebrates have limited access to water and feed on solid matter. As a consequence, they take up most of their nutrients by ingestion of foodstuffs that are also the vehicle for ingestion of contaminants. Many of the class ‘a’, metals that are taken up are found in membrane-bound granules in the cells of the hepatopancreas, although uncertainties remain as to the initiation of granule formation. Other metals, such as the class ‘b’ metal cadmium, may be in the granule or may be bound to a metallothionein type protein. There are studies on the uptake of contaminant metals into terrestrial molluscs from contaminated sites [103] and from food to which metal salts (Ca, Co, Fe, Mn, Zn) had been added [104]. The metals accumulate in the animal’s digestive gland where histological and ultrastructural studies indicate that a major route of uptake is by phagocytosis [105,106]. 6.4 6.4.1

ENDOCYTOSIS OF AIRBORNE PARTICLES Introduction

The most convincing evidence for the endocytosis of pollutant particulate matter into cells comes from the inhalation of airborne particles by humans. A full account of the composition, properties and distribution of particles in the atmosphere is given in Volume 5 of this series [3]. The particles can arise from natural sources such as volcanoes, or from anthropogenic industrial processes. The particles may be localised around mines, or can be distributed widely, depending on prevailing winds and precipitation, as occurred following the Chernobyl nuclear reactor accident. Among the more extensively studied particulates is asbestos, and it is now more than 40 years since it was implicated in mesothelioma [85]. Recognition that this was an environmental problem came when many victims who had not worked directly with asbestos but had lived near the asbestos fields in South Africa, or had other close contact with workers, developed asbestos-related conditions. The asbestos fibres are rapidly phagocytosed into lung epithelial cells. Although there is general agreement

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that asbestos fibres have the potential for DNA damage, the actual mechanisms are more elusive. Many mechanisms have been proposed, including the ability of the fibres to disrupt the phagolysosomal membrane, releasing hydrolytic enzymes which may poison the cell. A role has also been proposed for the iron content associated with the asbestos fibres in its ability to generate freeradical reactions. However, asbestos fibres themselves are considered to be physical carcinogens, as their size and shape appear to be the most important factor in inducing tumours [107]. Long (>4 mm), thin (<0:25 mm) fibres are more hazardous than short thicker ones. In a study using lung epithelial cells of the newt Taricha granulosa (which are similar in their structural organisation and biochemistry to their human counterparts) high-resolution time-lapse light microscopy showed that, while most of the crocidolite fibres were retained in the phagolysosomes, the thin fibres could be caught in the keratin cage during mitosis and, if long enough, were able to snag or block moving chromosomes [107]. A role for iron has been suggested in pathological effects derived from reactive oxygen following the inhalation of other particulate matter in the atmosphere. As with asbestos, the size of the particles is especially important, and particles with an aerodynamic diameter of less than 10 mm have been associated with increased mortality and morbidity. 6.4.2

Diesel Exhaust Particles and Fly-Ash

Many airborne particles, such as diesel exhaust particles and fly-ash from oil and coal combustion, contain carbon aggregates with various metals, acid salts and organic pollutants such as polyaromatic hydrocarbons, quinones and others [108]. Following inhalation, the particles are phagocytosed by epithelial cells of the airway and alveoli. The presence of oxidising species such as iron and quinone have led to the hypothesis that oxidative stress may lead to the pathologies. It was demonstrated that iron could be mobilised intracellularly from endocytosed coal fly-ash in a human airway epithelial cell line. This was determined by the increase of iron as ferritin in the cells which had been exposed to the smaller particles. It was suggested that this increase could lead to an intracellular iron overload, resulting in damage to the lung from reactive oxygen species. Since it was found that smaller particles are more readily endocytosed by epithelial cells [109], a new standard was issued by the Environmental Protection Agency (EPA) to include sizes down to 2:5 mm. A study investigating the consequences of diesel exhaust particles in human airway epithelial cells also concluded that any effects of these particles occurred after their endocytosis. However, organic components rather than the metals on the surface of the particles were considered to be responsible for subsequent events. Thus, treatment with the iron chelator desferrioxamine had no inhibitory effect on the secretion of the inflammatory cytokines interleukin-8,

390 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

interleukin-1b and an increase of GM–CSF (granulocyte macrophage colony stimulating factors) release [108]. Another study on the effects of diesel exhaust particles on primary alveolar macrophages supported the conclusion that it was the organic matter (polyaromatic hydrocarbons, halogenated hydrocarbons and quinines) which was responsible for the production of reactive oxygen radicals, and which eventually led to apoptosis of the phagocytotic cells [110]. 6.4.3

Nickel Compounds

Other notable examples that highlight the importance of the deleterious effects of inhaled particles arising from occupational exposure are iron and nickel oxides and sulfides derived from industrial processes. Nickel compounds are accepted as potent carcinogens, acting as agents for DNA strand breaks [111]. The hazard is greatest for nickel refinery dust (a mixture of nickel oxides and sulfides), but also for nickel oxide (NiO) on its own and nickel sub sulfide (Ni3 S2 ). However, the evidence is equivocal for soluble nickel compounds. The site of deposited particles following inhalation is determined in part by size. Most sizes can be trapped in the nasal passages, possibly giving rise to nasal cancer, while particles <10 mm can penetrate the alveolar regions, where they are phagocytosed [112,113]. Dissolution occurs in lysosomes. Nickel-containing vesicles have been observed around the nuclear membrane [114,115]. Studies with nickel compounds administered to rats and mice indicate that the appearance of neoplasms can be species specific with some compounds. Following chronic exposure of nickel oxide and nickel subsulfide, rats developed neoplasms, but neoplasms were only observed in female mice with nickel oxide exposure. No neoplasms were observed with soluble NiSO4 :6H2 O, and it was concluded that cell entry by the phagocytotic pathway was the crucial factor in the development of neoplasms [116]. 6.4.4

Lead Chromate Particles

Occupational inhalation of lead chromate particles which contain Cr(VI) has been associated with lung cancer and respiratory tract toxicity. Heavy levels of chromate particles and precancerous lesions have been seen at bronchial bifurcations 15 years after cessation of exposure. Animal studies show that soluble chromates are probably not carcinogenic, as organisms are able to reduce the Cr(VI) to the less-harmful Cr(III), whereas less-soluble and insoluble particulate chromates are able to induce tumours. In a study exposing normal human lung epithelial cells to lead chromate particles with a mean size of 2 mm, lead chromate particles and lead inclusion bodies were detected in the cells. Both Cr–DNA adducts and DNA-associated Pb ions were significantly increased following exposure to lead chromate. Treatment with lead chromate particles and soluble sodium chromate significantly increased apoptosis [117]. Two

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mechanisms have been proposed for the entry into the cell. The first suggests that lead chromate particles adhering to the cell membrane dissolve and the released chromate is transported into the cell via membrane anion transporters, and the second suggests that the particles are phagocytosed and then dissolved intracellularly [118,119].

7

CONCLUSIONS

It is quite clear that many if not most contaminants can be present in the environment as colloids or particulates. These may consist of pure aggregated molecules, or they may exist in various associations with other molecules. Whatever the form, they may be taken up by the relatively poorly studied process of endocytosis, which has recently been comprehensively reviewed [120], and they may contribute to deleterious effects, either directly in the exposed organism or indirectly through the food chain. Perhaps for obvious reasons, the pathological conditions in humans have related mainly to the inhalation of contaminant particles where the role of endocytosis is clearly established. For other organisms living in terrestrial and aquatic environments, it is well established that contaminants tend to be concentrated on to soil particles and into sediments, where their long-term fate is poorly understood. Anthropogenic discharges have been measured and the transport of colloidal and particulate pollutants in rivers, estuaries and oceans has been tracked. What is more difficult to determine is the bioavailability of these pollutants. In the United States, sediment-quality guidelines (SQGs) have been proposed, based on two criteria. The first estimates the impact of toxicity using waterquality criteria, with the assumption that there is an ‘equilibrium between sediment and pore water’. The second is based on ‘compilations of simultaneously measured biological characteristics and bulk chemical concentrations’. These concepts have been critically reviewed [25], with the suggestion that chemical data by themselves are not generally useful in predicting biological hazards, except possibly in cases of extreme contamination. Bioavailability can depend on pH, speciation, partitioning between water and sediment, the presence or absence of organic layers on particles, and the possible occurrence of turbulent activity in the environment. Bioassays can also be unreliable, as there is much variation in the way that diverse feeding and digestive strategies impact upon sediment colloids and particles in different species. These points, however, do not address the central question of how organisms deal with a contaminated environment with which they have to interact in order to obtain energy and metabolites. Crucial to these processes are the cellular processes which can modify the ionisation of molecules, their hydrophilic/ hydrophobic properties, and the matrix within which they exist. Many of these changes occur in the alimentary tract but they also occur at the cellular

392 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

level in endocytosis, which is a poorly studied process that can occur in a great diversity of cells and a great variety of physiological pathways. Unfortunately, the process is difficult to characterise experimentally, and in order to assess its importance we suggest the following criteria that need to be provided in any definitive study: (1) (2) (3) (4) (5) (6) (7) (8) (9)

binding of the contaminant to the colloid or particle surface; characterisation of this process in terms of effects of ionic strength and pH; presence of surface ligands on the colloid or particle/contaminant complex; presence of membrane receptors capable of interacting with surface ligands; demonstration that these receptors occur in specific phagocytic cells; demonstration of colloids or particles inside cells; involvement of endocytosis with phagosome dynamics, fusion to endosomes, lysosomes and exocytosis; correlation between occurrence of colloids or particles and enhanced cell accumulation of pollutant; evidence that the contaminant persists in tissue after colloids or particles have been exocytosed.

At the present time, all of these criteria have not been achieved in any specific system. There is, therefore, considerable circumstantial evidence that endocytosis presents a relatively unprotected route for the uptake of colloidal and particle-bound pollutants into cells. However, this important pathway has not yet been sufficiently well characterised to be capable of quantitative assessment.

GLOSSARY ABBREVIATIONS AE CF CFF DCT1 EDTA EPA FFF GED GM–CSF PC PS

Assimilation efficiency Concentration factor Cross-flow filtration Divalent cation/metal ion transfer Ethylenediamine tetra-acetic acid Environmental Protection Agency Field flow fractionation GTPase effector domains Granulocyte macrophage colony stimulating factor Phosphatidyl choline Phosphatidyl serine

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Receptor-mediated endocytosis Sediment-quality guidelines Tributyltin

SYMBOLS cs cw K Km fcoll cA cw cf cf , ss cw, ss cp kew ke g IR Ksw KD k ctd ctru ku

Activity in shrimp tissues (Bq ml1 ) Activity in treatment solution (Bq ml1 ) Affinity constant (mol dm3 )1 Binding affinity (mol dm3 ) Colloidal fraction Chemical concentration in animals (mg g1 ) Chemical concentration in dissolved phase (mg dm3 ) Concentration in ingested particles (mg mg1 ) Concentration in organism from food (mg g1 ) Concentration in organism from the water (mg g1 ) Concentration of shrimp mass in the water (g ml1 ) Corresponding efflux rate from the water (d1 ) Efflux rate constant (d1 ) Growth rate constant (d1 ) 1 Ingestion rate (mg g1 d ) Partition constant at equilibrium k1 =k2 Partition constant (ratio TBT sediment/TBT water) Rate constant Total dissolved concentration Truly dissolved concentration Uptake rate constant from the dissolved phase 1 (dm3 g1 d )

Equation (2)

Equation (1) Equation (11)

Equation (13) Equation (12) Equation (6)

Equation (5)

REFERENCES 1.

Buffle, J. and van Leeuwen, H. P. eds. (1992). Environmental Particles. IUPAC Series on Environmental Analytical and Physical Chemistry, Vol. 1, Lewis, Boca Raton, Ann Arbor. 2. Buffle, J. and van Leewen, H. P. eds. (1993). Environmental Particles. IUPAC Series on Environmental Analytical and Physical Chemistry, Vol. 2, Lewis, Boca Raton, Ann Arbor. 3. Harrison, R. M. and van Grieken, R. E. eds. (1998). Atmospheric Particles. Vol. 5, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle J. and van Leeuwen, H. P., John Wiley & Sons Ltd, Chichester, UK.

394 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 4.

5. 6. 7.

8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.

US Environmental Protection Agency (1994). Methods for measuring the toxicity and bioaccumulation of sediment-associated contaminants with freshwater invertebrates. EPA 600/R-94/024. Office of Research and Development, Duluth, MN. US Environmental Protection Agency (1994). Methods for assessing the toxicity of sediment-associated contaminants with estuarine and marine amphipods. EPA 600/ R-94/025. Office of Research and Development, Narragansett, RI. Shaw, D. J. (1992). Introduction to Colloid and Surface Chemistry. 4th edn, Butterworth-Heinemann, Oxford. Beckett, R. and Hart, B. T. (1993). Use of field flow fractionation techniques to characterize aquatic particles, colloids and macromolecules. In Environmental Particles. eds. Buffle, J. and van Leeuwen, H. P., Vol. 2, IUPAC Series on Environmental Analytical and Physical Chemistry, Lewis, Boca Raton, Ann Arbor, pp. 165–205. Ross, J. M. and Sherrell, R. M. (1999). The role of colloids in trace metal transport and adsorption behavior in New Jersey Pinelands streams, Limnol. Oceanogr., 44, 1019–1034. Atkins, P. W. (1998). Physical Chemistry. 6th edn, Oxford University Press, Oxford, p. 705. Kraepiel, A. M. L., Keller, K. and Morel, F. M. M. (1999). A model for metal adsorption on montmorillonite, J. Coll. Interf. Sci., 210, 43–54. Hart, B. T. (1982). Trace metals in natural waters. I. Speciation, Chem. Aust., 49, 260–265. Pinheiro, J. P., Mota, A. M., Simo˜es Gonc¸alves, M. L. S. and van Leeuwen, H. P. (1998). The pH effect in the diffusion coefficient of humic matter: influence in speciation studies using voltammetric techniques, Coll. Surf. A, 137, 165–170. Avena, M. J. and Koopal, L. K. (1999). Kinetics of humic acid adsorption at solid– water interfaces, Environ. Sci. Technol., 33, 2739–2744. Vigneault, B., Percot, A., Lafleur, M. and Campbell, P. G. C. (2000). Permeability changes in model and phytoplankton membranes in the presence of aquatic humic substances, Environ. Sci. Technol., 34, 3907–3913. Schlekat, C. E., Decho, A. W. and Chandler, G. T. (1998). Sorption of cadmium to bacterial extracellular polymeric sediment coatings under estuarine conditions, Environ. Toxicol. Chem., 17, 1867–1874. Fowler, S. W. and Knauer, G. A. (1986). Role of large particles in the transport of elements and organic compounds through the oceanic water column, Prog. Oceanogr., 16, 147–194. Collier, R. and Edmond, J. (1984). The trace element geochemistry of marine biogenic particulate matter, Prog. Oceanogr., 13, 113–199. Champion, J. T., Gilkey, J. C., Lamparski, H., Retterer, J. and Miller, R. M. (1995). Electron microscopy of rhamnolipid (biosurfactant) morphology: effects of pH, cadmium, and octadecane, J. Coll. Interf. Sci., 170, 569–574. Cosma, B., Frache, R., Baffi, F. and Dadone, A. (1982). Trace metals in sediments from the Ligurian Coast, Italy, Mar. Poll. Bull., 13, 127–132. Borg, H. and Jonsson, P. (1996). Large-scale metal distribution in Baltic sea sediments, Mar. Poll. Bull., 32, 8–21. McManus, J. P. and Prandle, D. (1996). Determination of source concentrations of dissolved and particulate trace metals in the southern North Sea, Mar. Poll. Bull., 32, 504–512. Schiff, K. C. (2000). Sediment chemistry on the mainland shelf of the Southern California Bight, Mar. Poll. Bull., 40, 268–276.

M. G. TAYLOR AND K. SIMKISS 23. 24. 25. 26.

27.

28. 29.

30.

31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41.

395

Bryan, G. W. and Langston, W. J. (1992). Bioavailability, accumulation and effects of heavy metals in sediments with special reference to UK estuaries: a review, Environ. Poll., 76, 89–131. Luoma, S. N. (1989). Can we determine the biological availability of sedimentbound trace elements? Hydrobiologia, 176/177, 379–396. O’Connor, T. P. and Paul, J. F. (2000). Misfit between sediment toxicity and chemistry, Mar. Poll. Bull., 40, 59–64. Selck, H., Decho, A. W. and Forbes, V. E. (1999). Effects of chronic metal exposure and sediment organic matter on digestive absorption efficiency of Cd by the deposit-feeding polychaete Capitella species I, Environ. Toxicol. Chem., 18, 1289–1297. van Ginnekin, L. and Blust, R. (2000). Determination of conditional stability constants of cadmium–humic acid complexes in freshwater by use of a competitive ligand equilibration-solvent extraction technique, Environ. Toxicol. Chem., 19, 283–292. Selck, H., Forbes, V. E. and Forbes, T. L. (1998). Toxicity and toxicokinetics of cadmium in Capitella sp, I: relative importance of water and sediment as routes of cadmium uptake, Mar. Ecol. Progr. Ser., 164, 167–178. Carvalho, R. A., Benfield, M. C. and Santschi, P. H. (1999). Comparative bioaccumulation studies of colloidally complexed and free-ionic heavy metals in juvenile brown shrimp Penaeus aztecus (Crustacea: Decapoda: Penaeidae), Limnol. Oceanogr., 44, 403–414. Farrington, J. W. and Westall, J. (1986). Organic chemical pollutants in the oceans and groundwater: a review of fundamental chemical properties and biogeochemistry. In The Role of the Oceans as a Waste Disposal Option. ed. Kullenberg, G., NATO ASI Series, D. Reidel, Boston, pp. 361–425. Bell, R. A. and Kramer, J. R. (1999). Structural chemistry and geochemistry of silver–sulfur compounds: critical review, Environ. Toxicol. Chem., 18, 9–22. Adams, N. W. H. and Kramer, J. R. (1999). Silver speciation in waste water effluent, surface waters, and pore waters, Environ. Toxicol. Chem., 18, 2667–2673. Ratte, H. T. (1999). Bioaccumulation and toxicity of silver compounds: a review, Environ. Toxicol. Chem., 18, 89–108. Connell, D. B., Sanders, J. G., Reidel, G. F. and Abbe, G. R. (1991). Pathways of silver uptake and trophic transfer in estuarine organisms, Environ. Sci. Technol., 25, 921–924. Hirsch, M. P. (1998). Bioaccumulation of silver from laboratory-spiked sediments in the oligochaete (Lumbriculus variegatus), Environ. Toxicol. Chem., 17, 605–609. Fretter, V. and Graham, A. (1976). A Functional Anatomy of Invertebrates. Academic Press, London. Owen, G. (1974). Feeding and digestion in the Bivalvia, Adv. Comp. Physiol. Biochem., 5, 1–35. Luoma, S. N., Ho, Y. B. and Bryan, G. W. (1995). Fate, bioavailability and toxicity of silver in estuarine environments, Mar. Poll. Bull., 31, 44–54. Luoma, S. N. and Bryan, G. W. (1981). A statistical assessment of the form of trace metals in oxidized estuarine sediments employing chemical extractants, Sci. Total Environ., 17, 165–196. Evans, S. M., Birchenough, A. C. and Brancato, M. S. (2000). The TBT ban: out of the frying pan into the fire? Mar. Poll. Bull., 40, 204–211. Pelletier, E. (1995). Environmental organometallic chemistry of mercury, tin, and lead: present status and perspectives. In Metal Speciation and Bioavailability in Aquatic Systems. eds. Tessier, A. and Turner, D. R., Vol. 3, IUPAC Series on

396 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

42. 43. 44.

45.

46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59.

Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Ltd, Chichester, pp. 103–148. Langston, W. J. and Burt, G. R. (1991). Bioavailability and effects of sediment-bound TBT in deposit feeding clams, Scrobicularia plana, Mar. Environ. Res., 32, 61–77. Langston, W. J. and Pope, N. D. (1995). Determinants of TBT adsorption and desorption in estuarine sediments, Mar. Poll. Bull., 31, 32–43. Mason, A. Z. and Jenkins, K. D. (1995). Metal detoxification in aquatic organisms. In Metal Speciation and Bioavailability in Aquatic Systems. eds. Tessier, A. and Turner, D. R., Vol.3, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems. Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Ltd, Chichester, pp. 479–608. Simkiss, K. and Taylor, M. G. (1995). Transport of metals across membranes. In Metal Speciation and Bioavailability in Aquatic Systems. eds. Tessier, A. and Turner, D. R., Vol. 3, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems. Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Ltd, Chichester, pp. 1–44. Gottesman, M. M. and Pastan, I. (1993). Biochemistry of multidrug-resistance mediated by the multidrug transporter, Ann. Rev. Biochem., 62, 385–427. Stein, W. D. (1997). Kinetics of the multidrug transporter (P-glycoprotein) and its reversal, Physiol. Rev., 77, 545–590. Hille, B. (1992). Ionic Channels of Excitable Membranes. 2nd edn, Sinauer Associates, Sunderland, MA. Simkiss, K. (1996). Ecotoxicants at the cell-membrane barrier. In Ecotoxicology – a Hierarchical Treatment. eds. Newman, M. C. and Jagae, C. H., CRC Lewis, Boca Raton, FL, pp. 59–83. Marks, B., Stowell, M. H. B., Vallis, Y., Mills, I. G., Gibson, A., Hopkins, C. R. and McMahon, H. T. (2001). GTPase activity of dynamin and resulting conformation change are essential for endocytosis, Nature, 410, 231–235. Gold, E. S., Underhill, D. M., Morrissette, N. S., Guo, J., McNiven, M. A. and Aderem, A. (1999). Dynamin 2 is required for phagocytosis in macrophages, J. Exp. Med., 190, 1849–1856. Mellman, I. (1996). Endocytosis and molecular sorting, Ann. Rev. Cell Dev. Biol., 12, 575–625. Gerasimenko, J. V., Tepikin, A. V., Petersen, O. H. and Gerasimenko, O. V. (1998). Calcium uptake via endocytosis with rapid release from acidifying endosomes, Current Biol., 8, 1335–1338. van Deurs, B., Petersen, O. W., Olsnes, S. and Sandvig, K. (1989). The ways of endocytosis, Int. Rev. Cytol., 117, 131–177. Allen, R. D., Schroeder, C. C. and Fok, A. K. (1992). Endosomal system of Paramecium: coated pits to early endosomes, J. Cell Sci., 101, 449–461. Kwiatkowska, K. and Sobota, A. (1999). Signalling pathways in phagocytosis, Bioessays, 21, 422–431. Lee, K.-D., Hong, K. and Papahadjopoulos, D. (1992). Recognition of liposomes by cells: in vitro binding and endocytosis mediated by specific lipid headgroups and surface charge density, Biochim. Biophys. Acta, 1103, 185–197. Lee, K.-D., Nir, S. and Papahadjopoulos, D. (1993). Quantitative analysis of liposome–cell interactions in vitro: rate constants of binding and endocytosis with suspension and adherent J774 cells and human monocytes, Biochemistry, 32, 889–899. Chenevier, P., Veyret, B., Roux, D. and Henry-Touleme´, N. (2000). Interaction of cationic colloids at the surface of J774 cells: a kinetic analysis, Biophys. J., 79, 1298–1309.

M. G. TAYLOR AND K. SIMKISS 60. 61. 62. 63. 64.

65.

66. 67. 68. 69. 70. 71. 72. 73.

74. 75. 76. 77. 78.

397

Chubb, J. R., Wilkins, A., Thomas, G. M. and Insall, R. H. (2000). The Dictyostelium RasS protein is required for macropinocytosis, phagocytosis and the control of cell movement, J. Cell Sci., 113, 709–719. Synnes, M., Prydz, K., Lovdal, T., Brech, A. and Berg, T. (1999). Fluid phase endocytosis and galactosyl receptor-mediated endocytosis employ different early endosomes, Biochim. Biophys. Acta-Biomembranes, 1421, 317–328. Parton, R. G. (1996). Caveolae and caveolins, Curr. Opin. Cell Biol., 8, 542–548. Rolfs, A. and Hediger, M. A. (1999). Metal ion transporters in mammals: structure, function and pathological implications, J. Physiol., 518, 1–12. Gunshin, H., Mackenzie, B., Berger, U. V., Gunshin, Y., Romero, M. F., Boron, W. F., Nussberger, S., Gollan, J. L. and Hediger, M. A. (1997). Cloning and characterization of a mammalian proton-coupled metal-ion transporter, Nature, 388, 482–488. Gruenheid, S., Canonne-Hergaux, F., Gauthier, S., Hackman, D. J., Grinstein, S. and Gros, P. (1999). The iron transport protein NRAMP2 is an integral membrane glycoprotein that colocalizes with transferrin in recycling endosomes, J. Exp. Med., 189, 831–841. Yokel, R. A., Allen, D. D. and Ackley, D. C. (1999). The distribution of aluminium into and out of the brain, J. Inorg. Biochem., 76, 127–132. Nilsson, J. R. (1979). Phagotrophy in Tetrahymena. In Biochemistry and Physiology of Protozoa. eds. Levandowsky, M. and Hunter, S. H., Academic Press, New York, pp. 330–379. Decho, A. W. and Luoma, S. N. (1996). Flexible digestion strategies and trace metal assimilation in marine bivalves, Limnol. Oceanogr., 41, 568–572. Owen, G. (1970). The fine structure of the digestive tubules of the marine bivalve Cardium edule, Phil. Trans. Roy. Soc. Lond. Ser. B., 258, 245–260. Owen, G. (1972). Lysosomes, peroxisomes and bivalves, Sci. Prog. Oxford, 60, 299–318. Moore, M. N. and Viarengo, A. (1987). Lysosomal membrane fragility and catabolism of cytosolic proteins: evidence for a direct relationship, Experientia, 15, 320–323. Spurgeon, D. J., Svendsen, C., Rimmer, V. R., Hopkin, S. P. and Weeks, J. M. (2000). Relative sensitivity of life cycle and biomarker responses in four earthworm species exposed to zinc, Environ. Toxicol. Chem., 19, 1800–1808. Scott-Fordsmand, J. J., Weeks, J. M. and Hopkin, S. P. (2000). Importance of contamination history for understanding toxicity of copper to earthworm Eisenia fetica (Oligochaeta: annelida) using neutral-red retention assay, Environ. Toxicol. Chem., 19, 1774–1780. Grundy, M. M., Moore, M. N., Howell, S. M. and Ratcliffe, N. A. (1996). Phagocytic reduction and effects on lysosomal membranes by polycyclic aromatic hydrocarbons, in haemocytes of Mytilus edulis, Aquat. Toxicol., 34, 273–290. Svendsen, C. and Weeks, J. M. (1995). The use of a lysosome assay for the rapid assessment of cellular stress from copper to the fresh water snail Viviparus contectus (Millet), Mar. Poll. Bull., 31, 139–142. Reade, P. and Reade, E. (1976). Phagocytosis in invertebrates: studies on the hemocytes of the clam Tridacna maxima, J. Invert. Pathol., 28, 281–290. Fankboner, P. V. (1971). Intracellular digestion of symbiotic zooxanthellae by host amoebocytes in giant clams (Bivalvia: Tridacnidae) with a note on the nutritional role of the hypertrophied siphonal epidermis, Biol. Bull., 141, 222–234. Rasmussen, L. and Kludt, T. A. (1970). Particulate material as a prerequisite for rapid cell multiplication in Tetrahymena culture, Exp. Cell Res., 59, 457–463.

398 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 79. 80. 81. 82.

83. 84. 85. 86. 87. 88. 89.

90. 91.

92. 93. 94. 95.

Nilsson, J. R. (1979). Intracellular distribution of lead in Tetrahymena during continuous exposure to the metal, J. Cell Sci., 39, 383–396. Asai, D. J. and Fornay, J. D. eds. (2000). Tetrahymena thermophilia. In Methods in Cell Biology. Vol. 62, Series eds. Wilson, L. and Matsudarira, P., Academic Press, pp. 1–580. Orias, E. and Rasmussen, L. (1976). Dual capacity for nutrient uptake in Tetrahymena: IV Growth without food vacuoles and its implications, Exp. Cell Res., 102, 127–137. Luoma, S. N. (1995). Prediction of metal toxicity in nature from bioassays. In Metal Speciation and Bioavailability in Aquatic Systems. eds. Tessier, A. and Turner, D. R., Vol. 3, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems. Series eds. Buffle J. and van Leeuwen H. P., John Wiley & Sons, Ltd, Chichester, pp. 609–659. Langston, W. J., Bebianno, M. J. and Burt, G. R. (1998). Metal handling strategies in molluscs. In Metal Metabolism in Aquatic Environments. eds. Langston, W. J. and Bebianno, M. J., Chapman and Hall, London, pp. 219–283. George, S. G., Pirie, B. J. S. and Coombs, T. L. (1976). The kinetics of accumulation and excretion of ferric hydroxide in Mytilus edulis (L.) and its distribution in the tissues, J. Exp. Mar. Biol. Ecol., 23, 71–84. Wagner, J. C. (1991). The discovery of the association between blue asbestos and mesotheliomas and the aftermath, Brit. J. Ind. Med., 48, 399–403. Moore, M. N. and Willows, R. I. (1998). A model for cellular uptake and intracellular behaviour of particulate-bound micropollutants, Mar. Environ. Res., 46, 509–514. Viarengo, A. (1989). Heavy metals in marine invertebrates: mechanisms of regulation and toxicity at the cellular level, Rev. Aquat. Sci., 1, 295–317. Roditi, H. A. and Fisher, N. S. (1999). Rates and routes of trace element uptake in zebra mussels, Limnol. Oceanogr., 44, 1730–1749. Decho, A. W. and Luoma, S. N. (1991). Time-courses in the retention of food material in the bivalves Potamocorbula amurensis and Macoma balthica: significance to the absorption of carbon and chromium, Mar. Ecol. Prog. Ser., 78, 303–314. Pirie, B. J. S., George, S. G., Lytton, D. G. and Thomson, J. D. (1984). Metalcontaining blood cells of oysters: ultrastructure, histochemistry and X-ray microanalysis, J. Mar. Biol. Assoc. UK, 64, 115–123. Fisher, N. S. and Reinfelder, J. R. (1995). The trophic transfer of metals in marine systems, In Metal Speciation and Bioavailability in Aquatic Systems. eds. Tessier, A. and Turner, D. R., Vol. 3, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems. Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Ltd, Chichester, pp. 363–406. Reiswig, H. M. (1971). Particle feeding in natural populations of three marine demosponges, Biol. Bull., 141, 568–591. Luoma, S. N., Johns, C., Fisher, N. S., Steinberg, N. A., Oremland, R. S. and Reinfelder, J. R. (1992). Determination of selenium bioavailability to a benthic bivalve from particulate and solute pathways, Environ. Sci. Technol., 26, 485–491. Wang, W.-X. and Fisher, N. S. (1996). Assimilation of trace elements and carbon by the mussel Mytilus edulis: effects of food composition, Limnol. Oceanogr., 41, 197–207. Wang, W.-X. and Fisher, N. S. (1999). Assimilation efficiencies of chemical contaminants in aquatic invertebrates: a synthesis, Environ. Toxicol. Chem., 18, 2034–2045.

M. G. TAYLOR AND K. SIMKISS 96. 97. 98. 99. 100. 101. 102. 103.

104. 105. 106. 107. 108. 109. 110. 111. 112.

113.

399

Landrum, P. F., Lee, H. II and Lydy, M. J. (1992). Toxicokinetics in aquatic systems: model comparisons and use in hazard assessment, Environ. Toxicol. Chem., 11, 1709–1725. Chong, K. and Wang, W.-X. (2000). Assimilation of Cd, Cr, and Zn by the green mussel Perna viridis and the clam Ruditapes philippinarum, Environ. Toxicol. Chem., 19, 1660–1667. Wildgust, M. A., McDonald, P. and White, K. N. (2000). Assimilation of 210 Po by the mussel Mytilus edulis from the alga Isochrysis galbana, Mar. Biol., 136, 49–53. Langston, W. J. (1996). Recent developments in TBT ecotoxicology, Toxicol. Ecotoxicol. News, 3, 179–187. Davies, N. A., Taylor, M. G. and Simkiss, K. (1997). The influence of particle surface characteristics on pollutant metal uptake by cells, Environ. Poll., 96, 179–184. Davies, N. A. and Simkiss, K. (1996). The uptake of Zn from artificial sediments by Mytilus edulis, J. Mar. Biol. Assoc. UK, 76, 1073–1079. Boucaud-Camou, E. and Yin, M. (1980). Fine structure and function of the digestive cell of Sepia officinalis (Mollusca: Cephalopoda), J. Zool. Lond., 191, 89–105. Coughtrey, P. J. and Martin, M. H. (1977). The uptake of lead, cadmium and copper by the pulmonate mollusc, Helix aspersa Muller and its relevance to the monitoring of heavy metal contamination of the environment, Oecologica, 27, 65–74. Taylor, M. G., Greaves, G. N. and Simkiss, K. (1990). Biotransformation of intracellular minerals by zinc ions in vivo and in vitro, Eur. J. Biochem., 192, 783–789. Howard, B. J. (1983). Heavy Metal Metabolism in Helix aspersa Muller. Ph. D. Thesis, University of Reading, UK. Sumner, A. T. (1965). The cytology and histochemistry of the digestive gland cells of Helix, Quart. J. Micr. Sci., 106, 173–192. Ault, J. G., Cole, R. W., Jensen, C. G., Jensen, L. C. W., Bachert, L. A. and Rieder, C. L. (1995). Behavior of crocidolite asbestos during mitosis in living vertebrate lung epithelial cells, Cancer Res., 55, 792–798. Baeza-Squiban, A., Bonvallot, V., Boland, S. and Marano, F. (1999). Airborne particles evoke an inflammatory response in human airway epithelium. Activation of transcription factors, Cell Biol. Toxicol., 15, 375–380. Boland, S., Bonvallot, V., Fournier, T., Baeza-Squiban, A., Aubier, M. and Marano, F. (2000). Mechanisms of GM-CSF increase by diesel exhaust particles in human airway epithelial cells, Am. J. Physiol., 278, L25–L32. Hiura, T. S., Kaszubowski, M. P., Li, N. and Nel, A. E. (1999). Chemicals in diesel exhaust particles generate reactive oxygen radicals and induce apoptosis in macrophages, J. Immunol., 163, 5582–5591. Zhuang, Z. X., Shen, Y., Shen, H. M., Ng, V. and Ong, C. N. (1996). DNA strand breaks and poly(ADP-ribose) polymerase activation induced by crystalline nickel subsulfide in MRC-5 lung fibroblast cells, Human Exper. Toxicol., 15, 891–897. Nieboer, E., Tom, T. T. and Sandford, W. E. (1988). Nickel metabolism in man and animals. In Nickel and its Role in Biology. Vol. 23, Metal Ions in Biological Systems. eds. Sigel, H. and Sigel, A., Marcel Dekker, New York, pp. 91–121. Nieboer, E., Rossetto, F. E. and Menon, C. R. (1988). Toxicology of nickel compounds, In Nickel and its Role in Biology. Vol. 23, Metal Ions in Biological Systems. eds. Sigel, H. and Sigel, A., Marcel Dekker, New York, pp. 359–402.

400 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 114. Costa, M., Heck, J. D. and Robison, S. H. (1982). Selective phagocytosis of crystalline metal sulfide particles and DNA strand breaks as a mechanism for the induction of cellular transformation, Cancer Res., 42, 2757–2763. 115. Costa, M., Simmons-Hansen, J., Bedrossian, C. W. M., Bonura, J. and Caprioli, R. M. (1981). Phagocytosis, cellular distribution, and carcinogenic activity of particulate nickel compounds in tissue culture, Cancer Res., 41, 2868–2876. 116. Dunnick, J. K., Elwell, M. R., Radovsky, A. E., Benson, J. M., Hahn, F. F., Nikula, K. J., Barr, E. B. and Hobbs, C. H. (1995). Comparative carcinogenic effects of nickel subsulfide, nickel oxide, or nickel sulfate hexahydrate chronic exposures in the lung, Cancer Res., 55, 5251–5256. 117. Singh, J., Pritchard, D. E., Carlisle, D. L., McClean, J. A., Montaser, A., Orenstein, J. M. and Patierno, S. R. (1999). Internalization of carcinogenic lead chromate particles by cultured normal human lung epithelial cells: formation of intracellular lead-inclusion bodies and induction of apoptosis, Toxicol. Appl. Pharmacol., 161, 240–248. 118. Wise, J. P., Orenstein, J. M. and Patierno, S. R. (1993). Inhibition of lead chromate clastogenesis by ascorbate: relationship to particle dissolution and uptake, Carcinogenesis, 14, 429–434. 119. De Flora, S. and Wetterhahn, K. E. (1989). Mechanisms of chromium metabolism and genotoxicity, Life Chem. Rep., 7, 169–244. 120. Conner, S. D. and Schmid, S. L. (2003). Regulated portals of entry into the cell, Nature, 422, 37–44.

9 Mobilisation of Organic Compounds and Iron by Microorganisms HAUKE HARMS AND LUKAS Y. WICK Swiss Federal Institute of Technology, ENAC–ISTE–LPE, Baˆtiment GR, CH-1015 Lausanne (EPFL), Switzerland

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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Active Versus Passive Mobilisation of Substrate . . . . . . . . . . 1.2 Reasons for Studying the Mobilisation of Organic Compounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Mechanisms and Principles of Biological Substrate Mobilisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Passive Mechanisms of Substrate Mobilisation. . . . . . . . . . . . . . . . 2.1 The Specific Affinity of Substrate Uptake . . . . . . . . . . . . . . . 2.2 The Concept of Specific Affinity as a Driving Force for Diffusive Substrate Transfer. . . . . . . . . . . . . . . . . . . . . . . . 2.3 The Role of Substrate Diffusion . . . . . . . . . . . . . . . . . . . . . . . 2.4 The Role of Adhesion and Bacterial Cell Surfaces in the Promotion of Passive Substrate Transfer . . . . . . . . . . . . . Active Mechanisms of Substrate Mobilisation . . . . . . . . . . . . . . . . 3.1 Chemotaxis to Poorly Bioavailable Substrates. . . . . . . . . . . . 3.2 Does Cell Contact with a Substrate Reservoir Allow the Direct Uptake of Sorbed, Liquid, Gaseous, and Solid Substrates? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Solid Substrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Liquid Substrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Sorbed Substrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Mobilisation of Hydrophobic Organic Substrates Using Biosurfactants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Mobilisation of Liquid, Solid or Sorbed Substrates by Solubilisation in Biosurfactant Micelles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Mobilisation of Liquid Substrates by Emulsification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Mobilisation of Substrates Using Extracellular Enzymes . . .

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3.5 Mobilisation of Iron Using Siderophores. . . . . . . . . . . . . . . . 4 Limits to the Mobilisation of Chemicals . . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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INTRODUCTION

Microorganisms may need to mobilise their organic substrates or essential mineral nutrients, because these chemicals are either out of their reach or present in effectively unavailable physical or chemical states. Various evolutionary adaptations help microorganisms to cope with limited access to chemicals. These adaptations range from the particularly high substrate affinities of their uptake systems (resulting in very efficient extraction of chemicals), to the use of specific carriers such as surface-active agents, bioemulsifiers, siderophores, and extracellular enzymes. Chemotactic movement and attachment to substrate sources may also be involved in the acquisition of chemicals. In this chapter, the present knowledge of the biophysical constraints for survival with poorly available substrates; the various microbial strategies to mobilise and compete for poorly available chemicals; and the underlying biological adaptations, are critically discussed. 1.1

ACTIVE VERSUS PASSIVE MOBILISATION OF SUBSTRATE

Heterotrophic organisms make use of different mechanisms to obtain their growth substrates (Figure 1). Their first option is to passively wait for the substrate to approach. This strategy is known from sessile animals, but is also used by many microorganisms, e.g. those living immobilised in biofilms. An obvious advantage of this strategy is its low-energy expenditure. Its success, however, depends on the abundance and mobility of the substrate. An adequate contact frequency can be assured by active movement of prey organisms, or by means of physical transport of otherwise immobile substrates by convection, diffusion or sedimentation. Strictly speaking, acquisition of diffusing substrate may already be regarded as a mechanism to acquire the food, as it is the consumption of substrate by the organism that creates the concentration gradient, which in turn, drives the directed flux of the dissolved substrate. As we will see later in this chapter, organisms may, to a certain extent, control the arising concentration gradient. Clearly, active mechanisms of obtaining food involve: (1) the active movement of organisms to their food, followed by its ingestion, e.g. hunting prey organisms, or chemotactically following increasing concentrations of substrate molecules;

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Strategy Waiting for substrate to approach by active movement, convection, or sedimentation

Low

Optimising substrate diffusion using high affinity uptake systems

Releasing carriers such as siderophores and biosurfactants

Releasing

exo enzymes

Moving liquid containing dissolved or suspended substrate

Degree of activity (energy expenditure) involved

Moving actively to graze food or swim up substrate gradients (chemotaxis)

Hunting prey

High

Figure 1. Scheme showing the strategies of microorganisms to obtain growth substrates and nutrients. It should be noted that the degree of activity needed or the energy expenditure involved, and consequently the exact order of the strategies, depend largely on factors such as the type and density of substrate. Strategies dealt with in this chapter are placed in boxes

(2) sending out carrier molecules or extracellular enzymes to access and mobilise remote organic substrates; or (3) creating movement of the medium containing the substrates. The subject of this chapter will be the most important mechanisms by which microorganisms mobilise substrates. We will thereby focus on the mobilisation of nonliving food molecules, and will not deal with living food organisms. Besides organic compounds, we will also treat the biological mechanisms to acquire iron as the least bioavailable inorganic nutrient in many environments. 1.2 REASONS FOR STUDYING THE MOBILISATION OF ORGANIC COMPOUNDS Besides its obvious role in the nutrition of heterotrophic organisms, the mobilisation of organic substrates also has various implications for the biogeochemical cycling of bioelements and for environmental quality. Many organic compounds are not readily bioavailable, and terrestrial habitats in particular are frequently carbon-limited, although the absolute concentrations of organic carbon can be quite high [1]. This apparent discrepancy results from the fact that natural organic matter can be (bio)chemically very stable, due to its polymeric nature and the high degree of structural heterogeneity, and in many instances it thus does not represent an easily accessible food source. Other environmental organic chemicals may be poorly bioavailable, although they are neither polymeric nor structurally heterogeneous. This results from the

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fact that many major pollutants are sparingly water-soluble, and therefore have the tendency to interact with natural organic matter and other soil constituents – processes which render them poorly mobile and barely accessible to microorganisms [2]. To cope with weakly degradable natural organic matter and with hardly accessible, immobilised environmental pollutants, microorganisms have developed mechanisms that help to mobilise both types of refractory substrates. From our anthropocentric perspective, we are concerned about the biodegradation of natural organic matter, as it represents a major reservoir of carbon that we want to continue to exist. We are also concerned about the accessibility of environmental pollutants for microbial degradation, as we want microorganisms to clean up polluted environments. We are furthermore concerned about the mobility of pollutants, as they may affect the quality of drinking water and food, and thereby threaten the integrity and functioning of ecosystems, as well as our own health. 1.3 MECHANISMS AND PRINCIPLES OF BIOLOGICAL SUBSTRATE MOBILISATION The requirements for biological mechanisms for the mobilisation of chemicals depend on the chemical and physical characteristics of these compounds, their abundance, and spatial distribution. Substrate mobilisation serves to overcome the distance between a substrate source and the uptake system of an organism, such as, for instance, the surface of a bacterial cell. It is therefore clear that the cost–gain ratio of the mobilisation process is minimised when the organism reduces its distance from the substrate. Organisms achieve this by enlarging their external surface areas and by developing structures of high fractal dimensions that optimally exploit the three-dimensional space containing the substrate. The hyphal network of fungi, the high surface to volume ratio of bacteria, and the microvilli of intestinal epithelia are examples of this principle. The same principle is realised in the root system of plants, a structure whose purpose is the exploitation of nutrients and water present in the rooted soil volume. Such largely ramified structures maximise the substrate uptake by shortening the average distance to their target chemicals, regardless of whether active mobilisation of substrate molecules is involved in the transport. However, the efficacy of carriers for substrate molecules benefits particularly from an optimal spatial arrangement, as the released carrier has to overcome the distance to the substrate, and then the substrate molecule, together with carrier, has to move back to the biological uptake system. The type of carrier that is involved in substrate mobilisation largely depends on the chemical and physical state of the substrate. It is generally agreed that most microorganisms rely on the presence of water-dissolved substrate molecules. This is because microbial cell walls exclude the uptake of molecules larger than about 600 g mol
1 [3]. Furthermore, the activity and growth of most

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microorganisms relies on the water phase, and these microorganisms are completely surrounded by water. Even when in contact with the solid phase, the specific mechanism of the adhesion, e.g. by colloidal forces, and the fact that microbial cells are more or less spherical objects, implies that the major part (if not all) of a microbe’s surface remains in contact with the aqueous phase. Substrate mobilisation therefore normally occurs via an aqueous phase. Mobilisation of a low-molar mass substrate that is dissolved in the water phase may be simply forced by consumption-driven diffusion. This appears trivial in the way that every kind of removal of dissolved substrate molecules inevitably creates concentration gradients, which in turn induce directed substrate diffusion. However, organism-specific characteristics influence the extent of this driving force of diffusion, as will be shown in the next section about passive mechanisms of substrate mobilisation. Thereafter, mechanisms of substrate mobilisation relying on the mobility of the organism are considered, before finally discussing mechanisms employing carrier agents that are sent out by the organisms.

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PASSIVE MECHANISMS OF SUBSTRATE MOBILISATION

At first glance, it appears illogical to use the term ‘passive’ to describe a form of substrate mobilisation. ‘Passive’ in this context means that the organism itself does not expend energy to achieve the mobilisation of its substrate. Rather, the mechanisms employed by the organism consist of an evolutionary adaptation to the fact that a substrate tends to be poorly available, i.e. because of low water solubility. Two kinds of such adaptations will be discussed. Firstly, there is an apparent tendency of microorganisms to adapt the specific affinity of their uptake systems to the prevailing concentration of their dissolved substrate molecules [4]. Secondly, it has been suggested that the cell-surface characteristics of bacteria, particularly their hydrophobicity, improve the uptake of hydrophobic substrates by facilitating the adhesion to either the hydrophobic substrates themselves or the organic sorbents or nonaqueous phase liquids containing these substrates [4]. On this occasion, hydrophobic cell walls may act as a reservoir for hydrophobic substrates and, by means of efficiently extracting them from the aqueous environment, increase the diffusive mass transfer to the cell. Figure 2 shows the influences of specific affinity and attachment to substrate sources, as will be detailed in the following section. 2.1

THE SPECIFIC AFFINITY OF SUBSTRATE UPTAKE

At low substrate concentrations, the passage through the cytoplasmic membrane, rather than enzymatic metabolism inside the cell is the major

Concentration

406 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

cd

(a)

Concentration

Distance

cd

(b)

Distance

Figure 2. Schematic visualisation of how increased specific substrate affinity resulting in lowered cell surface substrate concentration (a) and closer approach to a substrate source, e.g. by attachment to the substrate (b) steepens concentration gradients and thereby increases the diffusion flux from a distant substrate source (cd )

rate-limiting step for degradation [5]. Bacterial substrate consumption is therefore best described by a hyperbolic function referred to as the whole-cell Michaelis–Menten kinetics of substrate uptake [6] (Figure 3): Q ¼ Qmax c=ðKT þ cÞ

(1)

where Q is the substrate uptake rate, Qmax the biologically determined Q, c the substrate concentration and KT the concentration, resulting in Q ¼ Qmax =2. This concept was adopted from the classical Michaelis–Menten relationship [7], which describes the concentration dependency of enzymatic substrate conversion. At substrate concentrations c  KT equation (1) reduces to: Q  Qmax whereas at concentrations c  KT it becomes:

(2)

H. HARMS AND L. Y. WICK

407

Substrate uptake rate

a0A

Qmax

Qmax/2

The specific affinity a0A equals the slope of the first-order part of the curve at c << KT

Substrate concentration

KT

Figure 3. Schematic view of the substrate uptake rate versus concentration relationship as described by the whole-cell Michaelis–Menten kinetics. Q is the substrate uptake rate, Qmax the biologically determined maximum uptake rate per biomass, c the substrate concentration, and KT the whole-cell Michaelis constant, i.e. the concentration resulting in Qmax =2 (mass of substrate per volume). At c  KT , the slope of the first-order part of the uptake-rate versus concentration plot can be expressed by the specific affinity a0A (volume per biomass per unit time), which equals Qmax KT

Q  Qmax c=KT

(3)

Q ¼ aoA c

(4)

and can also be written as [8]:

with aoA ¼ Qmax =KT being the specific affinity of the uptake system. aoA indicates the ability of a biological transporter to accumulate a substrate from a dilute solution, and is the slope of the first-order part of the uptake-rate versus concentration plot [8]. Because of its prominent appearance in the whole cell Michaelis–Menten equation, KT is frequently mistaken as a measure of the substrate affinity. However, from equations (2) and (4), it becomes obvious that the activity versus concentration relationship is characterised by the two independent parameters, Qmax , as a descriptor of the zero-order part at high substrate concentration, and aoA , as a descriptor of the slope of the first-order part of the curve. In his muchcited review paper, Button [9] has listed the specific affinities of various organisms for a range of carbon sources and other elements. Reported variations for the same substrates extend over up to four orders of magnitude. Table 1 updates

408 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES Table 1. Specific affinities, a0A , of selected bacteria degrading hydrocarbons and aromatic compounds Organism Mycobacterium sp. LB501T Pseudomonas putida G7 Pseudomonas stutzeri P-16 Mixed cultures

Substrate

Anthracene Naphthalene Phenanthrene Naphthalene Phenanthrene Pyrene 2-Methylnaphthalene Sphingomonas sp. HH19k Dibenzofuran 3-Chlorodibenzofuran Pseudomonas sp. T2 3-Methylcatechol Uninduced cells Toluene Induced cells Toluene Pseudomonas putida Phenol Methylphenol 4-Chlorophenol Methylosinus trichosporium Methane Corynebacterium sp. strain 198 Dodecane


1 a0A (m3 kg
1 protein s )

9.028 1.389 0.278 0.006–0.139 0.008–0.026 0.0039 0.028 17.417 0.889 0.0003 0.0001 0.278 0.001 0.001 0.0003 0.008 0.0001

Ref. [4] [155] [156] [157] [107] [158] [158] [14] [14] [9] [9] [9] [159] [159] [159] [160] [8]

this list with a couple of new specific affinities reported for environmental chemicals. In a later work, Button [6] considered the concentration dependency of nutrient-limited transport as being controlled by kinetic contributions of two sequential processes (i.e. transporter and metabolism). From this theoretical work, he concluded that aoA depends strongly on the characteristics of the transport into the cell, but only weakly on the amount and the characteristics of the rate-limiting enzyme within the cell. Surprisingly, the whole-cell Michaelis constant, which depends on the ratio of rate-limiting enzyme to transporter, was found to be relatively independent of changes of aoA , and is thus not a good indicator of substrate affinity, in contrast to what is generally believed. KT is best used to describe the concentration at which degradation rates start to deviate from first-order kinetics because saturation begins to occur. Good oligotrophs, i.e. organisms that cope well with low substrate concentrations, are characterised by a large aoA . That they also have a small KT results from the fact that these substrate-limited cells have a small Qmax for reasons of enzyme economy [6], i.e. saturation, and thus half-saturation, is achieved at low substrate concentration. Degradation of environmental chemicals in terrestrial systems has frequently been found to follow first-order kinetics (e.g. [10]), which means that effective substrate concentrations in these environments are far from saturating the microbial uptake systems, and that the specific affinity entirely controls the degradation rate. The first-order degradation rates of different organisms are therefore proportional to their respective specific affinities for the substrate.

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409

In 1998, Kova´rova´-Kovar and Egli [11] reviewed bacterial growth kinetics. They observed that drastic variations in the reported kinetic parameters of bacterial strains can be attributed to different cultivation histories. In chemostat experiments, the same researchers found that cultivation at a high growth rate/high concentration regime led to increased intrinsic maximum substrate consumption rates and lowered specific affinities, whereas maximum specific affinity resulted from slow growth/low substrate concentrations. This relatively late recognition of the variation of whole-cell kinetic parameters due to regulation may be attributed to the fact that, because of their formal similarity, Monod parameters describing culture growth are often seen as analogous to Michaelis–Menten kinetics, although this is not necessarily valid. The kinetic parameters of an enzyme, as described by the Michaelis–Menten equation, reflect the genetically determined structure of this enzyme. They are determined by exposing a given preparation of this enzyme to varying substrate concentrations and then measuring conversion rates. Reported values of the maximal specific conversion rate,
max , and the half-saturation constant, KM , are therefore invariable. Likewise, whole-cell Michaelis–Menten parameters are determined by exposing a given cell suspension to a range of substrate concentrations and measuring substrate uptake. Kova´rova´-Kovar and Egli [11] have pointed out that it has been often overlooked that the determination of the two Monod parameters, mmax and Ks , in contrast to the foregoing, is performed stepwise with nonidentical biological materials. Whereas mmax is usually determined in chemostat washout experiments at high dilution rates DR, and high substrate concentrations, Ks is the much lower steady-state substrate concentration in the chemostat at mmax =2. The shift from DR ¼ mmax to DR ¼ mmax =2 implies the necessity to wait for a drastically reduced, new steady-state substrate concentration to establish. This allows the cells to adapt to the changed substrate regime: formerly copiotrophic bacteria become oligotrophic. The quasi-general observation of first-order kinetics in environmental contaminant degradation suggests that, in situ, microorganisms exploit their oligotrophic capacity. 2.2 THE CONCEPT OF SPECIFIC AFFINITY AS A DRIVING FORCE FOR DIFFUSIVE SUBSTRATE TRANSFER Model calculations have demonstrated that active cells are surrounded by zones containing substrate concentrations lower than those of the bulk liquid [12–14]. This concentration gradient results from the dynamic interplay between the rates of substrate uptake and diffusion through the diffusion layer surrounding the cell (see [15] for details). Boone et al. [13] developed a model using spherical coordinates that allows calculation of the diffusive substrate flux to a suspended spherical cell. In their model calculations, the cell surface concentration was set to arbitrary values between zero and about half of the bulk concentration. It

410 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

was found that for bacterium-sized organisms, steady-state concentration profiles establish within seconds, and that the extension of the zones of reduced substrate concentration is in the order of 10 mm. A theoretical concept developed by Harms and Zehnder [14] recognised that it is the substrate concentration at the cell surface that controls the uptake rate, and that a cell surface concentration of zero is illogical, because, according to the Michaelis–Menten relationship this would result in zero substrate uptake. Their extended model assumed that the actual substrate concentration at the cell’s surface is controlled by the dynamic interplay of substrate consumption by the cell and the resupply of substrate by diffusion from the bulk substrate solution towards the cell. The main parameters controlling the steady-state substrate concentration are the biologically determined substrate uptake rate and the diffusion coefficient [16]. Surprisingly, calculations showed that the cell surface substrate concentrations were generally only marginally reduced, i.e. that bacterial cells are far from being perfect sinks. This is due to the high aqueous diffusivity of low-molar mass substrates that easily compensates the substrate uptake. Calculations of the concentration reductions at the surface of Sphingomonas sp. HH19 showed that chlorodibenzofuran and dibenzofuran were reduced only by 1.1% and 17% as compared with the steady-state bulk substrate concentration [14] despite the respective high specific affinities of 0.889 and
1 17:417 m3 kgprotein s
1 for these substrates. It is this slight concentration difference that assures the cell’s substrate provision. Differences between developing concentration gradients depend strongly on the specific affinity. Figure 2a shows the influence of a higher specific affinity on concentration gradients driving substrate dissolution, and Figure 4 shows the extent of this effect on steady-state diffusive anthracene fluxes into cells of Mycobacterium sp. LB501T for several hypothetical distant (bulk) aqueous substrate concentrations cd (adapted from [14,17]). At cd  KT (Figure 4a), the substrate flux is relatively insensitive to both aoA and to the separation distance, whereas the flux becomes very sensitive to both parameters at cd  KT (Figure 4b) and even more so when cd < KT (Figure 4c). Under lownutrient conditions, the diffusive substrate flux towards the cell will largely depend on a cell’s oligotrophic capacity. Under real environmental conditions, cd is typically the aqueous solubility of a nonaqueous liquid or a crystalline contaminant or the aqueous (pseudo)equilibrium concentration of a sorbed or nonaqueous phase liquid (NAPL)-dissolved contaminant. 2.3

THE ROLE OF SUBSTRATE DIFFUSION

The model calculations in Figure 4 represent an idealised situation, as the diffusion coefficient Dw of anthracene in aqueous solution was used. Diffusion coefficients of low molar-mass-compounds in water at ambient temperature are
1 in the range of 5  10
10 to 1  10
9 m2 s [2,18]. Due to physical restriction

H. HARMS AND L. Y. WICK

411

and sorption, effective diffusion coefficients, Deff in soil or sediments can be
1 orders of magnitude lower (9  10
12 to 2  10
21 m2 s ) [19]. The lowest of the reported values correspond with average diffusion distances of 1:2  10
11 m s
1 (1 mm d
1 ) or less in soil or sediments as opposed to 1:2  10
7 m s
1 (1 cm d
1 ) in water. Bosma et al. [1] have proposed including the details of extracellular substrate transport in the calculation of whole-cell Michaelis–Menten kinetics. For the situation of a quasi-steady-state (i.e. when the transport flux and the rate of degradation of the substrate are equal) the consumption of substrate by a microorganism is represented as a function of the distant, and effectively unavailable, substrate concentration cd :
Q ¼ Qmax

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi #  " cd þ KT þ Qmax k
1 1
4cd Qmax k
1  1
1
2
1 2Qmax k ðcd þ KT þ Qmax k
1 Þ

(5)

This adaptation of the so-called Best Equation (for the derivation see [20–22]), describes the substrate uptake Q as a function of cd , Qmax , KT , and the mass transfer coefficient k of the substrate in the environment around the cell. In porous media, mass transfer coefficients depend heavily on Deff and can, for example, be expressed as Deff A=x for linear diffusion [21], Deff 8ro for radial diffusion [21], and kd Asw for the dissolution of solids or separate phase liquids [17,23]. A is the area through which the diffusion takes place, x is the distance, ro is the radius of a cell, kd is the rate constant of dissolution, and Asw is the contact area between a separate phase chemical and the water phase. Equation (5) expresses the interplay between physical mass transfer to the cells, as represented by k, and the oligotrophic capacity of the bacteria, as represented by the quotient of Qmax and KT . A further strength of the concept of Bosma and colleagues [1] is the possibility of estimating the relative physical and biological contributions to the overall degradation rate by extracting and comparing volume-normalised physical and biological rate coefficients. Mostly physically (bioavailability)-limited contaminant degradation rates can thus be distinguished from mostly biologically (e.g. biomass)-limited degradation, although equation (5) illustrates that purely physically or purely biologically determined degradation rates are unlikely to exist. Analysis of experimental data revealed that degradation of hydrophobic substrates in soil and sediments are dominated by mass transfer limitation. 2.4 THE ROLE OF ADHESION AND BACTERIAL CELL SURFACES IN THE PROMOTION OF PASSIVE SUBSTRATE TRANSFER Bacterial adhesion and the formation of biofilms have been frequently reported to occur under mass-transfer-limited conditions. For instance, biofilm

10

−3

10 x a0A

1 x a0A 0.1 x a0A

Substrate flux to the cell / mol s

−1

kg

−1

412 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

10

−4

0.01 x a0A

−5

10

(a) −6

10 x a0A

−3

10

1x

a0A

Substrate flux to the cell/mol s

−1

kg

−1

10

0.1 x a0A −4

10

0.01 x a0A −5

10

(b) −6

−3

10

10 x a0A

Substrate flux to the cell/mol s

−1

kg

−1

10

1 x a0A −4

10

0.1 x a0A −5

10

(c)

0.01 x a0A −6

10

0.1

1 10 Distance to the substrate source/µm

100

Figure 4. Calculation of the substrate uptake driven diffusive transfer of the polycyclic aromatic hydrocarbon anthracene to Mycobacterium sp. LB501T (solid line) and three other imaginary bacterial strains differing from strain LB501T by their 100-fold lower (dots), 10-fold lower (long dashes) and 10-fold higher (short dashes) specific affinities,

H. HARMS AND L. Y. WICK

413

formation and bacterial surface growth have been observed on poorly soluble solid polycyclic aromatic hydrocarbons (PAH) [4,24–26] and liquid hydrocarbons [27–32]. Increased substrate transfer due to bacterial adhesion has been inferred from faster degradation of sorbed or solid PAH than desorption or partitioning rates in the absence of bacteria would suggest [33–35]. Further evidence for the importance of close contact to the substrate comes from the observed drastic loss of microbial activity when the attachment to the substrate source is suppressed with nontoxic surfactants or when adhesion-hindered mutants are used [29,36–40]. Theoretical considerations show that bacterial adhesion to solid, liquid, or sorbed substrates is a powerful mechanism to improve substrate mass transfer. According to Fick’s law, the diffusive mass flux of a substrate towards the cell surface J is strongly affected by the space coordinate in direction of the transport: J ¼ Deff qc=qx

(6)

where qc is the concentration difference between the cell surface and the substrate source. The reduction of the distance between a substrate and the microorganism thus enhances the mass transfer by steepening the concentration gradient. This effect is shown in Figure 2b. It should be noted, however, that when coupled to microbial degradation, the actual diffusion flux is not inversely proportional to the distance, as equation (6) would suggest. Bacteria are not perfect sinks and, as illustrated by the Michaelis–Menten relationship (equation (1) ), the aqueous substrate concentration at their cell surface rises somewhat with increased mass transfer, thereby partly diminishing the gradient. Adhesion of bacteria to surfaces is believed to be mediated by long-ranging colloidal interactions, which hold bacteria in the close proximity of surfaces, thereby facilitating short-ranging hydrophobic interactions and adsorption of cell surface polymers to the surface. The extent of these interactions, and particularly the hydrophobic ones, depends strongly on the properties of

assuming linear pollutant diffusion to the cells (adapted from [17]). Distant aqueous substrate concentrations (cd ) were hypothetically set to 10-fold (a), one-fold (b), and 0.1fold (c) the maximum aqueous solubility of anthracene (cmax ¼ 3:4  10
10 mol m
3 ), corresponding with about 14-, 1.4-, and 0.14-times the whole-cell Michaelis constant (KT ) of strain LB501T. At cd  KT (a), the calculated substrate flux is insensitive to both the specific affinity (a0A ) and the distance from the cell surface, whereas the flux becomes very sensitive to both parameters at cd  KT (b) and cd < KT (c). At dilute substrate concentrations, a high specific affinity leads to more efficient pollutant uptake, resulting in higher pollutant depletion, lower near cell surface concentrations, and higher substrate transfer rates, and indicates the ability of a biological transporter to accumulate a substrate from a dilute solution, respectively [8]

414 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

the interacting cells and surfaces. The cell surface hydrophobicity as a key parameter for adhesion is often expressed as the contact angle (yw ) [41], i.e. the angle included between the tangent plane to the surface of a drop of water and the tangent plane to the surface of a layer of bacteria. Bacteria exhibiting yw < 308 are hydrophilic, whereas yw values of > 708 are considered hydrophobic. Preferences of hydrophobic bacteria for hydrophobic surfaces may explain the finding that particularly hydrophobic bacteria were isolated when hydrophobic membranes were used to extract them from soil instead of using a conventional water extraction protocol [42]. Studies on the efficient PAHdegrading Mycobacterium sp. LB501T that was isolated in this way have shown that bacteria may specifically respond to the low aqueous solubility and low bioavailability of anthracene by modifying their cell envelope [4,43]. Anthracene-grown cells exhibited a higher cell-surface hydrophobicity and adhered up to 70-fold better to hydrophobic surfaces than glucose-grown cells. It was furthermore found that mycobacteria growing on poorly watersoluble substrates exhibited later eluting, more hydrophobic long-chain fatty acids (mycolic acids) in their outer cell wall than cells grown on glucose. This finding is of interest, as mycolic acids are believed to stimulate attachment to hydrophobic surfaces, and hence to increase access to hydrophobic substrates [44,45]. Mycolic acids, which contribute up to 60% of the dry mass of the cell wall, may also significantly increase the sorption of hydrophobic substrates to the cell envelope. Several studies have shown that sorption processes to bacterial biomass may highly influence the distribution and fate of hydrophobic substrates in the environment, for instance by giving rise to bacteriafacilitated transport [46]. The importance of biofilms as a possible sink for dissolved organic and inorganic matter was also investigated. It was found that, despite their hydrogel-like character (96–98% water), biofilm extracellular polymeric substances (EPS) contained about 60–70% of all extracted BTX (benzene, toluene and xylenes), whereas the cells contained less than 20% of the BTX [47]. In a more general approach, Baughman and Paris [48] correlated the n-octanol–water partition constants, Kow , of hydrophobic organic contaminants (HOC) to the microbial sorption coefficient, KB : KB is the ratio of the cell-associated equilibrium HOC-concentration to the HOCconcentration dissolved in the aqueous medium. Close similarities between KB and the Kow of the HOC were found [48,49]. This points to the importance of bioaccumulation of hydrophobic substances in hydrophobic cell walls, cell membranes and the cytoplasm. As no differences between dead and living organisms were found, the bioaccumulation process appears to be passive, i.e. driven by large HOC-activity coefficients (fugacity) promoting HOCexpulsion from the dissolved state by physical processes. It is thus likely that hydrophobic cell envelopes act as transient reservoirs of hydrophobic substances.

H. HARMS AND L. Y. WICK

3 3.1

415

ACTIVE MECHANISMS OF SUBSTRATE MOBILISATION CHEMOTAXIS TO POORLY BIOAVAILABLE SUBSTRATES

As many natural or anthropogenic carbon sources are poorly mobile, their exploitation as food may require the active displacement of organisms to them. This can occur by random movement or in a directed manner. Motile bacteria possess the capability to sense and swim up concentration gradients of chemicals, a behaviour that has been referred to as positive chemotaxis. It is well known that plant root exudates and other plant products are potent attractants for soil bacteria [50]. More recently, several cases of chemotaxis towards environmental contaminants, such as naphthalene, biphenyl, toluene, benzene, nitroaromatic compounds, 2,4-dichlorophenoxyacetate, and various chlorinated ethylenes (reviewed in [51]) have been reported. These attractants have in common the fact that their aqueous solubilities are in the milligram per litre range or higher. This is in contrast to many priority contaminants whose solubilities are much lower. More research will be needed to find out whether less-soluble chemicals can bring about concentration gradients in water that are sufficient for bacterial chemotaxis. For natural polymeric substances, it has been suggested that chemotactic behaviour, in combination with the use of extracellular enzymes to release the monomeric chemoattractants, represents a fast means to search for particulate food sources [52]. Chemotaxis of a marine bacterium to an effectively insoluble polymeric substrate was observed microscopically [53]. The bacterium swam along the gradient of breakdown products generated by a Flavobacterium sp. immobilised in an alginate–agar bead. The chemoattractant was probably derived from protein present as a contaminant in the alginate. It appears unlikely that a similar mechanism employing exoenzymes is involved in the chemodetection of environmental chemicals, whose degradation requires precious cofactors such as NADH that have to be renewed after each reaction. This is, for example, the case for the bacterial dioxygenases involved in the initial attack of many aromatic chemicals. Products of the degradation of natural organic matter (wood) and environmental chemicals by fungal exoenzymes, however, resemble known aromatic attractants [51]. A recent experiment compared for the first time pollutant degradation by chemotactic bacteria and nonchemotactic mutants [54]. The result suggested an important role of chemotaxis in the bioremediation of contaminated soils. In a heterogeneous system, in which naphthalene was supplied from a microcapillary, a 90% reduction in the initial amount of naphthalene took six hours with the chemotactic wild-type Pseudomonas putida PpG7, while a similar reduction with either a chemotaxis-negative or a nonmotile mutant strain took about five times longer. Only the systems inoculated with the chemotactic strain exhibited degradation rates in excess of the rate of naphthalene diffusion from the

416 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

capillary. This suggests that chemotaxis to pollutants can overcome the masstransfer limitations that govern biodegradation rates. 3.2 DOES CELL CONTACT WITH A SUBSTRATE RESERVOIR ALLOW THE DIRECT UPTAKE OF SORBED, LIQUID, GASEOUS, AND SOLID SUBSTRATES? We have discussed the positive effects that bacterial displacement and adhesion to substrates exerts on the diffusive mass transfer. Theoretically, direct contact with the substrate could also allow microorganisms to employ other modes of uptake in addition to absorption of water-dissolved molecules. So, which are the physical states for which chemicals can be ingested by microorganisms? Environmental chemicals occur as pure liquid or solid compounds, dissolved in water or in nonaqueous liquids, volatilised in gases, dissolved in solids (absorbed) or bound to interfaces (adsorbed). Figure 5 gives a schematic view of the different physical states at which substrates are taken up by microbial cells. There is a consensus that water-dissolved chemicals are available to microbes. This is obvious for readily soluble chemicals, but there is also clear evidence for microbial uptake of the small dissolved fractions of poorly water soluble compounds. Rogoff already had shown in 1962 that bacteria take up phenanthrene from aqueous solution [55]. In the intervening time many other researchers have made the same observation with various combinations of microorganisms and poorly soluble compounds [14,56,57].

?

NAPL-bound or liquid substrate

Emulsified substrate

Volatilised substrate

?

Water-dissolved substrate

(Bio-)surfactant-bound substrate

Solid substrate

Adsorbed substrate

Absorbed substrate

Figure 5. Schematic representation of the different physical states at which environmental chemicals occur, with an indication of how these substrates are taken up by bacteria. Note that there is unanimous agreement only on the uptake of water-dissolved low-molecular-weight molecules

H. HARMS AND L. Y. WICK

417

Regarding the architecture of microbial surfaces, the water-dissolved state intuitively appears to be most suitable for the uptake. The cell walls of many bacteria and fungi represent hydrated polymeric layers similar to aqueous gels (see, for example, [58]) through which molecules diffuse before they come into contact with a transporter protein or the lipid bilayer of the cell membrane. There is still discussion about the ingestion of chemicals in all other physical states. It often seemed that substrates which occur in pure form or sorbed to a solid had to dissolve or to desorb, respectively, to become available for microbial uptake [59,60]. A smaller number of observations indicated that undissolved substrate molecules can also be taken up by microorganisms. There are two principal ways to prove the uptake of molecules in a form other than the water-dissolved state. The direct proof would be the microscopic observation of, for instance, the ingestion of substrate crystals. But also indirect proof is conceivable. If only water-dissolved molecules were available for uptake, the maximum uptake rate of poorly soluble compounds would be set by the maximum water-soluble concentration of the chemical. The observation of uptake rates in the presence of separate phase compounds higher than those that can be achieved with saturated aqueous solutions would then strongly indicate the ingestibility of the nondissolved compound. This approach has frequently been taken to investigate the possible direct availability of sorbed substrates [34,61–64]. Experimental data included in coupled desorption/degradation models seem indeed to support the direct accessibility of the sorbed molecules. Comparison of initial desorption rates in the absence of bacteria with degradation rates in the presence of bacteria, indicated the degradation of compounds that would not have been released in the water phase in a sterile system. This discrepancy is regarded as a proof for the direct interaction of the bacteria with the sorbed molecules. Closer inspection of model assumptions and theoretical consideration of possible mechanisms of sorbed-compound bioavailability, however, show that these reports are not conclusive. From a mechanistic perspective, the problem boils down to the question as to whether bacteria are able: (1) to enzymatically attack molecules that are still sorbed while the enzymesubstrate-complex is formed; (2) to take up molecules that are still sorbed while the transporter-substratecomplex is formed; or (3) to passively take up molecules without involvement of desorption into the aqueous phase. The release of sorbed molecules into the bulk water can be described as a sequence of a maximum of three processes: the transfer of absorbed or micro pore-sequestered molecules to the sorbent–water interface, the desorption in the narrow sense, i.e. the subnanometre movement of the sorbate that replaces its

418 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

solid environment by an aqueous one, and film diffusion to the bulk water. In many cases, the intra-sorbent transfer to the sorbent–water interface has been found to control the overall desorption rate of absorbed or pore-sequestered, i.e. aged, molecules [65,66]. It can be assumed, however, that direct contact of bacteria with these molecules is not possible before the molecules appear at the sorbent–water interface that is accessible to bacteria. Molecules present at the sorbent–water interface, either formerly absorbed ones that have reached the interface, or truly adsorbed ones (e.g. adsorbed to mineral surfaces exposed to the water phase) desorb (in the narrow sense) into the water phase. Only if this desorption is the rate-limiting step of the whole release process, do mechanisms (1), (2) or (3) have an impact on the overall rate. At least for formerly absorbed or micro pore-sequestered molecules, limitation of the overall release by the desorption step at the interface is quite unlikely. The so-called film (or diffusion layer) diffusion is the limiting step in the dissolution of crystals and droplets (see e.g. [67]), and may also be the process that limits the rate of appearance of adsorbed molecules in the bulk water phase. Even under conditions of percolation or mild stirring, particles are surrounded by a diffusion layer, the mass transfer through which is controlled by molecular diffusion. With laminar flow such as encountered in groundwater, the diffusion layer is typically between 50 and 100 mm thick [68]. A bulk water phase containing a subequilibrium concentration of the sorbate will thus drive desorption from this distance of 50 to 100 mm. This results in a concentration gradient between the bulk phase concentration and the interfacial aqueous pseudo-equilibrium concentration extending over these 50 to 100 mm. Release rates that are obtained under abiotic conditions reflect this bulk-phase driven desorption. They enter into desorption/degradation models and serve for comparison with observed degradation rates. Bacteria can influence dissolution and desorption rates without directly interfering with the intraparticle mass transfer or the desorption step. When attached to the sorbent, bacteria drive desorption by substrate uptake from deep inside the diffusion layer. Their distance to the sorbent is below 1 mm, and the effect of this shortened distance can be easily calculated (see also Figure 4). Assuming that the aqueous substrate concentration at the cell’s surface is identical to the concentration in the bulk aqueous phase in a sterile setting, the much closer distance between adhered bacteria and the sorbent results in a roughly hundred-fold steeper concentration gradient. It can be concluded that comparison of abiotic desorption rates with degradation rates can be misleading unless distance effects are accounted for mathematically. Harms and Zehnder [33] found that the high degradation rate of sorbed 3-chlorodibenzofuran by sorbent-associated Sphingomonas sp. HH19k was in agreement with the assumption that only desorbing 3-chlorodibenzofuran, not the sorbed compound, was available for degradation. The same was found for the crystalline substrates naphthalene and phenanthrene [69]. Wick et al. [17] were able to explain the fast development of Mycobacterium sp. LB501T

H. HARMS AND L. Y. WICK

419

biofilm on anthracene crystals with anthracene dissolution and aqueous phase diffusion to the adjacent biofilm. This was surprising as anthracene has an aqueous solubility of only 3:47  10
10 mol m
3 at 25 8C [2]. It was found that the calculated diffusive anthracene flux critically depended on the assumption of a submicrometre distance between anthracene crystals and biofilm. Scanning electron microscope images taken at early stages of biofilm formation showed craters on the anthracene surface, some of which enclosed bacteria. These craters were absent on fresh anthracene crystals, and could be attributed to anthracene dissolution driven by anthracene consumption by surfaceassociated bacteria. In the following subsection, mechanistic considerations from a microbe’s perspective about the direct access to nonaqueous substrates will be made and discussed in the context of further experimental findings. 3.2.1

Solid Substrates

Theoretically, solid substrates could be taken up directly by phagocytosis [70]. However, this has never been observed, and it seems unlikely for bacteria, which are covered by rigid cell walls. Alternatively, solid-state molecules might dissolve in the membranes of adjacent bacteria upon physical contact. Several early investigations did not indicate such a mechanism. Wodzinski and Johnson [71] showed that growth rates of bacteria in the presence of either crystalline naphthalene, phenanthrene, or anthracene depended on the respective solubilities of these aromatic hydrocarbons in water. The same group showed that growth rates of bacteria on media containing only dissolved naphthalene or bibenzyl were equal to those on media containing the dissolved and solid chemicals [56]. Similarly, bacterial growth rates on crystalline naphthalene and 4-chlorobiphenyl fell abruptly after the dissolved fractions of the substrates were depleted from the medium [72]. Stucki and Alexander [57] studied the degradation of solid biphenyl by three different bacteria. They observed only small numbers of bacteria on the crystal surfaces, indicating that the degradation of biphenyl took place in the aqueous state. Calculations furthermore showed that the biphenyl consumption at any instant was smaller than the maximum dissolution rate of biphenyl, and thus explainable by exclusive utilisation of the dissolved fraction. Growth of two bacteria on phenanthrene was initially exponential, and later became linear. Calculations suggested that the dissolution rate of phenanthrene limited the biodegradation rate in the linear growth phase. Linear growth of bacteria on naphthalene was also ascribed to the limited dissolution of the crystalline substrate [73], since the growth rates were positively correlated with the total surface area of the naphthalene crystals. Growth rates were also in agreement with model predictions, which accounted for the bacterial growth kinetics and the dissolution kinetics of naphthalene. In a further study by the same authors [22], dissolution rates of crystalline naphthalene were inferred from bacterial growth and

420 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

compared with independently determined dissolution rates. The small apparent enhancement of naphthalene dissolution by several Pseudomonas strains could be attributed to inaccuracies of model parameters, since the bacteria neither grew in direct association with the crystals (as was observed microscopically), nor excreted surface active products which could have mobilised naphthalene. Growth curves with crystalline dibenzofuran and dibenzo-p-dioxin were generally characterised by a short exponential growth phase that was followed by an extended linear growth phase before the growth stopped [74–78]. The linear growth phase was found to be accompanied by dissolution-limited, zero-order consumption of the solid substrate [74]. When solid dibenzofuran was provided as large spheres with a much lower available surface area, the dissolution limitation of growth of Sphingomonas sp. HH19k was much more pronounced [78]. It can be concluded that in none of these reports were growth or degradation rates found that suggested the uptake of solid substrate in solid form. 3.2.2

Liquid Substrates

The following model for bacterial growth on poorly soluble liquid hydrocarbons has been proposed [79] and experimentally confirmed (e.g. [80]). Initially, bacteria grow exponentially in contact with hydrocarbon droplets until the interfacial area is covered with cells. Consequently, exponential growth lasts longer with greater interfacial area. As there is an equilibrium between attached and suspended cells, the exponential growth rate is higher, when more interfacial area is available, i.e. a higher fraction of the cells are in the growing, attached state. The exponential growth phase is followed by a linear growth phase, the rate of which is higher for larger interfacial areas supporting more biomass. Unfortunately, this model does not permit statements to be made about the mode of hydrocarbon uptake by the attached bacteria. Regarding the possibility of direct uptake of nonaqueous phase liquids by bacteria, three theoretical mechanisms can be conceived. Firstly, entire droplets of these liquids may be channelled through pores in the cell envelope into the cytoplasm. However, if such pores do exist, their maximum size would have to be very small, as they have never been observed electron microscopically. Secondly, entire droplets could enter the cell surrounded by parts of the cell membrane – a process known as pinocytosis. The organic liquid would remain separated from the cell content and could be slowly released into the cytoplasm or degraded by membrane-bound enzymes. An argument against such a mechanism is the dense texture of bacterial cell envelopes, which might prevent its penetration by droplets just as discussed before. Moreover, many utilisable environmental chemicals like PCBs and the components of petroleum and tar oil occur as mixtures of liquids or dissolved in organic solvents. It is likely that individual microorganisms only utilise some constituents corresponding with a

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small mass fraction of these mixtures. In the case of unselective uptake, such organisms would also require mechanisms to excrete or inactivate the remainder. Thirdly, it is conceivable that droplets may fuse with and flow into the lipid bilayer upon contacting a cell membrane. However, depending on the size of the droplets, this would result in drastic changes in the membrane composition, which are likely to affect the cell. Such an uptake mechanism would require a high tolerance of the cells against these changes, or an efficient selection system enabling the cell to recognise droplets of appropriate size and chemistry. A study by Sikkema et al. [81] showed that the accumulation of the hydrophobic compound tetralin in bacterial membranes from aqueous solution exerted considerable toxic effects by swelling the membrane. Several observations, nevertheless, suggest the direct uptake of nonaqueous liquids. Much of this work was performed in the context of the, later abandoned, production of single cell protein as animal feed from mineral oils around 1970. Johnson [82] discussed the possibility that when microorganisms attach to droplets of alkane, the long alkane chains become a part of the phospholipid bilayer of the cell membrane. This could involve a lipophilic pathway leading the chemical from the outside of the cell membrane to the locus of the enzyme responsible for the primary attack on the hydrocarbon. The author furthermore calculated – from diffusion kinetics and water solubilities – that appreciable growth rates cannot be obtained on dodecane and higher hydrocarbons unless a mechanism other than the uptake of water-dissolved substrate molecules is available. A similar conclusion was drawn by Aiba et al. [36,37] based on interfacial areas of oil droplets and growth characteristics of Candida guilliermondii. They calculated that the hexadecane consumption by the cells was approximately six orders of magnitude faster than the dissolution in the aqueous phase. Their conclusion was that the uptake of dissolved hydrocarbon can be neglected when longer-chain hydrocarbons such as hexadecane are used as a substrate. Yoshida and Yamane [83] observed that the rate of dissolution of hexadecane that was estimated from the solubility and diffusivity in the aqueous phase was much smaller than the value calculated from the growth rates of Candida tropicalis. They furthermore observed the formation of submicronsized droplets and assumed the direct uptake of these droplets by the yeast. A pinocytotic mechanism was also postulated for the transport of hydrocarbons in Candida lipolytica [84]. Transmission electron microscopy showed the accumulation of hexadecane and gas oil at the cell membrane and the release of pinocytotic vesicles from the cell membrane into the cytoplasm. However, it remained unclear whether the hydrocarbons penetrated the cell wall as complete droplets or as dissolved molecules that then recondensed at the cell membrane. Hori et al. [85] showed the importance of direct bacterial contact with a NAPL phase containing the growth substrate. The degradation of n-heneicosan dissolved in pristane by Acinetobacter sp. CR was suppressed by either fast agitation, reducing NAPL-attached cell numbers or subcritical

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micellisation concentration (c.m.c.) surfactant concentrations interfering chemically with bacterial attachment. Several other observations point to the exclusive uptake of monodispersed substrate. The presence of intracytoplasmic hydrocarbon inclusions in Acinetobacter sp. HO1-N during growth on hexadecane seemed to confirm the hypothesis that complete oil droplets can be taken up by bacteria [86]. However, no membrane-bound or cell-wall-bound intermediate stages of the uptake process were found that could have confirmed the uptake of entire droplets. Moreover, the limiting membrane of the hexadecane inclusions was a phospholipid-rich monolayer structure containing four or five major polypeptide bands, as determined by SDS-polyacrylamide gel electrophoresis [87]. The differences in the peptide banding pattern and lipid composition of this membrane fraction as compared with the other membrane fractions of the cell suggested de novo synthesis, rather than its derivation from the cytoplasmic or outer membrane. Consequently, it did not appear that the hydrocarbon droplets were transported by a pinocytotic mechanism, but were rather formed secondarily from molecules taken up in the water-dissolved state. A recent electron microscopic visualisation of carefully preserved interfaces between biosurfactant producing bacteria and droplets of waste oil showed a close association that was mediated by electron-dense bacterial excretion products [88]. The authors’ claim of an observation of direct uptake of nm-sized oil droplets is, however, not justified by the micrographs presented. 3.2.3

Sorbed Substrates

Theoretically, only adsorbed, i.e. surface-bound, molecules can be directly available for microbial uptake. As pointed out before, molecules which are absorbed, i.e. dissolved in a solid, are unlikely to be contacted by microorganisms unless they appear at the surface of the sorbent, i.e. they change from the absorbed to an ephemeral ‘adsorbed’ state. Therefore, the discussion of the direct availability of sorbed molecules will be restricted to adsorbed molecules. A model by Ogram et al. [59] assumed that soil-associated bacteria degraded only water-dissolved 2,4-dichlorophenoxyacetic acid (2,4-D), whereas the sorbed chemical was completely protected from degradation. This model could explain the experimentally observed kinetics of 2,4-D degradation. Ehrhardt and Rehm [89] ascribed the drastically reduced toxicity of phenol for Pseudomonas sp. in the presence of activated carbon to sorption of the phenol, which largely reduced the aqueous concentrations. They could also show that the sorbed phenol was degraded upon desorption and diffusion out of the activated carbon. Subba-Rao and Alexander [90] suggested that the mineralisation of montmorillionite-sorbed benzylamine was limited by the desorption of the chemical. The mineralisation rates measured at various solute to sorbent ratios were always equal to or smaller than the corresponding desorption rates.

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Alvarez-Cohen et al. [91] explicitly showed that microbial transformation rates of trichloroethylene (TCE) were proportional to the aqueous TCE concentrations and independent from zeolite-sorbed TCE concentrations. Apparently in contrast to these findings, Crocker et al. [92] reported on the direct bioavailability of naphthalene sorbed to hexadecyltrimethylammonium (HDTMA)modified smectite clay to Pseudomonas putida 17848, but not to Alcaligenes sp. strain NP-Alk. It should be noted that sorption to the hexadecyl chains of HDTMA resembles more the solubilisation by a surfactant than adsorption to a solid surface. Possibly, hydrophobic surface structures of strain 17848 allowed the close contact with HDTMA, thereby facilitating the uptake of naphthalene by a lipophilic pathway. The principal difference between adsorbed and solid substrates is that the latter are adsorbed to molecules of their own kind. With respect to their bioavailability, multilayer-sorbed molecules should behave like a solid substrate. A calculation shows that the direct uptake of truly adsorbed molecules is probably neither advantageous to bacteria nor can it be shown experimentally. Cells of the dibenzofuran-degrading Sphingomonas sp. HH19k consume at maximum 100 000 molecules per second [14]. Assuming that an adhered cell touches a sorbent with 1% of its cell surface at a time, as was proposed by van Loosdrecht et al. [60], it would contact about 100 000 sorbed molecules at a time, representing substrate for only one second. This does not contradict the possibility of direct uptake of truly adsorbed molecules, but it illustrates that such an uptake-mechanism would be relatively unimportant. It can be concluded that the uptake of molecules by microorganisms in other than the water-dissolved state seems to be the exception rather than the rule. Neither the observation of direct contact of microorganisms with nondissolved substrates, nor the fact that in some cases this contact is needed for microbial growth or substrate degradation, provide evidence for the direct uptake of the separate phase substrates. 3.3 MOBILISATION OF HYDROPHOBIC ORGANIC SUBSTRATES USING BIOSURFACTANTS Microbes were frequently found to synthesise surface-active molecules in order to mobilise hydrophobic organic substrates. These biosurfactants, which are either excreted by the producing organisms or remain bound to their cell surfaces, are composed of a hydrophilic part making them soluble in water and a lipophilic part making them accumulate at interfaces. With respect to their physical effects, one can distinguish two types of biosurfactants: firstly, molecules that drastically reduce the surface and interfacial tensions of gas– liquid, liquid–liquid and liquid–solid systems, and, secondly, compounds that stabilise emulsions of nonaqueous phase liquids in water, often also referred to as bioemulsifiers. The former molecules are typically low-molar-mass

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compounds, such as glycolipids or glycolipopeptides, whereas the latter ones are frequently high-molar-mass compounds composed of polysaccharides, proteins, lipopolysaccharides, or lipoproteins. Microbes are known that produce both types of compounds simultaneously [93]. Detailed information about structural features of biosurfactants is available in a recent review article [94], and data about the surface activities and emulsifying properties have been summarised by Lang [95]. 3.3.1 Mobilisation of Liquid, Solid or Sorbed Substrates by Solubilisation in Biosurfactant Micelles At concentrations above their aqueous solubility, the so-called c.m.c., lowmolar-mass biosurfactants form micelles in the aqueous phase. Micelles are spherical or lamellar aggregates with a hydrophobic core and a hydrophilic outer surface. They are capable of solubilising nonpolar chemicals in their hydrophobic interior, and can thereby mobilise separate phase (liquid, solid or sorbed) hydrophobic organic compounds. The characteristics for the efficiency of (bio)surfactants are the extent of the reduction of the surface or interfacial tension, the c.m.c. as a measure of the concentration needed to bring about this reduction, and the molar solubilisation ratio MSR, which is the number of moles of a chemical solubilised per mole of surfactant in the form of micelles [96]. Micelles forming above the c.m.c. incorporate hydrophobic molecules in addition to those dissolved in the aqueous phase, which results in apparently increased aqueous concentrations. It has to be noted, however, that a micellesolubilised chemical is not truly water-dissolved, and, as a consequence, is differently bioavailable than a water-dissolved chemical. The bioavailability of hydrophobic organic compounds was, for instance, reduced by the addition of surfactant micelles when no excess separate phase compound was present and water-dissolved molecules became solubilised by the micelles [69]. In these experiments, bacterial uptake rates were a function of the truly water-dissolved substrate concentration. It seems therefore that micellar solubilisation increases bioavailability only when it transfers additional separate phase substrate into the aqueous phase, e.g. by increasing the rates of desorption or dissolution, and when micelle-solubilised substrate is efficiently transferred to the microorganisms. Theoretically, this transfer can occur exclusively via the water phase, involving release of substrate molecules from micelles, molecular diffusion through the aqueous phase and microbial uptake of water-dissolved molecules. This was obviously the case, when bacterial uptake rates of naphthalene and phenanthrene responded directly to micelle-mediated lowered truly waterdissolved concentrations of these chemicals [69]. These authors concluded from their experiments that micellar naphthalene and phenanthrene had to leave the micellar phase and diffuse through the water phase to become

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available for bacterial uptake. A similar conclusion was drawn by Grimberg et al. [97] for micellar phenanthrene. They clearly showed the unavailability of micellar phenanthrene for uptake by Pseudomonas stutzeri. When micelle-solubilised substrate is not directly available for microbial uptake, positive effects of substrate-solubilisation may nevertheless be observed, e.g. from faster dissolution or desorption or because a bigger substrate reservoir is present in the aqueous surroundings of the cells, assuring better resupply of consumed substrate and, possibly, from faster effective diffusion of substrate in micellar form. In a recent study, Garcia et al. [78] showed that micelles of the surfactant Brij 35 facilitated the diffusive transfer of dibenzofuran. Experimental results indicated, and calculations confirmed, that the effective diffusion of micellar dibenzofuran was slightly faster than diffusion of dissolved dibenzofuran. Surfactant micelles of assumed 4  10
9 m diameter diffused 7.9 times slower than individual dibenzofuran molecules, while they contained on average 14.6 dibenzofuran molecules. The extent of dibenzofuran solubilisation overcompensated the reduced diffusivity of micelles, and resulted in roughly two times faster effective diffusion of micellar dibenzofuran as an additional transport process besides diffusion of truly dissolved dibenzofuran. In the same study, the degree of dispersion of micelle-solubilised dibenzofuran and its effect on substrate bioavailability was calculated. It turned out that under the experimental conditions, the average distance between individual micelles (or between a bacterium and the nearest micelles) was in the order of 10
7 m, a distance that a molecule leaving such a micelle would pass through by aqueous diffusion in only 10
5 s. Theoretically, increased bioavailability could also result from direct uptake of biosurfactant micelles by microorganisms, or by direct transfer (not involving aqueous diffusion) of substrate molecules via a hydrophobic path from micelles to bacteria. In view of the fact that many bacterial surfactants represent cell membrane constituents, which are released by the cells [98,99], the possibility of a reintegration of biosurfactant micelles into the bacterial cell surface is not far-fetched. Such a fusion would be controlled by colloidal forces. Fusion of surfactant micelles with bacterial membranes would be a reasonable explanation for the frequently observed toxic effects of these agents at concentrations above, but not below the c.m.c. [100–104]. It may also explain the usually higher toxicity of cationic surfactants [103], which are electrostatically attracted by negatively charged cells. Although direct uptake of (bio)surfactant micelles by bacteria has been suggested [104], it has not been observed microscopically, yet. However, molecules of the Bacillus subtilis biosurfactant surfactin were found to be perfectly miscible with phospholipids, and to penetrate spontaneously into lipid membranes by means of hydrophobic interactions [105]. Miller and Bartha [106] postulated that unilamellar liposomes could easily pass through Gram-negative cell walls and fuse with the cell membrane. Encapsulated chemicals would then be delivered directly to membrane-bound enzyme systems of

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the intact cells. Experiments showed that liposome-carried 14 C-octadecane was indeed more rapidly delivered to a Pseudomonas isolate than free octadecane, and resulted in faster growth. However, the determination of 14 C-octadecane uptake probably did not discriminate between membrane-incorporation of liposomes and a loose association of entire liposomes with the cell surface. It may well be that the faster octadecane uptake resulted from its efficient release from the large specific surface area of liposome preparations, as compared with the much lower surface area of octadecane droplets. This was supported by the fact that sonication of octadecane in the absence of liposomes also resulted in increased uptake. Guha and Jaffe´ [107] measured phenanthrene biodegradation rates in the presence of four non-ionic surfactants. These rates were compared with model calculations accounting for the partitioning of phenanthrene between the micellar and water-dissolved phase and for bacterial kinetic parameters. The data indicated the direct availability of phenanthrene when solubilised by three of the surfactants. When solubilised by Brij 35, the surfactant with the longest hydrophilic residue, phenanthrene, was unavailable for bacterial uptake. The authors suggested that the interaction of the cell surfaces with the latter micelles was unfavourable. The fact that many biosurfactants are biodegraded, i.e. taken up along with their hydrophobic solubilisates is another good argument for direct uptake of biosurfactant micelles. Bury and Miller [108] reported on the stimulation of decane and tetradecane uptake by a simultaneously biodegraded biosurfactant. Further indirect support for the direct uptake of biosurfactant micelles comes from the finding that the bioavailability of micellar substrates is often strainspecific and dependent on the energy status of the receiving cells. Specificity of biosurfactant-solubilised substrate uptake indicates physical interaction between bacteria and biosurfactant micelles, which should be controlled by physicochemical cell characteristics. In accordance with this, surface-active agents synthesized by the yeast Yarrowia lipolytica 180 enhanced the oil-degrading activity of hydrophilic Moraxella sp. K12-7, whereas they inhibited the oildegrading activity of the hydrophobic Pseudomonas sp. K12-5 [109]. High specificity of biosurfactant action was also observed in a study of polychlorinated biphenyl degradation [110]. Rhamnolipids produced by Pseudomonas aeruginosa UG2 that were exogeneously added to cultures of this bacterium improved hexadecane degradation [111]. The same biosurfactant did not stimulate hexadecane degradation by four other hexadecane-degrading bacteria to the same extent, and neither did the biosurfactants produced by these other organisms. Uptake of rhamnolipid-solubilised 1-naphthylphenylamine by Pseudomonas aeruginosa UG2 was also enhanced, although not in de-energised cells, indicating energy-dependent uptake. The influence of rhamnolipid on the bacterial hexadecane uptake was supported in a separate study, where Noordman et al. [112] employed various experimental systems, in which either the physical mass transfer or the biological uptake of hexadecane by Pseudomonas

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aeruginosa UG2 was the limiting step. They could show that the addition of rhamnolipid stimulated the hexadecane uptake by the bacteria rather than the mass transfer to the bacteria. Both a positive influence and energy-dependency of the uptake of rhamnolipid-solubilised hexadecane were also found in Pseudomonas aeruginosa PG201 [113]. Species-specific action of a biosurfactant was also found for sophorolipid, a biosurfactant produced by Candida bombicola ATCC 22214, which showed antimicrobial activity against Bacillus subtilis, Staphylococcus xylosus, Streptococcus mutans, Propionibacterium acne, and the plant pathogenic fungus, Botrytis cineria, resulting in leakage of intracellular enzymes [114]. No effect on Escherichia coli was found, indicating that the selective antimicrobial activity of sophorolipid depended on the cell wall structure. A different mechanism of solubilisation was reported for the protein AlnA that had been purified from the multicomponent emulsifier alasan synthesised by Acinetobacter radioresistens KA53 [115]. Native gel electrophoresis indicated that AlnA, which is characterised by four hydrophobic regions, formed hexamers in the presence of PAH compounds. At low molar ratios of fluorene to AlnA, only the monomer was observed, whereas hexamers were detected at higher ratios. This indicated that single fluorene molecules bind to the monomeric form of AlnA, and, as the amount increases above one bound fluorene molecule per AlnA, the protein aggregates to form a specific oligomer of five to eight monomers, which allows for the binding and solubilisation of more fluorene. With 12 PAHs, maximum molar ratios between 4.3 and 55.8 were observed. The reduction of interfacial tensions by biosurfactants can also result in macroscopic mobilisation of hydrophobic organic chemicals. Rhamnolipids at a concentration of 0.25% greatly enhanced pyrene transport in sand, and could facilitate contaminant recovery [116]. An economically important field of application of biosurfactant-producing microorganisms is the extraction of mineral oil. One of the most important factors that limits oil production is the entrapment of oil in small pores by capillary forces. Here, biosurfactants are potentially very useful, as they drastically decrease the interfacial tension between the oil and the oil-containing rock. The reduction of the interfacial forces between the oil and brine will release the entrapped oil, and may be the most important mechanism for microbially enhanced oil recovery. Other bacteria expose amphiphilic molecules on their outer surface and act as emulgating agents, thereby positively influencing the ratio between oil and brine in the extracted liquid [117,118]. 3.3.2

Mobilisation of Liquid Substrates by Emulsification

Many high-molar-mass bacterial surfactants, or bioemulsifiers, are relatively inefficient in reducing interfacial tensions, but rather stabilise emulsions of

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nonaqueous phase liquids in water by preventing their coalescence [119]. Emulsification is distinguished from micellar solubilisation, in that entire nonaqueous micro-droplets are stabilised by surface-attached amphiphilic molecules or microorganisms. The primary effect of emulsification regarding the bioavailability of hydrophobic compounds is the enlargement of the interfacial area between the aqueous phase and the nonaqueous liquid, resulting in higher dissolution rates and providing additional interface for microbial attachment. Growth on poorly soluble liquids is typically exponential until the interface is covered by cells. Therefore, exponential growth lasts longer when more interfacial area is available. The mass ratios of bioemulsifiers to emulsified hydrocarbon are typically lower than between micelle-forming biosurfactants and their solubilisates. The emulsifying activity is usually quantified by turbidity measurement after emulsification by 30 min of intense vortexing of standard quantities of emulsifier, nonaqueous phase liquid and water, and expressed in turbidity units [120]. The stability of the emulsion is checked by a second turbidity measurement of the emulsion that had been left undisturbed for 24 h and expressed in per cent of the initial measurement. Unfortunately, turbidities cannot be easily converted into masses of nonaqueous phase liquid emulsified per mass of emulsifier, and comparison of emulsifying activities from different studies is hardly possible. As the enlargement of the nonaqueous liquid–water interface is the primary effect of emulsification, gain in interface per total liquid volume per mass unit of emulsifier might be an appropriate dimension for the activity of an emulsifier. In some cases, the droplet size of emulsion was determined by microscopy [85,121] or laser diffraction [122]. A well-studied example of a bioemulsifier is emulsan, a cell surface-exposed molecule that allows Acinetobacter calcoaceticus RAG-1 to attach to crude oil droplets [123]. Upon depletion of the short-chain alkanes utilised by this strain, the emulsan molecules were released from the bacterial surface, thereby allowing the cells to leave the oil droplet and to find a new substrate. Important positive side-effects of this mechanism seem to be that the remaining emulsan hydrophilises the droplet and prevents both the reattachment of A. calcoaceticus RAG-1 and the coalescence of the used oil droplet with other droplets that still contain unexploited alkanes. Bredholt et al. [124] studied the oilemulsifying activity of Rhodococcus sp. strain 094. When exposed to inducers of crude-oil emulsification, the cells developed a strongly hydrophobic character, which was rapidly lost when crude-oil emulsification started. This indicated that the components responsible for the formation of cell-surface hydrophobicity acted as emulsion stabilisers after release from the cells. Willumsen and Karlson [125] screened 57 PAH-degrading bacteria isolated from PAH-contaminated soil for the production of biosurfactant compounds. The majority of the strains isolated on phenanthrene, pyrene, and fluoranthene were better emulsifiers than surface-tension reducers, and the stability of the

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formed emulsions was in general high. The strains isolated on anthracene were in general better in lowering the surface tension than in forming emulsions. In all strains, reduction of surface tension and emulsion formation did not correlate. However, in the majority of strains the two factors were associated with the bacterial cell surfaces, rather than the culture supernatants. Besides its solubilising activity, the protein AlnA of Acinetobacter radioresistens KA53 was also found to have strong substrate-specific emulsifying activity [126]. The 45 kg mol
1 protein was more effective in emulsifying hexylbenzene, hexadecane, and crude oil than in emulsifying low-molar-mass aliphatic and aromatic hydrocarbons. A Pseudomonas aeruginosa isolated from polluted soil was found to produce a 14 kg mol
1 peptidoglycolipid with high emulsifying activity [127]. Bioemulsifiers were also reported to facilitate the degradation of diesel oil [128], crude oil [129], n-alkanes [122], middle-length chain alkanes [130], heptadecane [131], petroleum fuels [121], aromatic and aliphatic hydrocarbons, crude oil, creosote [132], and benzo-(a)-pyrene dissolved in diesel-oil [133]. It has been argued that the evolutionary advantage of bioemulsifiers for the producing organisms is unclear, as concentrations needed for emulsification can hardly be achieved in open natural systems. However, in the immediate vicinity of cell surfaces and in shielded environments such as soil pores, the enrichment of bioemulsifier may be sufficient to result in substrate mobilisation [94]. Interesting in this respect is the recent finding that the production of low- and high-molar-mass biosurfactants by some bacteria is up-regulated in a culture density-dependent manner. The best-studied example is the quorum sensingcontrolled synthesis of rhamnolipids by Pseudomonas aeruginosa [134,135]. 3.4 MOBILISATION OF SUBSTRATES USING EXTRACELLULAR ENZYMES A large fraction of all natural organic matter in aqueous and terrestrial systems is polymeric in nature and not directly available for microbial uptake. Even the generally more permeable cell walls of Gram-negative bacteria exclude the uptake of molecules larger than about 0:6 kg mol
1 , a limit that is set by the size of unspecific channel proteins in the outer membranes – referred to as porins [3]. Microorganisms therefore exploit this major reservoir of metabolisable carbon using extracellular enzymes that may either remain cell surface bound or be released from the organism. Microorganisms excrete specific hydrolases for all classes of hydrolysable polymers of biological origin, including polysaccharides, polypeptides, nucleic acids and lipids. Non-hydrolysable biopolymers such as lignins are attacked by extracellular enzymes of fungal origin, such as laccases, peroxidases and ligninases. In an exhaustive theoretical treatment, Vetter et al. [52] have elaborated on the potential costs and benefits of the use of freely released extracellular enzymes for particulate organic-matter degradation. Although their main focus was on organic-matter degradation in

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marine sediments, the thorough sensitivity analysis of their mechanistic model, involving large variations of model parameters, expands the scope of their considerations to various other environmental systems, and to other mobilising agents such as biosurfactants or siderophores. They considered the case of a single spherical microbe immobilised in the centre of an aggregate that is composed of exploitable particulate organic matter, inert particles and waterfilled pores. The flux of excreted extracellular enzymes away from the bacterium and the flux of hydrolysate was treated in terms of diffusive transport in spherical coordinates. The influences of 16 independent variables were considered in model calculations. Cost–benefit considerations were based on the conservative assumption that the mass ratio between hydrolysate reaching the cell and enzyme excreted has to be at least 10 to result in a net benefit for the cell. This ratio can be much smaller when, for example, growth-limiting elements are mobilised by the action of the exoenzyme. Model calculations led to the following general conclusions: (1) extracellular enzymes can support microbial growth under a large range of environmental conditions; (2) exploited distances are typically in the range of 10 to 50 mm; (3) the efficacy of extracellular enzymes is most sensitive to the specificity of enzyme-substrate binding and the enzyme inactivation rate; (4) low observed concentrations of free extracellular enzymes [136] may reflect high binding constants with the particulate substrates; (5) excess solubilisation, i.e. hydrolysate diffusion away from the microbe is between one to two orders of magnitude higher than hydrolysate diffusion to the microbe; (6) enclosure of bacteria in microaggregates, e.g. in pores and shielding by surfaces, increases the efficacy of the use of extracellular enzymes by constraining hydrolysate diffusion; and (7) steady-state concentration profiles of extracellular enzymes and hydrolysates establish within seconds, suggesting that extracellular enzymes in combination with chemotaxis represent a fast means of searching for particulate food sources. 3.5

MOBILISATION OF IRON USING SIDEROPHORES

Iron is an essential cofactor of numerous enzymes, involved in, for instance, electron transfer and oxygen metabolism. It seems counterintuitive that the fourth most abundant element in the biosphere is in many instances the least bioavailable bioelement and therefore the limiting growth factor. The reason for this lies in the extremely low solubility of ferric iron (Fe3þ ) – the prevailing form of iron under oxic conditions. Iron is precipitated as Fe(OH)3 with a solubility product of 10
39 , which limits the aqueous concentration of ferric ion

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to about 10
18 mol dm
3 at neutral pH, whereas microorganisms require a minimum effective concentration of 10
8 mol dm
3 for growth [137]. An exception is the soil bacterium Lactobacillus plantarum, which does not require iron because it activates all its enzymatic functions with metals other than iron [138]. Whereas animals ingest iron by feeding on prey organisms, plants and microorganisms rely on the uptake of iron from their aqueous environment. Particular problems arise for pathogenic microorganisms, which have to compete for iron with efficient iron carriers in the body fluids of their host organisms. In vertebrates most of the iron is bound by transferrin, lactoferrin, and in red blood cells. Restricting the access of bacterial pathogens to iron is considered as an important component of the mammalian host defense [139]. It has been reported, however, that bacterial pathogens can scavenge iron from host storage compounds [140]. Another example of an extremely iron-deficient habitat is the surface water of oceans, where typical iron concentrations range between 2  10
11 to 10
9 mol dm
3 . In these systems more than 99% of ferric ion is complexed by yet unknown organic ligands having stability constants on the
1 order of 1019 to 1022 dm3 mol [141]. To be able to overcome this strong binding of iron, biological mobilisation and uptake systems should possess stability constants of at least the same magnitude. An original suggestion is that the organic ligands of ferric iron in ocean water in fact represent unknown iron chelators excreted by marine phytoplankton and/or bacteria [141]. The problem of iron acquisition has indeed been solved by many bacteria, fungi, and plants, by producing and releasing small, soluble iron chelators known as siderophores. A fundamental difference between how extracellular enzymes and siderophores mobilise their target substrates is that the latter ones have to diffuse back to the excreting organism together with a single target ion. Common properties of siderophores are iron-regulated biosynthesis, ferric ion chelating capability and active transport through the cell membrane [142]. Further important features of siderophores are their high selectivity for iron and the specificity of the membrane-bound uptake systems. An exception to this rule seems to be the iron-uptake system first described for Aeromonas hydrophila, which will be described below [143]. With few reported exceptions, it appears that the chelated iron is reserved for the species that released the siderophore. Countermeasures of competing species would therefore be restricted to the production of siderophores of even higher stability constants. Given the strong competition for the scarce iron, there is a high selection pressure towards the evolutionary invention of siderophores with high stability constants. Bacterial siderophores are typically small peptidic molecules, which contain side chains and functional groups that can provide high-affinity ligands for coordination of ferric ions. The structures of some siderophores are shown in Drechsel and Jung [142]. Siderophore synthesis occurs via enzymatic assembly by nonribosomal peptide synthetases [144]. In bacteria, siderophore synthesis is

432 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

typically negatively regulated by the universal repressor, Fur. In the presence of abundant iron, the Fe2þ –Fur complex binds to a Fur-binding sequence, thereby repressing siderophore synthesis. For a detailed discussion of siderophore regulation in bacteria, the reader is referred to Crosa and Walsh [144]. Iron(III) preferably forms hexacoordinate (octahedral) complexes. A peculiarity of siderophores is that they usually provide the six required coordination sites (mostly oxygen functions) in a single molecule. Bacteria appear to have developed the broadest variety of siderophores, as four classes are known: carboxylates, hydroxamates, hydroxypyridonates, and catecholates, named after the coordination groups, as well as various mixed forms. The stability constants of the pure forms of these siderophores are in the range of 1021 dm3 mol
1 for pure carboxylates such as rhizoferrin, and around 1030 dm3 mol
1 for trihydroxamates such as the ferrichromes. The stability constants of mixed forms such as dihydroxamate/carboxylates lie somewhere in between. In the powerful tricatecholate siderophore enterobactin of Escherichia coli, three catecholic side chains provide a perfect hexadentate ligation of ferric iron, resulting in an estimated stability constant of 1052 dm3 mol
1 [145]. An equally high stability constant was reported for alterobactin A from the marine bacterium Alteromonas luteoviolaceum, a b-hydroxyaspartate/catecholate siderophore [146]. An advantage of the seemingly least competitive carboxylate siderophores with respect to their stability constants is their high stability at pH down to 4. This is corroborated by the observation that carboxylates are preferably produced by organisms living at mildly acidic pH. The uptake of siderophore–iron complexes by Gram-negative bacteria is energy dependent and occurs via specific outer membrane proteins. In the periplasmic space, it binds to its cognate periplasmic binding protein and is then actively transported across the cytoplasmic membrane by an ATP-transporter protein. Three principal mechanisms for transport through the outer membrane have been described: (1) a ferric siderophore is bound to a specific protein receptor, causing a conformational change in the latter, which pumps the siderophore into the periplasmatic space, whereby it returns to its original conformation [147]. (2) pyoverdin, a siderophore synthesised by Pseudomonas aeruginosa binds tightly in its iron-free form to its outer membrane receptor, where it might scavenge Fe3þ directly from the medium before being transported into the periplasmic space via a conformational change of the receptor. The bound iron-free pyoverdin may also be exchanged by an approaching dissolved Fe3þ –pyoverdin complex, that is then transported through the outer membrane [148]. (3) siderophore uptake by the freshwater bacterium Aeromonas hydrophila involves a ligand exchange [143]. Here, the ferric siderophore binds to a

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receptor carrying a second, iron-free siderophore. Iron exchange between the two siderophores causes the receptor protein to change its conformation thereby releasing the iron together with the second siderophore into the periplasmic space before returning to its original conformation. This latter mechanism appears to be very efficient at low concentrations of ferric siderophores and is very unspecific, as 20 heterologous siderophores and siderophore analogues were shown to mediate iron uptake by Aeromonas hydrophila. The energy for the siderophore transport is provided to the outer membrane by energy transduction from the cytoplasmic membrane via the proteins TonB, ExB, and ExD. Interestingly, genome analysis of Pseudomonas aeruginosa and of Caulobacter crescentus predicts 34 and 65 TonB-dependent outer membrane transport proteins, respectively. This suggests the energydependent uptake of further micronutrients via specific outer membrane proteins [149]. Siderophore transport across the cytoplasmic membrane is mediated by ATP-binding cassette transporters [150]. It involves a periplasmic binding protein of broad substrate specificity, a siderophore channel through the cytoplasmic membrane, and an ATPase providing the energy for the transport [151]. In the cytoplasm, the iron is transferred to iron transport and iron storage components such as ferritins and bacterioferritins (for review see [152]), which fulfill the twofold role of storing essential iron and reducing the toxic effects of excess ferrous iron such as oxidative stress [153]. These cytoplasmic ion carriers cannot compete with the high stability constants of siderophores, which necessitates release mechanisms such as the degradation of the siderophore ligand or the reduction of the ferric ion to the ferrous ion with much less affinity to the siderophore ligand [142].

4

LIMITS TO THE MOBILISATION OF CHEMICALS

The capacity of microbes to mobilise chemicals is not an evolutionary new invention as a response to the advent of anthropogenic environmental chemicals. Microbial communities have always been – and still are – opportunistic, in that they claim and exploit the maximally available substrate first. Degradation of easy degradable and accessible fractions of newly added organic material by so-called r-strategists results in increasing average biochemical stability and decreasing average physical accessibility of the remaining fraction. It is, nevertheless, true that more than the immediately accessible fraction of the global primary production is microbially recycled within short periods ranging from days to centuries, and that only a tiny fraction is buried for geological timescales. A difference between natural refractory compounds and environmental chemicals might be that the former ones, for example lignin, are chemically

434 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

challenging to cope with, and that their degradation required biochemical adaptations, whereas the latter ones are typically unavailable due to physical characteristics that need to be overcome by physical adaptations of microorganisms. This distinction, however, is not stringent, as e.g. crude oil already reentered the biosphere before it was technically exploited, and anthropogenic compounds may well be biochemically inert because they are polymeric, and consequently not absorbable by microorganisms. With respect to some anthropogenic polymers, the limits of biological mobilisation may indeed be reached, because cost–gain ratios may preclude their exploitation. Whereas most natural polymers such as proteins, polysaccharides and nucleic acids, are hydrolysable in autonomous, extracellular enzymatic reactions, the degradation of structurally different anthropogenic polymers may require cofactors that have to be reactivated after each reaction cycle. Highly halogenated organic compounds such as polychlorinated biphenyls and perchloroethylene appear to be too highly oxidised and low in energy content to serve as sources of electrons and energy for microbial metabolism. Bacteria are more likely to use them as electron acceptors in cell-membranebased respiration processes [154]. The environmental fate of halogenated polymers such as polyvinylchloride or Teflon2 may depend on the question of whether it will be appropriate to sustain de-halorespiration processes.

5

CONCLUSIONS

The acquisition and assimilation of bioelements are the most fundamental processes in an organism’s struggle for life. It is therefore obvious that in complex natural systems the competition between thousands of species for limited quantities of a small number of elements is a major evolutionary factor. However, the individual contributions of the physical and biochemical aspects of nutrition to the fitness of an organism are widely unknown. The frequent observation that biodegradation processes, e.g. in soil remediation, are limited by physical obstacles to substrate acquisition, rather than by biochemical incapacities, points at the importance of substrate mobilisation strategies. Microorganisms have evolved various strategies to obtain essential chemicals. Evolutionary adaptations support the peculiar mechanism of microbial nutrition, i.e. uptake of compounds via a passage through the cell membranes. They either (1) increase the contact frequency of the organism’s membrane with its substrate e.g. by chemotaxis or attachment to substrate sources; (2) increase the efficiency of the uptake by employing uptake systems of high specific affinity and, possibly, direct uptake (without passage through an aqueous phase) of nonaqueous phase liquids or micelle-solubilised compounds; or (3) force the release of compounds from effectively bio-unavailable physical

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(biosurfactants, siderophores) or chemical (exoenzymes) states. It appears that they may even (4) outcompete other organisms by claiming substrates prior to uptake by using specific siderophores or biosurfactants.

GLOSSARY A Asw a0A BTX c cd c.m.c. Deff DR Dw HDTMA HOC J KB KM Kow Ks KT k kd MSR NAPL PAH Q Qmax r0 TCE
max x mmax yw 2,4-D

Area through which diffusion takes place Contact area between separate phase and water Specific affinity of the uptake system Benzene–toluene–xylene Substrate concentration Distant (bulk) aqueous substrate concentrations Critical micellisation concentration Diffusion coefficient in environmental matrix Dilution rate Diffusion coefficient in aqueous solution Hexadecyltrimethylammonium Hydrophobic organic contaminant Mass flux towards the cell surface Biomass–water partition coefficient Michaelis constant Octanol–water partition coefficient Substrate saturation constant Whole-cell Michaelis constant Mass transfer coefficient Dissolution rate constant Molar solubilisation ratio Nonaqueous phase liquid Polycyclic aromatic hydrocarbon Substrate uptake rate Biologically determined maximum uptake Cell radius Trichloroethylene Maximum specific substrate conversion rate Distance Maximum growth rate Contact angle with water 2,4-Dichlorophenoxyacetate

(m2 ) (m2 )
1 m3 kg
1 protein s mol m
3 mol m
3 kg m
3 m2 s
1 s
1 m2 s
1

mol m
2 s
1 kg m
3 mol m
3 m3 m
3 mol m
3 mol m
3 m3 s
1 m s
1 mol mol
1
1 mol kg
1 biomass s
1 mol kg
1 biomass s m
1 mol kg
1 biomass s m s
1 8

436 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

14. 15.

16.

Bosma, T. N. P., Middeldorp, P. J. M, Schraa, G. and Zehnder, A. J. B. (1997). Mass transfer limitation of biotransformation: quantifying bioavailability, Environ. Sci. Technol., 31, 248–252. Schwarzenbach, R. P., Gschwend, P. M. and Imboden, D. M. (2003). Environmental Organic Chemistry. John Wiley & Sons, Ltd, Hoboken, NJ. Weiss, M. S., Abele, U., Weckesser, J., Welte, W., Schlitz, E. and Schultz, G. E. (1991). Molecular architecture and electrostatic properties of a bacterial porin, Science, 254, 1627–1630. Wick, L. Y., Ruiz de Munain, A., Springael, D. and Harms, H. (2002). Responses of Mycobacterium sp. LB501T to the low bioavailability of solid anthracene, Appl. Microbiol. Biotechnol., 58, 378–385. Koch, A. L. (1997). Microbial physiology and ecology of slow growth, Microbiol. Mol. Biol. Rev., 61, 305–317. Button, D. K. (1991). Biochemical basis for whole-cell uptake kinetics: specific affinity, oligotrophic capacity, and the meaning of the Michaelis constant, Appl. Environ. Microbiol., 57, 2033–2038. Michaelis, L. and Menten, M. M. L. (1913). Die Kinetik der Invertinwirkung, Biochem. Z., 49, 333–369. Law, A. T. and Button, D. K. (1977). Multiple-carbon-source-limited growth kinetics of a marine coryneform bacterium, J. Bacteriol., 129, 115–123. Button, D. K. (1985). Kinetics of nutrient-limited transport and microbial growth, Microbiol. Rev., 49, 270–297. Nielsen, P. H., Bjerg, P. L., Nielsen, P., Smith, P. and Christensen, T. H. (1996). In situ and laboratory determined first order degradation rate constants of specific organic compounds in an aerobic aquifer, Environ. Sci. Technol., 30, 31–37. Kova´rova´-Kovar, K. and Egli, T. (1998). Growth kinetics of suspended microbial cells: from single-substrate-controlled growth to mixed-substrate kinetics, Microbiol. Mol. Biol. Rev., 62, 646–666. Pasciak, W. J. and Lippert, K. D. (1974). Transport limitation of nutrient uptake in phytoplankton, Limnol. Oceanogr., 19, 881–888. Boone, D. R., Johnson, R. L. and Liu, Y. (1989). Diffusion of the interspecies electron carriers H2 and formate in methanogenic ecosystems and its implications in the measurement of Km for H2 or formate uptake, Appl. Environ. Microbiol., 55, 1735–1741. Harms, H. and Zehnder, A. J. B. (1994). Influence of substrate diffusion on degradation of dibenzofuran and 3-chlorodibenzofuran by attached and suspended bacteria, Appl. Environ. Microbiol., 60, 2736–2745. van Leeuwen, H. P. and Galceran, J. (2004). Biointerfaces and mass transfer. In Physicochemical Kinetics and Transport at Biointerfaces. eds. van Leeuwen, H. P. and Ko¨ster, W., Vol. 9, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle J. and van Leeuwen, H. P., John Wiley & Sons Ltd, Chichester, UK, pp. 113–146. Galceran, J. and van Leeuwen, H. P. (2004). Dynamics of biouptake processes. The role of transport, adsorption and internalisation. In Physiochemical Kinetics and Transport at Biointerfaces. eds. van Leeuwen, H. P. and Ko¨ster, W., Vol. 9, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems. Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons Ltd, Chichester, UK, pp. 147–203.

H. HARMS AND L. Y. WICK 17. 18. 19. 20. 21. 22.

23. 24. 25.

26. 27. 28. 29. 30. 31. 32. 33. 34. 35.

437

Wick, L. Y., Colangelo-Failla, T. and Harms, H. (2001). Kinetics of mass transferlimited microbial growth on solid PAHs, Environ. Sci. Technol., 35, 354–361. Weast, R. C., ed. (1984). CRC Handbook of Chemistry and Physics. 64th edn, CRC Press Boca Raton. Harms, H. and Bosma, T. N. P. (1997). Mass transfer limitation of microbial growth and pollutant degradation, J. Indust. Microbiol., 18, 97–105. Best, J. B. (1955). The interference of intracellular enzymatic properties from kinetic data obtained on living cells. I. Some kinetic considerations regarding an enzyme enclosed by a diffusion barrier, J. Cell. Comp. Physiol., 46, 1–27. Koch, A. L. (1990). Diffusion. The crucial process in many aspects of the biology of bacteria, Adv. Microbiol. Ecol., 11, 37–69. Wilkinson, K. J. and Buffle, J. (2004). Critical evaluation of physicochemical parameters and processes for modelling the biological uptake of trace metals in environmental (aquatic) systems. In Physiochemical Kinetics and Transport at Biointerfaces. eds. van Leeuwen, H. P. and Ko¨ster, W., Vol. 9, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Ltd, Chichester, UK, pp. 445–533. Volkering, F., Breure, A. M. and van Andel, J. G. (1993). Effect of microorganisms on the bioavailability and biodegradation of crystalline naphthalene, Appl. Microbiol Biotechnol., 40, 535–540. Eriksson, M., Dalhammar, G. and Mohn, W. W. (2002). Bacterial growth and biofilm production on pyrene, FEMS Microbiol. Ecol., 40, 21–27. Mulder, H., Breure, A. M., van Honschooten, D., Grotenhuis, J. T., van Andel, J. G. and Rulkens, W. H. (1998). Effect of biofilm formation by Pseudomonas 8909N on the bioavailability of solid naphthalene, Appl. Microbiol. Biotechnol., 50, 277–283. Tongpim, S. and Pickard, M. A. (1996). Growth of Rhodococcus S1 on anthracene, Can. J. Microbiol., 42, 289–294. McLee, A. G. and Davies, S. L. (1972). Linear growth of a Torulopsis sp. on n-alkanes, Can. J. Microbiol., 18, 315–319. Kirschner-Zilber, I., Rosenberg, E. and Gutnick, G. (1980). Incorporation of 32 P and growth of pseudomonad UP-2 on n-tetracosane, Appl. Environ. Microbiol., 40, 1086–1093. Rosenberg, M. and Rosenberg, E. (1981). Role of adherence in growth of Acinetobacter cacoaceticus RAG-1 on hexadecane, J. Bacteriol., 148, 51–57. Thomas, J. M. and Alexander, M. (1987). Colonization and mineralization of palmitic acid by Pseudomonas pseudoflava, Microb. Ecol., 14, 75–80. Goswami, P. and Singh, H. D. (1990). Different modes of hydrocarbon uptake by two Pseudomonas species, Biotechnol. Bioeng., 37, 1–11. Bouchez, M., Blanchet, D. and Vandecasteele, J. P. (1997). An interfacial uptake mechanism for the degradation of pyrene by a Rhodococcus strain, Microbiology, 143, 1087–1093. Harms, H. and Zehnder, A. J. B. (1995). Bioavailability of sorbed 3-chlorodibenzofuran, Appl. Environ. Microbiol., 61, 27–33. Calvillo, Y. M. and Alexander, M. (1996). Mechanism of microbial utilization of biphenyl sorbed to polyacrylic beads, Appl. Microbiol. Biotechnol., 45, 383–390. Lahlou, M. and Ortega-Calvo, J. J. (1999). Bioavailability of labile and desorptionresistant phenanthrene sorbed to montmorillonite clay containing humic acids, Environ. Toxicol. Chem., 18, 2729–2735.

438 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 36. 37. 38. 39. 40. 41.

42.

43. 44.

45. 46. 47. 48. 49. 50. 51. 52. 53.

Aiba, S., Moritz, V., Someya, J. and Haung, K. L. (1969). Cultivation of yeast cells by using n-alkanes as the sole carbon source. I. Batch culture, J. Ferm. Technol., 47, 203–210. Aiba, S., Moritz, V., Someya, J. and Haung, K. L. (1969). Cultivation of yeast cells by using n-alkanes as the sole carbon source. II. An approach to the mechanism of the microbial uptake of n-alkanes, J. Ferm. Technol., 47, 211–219. Efroymson, R. A. and Alexander, M. (1991). Biodegradation by an arthrobacter species of hydrocarbon partitioned into an organic solvent, Appl. Environ. Microbiol., 57, 1441–1447. Koch, A. K., Ka¨ppeli, O., Fiechter, A. and Reiser, J. (1991). Hydrocarbon assimilation and biosurfactant production in Pseudomonas aeruginosa mutants, J. Bacteriol., 173, 4212–4219. Stelmack, P. L., Gray, M. R. and Pickard, M. A. (1999). Bacterial adhesion to soil contaminants in the presence of surfactants, Appl. Environ. Microbiol., 65, 163–168. van der Mei, H. C., Rosenberg, M. and Busscher, H. J. (1994). Assessment of microbial cell surface hydrophobicity. In Microbial Cell Surface Analysis. eds. Mozes, N., Handley, P. S., Busscher, H. J. and Rouxhlet, P. G., VCH, New York, pp. 261–287. Bastiaens, L., Springael, D., Wattiau, P., Harms, H., de Wachter, R., Verachtert, H. and Diels, L. (2000). Isolation of adherent polycyclic aromatic hydrocarbon (PAH) degrading bacteria using PAH sorbing carriers, Appl. Environ. Microbiol., 66, 1834–1843. Wick, L. Y., Wattiau, P. and Harms, H. (2002). Influence of the growth substrate on the mycolic acid profiles of mycobacteria, Environ. Microbiol., 4, 612–616. Bendinger, B., Rijnaarts, H. H. M., Altendorf, K. and Zehnder, A. J. B. (1993). Physicochemical cell-surface and adhesive properties of coryneform bacteria related to the presence and chain-length of mycolic acids, Appl. Environ. Microbiol., 59, 3973–3977. Borrego, S., Nubio, E., Ancheta, O. and Espinosa, M. E. (2000). Study of the microbial aggregation in mycobacterium using image analysis and electron microscopy, Tissue Cell, 32, 494–500. Bellin, C. A. and Rao, P. S. C. (1993). Impact of bacterial biomass on contaminant sorption and transport in a subsurface soil, Appl. Environ. Microbiol., 59, 1813–1820. Spa¨th, R., Flemming, H. C. and Wuertz, S. (1998). Sorption properties of biofilms, Wat. Sci. Technol., 37, 207–210. Baughman, G. L. and Paris, D. F. (1981). Microbial bioconcentration of organic pollutants from aquatic systems – a critical review, CRC Critical Rev. Microbiol., 8, 205–228. Sikkema, J., de Bont, J. A. M. and Poolman, B. (1995). Mechanisms of membrane toxicity of hydrocarbons, Microbiol. Rev., 59, 201–222. Harwood, C. S., Rivelli, M. and Ornston, L. N. (1984). Aromatic acids are chemoattractants for Pseudomonas putida, J. Bacteriol., 160, 622–628. Parales, R. E. and Harwood, C. S. (2002). Bacterial chemotaxis to pollutants and plant-derived aromatic molecules, Curr. Opin. Microbiol., 5, 266–273. Vetter, Y. A., Deming, J. W., Jumars, P. A. and Krieger-Brockett, B. B. (1998). A predictive model of bacterial foraging by means of freely released extracellular enzymes, Microb. Ecol., 36, 75–92. Malmcrona-Friberg, K., Blainey, B. L. and Marshall, K. C. (1991). Chemotactic response of a marine bacterium to breakdown products of an insoluble substrate, FEMS Microb. Ecol., 85, 199–206.

H. HARMS AND L. Y. WICK 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65.

66. 67. 68. 69. 70.

71. 72.

439

Marx, R. B. and Aitken, M. D. (2000). Bacterial chemotaxis enhances naphthalene degradation in a heterogeneous aqueous system, Environ. Sci. Technol., 34, 3379–3383. Rogoff, M. H. (1962). Chemistry of oxidation of polycyclic aromatic hydrocarbons by soil Pseudomonads, J. Bacteriol., 83, 998–1004. Wodzinski, R. S. and Bertolini, D. (1972). Physical state in which naphthalene and bibenzyl are utilised by bacteria, Appl. Microbiol., 23, 1077–1081. Stucki, G. and Alexander, M. (1987). Role of dissolution rate and solubility in biodegradation of aromatic compounds, Appl. Environ. Microbiol., 53, 292– 297. Jucker, B. A., Harms, H. and Zehnder, A. J. B. (1998). Polymer interactions between bacterial cells and glass investigated using LPS micelles, Coll. Surf. B, 11, 33–45. Ogram, A. V., Jessup, R. E., Ou, L.-T. and Rao, P. S. C. (1985). Effects of sorption on biological degradation rates of (2,4-dichlorophenoxy)acetic acid in soils, Appl. Environ. Microbiol., 49, 582–587. van Loosdrecht, M. C. M., Lyklema, J., Norde, W. and Zehnder, A. J. B. (1990). Influence of interfaces on microbial activity, Microbiol. Rev., 54, 75–87. Guerin, W. F. and Boyd, S. A. (1992). Differential bioavailability of soil-sorbed naphthalene to two bacterial strains, Appl. Environ. Microbiol., 58, 1142–1152. Tang, J. M., White, J. C. and Alexander, M. (1998). Utilization of sorbed compounds by microorganisms specifically isolated for that purpose, Appl. Microbiol. Biotechnol., 49, 117–121. Feng, Y. C., Park, J. H., Voice, T. C. and Boyd, S. A. (2000). Bioavailability of soilsorbed biphenyl to bacteria, Environ. Sci. Technol., 34, 1977–1984. Park, J. H., Zhao, X. D. and Voice, T. C. (2001). Biodegradation of nondesorbable naphthalene in soils, Environ. Sci. Technol., 35, 2734–2740. Luthy, R. G., Aiken, G. R., Brusseau, M. L., Cunningham, S. D., Gschwend, P. M., Pignatello, J. J., Reinhard, M., Traina, S. J., Weber Jr, W. J. and Westall, J. C. (1997). Sequestration of hydrophobic organic contaminants by geosorbents, Environ. Sci. Technol., 31, 3341–3347. Alexander, M. (2000). Aging, bioavailability, and overestimation of risk from environmental pollutants, Environ. Sci. Technol., 34, 4259–4265. Bird, R. B., Stewart, W. E. and Lightfoot, E. N. (1960). Transport Phenomena. John Wiley & Sons, Ltd, New York. Levich, V. G. (1962). Physicochemical Hydrodynamics. Prentice Hall, Englewood Cliffs, NJ. Volkering, F., Breure, A. M., van Andel, J. G. and Rulkens, W. H. (1995). Influence of nonionic surfactants on bioavailability and biodegradation of polycyclic aromatic hydrocarbons, Appl. Environ. Microbiol., 61, 1699–1705. Taylor, M. G. and Simkiss, K. (2004). Transport of colloids and particles across biological membranes. In Physiochemical Kinetics and Transport at Biointerfaces. eds. van Leeuwen, H. P. and Ko¨ster, W., Vol. 9, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Ltd, Chichester, UK, pp. 357–400. Wodzinski, R. S. and Johnson, M. J. (1968). Yields of bacterial cells from hydracarbons [sic], Appl. Microbiol., 16, 1886–1891. Thomas, J. M., Yordy, J. R., Amador, J. A. and Alexander, M. (1986). Rates of dissolution and biodegradation of aromatic compounds, Appl. Environ. Microbiol., 52, 290–296.

440 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 73. 74. 75.

76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90.

Volkering, F., Breure, A. M., Sterkenburg, A. and van Andel, J. G. (1992). Microbial degradation of polycyclic aromatic hydrocarbons: effect of substrate availability on bacterial growth kinetics, Appl. Microbiol. Biotechnol., 36, 548–552. Fortnagel, P., Harms, H., Wittich, R.-M., Francke, W., Krohn, S. and Meyer, H. (1989). Cleavage of dibenzofuran and dibenzo-p-dioxin ring systems by a Pseudomonas bacterium, Naturwissenschaften, 76, 222–223. Strubel, V., Rast, H. G., Fietz, W., Knackmuss, H. J. and Engesser, K. H. (1989). Enrichment of dibenzofuran utilizing bacteria with co-metabolic potential toward dibenzodioxin and other anellated aromatics, FEMS Microbiol. Lett., 58, 233–238. Wittich, R.-M., Wilkes, H., Sinnwell, V., Francke, W. and Fortnagel, P. (1992). Metabolism of dibenzo-p-dioxin by Sphingomonas sp. strain RW1, Appl. Environ. Microbiol., 58, 1005–1010. Monna, L., Omori, T. and Kodama, T. (1993). Microbial degradation of dibenzofuran, fluorene, and dibenzo-p-dioxin by Staphylococcus auriculans DBF63, Appl. Environ. Microbiol., 59, 285–289. Garcia, J. M., Wick, L. Y. and Harms, H. (2001). Influence of the nonionic surfactant Brij 35 on the bioavailability of solid and sorbed dibenzofuran, Environ. Sci. Technol., 35, 2033–2039. Dunn, I. J. (1968). An interfacial kinetics model for hydrocarbons oxidation, Biotechnol. Bioeng., 11, 467–487. Bouchez-Naı¨tali, M., Blanchet, D., Bardin, V. and Vandecasteele, J.-P. (2001). Evidence for interfacial uptake in hexadecane degradation by Rhodococcus equi: the importance of cell flocculation, Microbiology, 147, 2537–2543. Sikkema, J., Poolman, B., Konings, W. N. and de Bont, J. A. M. (1992). Effects of the membrane action of tetralin on the functional and structural properties of artificial and bacterial membranes, J. Bacteriol., 174, 2986–2992. Johnson, M. J. (1964). Utilisation of hydrocarbons by micro-organisms, Chem. Ind., 36, 1532–1537. Yoshida, F. and Yamane, T. (1971). Hydrocarbon uptake by microorganisms – a supplementary study, Biotechnol. Bioeng., 13, 691–695. Ludvik, J., Munk, V. and Dostalek, M. (1968). Ultrastructural changes in the yeast Candida lipolytica caused by penetration of hydrocarbons into the cell, Experientia, 24, 1066–1068. Hori, K., Matsuzaki, Y., Tanji, Y. and Unno, H. (2002). Effect of dispersing oil phase on the biodegradability of a solid alkane dissolved in non-biodegradable oil, Appl. Microbiol. Biotechnol., 59, 574–579. Kennedy, R. S., Finnerty, W. R., Sundarsanan, K. and Young, R. A. (1975). Microbial assimilation of hydrocarbons. I. The fine-structure of a hydrocarbon oxidizing Acinetobacter sp., Arch. Microbiol., 102, 75–83. Scott, C. C. L. and Finnerty, W. R. (1976). Characterization of intracytoplasmic hydrocarbon inclusions from the hydrocarbon-oxidizing Acinetobacter species HO1-N, J. Bacteriol., 127, 481–489. Southam, G., Whitney, M. and Knickerbocker, C. (2001). Structural chracterization of the hydrocarbon degrading bacteria–oil interface: implications for bioremediation, Int. Biodeter. Biodegr., 47, 197–201. Ehrhardt, H. M. and Rehm, H. J. (1985). Phenol degradation by microorganisms adsorbed on activated carbon, Appl. Microbiol. Biotechnol., 21, 32–36. Subba-Rao, R. V. and Alexander, M. (1982). Effect of sorption on mineralization of low concentrations of aromatic compounds in lake water samples, Appl. Environ. Microbiol., 44, 659–668.

H. HARMS AND L. Y. WICK 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103.

104.

105. 106. 107. 108. 109.

441

Alvarez-Cohen, L., McCarty, P. L. and Roberts, P. V. (1993). Sorption of trichloroethylene onto a zeolite accompanied by methanotrophic biotransformation, Environ. Sci. Technol., 27, 2141–2148. Crocker, F. H., Guerin, W. F. and Boyd, S. A. (1995). Bioavailability of naphthalene sorbed to cationic surfactant-modified smectite clay, Environ. Sci. Technol., 29, 2953–2958. Kim, S. H., Lim, E. J., Lee, S. O., Lee, J. D. and Lee, T. H. (2000). Purification and characterization of biosurfactants from Nocardia sp. L-417, Biotechnol. Appl. Biochem., 31, 249–253. Rosenberg, E. and Ron, E. Z. (1999). High- and low-molecular-mass microbial surfactants, Appl. Microbiol. Biotechnol., 52, 154–162. Lang, S. (2002). Biological amphiphiles (microbial biosurfactants), Curr. Opin. Coll. Interf. Sci., 7, 12–20. Edwards, D. A., Luthy, R. G. and Liu, Z. (1991). Solubilisation of polycyclic aromatic hydrocarbons in micellar nonionic surfactant solutions, Environ. Sci. Technol., 25, 127–133. Grimberg, S. J., Stringfellow, W. T. and Aitken, M. D. (1996). Quantifying the biodegradation of phenanthrene by Pseudomonas stutzeri P16 in the presence of a nonionic surfactant, Appl. Environ. Microbiol., 62, 2387–2392. Neu, T. R. (1996). Significance of bacterial surface-active compounds in interaction of bacteria with interfaces, Microbiol. Rev., 60, 151–166. Zajic, J. E. and Seffens, W. (1984). Biosurfactants, Crit. Rev. Biotechnol., 1, 87–107. Jimenez, I. Y. and Bartha, R. (1996). Solvent-augmented mineralization of pyrene by a Mycobacterium sp., Appl. Environ. Microbiol., 62, 2311–2316. Laha, S. and Luthy, R. G. (1991). Inhibition of phenanthrene mineralization by nonionic surfactants in soil–water systems, Environ. Sci. Technol., 25, 1920– 1930. Laha, S. and Luthy, R. G. (1992). Effects of nonionic surfactants on the solubilisation and mineralization of phenanthrene in soil–water systems, Biotechnol. Bioeng., 40, 1367–1380. Arechabala, B., Coiffard, C., Rivalland, P., Coiffard, L. J. M. and de RoeckHoltzhauer, Y. (1999). Comparison of cytotoxicity of various surfactants tested on normal human fibroblast cultures using the neutral red test, MTT assay and LDH, J. Appl. Toxicol., 19, 163–165. Ghosh, M. M., Robinson, K. G., Yeom, I. T. and Z. Shi, Z. (1994). Bioremediation of PAH- and PCB-contaminated soils using surfactants. In Innovative Solutions for Contaminant Site Management. Water Environment Federation, Specialty Conference Series Proceedings, Alexandria, VA, pp. 663–666. Magetdana, R. and Ptak, M. (1995). Interactions of surfactin with membrane models, Biophys. J., 68, 1937–1943. Miller, R. M. and Bartha, R. (1989). Evidence from liposome encapsulation for transport-limited microbial metabolism of solid alkanes, Appl. Environ. Microbiol., 55, 269–274. Guha, S. and Jaffe´, P. R. (1996). Biodegradation kinetics of phenanthrene partitioned into the micellar phase of nonionic surfactants, Environ. Sci. Technol., 30, 605–611. Bury, S. J. and Miller, C. A. (1993). Effect of micellar solubilisation on biodegradation rates of hydrocarbons, Environ. Sci. Technol., 27, 104–110. Kim, T. H., Oh, Y. S. and Kim, S. J. (2000). The possible involvement of the cell surface in aliphatic hydrocarbon utilization by an oil-degrading yeast, Yarrowia lipolytica 180, J. Microbiol. Biotechnol., 10, 333–337.

442 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 110. Golyshin, P. M., Fredrickson, H. L., Giuliano, L., Rothmel, R., Timmis, K. N. and Yakimov, M. M. (1999). Effect of novel biosurfactants on biodegradation of polychlorinated biphenyls by pure and mixed bacterial cultures, Microbiologica, 22, 257–267. 111. Noordman, W. H. and Janssen, D. B. (2002). Rhamnolipid stimulates uptake of hydrophobic compounds by Pseudomonas aeruginosa, Appl. Environ. Microbiol., 68, 4502–4508. 112. Noordman, W. H., Wachter, J. H. J., De Boer, G. and Janssen, D. B. (2002). The enhancement by surfactants of hexadecane degradation by Pseudomonas aeruginosa varies with substrate availability, J. Biotechnol., 94, 195–212. 113. Beal, R. and Betts, W. B. (2000). Role of rhamnolipid biosurfactants in the uptake and mineralization of hexadecane in Pseudomonas aeruginosa, J. Appl. Microbiol., 89, 158–168. 114. Kim, K., Yoo, D., Kim, Y., Lee, B., Shin, D. and Kim, E. K. (2002). Characteristics of sophorolipid as an antimicrobial agent, J. Biotechnol. Microbiol., 12, 235–241. 115. Toren, A., Ron, E. Z., Bekerman, R. and Rosenberg, E. (2002). Solubilisation of polyaromatic hydrocarbons by recombinant bioemulsifier AlnA, Appl. Microbiol. Biotechnol., 59, 580–584. 116. Lafrance, P. and Lapointe, M. (1998). Mobilisation and co-transport of pyrene in the presence of Pseudomonas aeruginosa UG2 biosurfactants in sandy soil columns, Ground Wat. Monit. Remediat., 18, 139–147. 117. Adkins, J. P., Tanner, R. S., Udegbunam, E. O., McInerney, M. J. and Knapp, R. M. (1993). Microbially enhanced oil recovery from unconsolidated limestone cores, Geomicrobiol. J., 10, 77–86. 118. McInerney, M. J. and Westlake, D. W. S. (1990). Microbially enhanced oil recovery. In Microbial Mineral Recovery. eds. Ehrlich, H. L. and Brierley, C. L., McGraw-Hill, New York, pp. 409–445. 119. Ron, E. Z. and Rosenberg, E. (2002). Biosurfactants and oil bioremediation, Curr. Opin. Biotechnol., 13, 249–252. 120. Rubinovitz, C., Gutnick, D. L. and Rosenberg, E. (1982). Emulsan production by Acinetobacter calcoaceticus in the presence of chloramphenicol, J. Bacteriol., 152, 126–132. 121. Marin, M., Pedregosa, A. and Laborda, F. (1996). Emulsifier production and microscopical study of emulsions and biofilms formed by the hydrocarbonutilizing bacteria, Appl. Microbiol. Biotechnol., 44, 660–667. 122. Schmid, A., Kollmer, A. and Witholt, B. (1998). Effects of biosurfactant and emulsification on two-liquid phase Pseudomonas oleovorans cultures and cell-free emulsions containing n-decane, Enzyme Microb. Technol., 22, 487–493. 123. Rosenberg, E., Gottlieb, A. and Rosenberg, M. (1983). Inhibition of bacterial adherence to hydocarbons and epithelial cells by emulsan, Infect. Immun., 39, 1024–1028. 124. Bredholt, H., Bruheim, P., Potocky, M. and Eimhjellen, K. (2002). Hydrophobicity development, alkane oxidation, and crude-oil emulsification in a Rhodococcus species, Can. J. Microbiol., 48, 295–304. 125. Willumsen, P. A. and Karlson, U. (1997). Screening of bacteria, isolated from PAH-contaminated soils, for production of biosurfactants and bioemulsifiers, Biodegradation, 7, 415–423. 126. Toren, A., Navon-Venezia, S., Ron, E. Z. and Rosenberg, E. (2001). Emulsifying activities of purified alasan proteins from Acinetobacter radioresistens KA53, Appl. Environ. Microbiol., 67, 1102–1106.

H. HARMS AND L. Y. WICK

443

127. Ilori, M. O. and Amund, D. I. (2001). Production of a peptidoglycolipid bioemulsifier by Pseudomonas aeruginosa grown on hydrocarbon, Z. Naturforsch., 56, 547–552. 128. Fleck, L. C., Bicca, F. C. and Ayub, M. A. Z. (2000). Physiological aspects of hydrocarbon emulsification, metal resistance and DNA profile of biodegrading bacteria isolated from oil polluted sites, Biotechnol. Lett., 22, 285–289. 129. Bredholt, A., Josefsen, K., Vatland, A., Bruheim, P. and Eimhjellen, K. (1998). Emulsification of crude oil by an alkane-oxidizing Rhodococcus species isolated from seawater, Can. J. Microbiol., 44, 330–340. 130. de Acevedo, G. T. and McInerney, M. J. (1996). Emulsifying activity in thermophilic and extremely thermophilic microorganisms, J. Indust. Microbiol., 16, 1–7. 131. Bonin, P. and Bertrand, J.-C. (1999). Involvement of bioemulsifier in heptadecane uptake in Pseudomonas nautica, Chemosphere, 38, 1157–1164. 132. Burd, G. and Ward, O. P. (1996). Physicochemical properties of PM-factor, a surface-active agent produced by Pseudomonas marginalis, Can. J. Microbiol., 42, 243–251. 133. Kanaly, R. A., Bartha, R., Watanabe, K. and Harayama, S. (2000). Rapid mineralization of benzo[a]pyrene by a microbial consortium growing on diesel fuel, Appl. Environ. Microbiol., 66, 4205–4211. 134. Brint, J. M. and Ohman, D. E. (1995). Synthesis of multiple exoproducts in Pseudomonas aeruginosa is under control of RhlR–Rhll, another set of regulators in strain PAO1 with homology to the autoinducer-responsive LuxR–LuxI family, J. Bacteriol., 177, 4442–4451. 135. van Delden, C., Pesci, E. C., Pearson, J. P. and Iglewski, B. H. (1998). Starvation selection restores elastase and rhamnolipid production in a Pseudomonas aeruginosa quorum-sensing mutant, Infect. Immun., 66, 4499–4502. 136. Rego, J. V., Billen, G., Fontigny, A. and Somville, M. (1985). Free and attached proteolytic activity in water environments, Mar. Ecol. Prog. Ser., 21, 245–249. 137. Braun, V. and Hantke, K. (1997). Receptor-mediated bacterial iron transport. In Transition Metals in Microbial Metabolism. eds. Winkelmann, G. and Carrano, C. J., Harwood, Amsterdam, pp. 81–116. 138. Archibald, F. (1983). Lactobacillus plantarum, an organism not requiring iron, FEMS Microbiol. Lett., 19, 29–32. 139. Kontoghiorghes, G. J. and Weinberg, E. D. (1995). Iron: mammalian defense systems, mechanisms of disease, and chelation therapy approaches, Blood Rev., 9, 33–45. 140. Wolz, C., Hohloch, K., Ocaktan, A., Poole, K., Evans, R. W., Rochel, N., Albrecht-Gary, A.-M., Abdallah, M. A. and Doering, G. (1994). Iron release from transferrin by pyoverdin and elastase from Pseudomonas aeruginosa, Infect. Immunol., 62, 4021–4027. 141. Butler, A. (1998). Acquisition and utilization of transition metal ions by marine organisms, Science, 281, 207–209. 142. Drechsel, H. and Jung, G. (1998). Peptide siderophores, J. Peptide. Sci., 4, 147–181. 143. Stintzi, A., Barnes, C., Xu, J. and Raymond, K. N. (2000). Microbial iron transport via a siderophore shuttle: a membrane ion transport paradigm, Proc. Natl Acad. Sci., 97, 10 691–10 696. 144. Crosa, J. H. and Walsh, C. T. (2002). Genetics and assembly line enzymology of siderophore biosynthesis in bacteria, Microbiol. Mol. Biol. Rev., 66, 223–249. 145. Neilands, J. B. (1995). Siderophores: structure and function of microbial iron transport compounds, J. Biol. Chem., 270, 26 723–26 726.

444 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 146. Reid, R. T., Live, D. H., Faulkner, D. J. and Butler, A. (1993). A siderophore from a marine bacterium with an exceptional ferric iron affinity constant, Nature, 366, 455–458. 147. Braun, V., Hantke, K. and Ko¨ster, W. (1998). Bacterial iron transport: mechanisms, genetics, and regulation. In Metal Ions in Biological Systems: Iron Transport and Storage in Microorganisms. Vol. 35, eds. Sigel, A. and Sigel, H., Marcel Dekker, New York, pp. 67–145. 148. Schalk, U., Hennard, C., Dugave, C., Poole, K., Abdallah, M. A. and Pattus, F. (2001). Iron-free pyoverdin binds to its outer membrane receptor FpvA in Pseudomonas aeruginosa: a new mechanism for membrane iron transport, Mol. Microbiol., 39, 351–360. 149. Braun, V. and Braun, M. (2002). Active transport of iron and siderophore antibiotics, Curr. Opin. Microbiol., 5, 194–201. 150. Ko¨ster, W. (2001). ABC transporter-mediated uptake of iron, siderophores, heme and vitamin B12 , Res. Microbiol., 152, 291–301. 151. Ko¨ster, W. (2004). Transport of solutes across biological membranes: prokaryotes. In Physiochemical Kinetics and Transport at Biointerfaces. eds. van Leeuwen, H. P. and Ko¨ster, W., Vol. 9, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Ltd, Chichester, UK, pp. 271–335. 152. Andrews, S. C. (1998). Iron storage in bacteria, Adv. Microbial Physiol., 40, 281–351. 153. Chen, C.-Y. and Morse, S. A. (1999). Neisseria gonorrhoeae bacterioferritin: structural heterogeneity, involvement in iron storage and protection against oxidative stress, Microbiology, 145, 2967–2975. 154. Holliger, C., Wohlfahrt, G. and Diekert, G. (1998). Reductive dechlorination in the energy metabolism of anaerobic bacteria, FEMS Microbiol. Rev., 22, 383–398. 155. Ahn, I. S., Ghiorse, W. C., Lion, L. W. and Shuler, M. L. (1998). Growth kinetics of Pseudomonas putida G7 on naphthalene and occurrence of naphthalene toxicity during nutrient deprivation, Biotechnol. Bioeng., 59, 587–594. 156. Stringfellow, W. T. and Aitken, M. D. (1995). Competitive metabolism of naphthalene, methylnaphthalenes and fluorene by phenanthrene-degrading pseudomonads, Appl. Environ. Microbiol., 61, 357–362. 157. Guha, S., Peters, C. A. and Jaffe´, P. R. (1999). Multisubstrate biodegradation kinetics of naphthalene, phenanthrene, and pyrene mixtures, Biotechnol. Bioeng., 65, 491–499. 158. Bouwer, E. J., Chen, C. T. and Li, Y. H. (1992). Transformation of a petroleum mixture in biofilms, Wat. Sci. Technol., 26, 637–646. 159. Paris, D. F., Steen, W. C., Baughman, G. L. and Barnett, J. T. (1981). Secondorder model to predict microbial degradation of organic compounds in natural waters, Appl. Environ. Microbiol., 41, 603–609. 160. O’Neill, J. G. and Wilkinson, J. F. (1977). Oxidation of ammonia by methane oxidation, J. Gen. Microbiol., 100, 407–412.

10 Critical Evaluation of Physicochemical Parameters and Processes for Modelling the Biological Uptake of Trace Metals in Environmental (Aquatic) Systems KEVIN J. WILKINSON AND JACQUES BUFFLE CABE (Analytical and Biophysical Environmental Chemistry), 30 quai Ernest Ansermet, Universite´ de Gene`ve, CH-1211, Gene`ve 4, Switzerland

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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Important Physicochemical Processes Leading to Biological Uptake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mass Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Molecular Diffusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Effects of Fluid Motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Influence of Steady, Uniform Flows . . . . . . . . . . . . . . 3.2.2 Influence of Shear and Turbulent Flows . . . . . . . . . . 3.3 Influence of Organism Size, Shape and Microenvironment. . 3.4 Influence of Solute Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Examples of Mass Transport Limitation in Environmental Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1 Rapidly Accumulating Compounds . . . . . . . . . . . . . . 3.5.2 Slowly Diffusing Compounds. . . . . . . . . . . . . . . . . . . . 3.5.3 Cells in Aggregates, Flocs and Biofilms . . . . . . . . . . . Complexation and Dissociation: Thermodynamics and Chemical Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Nature of Metal Complexes in Aquatic Systems . . . . . . . . . . 4.2 Thermodynamic Stability of Aquatic Complexes . . . . . . . . . 4.2.1 Polyelectrolytic Effect . . . . . . . . . . . . . . . . . . . . . . . . . .

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4.2.2 Polyfunctionality Effect . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Interpreting Metal Complexation Data . . . . . . . . . . . 4.3 Dissociation Kinetics of Aquatic Complexes . . . . . . . . . . . . . 4.3.1 Simple Ligands: Eigen–Wilkens Mechanism . . . . . . . 4.3.2 Application of the Eigen–Wilkens Mechanism to Natural Waters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Heterogeneous Ligands . . . . . . . . . . . . . . . . . . . . . . . . 5 Adsorption and Desorption at the Biological Surface . . . . . . . . . . 5.1 Limitations in the Determination and Interpretation of Equilibrium and Kinetic Data . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Equilibrium and Rate Constants for the Adsorption at the Membrane Surface . . . . . . . . . . . . 5.1.2 Carrier Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Adsorption to Carriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Competition Among Metals . . . . . . . . . . . . . . . . . . . . 5.2.2 Ternary Complexes and Ligand Adsorption . . . . . . . 5.2.3 Chemical Heterogeneity Effects. . . . . . . . . . . . . . . . . . 5.2.4 Rate-Limiting Adsorption of Metal to Carriers . . . . 6 Trace Element Transport Across Biological Membranes . . . . . . . 6.1 Kinetics of the Important Transport Mechanisms . . . . . . . . 6.1.1 Passive Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.2 Carrier-Mediated Transport and Ion Channels. . . . . 6.1.3 Active Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Points of Caution When Interpreting Uptake Kinetics . . . . 6.2.1 Limitations of the Michaelis–Menten Approach. . . . 6.2.2 Cellular Responses Affecting Trace Element Internalisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 Population Responses Affecting Trace Element Internalisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.4 Indirect Biological Responses Affecting Trace Element Internalisation . . . . . . . . . . . . . . . . . . . 7 Coupled Dynamic Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Timescales and Limiting Permeabilities Related to the Various Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.1 Biological Uptake Limitation . . . . . . . . . . . . . . . . . . . 7.1.2 Diffusion Limitation . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Lability Criteria and Semi-Labile Complexes . . . . . . . . . . . . 7.3 Role of Ligand Excess and Chemical Heterogeneity . . . . . . 7.4 Nature of the Rate-Limiting Step for Metal Biouptake by Phytoplankton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Some Implications of a Rate-Limiting Diffusion . . . . . . . . . 7.5.1 Bioavailability of Colloidal Bound Metal . . . . . . . . .

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7.5.2 Requirements of Trace Metal Carriers . . . . . . . . . . . . 8 Future Perspectives and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

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INTRODUCTION

In environmental systems, trace metals are found in many different forms, including free hydrated ions, complexes with poorly defined natural ligands or as adsorbed species on the surfaces of particles and colloids [1,2]. Although it is now well accepted by both environmental scientists and government regulators that the biological effects of trace elements are greatly influenced by their chemical speciation in the external medium, no consensus currently exists as to the exact role of chemical speciation, especially for field conditions. Due to the absence of scientific consensus, most regulatory agencies still routinely employ total or ‘dissolved’ elemental concentrations when setting maximum acceptable levels for effluents and point sources of pollutants. In 1978, Jackson and Morgan [3] identified four difficulties that they considered were limiting our understanding of the effects of trace metals on microorganisms: (1) determination of the chemical speciation in solution; (2) understanding of interactions among metal ions; (3) ignorance concerning the rates and mechanisms of interaction of the metal with the biological interface; and (4) ignorance of the fate of the metals at the cellular level. For the most part, these difficulties still exist, since much of the data generated over the past 25 years has been empirical or semi-empirical. It is our view that progress towards a quantitative understanding of trace element uptake will require work in the areas that were identified by Jackson and Morgan 25 years ago. Such data should help refine the mechanistic (and hopefully predictive) models that will be required in order to quantitatively understand trace-element accumulation by aquatic organisms. The goals of this chapter are therefore: (1) the examination of the main dynamic, physicochemical processes required to understand and model biouptake fluxes; (2) the elaboration and refinement of a conceptual model describing the bioaccumulation of trace elements, including identification of the most important hypotheses underlying the model;

448 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

(3) the evaluation of important deviations from the conceptual model due to conditions found in ‘real’ environmental systems (due to heterogeneity, polydispersity, etc.); and (4) the identification of key parameters still required for modelling and key future experiments. This review will focus on the most important physicochemical and biological processes leading to biological uptake. The emphasis of the chapter will be on environmentally complex systems, since the basic biophysical processes have been examined in greater detail in the preceding chapters. While the processes that are involved in uptake are often applicable either to the bioaccumulation of hydrophilic (often metals) or hydrophobic (often organic) elements and compounds, many of the examples that follow will examine the uptake of trace metals in order to provide a focus for the chapter. The term solute will be used as the more general term signifying any chemical species being accumulated. In addition, in order to make the chapter as accessible as possible, most of the quantitative arguments focus on bioaccumulation from the perspective of a small, isolated planktonic microorganism, while a necessarily more qualitative approach is employed to evaluate the effects of organism size, motility or community formation.

2 IMPORTANT PHYSICOCHEMICAL PROCESSES LEADING TO BIOLOGICAL UPTAKE Several theoretical discussions have examined trace metal [4–8] or trace element [9,10] uptake by aquatic organisms. In practice, the differences among the models are due less to the model’s conceptual framework than to simplifying assumptions that are made in order to relate measurable parameters to induced biological effects. Nonetheless, a general consensus currently exists in the literature with respect to the key processes that control solute biouptake and bioavailability (Figure 1). In the first instance, the solute must be transferred from the external medium to near enough to the organism for an interaction to take place (mass transport). Compounds are not necessarily inert during transport, and varying physicochemical conditions (e.g. changing pH, metal or ligand concentrations, membrane potentials) may provoke modifications in the chemical speciation of the element (e.g. complexation/dissociation). It is assumed that to induce an effect, the solute must react with a sensitive site on the biological membrane (adsorption/desorption), often but not necessarily followed by biological transport (internalisation). The magnitude of each of the fluxes will vary, depending upon the chemical nature of the compounds being accumulated, the size and type of organism, the physicochemical nature of the surrounding medium, etc.

K. J. WILKINSON AND J. BUFFLE

Physicochemistry of the bulk solution

Biological effects

ML5 (toxic)

ML4 (storage)

449

Passive diffusion ML1

ML1 (hydrophobic)

Carrier Mass transport mediated transport Mz+ Mz+ M Internalisation Adsorption/ Desorption Complexation / Dissociation ML2 (hydrophilic)

ML3 (essential) Efflux

Figure 1. Conceptual model of the important physicochemical processes, leading to the uptake of a trace element by an aquatic microorganism

Two major classes of models can be distinguished depending on whether or not the processes that are external to the organism are at thermodynamic equilibrium. For example, a slow, rate-limiting internalisation is the underlying hypothesis of most trace metal uptake models, including the free-ion activity model, FIAM [5,11,12] and the biotic ligand model, BLM [13–17]. On the other hand, models examining nutrient or organic pollutant uptake generally place more emphasis on the possibility of a rate-limiting mass transport [9,18,19] or an equilibrium-based partitioning of the solute [20–22]. In the thermodynamic models (FIAM and BLM), the internalisation flux is assumed to be rate-limiting, and the concentration of carriers or sensitive sites bound by the solute of interest negligible with respect to the total number of carriers (i.e. free carrier concentration constant). The fundamental equations describing the equilibrium models can be summarised as: M þ L $ ML

(1)

[ML] ¼ K1 [M][L]

(2)

M þ Rcell $ M
Rcell

(3)

fM
Rcell g ¼ KS fRcell g[M]

(4)

450 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

where [] and {} are the bulk and surface concentrations, respectively, M and L are the metal and ligand in solution (charges omitted for simplicity), Rcell is a sensitive (physiologically active) site on the surface of the organism (e.g. transporter, carrier, ion channel) and K1 and KS are the stability constants defining the equilibrium reactions. Note that the convention for defining bulk concentrations of free metal, as [M] is equivalent to the formulation cM used in several of the previous chapters. In this chapter, c will be employed for the more general formulation of solute concentration. Where biological internalisation occurs (equation (5)), the corresponding uptake flux, Jint , is usually assumed to be a first-order function of any of the equilibrium species, including fM
Rcell g (equation (6)) or [M] (equation (7)). kint

k

f M
Rcell ! Mint þ Rcell M þ Rcell $ k

(5)

Jint ¼ kint fM
Rcell g

(6)

Jint ¼ kint KS fRcell g[M]

(7)

d

where kf , kd and kint are the formation, dissociation and internalisation rate constants. Mint represents the metal that has been internalised with a concurrent recycling of the membrane carrier ligands. This first-order assumption is the biological equivalent of assuming that membrane permeability (P ¼ Jint =[M]) is independent of free solute concentration in the external medium. While equations (6) and (7) are thermodynamically equivalent, equation (6) is the basis of the BLM, while equation (7) is the basis of FIAM (for constant concentrations of fRcell g, i.e. well below saturation). Despite the fact that they have been applied across a wide range of conditions for a wide range of aquatic organisms, the above models (BLM, FIAM) are only strictly applicable for cases where [12,23]: . the plasma membrane is the primary site of interaction of the trace metal with living organisms (Section 6.1); . mass transport towards the membrane is not rate-limiting (Section 3); . surface complexation kinetics at the biological interface are not rate-limiting (Section 5.2.5); . in cases where competition occurs for transport sites, it can be predicted by thermodynamic constants (Section 5.2.1); . chemical gradients at the bulk solution–biological interphase (e.g. concentration or pH gradients, etc.) do not affect transport to or reactions with the transport sites (Section 6.5.4); . carrier ligands generally remain undersaturated (Section 6.1); . the membrane surface is chemically homogeneous (i.e. it only contains one type of site) (Section 5.2.4, cf. Chapter 6 [24]);

K. J. WILKINSON AND J. BUFFLE

451

. chemical reactions of the solutes with the cell walls are either negligible or very fast (at equilibrium) compared with internalisation (Section 5.2.3); . the induced biological response is directly proportional to metal internalisation fluxes, Jint , or concentrations of the surface complex fM
Rcell g. Clearly, a FIAM or BLM response requires many, perhaps unrealistic, assumptions to be fulfilled. For instance, several other less-limiting models (e.g. [3]) take into account a potential mass transport limitation on biouptake. If mass transport is limiting, it will set an upper limit to the uptake flux that can be accessed by the organism and the movement of the biological cells or of the surrounding water will enhance advective solute supply [25–27] by decreasing the thickness of the diffusion boundary layer [28]. Due to an imperfect capacity to absorb nutrients brought to the surface of the organism by mass transfer, many intermediate cases also exist for which the organism can only partially exploit transport increases [29,30]. Nonetheless, for various reasons, few studies have rigorously examined the uptake of environmental solutes in the context of models other than the simple thermodynamic ones. Due to this lack of experimental verification, it is currently unclear to what extent chemical reactions, mass transport and surface charges may influence solute fluxes. By definition, the flux, Ji , of a solute i is given by: J¼

1 dN A dt

(8)

where N represents the number of moles of solute passing through a surface of area, A, per unit time, t. By convention [31], a positive flux indicates a flux towards the cell, while a negative flux indicates a flux leaving the cell. As discussed in a previous chapter [32], under steady-state conditions, the flux of solute is related to the concentration change of solute at a given location and time by: qci ¼
divJi þ kf cj
kr ci qt

(9)

where kf and kr are the forward and reverse reaction rate constants and ci and cj (mol dm
3 ) are the concentrations of the solute i, and reaction product, j. A suitable starting point for describing the flux of a solute can be given by the onedimensional Nernst–Planck equation, obtained by taking into account diffusion, liquid flow and electrical potential gradients (see Chapter 3 for details [32,33]): Ji ¼ Di

q2 ci qx2

diffusion

þ

v

qci qx

þ

advection

qc jzi j ci ui qx zi conduction

(10)

452 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES
1

where x (m) is the distance from the surface, Di (m2 s ) is the diffusion coefficient, z is the ionic charge, ui is the ionic mobility, c is the electrical potential and v is the velocity of the liquid. In the following discussion, the role of each of the terms of equations (9) and (10) will be examined with respect to solute bioaccumulation. One model will not be favoured over another, but instead each of the main physicochemical processes will be considered separately, as if it were the rate-limiting step. We recognise that it is somewhat artificial to consider each process individually, since in reality they are coupled, nonindependent processes. Nonetheless, this approach allows for an easier identification and discussion of the rate-limiting steps. We will attempt to reconcile this problem at the end of the chapter by providing several examples of coupled fluxes.

3

MASS TRANSPORT

It is not the goal of this section to provide a thorough review of the role of hydrodynamics on nutrient uptake to plankton. Indeed, the reader is referred to more complete treatments on the subject [25–27,34–37], including work found in Chapter 3 of this volume [32]. Instead, the main objective of this section is (1) to characterise the nature and role of diffusive mass transport (Section 3.1); (2) to describe the most important hydrodynamic conditions that are pertinent to environmental conditions (Section 3.2); (3) to identify specific circumstances for which bioaccumulation may be affected by fluid motion (Sections 3.3–3.4); (4) to provide literature examples for which mass transport limitation appears to have occurred (Section 3.5); and (5) to direct the reader to some of the most important related literature for more detailed information. Such considerations are important for both the planning and interpretation of biouptake experiments. 3.1

MOLECULAR DIFFUSION

Fick [38] defined a total one-dimensional diffusional flux of a solute towards a planar surface as: Jd,p ¼ D

qc qx

(11)

where Jd,p is the planar diffusive flux (mol m
2 s
1 ). Fick’s second law (corresponding with the first term in equation (10)) is the basic equation for one-

K. J. WILKINSON AND J. BUFFLE

453

dimensional, unsteady-state diffusion that describes the change in concentration, c, with time, t, at distance x, as a function of the change in concentration gradient with distance: qc q2 c ¼D 2 qt q x

(12)

For small microorganisms, radial rather than planar diffusion will occur [39], such that: qc q2 c 2 qc ¼D 2 þ qt q r r qr

(13)

where r is the radial distance from the centre of the microorganism. After a transient period, a steady-state flux will occur that is given by [40]:  
 1 1 þ Jdss,s ¼ D c
c0 d r0

(14)

where the superscript ss refers to the steady-state, the subscript d,s refers to spherical diffusion, and c is a concentration, either in the bulk solution (superscript *) or at the membrane surface (superscript 0). The d is the diffusion boundary layer thickness and r0 is the cell radius. Thus Jdss,s is the flux that is created at the biological interface if biological uptake exceeds mass transport [18,27,28,37]. From this equation, it can be seen that diffusive fluxes to microorganisms will increase with decreasing solute size (i.e. larger D), increasing concentration difference between the bulk solution and biological surface (i.e. more solute in the bulk or less at the organism surface), and for smaller organisms or smaller diffusion boundary layers [27,41,42]. The diffusion boundary layer thickness depends on D, and consequently the viscosity of the medium, Z, and the geometry of the microorganism. In the absence of flow, the diffusion boundary layer of large or planar surfaces (r0  d) can be defined by [40,43]: d¼

pffiffiffiffiffiffiffiffiffiffiffiffi pDtd

(15)

where td is the time after the theoretical initiation of the biouptake process by the microorganism. As can be seen from this equation and from Figure 2a, for large surfaces, in the absence of flow, d will increase continually with time. In this case, the concentration profiles that develop with time are fairly linear near the surface, and d can be rigorously defined by extrapolation of the linear part of the curve to the bulk concentration. Equation (15) implies that the
1 diffusion of a small solute with a typical diffusion coefficient of 6  10
10 m2 s

454 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES t = 0s t = 10 s

t = 1000 s

(a)

Relative concentration (c/c*)

t = 0.1 s

10 20 30 40 50 60 70 80 90 100 x/µm

t = 0s t =1000 s t =10 s

Steady-state

(b) 1

2

3

4

5

6

7

8

9

Relative concentration (c/c*)

t = 0.1 s

10

r / r0

Figure 2. Development of elemental concentration–distance profiles as a function of time for a mass-transport-limiting situation. (a) Diffusion to a ‘large’ (r0  d) organism, (b) Diffusion to a ‘small’ (r0  d) organism. For further details, refer to [41,45]

(e.g. a divalent cation, [44]) through a diffusion layer thickness of 10 mm will take on the order of 0.05 s, while 5 s would be required for d ¼ 100 mm. Equation (14) also shows that for microorganisms with radii that are less than a few microns with a typical diffusion layer thickness  10 mm, radial diffusion should predominate over linear diffusion [46]. Under steady-state conditions, the area integrated cellular flux (mol s
1 ), Q, for a small, spherical cell of surface ¼ 4pr20 , is given by:
 Q ¼ 4pr0 D c
c0

(16)

and concentration increases from the cell towards the bulk solution will be asymptotic to the bulk concentration (Figure 2b). Because, for radial diffusion,

K. J. WILKINSON AND J. BUFFLE

455

there is neither a continuous linear gradient nor an abrupt outer limit to the concentration boundary layer, it is more difficult to give a precise definition of d. For example, if the thickness of the boundary layer is considered to correspond to the distance at which the concentration attains 90% that of the bulk solution [25,47], then the time required to attain a steady-state diffusive flux, tss , can be estimated as < 1 s for the transport of a solute of similar characteristics to that examined earlier, i.e. D ¼ 6  10
10 m2 s
1 , towards a perfectly absorbing microorganism with a diameter of 5 mm. The preceding discussion demonstrates that in order to understand the role(s) of mass transfer with respect to trace element bioaccumulation, the following considerations must be examined: (1) what is the effect of hydrodynamic flow on d (Section 3.2)? (2) does radial (r0  d) or planar (r0  d) diffusion occur? (Note that for nonspherical organisms, shape corrections should be included, Section 3.3.) (3) in case of planar diffusion in a medium with flow, is the system: – at steady-state (i.e. overall flux ¼ Jdss,s ; d ¼ constant); – near equilibrium (overall flux  maximum Jdss,s ); or – in a non-steady-state regime? (4) in the case of radial diffusion, is the system at steady-state (i.e. total uptake time  td ), or under non-steady-state conditions (total uptake time < td )? To answer questions 2–4, the relationships between the external flow velocity and d should be known. The important roles of fluid motion are examined in Sections 3.2–3.4. 3.2

EFFECTS OF FLUID MOTION

As was seen in equation (14), it is possible to increase solute transport to the organism surface by: (1) decreasing the thickness of the diffusion boundary layer; (2) increasing the concentration gradient, c
c0 ; or (3) decreasing the size of the (micro)organism. Fluid motion acts to decrease the diffusion boundary layer thickness. Strategies of the microorganism to increase solute flux by decreasing its size or surface concentrations of the solute, c0 , will be examined in Section 6. In this section, the solute concentration at the surface of the organism, c0 , is assumed to be zero, i.e. the cell is a perfect absorber (sink), since this will provide an upper limit for the importance of fluid motion. It is clear that if fluid motion has no effect for a perfect absorber, it will have no effect for an imperfect one.

456 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

The size, shape and charge of the solute, the size and shape of the organism, the position of the organism with respect to other cells (plankton, flocs, biofilms), and the nature of the flow regime, are all important factors when describing solute fluxes in the presence of fluid motion. Unfortunately, the resolution of most hydrodynamics problems is extremely involved, and typically bioavailability problems under environmental conditions are in the range of problems for which analytical solutions are not available. For this reason, the mass transfer equation in the presence of fluid motion (equation (17), cf. equation (14)) is often simplified as [48]:    1 1
 (17) c
c0  bc Jad ¼ D þ d r0 where Jad is the advective flux, and b is a mass transfer coefficient (m s
1 ) that is strongly dependent upon the configuration of the system under consideration (i.e. flow velocity of the bulk solution, the length scales of interest, the size of the organism, the kinematic viscosity and D; [49]). Based upon this semi-empirical formulation, several complex environmental systems have been examined, including the sediment–water interface [48], phytoplankton aggregates [50,51], flow over corals [52,53] and kelp surfaces [54]. It should nonetheless be emphasised that equation (17) is in itself an oversimplification in real systems, since conductive and chemical reaction terms are neglected (equations (9)–(10)). In the following, examples of the effects of important (yet simplified) flow regimes: uniform flow, shear and turbulence, are examined in greater detail. 3.2.1

Influence of Steady, Uniform Flows

In natural waters, unattached microorganisms move with the bulk fluid [55], so that no flux enhancement will occur due to fluid motion for the uptake of typical (small) solutes by small, freely suspended microorganisms [25,27,35,41,56,57]. On the other hand, swimming and sedimentation have been postulated to alleviate diffusive transport limitation for larger organisms. Indeed, in the planar case (large r0 ), the diffusion boundary layer, d, has been shown to depend on advection and will vary with D according to a power function of Da (the value of a is between 0.3 and 0.7 [43,46,58]). For example, in Chapter 3, it was demonstrated that in the presence of a laminar flow parallel to a planar surface, the thickness of the diffusion boundary layer could be estimated by: d¼

2:95D1=3
~1=6 y1=2 v1=2

(18)
1

where
~ is the kinematic viscosity of the solution (m2 s ), v is the flow velocity of the bulk solution and y is the distance from the upstream edge of the surface. Similarly, for a spherical particle [32]:

K. J. WILKINSON AND J. BUFFLE

d¼

457

  1=3 1:29r0 D 1 y
sin 2y 2 sin y vr0

(19)

where y is a spatial variable that relates the direction of flow to the point of interest on the surface of the organism. As expected, in the spherical case, d attains a minimum on the upstream side of the cell (y ¼ 0), while, on the downstream side of the cell, the diffusion layer thickness is large compared with the cell radius. The exact assumptions and mathematical approximations for both of these equations are discussed in much greater detail in Chapter 3 of this volume. In natural waters, sinking rates (mathematically equivalent to the flow velocity for a stationary cell) are predicted to increase in proportion to the square of the cell radius according to a Stokes’ law dependency. For a spherical organism:

vsed ¼

 2gn r20 rorg
rwater 9Z

(20)

where vsed is the sedimentation velocity (m s
1 ), gn is the gravitational acceleration constant (m s
2 ), r are the densities of the organism and water (kg m
3 )
1 and Z is the dynamic viscosity of the water (kg m
1 s ). Sedimentation calculations using this assumption (e.g. [26,27]) have indicated that no significant increase in mass transport should be observed for organisms < 10 mm, while for microorganisms with a radius of 100 mm, advection due to sedimentation is predicted to increase the mass transport of small solutes by 10% [26] to 100% [27]. The variation across the literature results both from different assumptions (e.g. excess densities, rorg
rwater , can vary between 10 and 100 kg m
3 ; [59]), and from the experimental observation that Stokes’ law overestimates the sinking rate of large cells and underestimates the sinking rate of small cells [60], most probably due to the dependency of cell density on nutrient and light conditions and the growth phase of the cell [61–63]. For small microorganisms, encounter rates of solutes due to molecular diffusion are large compared with those generated by typical swimming speeds of 10–100 cell radii per second [36]. Therefore, small organisms cannot swim fast enough to significantly increase the mass transport of small molecules [35,41,64]. For example [35], in order to double its uptake, a 1 mm cell would
1 need to swim at 3 mm s
1 for a small compound (D ¼ 10
9 m2 s ) but only at
1
12 2
1 15 mm s for a larger compound (D ¼ 5  10 m s ). For somewhat larger organisms (> 5
10 mm), most calculations support the idea that the effect of swimming will be of a similar order of magnitude to sedimentation (e.g. [25–27,34,35]). For example, typical swimming speeds of microorganisms are from 20 mm s
1 to 500 mm s
1 [65,66], while measured sedimentation rates range from approximately 0 to 350 mm s
1 [63]. Unfortunately, general solutions for

458 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

the deformation of the diffusional boundary layer due to swimming are difficult to predict, since the hydrodynamics will vary greatly due to the mode of propulsion (e.g. planar or helical wave motion, flagellum-driven, rotational) and the shape of the organism. 3.2.2

Influence of Shear and Turbulent Flows

Turbulence is characterised by irregular flow and the importance of inertial forces. Turbulent flow is dissipated below the length scale of the smallest eddies, which in most natural waters is in the mm to cm range (Kolmogorov length,
3 =e0 )0:25 , where e0 ¼ turbulent kinetic energy dissipation rate [25,27,67]). Lv ¼ (~ Above these distances, turbulence is recognised to play an important role in regulating element bioavailability, by destroying the macroscopic vertical density structure of the water column [26] so as to homogenise solute concentrations. At smaller distances, including the microscopic interface between the organism and the bulk water, linear shear is assumed to dominate flow [27]. In such cases, as was observed for uniform laminar flows, it is unlikely that shear will have any influence on mass transport to small microorganisms, since shear rates would have to attain 106 s
1 to reduce d below 10 mm [64]. In the eutrophic zone of lakes and oceans, shear rates are thought to attain maximum values of 2 to 7 s
1 [55,68]. On the other hand, for a small solute
1 (D ¼ 10
9 m2 s ) and an organism diameter of 50 mm, mass transport is predicted to be increased by 2% [25] to 32% [27] in the presence of strong turbu
3 lence (e0 ¼ 10
2 cm2 s ). Lazier and Mann [25] showed that oceanic turbulence could increase nutrient uptake by spherically shaped cells of > 100 mm radius. Unfortunately, experimental verification of these theoretical results is difficult. Stirring conditions in experiments performed in the laboratory are generally not well controlled nor well quantified, so that no clear relationship between theoretical and experimental uptake fluxes can be determined, nor can the experiments be easily related to conditions found in the natural environment. Logan and Dettmer [56] got around some of these difficulties by using a flowthrough filtration system. In that case, for a flow field of 1 mm s
1 , leucine uptake by Zoogloea ramigera was 55–65% greater than uptake by cells without flow. On the other hand, their experiments also showed that leucine uptake was not affected by shear rates as large as 50 s
1 [56]. In summary, fluid motion cannot be expected to increase the uptake of small molecules by cells in the micrometre size range [69]. On the other hand, turbulence or shear forces are expected to homogenise the bulk solution concentrations, so as to maintain a constant concentration gradient at the organism surface. Furthermore, significant benefit may be gained from fluid motion, either for large cells or for the uptake of slowly diffusing molecules. This is especially important, since the cellular demand for nutrients increases with cell radius more quickly than does the area integrated cellular diffusive flux, Q

K. J. WILKINSON AND J. BUFFLE

459

(equation (16), [35]), so that fluid motion becomes more and more useful for cells exceeding several microns. The effects of solute and organism size and shape and the effect of cellular attachment to aggregates, biofilms or surfaces are examined in Sections 3.3–3.5. 3.3 INFLUENCE OF ORGANISM SIZE, SHAPE AND MICROENVIRONMENT For a small, spherical microorganism, the diffusive flux is inversely proportional to the cell radius (equation (14)), providing an advantage (i.e. for nutrients) to smaller organisms [46]. Unfortunately, natural organisms are rarely perfect spheres. Organism shape can influence diffusive transport by modifying both the surface:volume ratio and the diffusive transport per unit of surface area [67]. In the absence of flow, Koch [40] demonstrated theoretically that a long, filamentous organism would face a continually decreasing rate of nutrient supply (continual increase in d) in contrast to the spherical organism that would achieve a constant steady-state rate of uptake (cf. Section 3.1). Pahlow et al. [67] concluded that microorganism nonsphericity would enhance the diffusive supply of solute on a per volume basis, but decrease the solute flux per unit of surface area. On the other hand, they showed that the association of circular or spheroid shaped cells in a chain formation would result in a decrease in both the volume and surface-normalised diffusive supply. Pahlow et al. [67] have also carefully examined the role of cell shape on nutrient uptake by diatoms in the presence of advection, under the assumption that nonspherical cells will rotate intermittently. In that case, the relative increase in transport capacity is small for solitary, nonspherical cells with respect to spheres [67]. These authors found that advection could significantly increase transport for cell chains, even though it did not compensate for the loss in diffusive flux when calculations were made on a cell surface area basis. Therefore, although advection has a much greater effect on the supply of solute to chains than it does to solitary cells, solitary cells will always maintain an advantage over chains. As seen in Chapter 2 of this volume [70], the outer cell wall, outer membrane or S-layer can be a barrier to diffusion in microorganisms. In addition, many organisms can secrete hydrophilic exopolymers [71,72] that can cross-link by hydrogen or covalent bonds to form gel-like structures [18,73,74]. The gel layer usually has little effect on the molecular diffusion of nutrients and trace pollutants, since they are often very small with respect to the pore size. On the other hand, the solute may interact chemically with the cell wall or external gel layers [75,76], resulting in a significant decrease in the diffusion coefficients (i.e. ‘restrained’ diffusion). Furthermore, the exopolymer layers may minimise advective effects by reducing flow in the immediate cell environment, thus lowering the concentration gradient at the cell surface through an increase in d.

460 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

3.4

INFLUENCE OF SOLUTE SIZE

Solutes diffuse in proportion to their diffusion coefficient, which is inversely proportional to their hydrodynamic radii, aH , (Stokes–Einstein equation): aH ¼

kT 6pZD

(21)

where k is the Boltzman constant and T is the temperature. Based upon observed empirical relationships between molar mass and molecular size [77], this relationship implies that the diffusive flux decreases with the cubic or square root of the molar mass, or the two-thirds power of the molar volume (based on the assumption of a compact sphere [2]). Because many of the compounds accumulated by plankton have fairly low molar masses (M < 1000 g mol
1 ), they should diffuse fairly rapidly in unreactive media, and, under such conditions, diffusion is expected to limit uptake only in the case of very rapid biological internalisation fluxes. On the other hand, most trace compounds react with the colloids and biopolymers of natural reactive media (e.g. biological gels, sediments, soils), so that the effective diffusion coefficient may be orders of magnitude smaller than the intrinsic diffusion coefficient (Table 1), potentially limiting the transport flux. 3.5 EXAMPLES OF MASS TRANSPORT LIMITATION IN ENVIRONMENTAL SYSTEMS Four strategies are generally employed to demonstrate mass transfer limitation in aquatic systems. Most commonly, measured uptake rates are simply compared with calculated maximal mass transfer rates (equation (17)) (e.g. [48,49]). Uptake rates can also be compared under different flow conditions (e.g. [52,55,56,84]), or by varying the biomass under identical flow conditions (e.g. [85]). Finally, several recent, innovative experiments have demonstrated diffusion boundary layers using microsensors [50,51]. Of the documented examples of diffusion limitation, three major cases have been identified: (1) solute internalisation is very rapid; (2) solutes are large and slowly diffusing; or (3) solutes diffuse through highly complexing or viscous media (restrained diffusion). 3.5.1

Rapidly Accumulating Compounds

A higher susceptibility to mass transport limitation is generally related to a higher affinity of the cells for the solute, i.e. rapidly accumulating compounds [86]. Therefore, transport limitation has been hypothesised to occur mainly for

K. J. WILKINSON AND J. BUFFLE

461

Table 1. Properties of representative metal complexes, including effective labilities, thermodynamic stabilities and mobilities in environmental systems (modified from Buffle [2,78]). Diffusion coefficients are indicative only, and depend upon the exact physicochemical conditions that are examined: please consult original references for more precise values. Metal complex labilities and stabilities are discussed in Sections 4 and 7 Compound/System

D (10
10
1 m2 s )

Univalent inorganic ions (Cl
, F
, etc.) OH
Bivalent inorganic ions 2
(CO2
3 , SO4 , etc.) S(-II) Polysulfides Humic substances

Small specific organic ligands Proteins and peptides Metallothioneins, Phytochelatins, Siderophores, Porphyrins Aquatic polysaccharides Clay colloids Fe(III) and Mn(IV) oxyhydroxides

Effective complex lability

Thermodynamic stability of complex

Ref.

10–20

High

Weak

[44]

52.7

Low

Strong

[79]

5.5–9

High

Weak

[80]

7–11

Low Low From fully labile (high M/L; pH < 7) to fully inert (low M/L, pH > 7) Low

Strong Strong From low stability [81] (high M/L; pH < 7) to very high stability (low M/L, pH > 7) Often strong [82]

Low

Weak to very strong Very strong

Low Intermediate Intermediate to strong

[83]

1.5–2.5

1–8 0.1–2 1–2

0.05–1 High 0.005–0.5 Low < 0:1 Low

[2]

nutrients and hydrophobic organic contaminants. For example, Pasciak and Gavis [29] determined the ratio, j, between calculated maximal cellular fluxes due to spherical diffusion (equation (16)) and measured cellular nutrient uptake
 rates, vint ¼ vmax c0 = KM þ c0 : j¼

4pr0 DKM vmax

(22)

where KM (mol dm
3 ), vint (mol s
1 per cell) and vmax (mol s
1 per cell) are obtained from a Michaelis–Menten treatment of the data on a per cell basis (cf. Section 6.1). Values of j ¼ 1 (i.e. Q ¼ vint or Jd ¼ Jint ) indicate that diffusional transport will be rate-limiting. Although Pasciak and Gavis did not demonstrate unequivocally mass transport limitation (j values were close to,

462 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

but generally greater than 1), they concluded that, under certain circumstances, it could be possible. Nonetheless, they did show experimentally that fluid shear could increase nitrate uptake in a diatom with a radius of roughly 20 mm [30]. Using similar theoretical arguments, Mierle [87] attributed deviations from Michaelis–Menten kinetics at low phosphate concentrations to diffusion limitation. Finally, transport limitation of CO2 has been proposed to occur for phytoplankton [47,69,88] and seagrasses [89]. Among the trace metals, Hudson and Morel [7] postulated that Fe and Zn were closest to a diffusion-limited situation based upon measured cellular metal quotas and concentrations in marine systems (e.g. Zn would be diffusion limited for cells > 20 mm). Similarly, Hassler and Wilkinson [90] showed that for cells grown under of Zn starvation, transport was diffusion limited for

2þ  conditions
3 Zn < 10
12 mol dm . Fortin and Campbell [91] showed that, in the presence of chloride, the Ag transport flux to Chlamydomonas reinhardtii was close to a diffusion limitation at the lower Ag concentrations that were examined. Diffusion limitation of trace metals is most likely in systems where the concentrations are low and concentrations of competing metals are high, especially for essential metals that are taken up by passive diffusion across the membrane [8]. The final point of essentiality could be especially important when transport systems are upregulated in response to low metal concentrations (see also Section 2.2; [90,92]). 3.5.2

Slowly Diffusing Compounds

Although several theoretical treatments have demonstrated that the uptake of large, slowly diffusing solutes could be limited due to mass transfer (e.g. [6,25]), few experiments have thoroughly tested this hypothesis. Confer and Logan [84] have demonstrated increased bacterial uptake of a 65 kDa BSA (bovine serum albumin) and a 70.8 kDa dextran in stirred (with respect to nonstirred) samples, suggesting that nonstirred samples may have been mass transport limited. On the other hand, laminar fluid shear rates up to 50 s
1 had no effect on the uptake of low molar mass leucine and glucose [55,56]. 3.5.3

Cells in Aggregates, Flocs and Biofilms

For cells that are embedded in macroscopic gel-like structures such as flocs, biofilms or other porous media such as soil or sediment aggregates, mass transport to the cells can decrease due to: (1) complexation of the solute by the aggregate structure, with a resulting decrease in the effective diffusion coefficient (restrained diffusion); (2) increased consumption of the solute due to increased cell numbers in the structure leading to depletion of the solute; or (3) an increase of the diffusion layer thickness.

K. J. WILKINSON AND J. BUFFLE

463

On a per cell basis, uptake rates of attached microorganisms are generally greater than for free-living organisms [93–95]. Although a significant proportion of the observed increases in uptake rates are postulated to be due to size differences of the organisms [96,97], some of the additional rate increase may be due to a decrease in the diffusion boundary layer thickness due to advection, since, unlike planktonic microorganisms that move with the bulk fluid, attached organisms can experience advective flow past their surface [98]. Researchers examining the biodegradation of organic contaminants in biofilms, bioreactors, sediments or soils have also long observed differences between attached and unattached cells or in situations where some cells are buried beneath others (as in biofilms) [99,100]. For example, Bosma et al. [101] concluded that mass transfer limited the biodegradation of a-hexachlorocyclohexane by Sphingomonas. Harms and Zehnder [86] have shown that diffusive transport to cells on a crowded surface was lower than that determined for single attached cells. Their work also correlated a higher affinity of the cells for the solute with a higher susceptibility to a mass transport limitation. As observed earlier, most of the previous results have postulated mass transport limitation based upon the (sometimes tenuous) calculated values of the maximum diffusive flux. On the other hand, the direct observation of a diffusion boundary layer is sufficient proof of a mass transport limitation. Although microelectrodes are not yet able to identify diffusion boundary layers around individual cells, they have been useful for the determination of concentration gradients in microaggregates. For example, Ploug et al. [50,51], Ploug and Jorgenson [102] and Lubbers et al. [103] have mapped oxygen and pH gradients in laboratory-generated diatom (Phaeocystis) microaggregates using a microelectrode with a spatial resolution of < 50 mm. By comparing uptake kinetics between single free-living cells and cells living in a 1 mm large colony, they were able to demonstrate a diffusion limited supply of inorganic nitrogen and phosphate from the bulk water [51]. Cell-specific nutrient fluxes were lower than those of single free-living cells at low nutrient concentrations, due to the presence of relatively thick diffusion boundary layers [51]. The downfield diffusion boundary layer thickness, d, could be quantified: as expected, its downstream thickness (O2 : 420
1000 mm) was larger than that directly in the advective flow (170
380 mm) [102].

4 COMPLEXATION AND DISSOCIATION: THERMODYNAMICS AND CHEMICAL KINETICS As discussed in Chapter 5 of this volume [104], chemical speciation can be defined as the physicochemical distribution of a chemical among all of its possible forms. In environmental systems, ligands range from simple ligands

464 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 2


(e.g. CO2
3 , SO4 , OH , Cl , amino acids) to chemically heterogeneous compounds with several distinct chemical sites per molecule (e.g. humic substances (HS), polysaccharides, hydrous metal oxides, clays, etc.) [1]. Indeed, in natural aquatic systems, only a small fraction of trace metal is likely to be found as the free hydrated cation. In order to predict whether complexes are able to contribute to metal uptake fluxes, both thermodynamic and kinetic effects must be taken into account. As will be seen below, when compared with observations made in the absence of ligands, a reduction in biological uptake will have a thermodynamic origin for labile complexes (i.e. complexes that dissociate many times during their transport through the diffusion layer) and a kinetic origin for nonlabile complexes. In the following, the role(s) of thermodynamic stability (Section 4.2) and kinetic dissociation rates (Section 4.3) on biouptake will be examined for metal complexes formed with simple or heterogeneous ligands. The implications of the thermodynamic and kinetic chemical factors on the dynamic transfer of metals from the bulk solution to the membrane surface will be discussed in Sections 7.1–7.2.

4.1

NATURE OF METAL COMPLEXES IN AQUATIC SYSTEMS

The nature and properties of the major natural aquatic ligands are summarised in Table 1 [2,105] and in Chapter 5 of this volume. In the context of this chapter, they can be divided into the following groups:
(1) simple, well-characterised inorganic (e.g. CO2
3 , Cl ) or organic (e.g. amino acids, oxalic acid, tartaric acid) ligands for which equilibrium and kinetic constants for the protonation and complexation are relatively wellknown. Although some organic molecules such as the amino acids are potentially complexing, they are usually rapidly degraded by microorganisms in the water column [27,28]. On the other hand, carboxylic acids such as citric or tartric acid, may be found in sufficiently large concentrations so as to be complexing, especially in the rhizosphere. (2) metal oxides, clay minerals and silica are (generally) negatively charged, colloidal particles ranging from a few nm to several hundreds of mm. They may form surface coordination complexes with transition and b-metals [1,106]. Most natural metal oxides or coatings have high complexation capacities (up to several moles of trace metal per g) and low apparent dissociation rate constants, due mainly to the slow diffusion of trace metals inside the complexing particles. (3) polysaccharides or peptidoglycans are released by microorganisms, particularly in response to nutrient deficiency. The complexing sites include mainly carboxylic functional groups [2].

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(4) complexing sites located at the surface of aquatic microorganisms may represent a significant proportion of the complexing sites in a water body, depending upon its level of productivity. Complexing functional groups are found both at the membrane surface to facilitate elemental internalisation, and at sites located in the cell wall of the organisms. In the cell wall, metal-binding functional groups include mainly carboxylate, phosphate and amino groups [107–110]. (5) humic substances, HS, are formed in water bodies or soils from the microbial degradation and transformation of dead plants and microorganisms. Molar masses are thought to be between 600 and 10 000 g mol
1 , with a resulting molecular diameter between 1 and 5 nm [81,111–113]. They have predominantly carboxylate and phenolic groups in addition to a large number of poorly characterised, oxygen, nitrogen or sulfur-containing sites that, despite their small proportions [114–116], may be strongly complexing [2,117]. Due to the large number of carboxylate groups, HS possess a significant negative electric field at environmental pH. HS are thus chemically heterogeneous, polyfunctional and oligoelectrolytic. (6) strong specific ligands at extremely low concentrations (down to picomolar levels) have also been postulated in water, although rarely demonstrated unambiguously. Potential sources of such ligands in waters include [5]: anthropogenically produced ligands (e.g. EDTA) or plankton exudates or decomposition biproducts including metallothioneins, phytochelatins, siderophores, porphyrins, and phosphate granules [118–124]. Some strong chelators are also produced intracellularly by organisms in response to metal stress (e.g. phytochelatins, metallothioneins) or metal deficiency (e.g. siderophores), and can be released into the water either in response to metal exposure or following cell lysis [125–127]. Nonetheless, most of the information on biologically produced, chelating molecules has come from laboratory culture studies, e.g. [121,128]. Based upon their complexation properties, metals can be classified into three major groups: hard or a metals, including the alkaline and alkaline-earth metals; borderline metals (especially Mn, Fe, Co, Ni, and Cu) and soft or b metals that include Pb, Cd, and Hg. The hard metals predominantly bind oxygencontaining sites (e.g. ligand types 1 to 5 above), forming relatively weak complexes. The borderline metals form stronger complexes, especially with N- and S-containing sites (ligand types 1 to 6 ). The soft metals form the strongest complexes with the N and S containing (soft) ligands, in particular, the ligand types 5 and 6. Stability constants have only been well documented for metal complexes of the type 1 ligands (e.g. [129]) and some of the highly complexing anthropogenic ligands such as EDTA. There is still much debate [105,130,131] as to what extent specific, strongly binding ligands play a role in the complexation of metals in natural waters.

466 KINETICS AND TRANSPORT AT BIOINTERFACES 4.2 PHYSICOCHEMICAL THERMODYNAMIC STABILITY OF AQUATIC COMPLEXES

log ([M]b/DOC)

As seen above, a large proportion of aquatic complexes are not formed with simple well-characterised ligands (e.g. Figure 3a) with well-defined equilibrium and rate constants, but rather with heterogeneous ligands with poorly defined compositions, large numbers of sites and usually poorly defined equilibrium and rate constants (e.g. Cu [118,132–134]; Fe [123,135]; Pb [136–138]; Zn [133,137,139]; see also Chapter 5 [104] and reviews [131,140]). Indeed, although it is now well accepted that a large proportion of metals are complexed in natural waters, very few metal complexes have been unambiguously identified and characterised [121,127,130,131], especially those postulated to exist at picomolar concentrations. For the heterogeneous ligands, a key point is that

1

0

1 (a)

(b)

0

log[M] (mol dm−3)

log ([M]b/DOC) (mol g−1C)

−3

log[M] (mol dm−3)

(c)

Pb −4

Cd

−5

0.5 −6 10

8

6

4

logK *

Figure 3. (a) Schematic representation of a complexation titration curve for a mixture of simple ligands, and (b) Titration curve of a heterogeneous ligand: logarithmic plot of bound metal versus free metal in the presence of a fulvic acid. For further details, refer to [142]. (c) Variation of the complexation capacity as a function of the corresponding equilibrium constant, K  (i.e. value of K valid at a given ratio of [M]b =[DOC]), for the complexation of Pb and Cd by a peat humic acid [144]. [M]b refers to the concentration of bound metal, [DOC] is dissolved organic carbon concentration and [M] is the concentration of free metal ion. For further details, refer to [143]. Reprinted from: [145] Anal. Chim. Acta, 284, Pinheiro, J. P. et al., ‘Complexation study of humic acids with cadmium (II) and lead (II)’, pp. 525–537, Copyright (1994), with permission from Elsevier

K. J. WILKINSON AND J. BUFFLE

467

the values of the constants change with the metal to ligand ratio as stronger complexes are formed at lower metal/site ratios (Figure 3c) [131,141–143]. The observation of smeared titration curves (e.g. Figure 3b) can be attributed to both physical and chemical features of the heterogeneous ligands including [5,117,142,143]: (1) intrinsic chemical heterogeneity due to the existence of many different complexing groups in the same molecule; (2) poly- or oligoelectrolytic character due to a large number of charged functional groups on each macromolecule or colloid; and (3) conformational changes of the molecule or colloid due to specific binding of metals or modifications to the electrostatic interactions among functional groups. 4.2.1

Polyelectrolytic Effect

For charged surfaces, complex stability may be enhanced (or reduced) by the polyelectrolytic effect, if the pH is significantly different from the pH of zero charge, pHpzc , of the surface [106,146]. In that case, the equilibrium constant, K, between the solute and a surface site, S, can be expressed as: K¼

{MS} [M]0 {S}

(23)

where [M]0 is the volume concentration of metal at the charged surface. [M]0 differs from the bulk solution concentration, [M], by the Boltzmann factor: [M]0 ¼ [M] exp(
zF c=RT)

(24)

where z is the algebraic charge number of M, c is the surface potential of the particle, R is the gas constant, T is the temperature and F is the Faraday constant. For impermeable solid particles, the surface charge density, s, determined from the number of deprotonated sites at any given pH can be related to c [147]:      2Fcs z zF c 4 zF c tanh þ 2sinh s¼ k 2RT kr0 4RT

(25)

where cs is the salt concentration and k
1 is the double layer thickness on the particle. While somewhat more difficult, similar corrections for polyelectrolytic effects can also be performed for natural polysaccharides, peptidoglycans and HS [77]. In this case, the relationship between s and c is given by different mathematical expressions [77,148] that depend on the conformation of the

468 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

biopolymer in solution. To a good first approximation, the expression for charged permeable spheres would appear to be applicable to HS [149], due to their near-spherical conformation [150] and low apparent permeability [151]. Although systematic studies of the potential effect on metal complexation by HS are scarce [117], at pH ¼ 8, an average c value of
60 mV has been estimated for several HS of various origins [148,149] (ca. 5 meq g
1 COOH functional groups). 4.2.2

Polyfunctionality Effect

The polyfunctionality effect, due to the chemical heterogeneity of the ligand, is extremely important for HS, and will apply to a lesser degree to metal oxides, polysaccharides and proteins. Highly polyfunctional ligands, such as the HS, can have stability constants for a given metal that range over six or more orders of magnitude [105,131,152]. When such ligands are titrated by metal ions, the strongest sites are occupied first, while weaker and weaker sites are gradually filled until all sites are saturated [117,143]. When an equilibrium constant is computed at each titration point, a continuous decrease of the apparent K is observed with the increase of metal-to-ligand ratio (e.g. Figure 3c). 4.2.3

Interpreting Metal Complexation Data

At least three philosophical approaches are available when interpreting trace metal complexation data:

~ and complexation capacities, Cc , may be deduced for (1) average K values, K, each site type from titration curves using a Scatchard type data treatment. This approach is limited to ligands with a few ( 3) site types. For highly polyfunctional ligands, K values will vary continuously with the metal to ligand ratio, such that approaches (2) or (3) are preferred. (2) a more rigorous approach for polyfunctional ligands is to calculate a continuous affinity spectrum, i.e. site occupation probability as function of the complexation constant. This technique requires inverse deconvolution of the experimental data, which may be difficult, due to a potentially large error propagation [153]. Nonetheless, rigorous mathematical treatments are available (e.g. [154]). (3) a third approach for polyfunctional ligands consists in computing a differential equilibrium function, DEF ( log K  ¼ f ( log ([M]b =[L]t )); [143,155, 156]) from the experimental data. K  is a weighted average of all of the K values [105] in a particular complex [143,157], with a strong weighting for the sites that are half-saturated at a particular [M]b =[L]t ratio. [M]b is the concentration of bound metal and [L]t is the total concentration of ligand. At constant pH and ionic strength, a linear relationship is obtained:

K. J. WILKINSON AND J. BUFFLE

log K  ¼ log K0
G log ([M]b =[L]t )

469

(26)

where K0 is a constant that depends on the pH and ionic strength and the nature of the metal and ligand. G is a constant (0 < G < 1) representing the heterogeneity of the sample (lower values indicating greater heterogeneity; G ¼ 1 for the homogeneous case) that is obtained from the slope of the DEF curve. For HS, the value of G is generally observed to vary between 0.4 and 0.7 [158,159], although values as high as 0.9 have been observed for highly purified fulvic acids [160]. Similar approaches have been applied to samples of natural organic matter (reviewed in [131]), suggesting the existence of an extremely large number of site types in aquatic environments. Such a result is due in part to the large number of coordination sites present, but also to a change in ligand conformation due to a variable metal/ligand ratio. Recently, computer models have been developed that include such conformational changes in the speciation codes [117,161,162]. Nevertheless, when interpreting literature complexation data, several considerations are important to ensure that the constants provided by the models are physically realistic: (1) a minimum of operationally defined parameters should be employed; (2) the model should be applied over a wide range of [M]b =[L]t ; and (3) the model should not be dependent on the analytical technique and its ‘detection window’ [2,105,152,163]. 4.3

DISSOCIATION KINETICS OF AQUATIC COMPLEXES

Several comprehensive texts [164–166] and papers [167–170] have been published on complexation reaction kinetics in aqueous, including environmental, solutions. In this section, we shall briefly examine the Eigen–Wilkins mechanism as a starting point for estimating the rates of metal complexation reactions in environmental aqueous systems (Sections 4.3.2–4.3.3) and as a basis for the definition of the lability criteria (Section 7.2). 4.3.1

Simple Ligands: Eigen–Wilkens Mechanism

Detailed kinetic data are rare for natural aquatic ligands. For simple, not strongly binding ligands, it has been shown [164,165,171] that the dehydration of M(H2 O)zþ q subsequent to the formation of an outer sphere complex or ion pair (Eigen–Wilkens mechanism, equation (27)) is often the rate-limiting step in the formation of the metal complex, ML. This mechanism has often been applied to natural ligands [5,167,171] without further confirmation of its validity.

470 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES k
H2 O

Kos

zþ MðH2 OÞzþ q þL$MðH2 OÞq L
! MLðH2 OÞq
1

(27)

kf ¼ Kos k
H2 O

(28)

Under these conditions, the formation rate constant, kf , can be estimated from the product of the outer sphere stability constant, Kos , and the water loss rate constant, k
H2 O , (equation (28); Table 2). The outer sphere stability constant can be estimated from the free energy of electrostatic interaction between M(H2 O)zþ q and L and the ionic strength of the medium [5,164,172,173]. Consequently, Kos does not depend on the chemical nature of the ligand. A similar mechanism will also apply to a coordination complex with polydentate ligands, if the rate-limiting step is the formation of the first metal–ligand bond [5]. Values for the dissociation rate constants, kd , are usually estimated from the thermodynamic equilibrium constant, using calculated values of kf : K¼

4.3.2

kf kd

(29)

Application of the Eigen–Wilkens Mechanism to Natural Waters

The Eigens–Wilkens mechanism is not applicable for several environmentally relevant conditions [165,171]: (1) the presence of several ligands. The hydrolysis of multivalent cations can greatly (103
105 ) accelerate the rate of water loss and thus the kinetics Table 2. Representative values of the dehydration rate constant and the complex formation rate constant for a singly and a doubly charged anionic ligand for several metals in aqueous solutions. An ionic strength of 0:01 mol dm
3 was assumed. t1=2 is the half dissociation time (equivalent to 0:7=kd ) for a singly charged anionic ligand
1 with a stability constant of 106 dm3 mol . Based on [5,164,172]
1


1

Metal

k
H2 O =s
1

kf =dm3 mol
1 s , L ¼
1

kf =dm3 mol
1 s , L ¼
2

t1=2 =s

Pb2þ Hg2þ Cu2þ Cd2þ Zn2þ Co2þ Ni2þ Fe3þ Al3þ

7  109 2  109 1  109 3  108 7  107 2  106 3  104 2  102 1

3  1010 7  109 4  109 1  109 3  108 7  106 1  105 3  103 1  101

3  1011 9  1010 4  1010 1  1010 3  109 9  107 1  106 1  105 5  102

2  10
5 1  10
4 2  10
4 7  10
4 2  10
3 1  10
1 7  100 2  102 7  104

K. J. WILKINSON AND J. BUFFLE

471

of the coordination reaction, if OH
is bound more weakly than the incoming ligand [5]. This effect is especially important for Fe(III), Al(III) and Cr(III) [174–176]. For example, water-loss rates for Fe(OH)2þ are 1000 faster than those observed for Fe3þ [174]. Complexation by other inorganic ligands (e.g. Cl
, NH3 , CO2
3 ) is also predicted to have a similar effect, but of less important magnitude. For example, chloride complexation of Ni and Co has been shown to accelerate water loss by 10
20 [172]. (2) competition among metals for the same ligand. Slower than predicted complexation kinetics may occur in systems containing mixtures of competing metals [177]. Indeed, in natural systems, complexation often occurs 2þ in competition with other cations (e.g. Hþ , Ca2þ , Mg , transition metals) that are already bound to the ligand of interest [2]. Although kinetics for the competition reaction have not been well studied for natural organic complexes, for model chelators such as EDTA, exchange reactions are now fairly well understood. In that case, the formation rate of the ML complex is not controlled by the water-loss kinetics of M but rather by the dissociation rate of the competing complex. For that reason, the complexation of transition metals by protonated EDTA is rapid, whereas in the presence of high initial concentrations of Ca, as is often the case in natural waters, the presence of a Ca–EDTA complex will greatly reduce the metal-exchange kinetics [5,178]. Indeed, the formation times of Cd, Pb and Zn complexes with EDTA (from Ca–EDTA) are not in the 10
6 to 1 s range that would be expected if water loss were rate-limiting, but instead take between 10 min and 10 h [178]. (3) other coupled processes. In complicated environmental systems, complexation/dissociation reactions are coupled to other, not necessarily well identified processes such as diffusion or chemical phase transformations (e.g. redox, precipitation) that may be rate-limiting. For example, it has been shown that the decomplexation of Pb, Cu, Cd and Zn from freshwater colloidal clays and metal oxides takes several days [179–182] whereas subsecond times would be expected for a simple surface decomplexation based on a rate-limiting water exchange step. The observed slow desorption kinetics have been attributed to the diffusion of the metal ion out of the pores or interlamellar spaces of the colloids and to a limiting Kþ release from clays [183]. Nonetheless, more detailed studies are still required in order to fully understand this process. In summary, complexation kinetics for most 1:1 metal:ligand complexes are generally rapid, with water-loss rate constants, kf , ranging from 104 to 109 s
1 [164]. In many cases involving the formation of simple divalent metal complexes, the Eigen–Wilkens mechanism gives a reasonable estimate of a maximum value of kf . Nonetheless, it must be kept in mind that in complicated

472 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

mixtures and natural systems, reaction rates can be increased or (more frequently) decreased by orders of magnitude due to secondary factors such as ligand or metal competition, the coupling of diffusion or phase transformation reactions or by changes to the tertiary conformation of the ligands. The further role of ligand heterogeneity on reaction kinetics is examined in the next section. 4.3.3

Heterogeneous Ligands

As discussed above, in natural waters, most trace metals are bound to poorly defined colloidal or polymeric, chemically heterogeneous ligands, including HS. The current lack of understanding of the structure and reactivity of these ligands limits extrapolation of the mechanisms and rate laws established for simple ligands to natural systems. This section will attempt to establish guidelines in order to allow order of magnitude predictions of the dissociation kinetics of complexes with heterogeneous ligands. In the simplest case, it can be assumed that the water exchange reaction with a complexing site of a heterogeneous ligand will be governed by the Eigen– Wilkens mechanism as for complexes with simple ligands. In this case, equations (26) and (29) can be combined to yield: log kd ¼
log K0
log kf þ G logð[M]b =[L]t Þ

(30)

Indeed, if the Eigen–Wilkens mechanism is valid for each site, then kf is constant and independent of the site type and log kd is proportional to log ([M]b =[L]t ). In this case, a linear increase of the (log) dissociation rate constant is predicted as a function of the (log) metal/ligand ratio (Figure 4), reflecting the decreasing binding energy and increasing rate of dissociation of the metal complexes with the increasing metal/ligand ratio. While equation (30) is often valid for the dissociation kinetics of metal–fulvic acid or metal–humic acid complexes, dissociation kinetics for heterogeneous ligands are more generally described by a distribution function of rate constants [142] that describes the probability of finding any particular value of kd in the ligand of interest. In such cases, G also varies with the metal:ligand ratio, such that equation (30) is represented by a curve. Nonetheless, this approach is often hampered by the disproportionate influence of experimental errors on the calculations. The most important point to be retained from Figure 4 is that under environmental conditions, the values of the dissociation rate constants may be spread over several orders of magnitude, depending on the metal/ligand ratio. The complexes range from very rapidly dissociated, at high metal to ligand ratios to nearly inert complexes at low metal to ligand ratios. For example, at pH 8, more than one day is required for the dissociation of copper–fulvic acid complexes at < 10
2 mmol Cu g
1 C, while, for < 1 mmol Cu g
1 C, dissociation occurs in < 1 s [184].

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473

log ([M]b/DOC) (mol g−1)

−2 0.48 −3 −4 −5 12

10

8

6

4 log K*

−4

−2

0

2

4 log k * /s−1 d

1 d 1 h 1 min 1 s

1 ms

log t90

Figure 4. Copper complexation by a pond fulvic acid at pH 8 as a function of the logarithm of [Cu2þ ]. On the x-axis, complex stability constants and kinetic formation rate constants are given by assuming that the Eigen–Wilkens mechanism is valid at all [M]b =[L]t . The shaded zone represents the range of concentrations that are most often found in natural waters. The þ represent experimental data for the complexation of Cu by a soil-derived fulvic acid at various metal:ligand ratios. An average line, based on equations (26) and (30) is employed to fit the experimental data. Data are from Shuman et al. [2,184]

5 ADSORPTION AND DESORPTION AT THE BIOLOGICAL SURFACE In order to induce a biological effect, the solute must first be adsorbed to a sensitive site on the cell surface. For certain toxic substances, adsorption alone is sufficient to cause acute toxicity in aquatic organisms via the direct impairment of membrane function or through the catalysis of membrane degradation [185]. In the case of a bioaccumulated element, the concentration of the element adsorbed to sensitive sites on the biological membrane is often directly related to the uptake fluxes and biological effects. Indeed, with the exception of photochemical responses, the reversible binding of a solute to a specific site on a protein or nucleic acid is the primary mode used in vivo to initiate biological processes [186]. This is the underlying basis of the biotic ligand model that is currently receiving much attention in toxicology circles in spite of its serious limitations. Solute adsorption is therefore discussed in Sections 5.1 and 5.2. Because bioaccumulation mechanisms are most often deduced from indirect measurements with relatively large experimental errors, the limitations of these techniques are discussed in Section 5.1.1. In Section 6, we will examine

474 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

how internalisation fluxes are related to the concentrations of solute adsorbed to sensitive surface sites. 5.1 LIMITATIONS IN THE DETERMINATION AND INTERPRETATION OF EQUILIBRIUM AND KINETIC DATA As seen above (equation (5)), the basis of the simple bioaccumulation models is that the metal forms a complex with a carrier or channel protein at the surface of the biological membrane prior to internalisation. In the case of trace metals, it is extremely difficult to determine thermodynamic stability or kinetic rate constants for the adsorption, since for living cells it is nearly impossible to experimentally isolate adsorption to the membrane internalisation sites (equation (3)) from the other processes occurring simultaneously (e.g. mass transport; complexation; adsorption to other nonspecific sites, Scell , i , (equation (31)); internalisation). M þ Rcell $ M
Rcell

(3)

M þ Scell, i $ M
Scell, i

(31)

For this reason, thermodynamic and rate constants (Section 5.1.1) and carrier numbers (Section 5.1.2) are most often determined from kinetic measurements of uptake. The major limitations of this approach are discussed below. 5.1.1 Equilibrium and Rate Constants for the Adsorption at the Membrane Surface Because it is difficult to isolate the carrier-bound metal (or solute) from that bound to other cellular fractions, experiments are often performed under limiting conditions. For example, temperature or time may be manipulated in order to reduce internalisation fluxes while having less important or predictable effects on adsorption. This is due to the fact that binding to carriers is often driven by positive entropy changes [114], such that a decrease in temperature will generally result in only minor variations of equilibrium binding, while significantly reducing internalisation of the solute carrier complex across the biological membrane. Another common approach is to perform measurements of cellular metal following very short or very long equilibration times with the medium. While the adsorbed metal fraction is often negligible with respect to total cellular metal in long-term experiments, i.e. more than hours to days, it may predominate at short times (less than hours). For short exposure times (seconds to minutes), it is often assumed that the solute concentration in solution remains constant and that desorption is negligible with respect to adsorption (equation (32)). These greatly simplifying

K. J. WILKINSON AND J. BUFFLE

475

assumptions allow for the determination of a pseudo first-order constant (units ¼ s
1 ) that describes the forward rate of adsorption to the carriers. Practically, the condition of constant concentration in the bulk solution can be obtained by reducing cell numbers so that solute depletion is negligible over the time course of the experiments. On the other hand, some solutions have also been published for the non-steady-state situations [114]: Jads ¼ kf [M]fRcell g (forward reaction)

Jnet

(32)

Jnet ¼ kf [M](fRt g
fM
Rcell g)
kr fM
Rcell g (33)   n ¼ kf ([M]
fM
Rcell g ðfRt g
fM
Rcell gÞ
kr fM
Rcell g (34) NA

In equation (34), n is the number of cells and NA is Avogadro’s number, and {Rt } is the total carrier concentration (including both bound and free carriers). Solute depletion can be especially important in laboratory experiments, since large numbers of cells are generally employed at low solute concentrations that are typical of trace elements in natural waters. On the other hand, at high solute concentrations corresponding with carrier saturation, nonspecific adsorption to membrane components other than the carriers becomes important, and thus interpretation is much more difficult. In the biomedical literature (e.g. solute ¼ enzyme, drug, etc.), values of kf and kr are often estimated from kinetic experiments that do not distinguish between diffusive transport in the external medium and chemical reaction effects. In that case, reaction kinetics are generally assumed to be rate-limiting with respect to mass transport. This assumption is typically confirmed by comparing the adsorption transient to maximum rates of diffusive flux to the cell surface. Values of kf and kr are then determined from the start of short-term experiments with either no (determination of kf ) or a finite concentration (determination of kr ) of initial surface bound solute [189]. If the rate constant for the reaction at the cell surface is near or equal to 4pr0 D (cf. equation (16)), then binding is assumed to be diffusion limited. In this case, kinetic constants can be determined by distinguishing intracellular from bound solute using distinctions based upon time or chemical extraction techniques (e.g. [190,191]). For a diffusion-limited surface reaction, rate constants for the adsorption will not be constants but instead functions of the number of available free receptors [114]. In the case of trace metals, adsorption is typically much faster than the time intervals for which it is practically possible to separate the cells. Therefore, in practice, values of kf and kr are most often estimated by assuming that water loss from the hydrated cation is rate-limiting (Eigen–Wilkins mechanism, see Section 4.3.1 above). In some cases, uptake transients can be observed at the start of a short-term uptake experiment or by using pulse-chase experiments for which a metal solution containing a radioactive tracer is replaced by a solution

476 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

of nonradioactive metal [192]. The pulse-chase experiments allow for the verification of kd  kint that is required to validate the steady-state assumption, necessary when employing internalisation fluxes in the determination of the equilibrium constants. In the steady-state approach (equations (35) and (36)), no attempt is made to isolate the adsorption step from the internalisation of solutes. In this case, a Langmuir adsorption via membrane carriers is coupled to an irreversible and rate-limiting internalisation of the solute–carrier complex [186]. The process can be described by the Michaelis–Menten equation: kint kf M þ Rcell $ MRcell
! Mint þ Rcell kd Jint ¼

(5)

Jmax [M] KM þ [M]

(35)

kd þ kint kf

(36)

KM ¼

From a plot of the internalisation flux against the metal concentration in the bulk solution, it is possible to obtain a value of the Michaelis–Menten constant, KM and a maximum value of the internalisation flux, Jmax (equation (35)). Under the assumption that kd  kint for a nonlimiting diffusive flux, the apparent stability constant for the adsorption at sensitive sites, Ks , can be calculated from the inverse of the Michaelis–Menten constant (i.e.
1 ¼ Ks ¼ kf =kd ). The use of thermodynamic constants from flux measureKM ments can be problematic due to both practical and theoretical (see Chapter 4) limitations, including a bias in the values due to nonequilibrium conditions, difficulties in separating bound from free solute or the use of incorrect model assumptions [187,188]. 5.1.2

Carrier Numbers

As seen in equations (32)–(34), the forward adsorptive flux depends upon the concentration of free cell surface carriers. Unfortunately, there is only limited information in the literature on determinations of carrier concentrations for the uptake of trace metals. In principle, graphical and numerical methods can be used to determine carrier numbers and the equilibrium constant, Ks , corresponding to the formation of M
Rcell following measurement of [M] and fM
Rcell g. For example, a (Scatchard) plot of fM
Rcell g=[M] versus fM
Rcell g should yield a straight line with a slope equal to the reciprocal of the dissociation constant and abscissa-intercept equal to the total carrier numbers (e.g. [186]).

K. J. WILKINSON AND J. BUFFLE

fM
Rcell g ¼
Ks fM
Rcell g þ Rt Ks
1 [M]

477

(37)

Where competitive inhibition is observed between two solutes (i.e. binding to a single, identical carrier), it is also possible to estimate carrier concentrations using a steady-state treatment [193–195]. In that case, data from the competing solutes are used to generate a sufficient number of equilibrium expressions (e.g. equations (38) and (39)) and corresponding mass balance equations (e.g. equations (40) and (41)) to resolve for the total carrier concentration. fMi
Rcell g ½Mi fRcell g

Hj
Rcell Kj ¼  Hj fRcell g Ki ¼

(38)

(39)

 Mi, t ¼ ½Mi þ fMi
Rcell g

(40)



fRt ¼ fRcell g þ fMi
Rcell g þ Hj
Rcell

(41)

Carriers can also, in theory, be isolated from the membrane and quantified using gel electrophoresis (or similar techniques), although in practice, it is only possible to measure a protein content and not a carrier number (e.g. [196]). Note that in all of the cases mentioned above, carrier numbers are generally quantified by assuming a 1:1 stoichiometry with a labelled solute. The above procedures imply that (1) there is only a single type of site; (2) binding occurs only to the transporter site (usually not the case for trace metals), and (3) the internalisation flux is negligible for the equilibration times that are employed [197,198]. These conditions are rarely fulfilled for metal transporters. The interpretation of Scatchard plots is especially ambiguous in the presence of several independent sites. On the other hand, in the biomedical literature, where nonspecific adsorption is generally not a problem, values of 104 to 106 carriers per cell (ca. 10
13 to 10
11 carriers cm
2 of cell surface area), with even lower numbers determined for some receptors (e.g. haematopoetic growth factor [199]), are typically reported. There is only limited information in the literature on determinations of carrier numbers for the uptake of trace metals. Hudson and Morel [7] and later Sunda and Huntsman [200] argued that to enable Fe uptake, marine diatoms required extremely large numbers of carriers (enough to cover 50% of the cell surface area in some cases). For Pb uptake by Chlorella kesslerii, Slaveykova and Wilkinson [201] have also estimated large carrier numbers of 1:5  10
11 mol cm
2 (> 106 carriers per cell) using kinetic EDTA extraction techniques. Finally, using similar extraction kinetics, saturation of Zn

478 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

transporters has been observed to occur at 10
10 mol cm
2 [90]. It is notable that in each of the known estimates of metal carrier numbers, large numbers have been obtained, especially considering that, for cells of these sizes, physical space arguments alone would limit carrier numbers to ca. 107 per cell [7,201]. 5.2

ADSORPTION TO CARRIERS

Little effort has been made in the literature to distinguish adsorption to carrier sites from nonspecific adsorption to the cell wall and biological membrane. Typically, most quantitative determinations of intrinsic stability constants (including some BLM data) are obtained using equilibrium measurements on whole cells, while the more (ecologically) relevant, but conditional, stability constants for binding to metal carrier sites are determined using a Michaelis–Menten steady-state approach (e.g. Table 3, equation (35)). As discussed above, many assumptions must be fulfilled in order to assure the validity of the latter approach. In addition, competition among different metals, chemical heterogeneity effects, formation of ternary species and the non-steady-state adsorption of the metal are rarely examined, but important, problems in natural (heterogeneous) systems. These topics will be examined in the following sections (5.2.1–5.2.4). 5.2.1

Competition Among Metals

No carrier is completely specific for a given trace metal; metals of similar ionic radii and coordination geometry are also susceptible to being adsorbed at the same site. The binding of a competing metal to an uptake site will inhibit adsorption as a function of the respective concentrations and equilibrium constants (or kinetic rate constants, see below) of the metals. Indeed, this is one of the possible mechanisms by which toxic trace metals may enter cells using transport systems meant for nutrient metals. The reduced flux of a nutrient metal or the displacement of a nutrient metal from a metabolic site can often explain biological effects [92]. In the simplest case of a competitive uptake of two metals (or a metal and proton) for an identical uptake site under equilibrium conditions, the reduction of the uptake flux of the solute can be quantitatively predicted using the respective equilibrium formation constants (equations (38)–(41)). As can be seen in Table 3, for a given study, constants among the trace metals, protons and alkaline earth metals are often sufficiently similar for competition to be important. Nevertheless, competition is likely to be negligible under most environmentally relevant conditions where competition occurs between low concentrations of metals, such that the free carrier concentration remains approximately equal to the total receptor concentration. Although several examples of multiple metal experiments exist in the literature, few have quantitatively examined the role of competition on uptake fluxes,

K. J. WILKINSON AND J. BUFFLE

479

Table 3. Representative affinity constants for the binding of metal to transport sites or whole cells/organisms. Ionic strengths and pH values are given for the conditional constants. In the column ‘Comments’, information on the method of determination (KM ¼ Michaelis–Menten constant; WC ¼ whole-cell titrations); the type of constant (CC ¼ conditional constant; IC ¼ intrinsic constant) and special conditions (CI ¼ competitive inhibitors; NICA ¼ nonideal competitive adsorption) are given Metal

pH

Ionic strength (mmol dm
3 )

log KS

Comments

Ref.

Ni H Cd Ca Zn

7.5

100 10/100

4.7 8.7, 5.7 5.3, 2.3 5.3, 2.3 4.9, 2

CC; KM WC; IC; NICA interpretation

[202] [110]

Fungus Penicillium ochrochloron

Cu

3.0

100

Saccharomyces cerevisiae

Mn

6.5

5

Cd Cd Zn

7.0 6.8

30

Mn Zn Pb Co Mn Zn Zn

8.2

ca. 650

6.0 8.0

10

6.2

25

Mn Zn Cd Zn

8.2

ca. 650

8.2

ca. 650

Zn Cu Cd Ca H

7.5 6.2

ca. 3 ca. 1

Organism

Bacterium Rhodospirillum rubrum Rhodococcus erythropolis

Phytoplankton Chlorella pyrenoidosa Chlorella vulgaris

Chlamydomonas sp. Chlorella kesslerii Chlorella salina

Selenastrum capricornutum Diatoms Thalassiosira pseudonana

Emiliania huxleyi

Fish Oncorhynchus mykiss Pimephales promelas

CC; KM ; no saturation at pH 6 6.5, 4.2 CC; KM ; CI: Co, Zn 3.4

5.5 4.4 4.1

CC; KM WC; IC; Numerical resolution CC; KM

7.0 7.7 5.5 CC; KM 4.7, 3.6 CC; KM 5.7, 3.1 5.4, 3.2 8.2 CC; KM 7.1 7.5 8.1 8.4 9.6

[203]

[204]

[205] [193]

[206] [92] [201] [207] [208] [210]

CC; KM

[211] [92]

CC; KM Variable acclimation

[209]

5.1–5.4 CC; KM 7.4 WC; IC 8.6 5.0 6.7

[212] [17]

480 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

although this is currently an active area of research. A notable exception is the work of Sunda and Huntsman [213,214] and a few others (e.g. Table 3; [193–195,215]). For example, Cd has been shown to bind to Mn uptake sites, thereby competitively inhibiting Mn transport into the cells of marine phytoplankton [216,217]. In addition, Mn uptake by marine phytoplankton has been shown to be reduced by Cu and Zn [92,205,213,216], due both to an inhibition of direct binding to the transport sites and an apparent intracellular regulation of the uptake rate. The latter mechanism will be examined in greater detail in Section 6.5.2. 5.2.2

Ternary Complexes and Ligand Adsorption

Although it is not an absolute criterion of the conceptual model presented in Section 2, it is often assumed that only the free metal ion will react with the transporter. In fact, until recently, very few experiments have attempted to examine the chemical nature of the biological surface complex even though powerful techniques such as solid-state nuclear magnetic resonance spectroscopy (e.g. [218,219]) or the synchrotron-based X-ray microprobe techniques (e.g. [220]) are now making those experiments possible. In one such case, 19 F NMR was employed to show that in addition to fAl
Rm g complexes, ternary fF
Al
Rcell g complexes could be formed at the surface of cells isolated from the gills of Atlantic salmon [221]. The corresponding, in situ, toxicological results [222,223] showed that both the fF
Al
Rcell g complex and the fAl
Rcell g complex contributed in different manners to the observed bioaccumulation and toxicity of aluminium. Furthermore, based on toxicological results, several authors (e.g. [224–226]) have postulated the formation of HO
Al
Rcell complexes or the surface precipitation of aluminium hydroxides or polymeric Al at intermediate pH values. Although toxicity is indeed more important at pH 5–7 than can be explained by solution concentrations of Al3þ , analysis is not straightforward, since pH decreases cause both an increase in carrier protonation and a decrease in Al hydrolysis [227]. In the case of Al (and Fe(III)), the formation of ternary complexes is an attractive, if unproven, explanation since, as was shown above (Section 4.3), complexation with inorganic ligands can accelerate water loss, increasing significantly the rate of adsorption of the cations to surface sites. The behaviour of natural ligands has been discussed in Section 4.3.3. In addition to the direct effect of complexation that is related to a decrease in the free ion activity, it has been shown that some ligands, in particular the HS, can be sorbed directly to biological surfaces, in the presence or absence of the trace metal [228,229]. This result is likely due to the fact that HS and similar macromolecules contain hydrophobic moieties that facilitate their adsorption to the plasma membrane and cell wall [157,230,231]. Because adsorption is expected to occur primarily with sites that are independent of the transporters,

K. J. WILKINSON AND J. BUFFLE

481

it might be expected to have few effects on the cell function. However, this does not appear to be the case. The adsorption of HS has been shown to increase membrane permeability (Selenastrum capricornutum, [232]) and reverse permeability effects caused by metal adsorption (C. kesslerii [160,233]). Both the adsorption of HS and the resulting increases in membrane permeability have been observed to be much more important at slightly acidic pH values as compared with neutral pH [228,232]. 5.2.3

Chemical Heterogeneity Effects

It was shown above (Section 4.3.3) that for environmental ligands in solution, chemical heterogeneity, polydispersity and conformational effects play an important role in the binding of metals. As for ligands in solution, there is a tendency for the average stability constant, K  , to decrease with the complexation capacity of the biota ([131,234,235]; Figure 5). The lower slope of the log–log graph (near 0.5) is consistent with an underlying continuous distribution of functional groups of different complexation strengths that reflects cell wall/membrane heterogeneity. In this case, the heterogeneity parameter, G, ranged from 0.38 for Cu binding to 0.98 for Zn binding by the aquatic Gram-negative bacterium, Klebsiella pneumoniae [234]. The metal-binding

log ([M]b/{Scell,t}) (mol m−2)

−5.0 Cu pH 7.2

−5.5 −6.0

Cu pH 6.1 Pb pH 6.9 Zn pH 7.3

−6.5

Zn pH 5.7

−7.0

8

7

6

5

log K*

Figure 5. Variation of the complexation capacity of the bacteria Klebsiella pneumoniae as a function of the conditional differential equilibrium functions, K  , for Zn, Pb and Cu. Bound metal was determined as the difference between total and electrochemically (differential pulse anodic stripping voltammetry) labile metal. Bound metal was normal
1 ised to the bacterial surface area (ca. 170 m2 g ). As was observed for the hetereogeneous ligands such as humic substances (Figures 3 and 4), each of the slopes is smaller than unity (see text for explanation): Cu (pH 6.1: 0.33; pH 7.2: 0.38); Pb (pH 6.9: 0.46); Zn (pH 5.7: 0.33; pH 7.3: 0.25). Ionic strength was 10 mmol dm
3 . The pH values are given in the figure. Reprinted from: [235] Sci. Total Environ., 60, Gonc¸alves M. L. S. et al., ‘Metal ion binding by biological surfaces: voltammetric assessment in the presence of bacteria’, pp. 105–119, Copyright (1998), with permission from Elsevier

482 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

heterogeneity of other microorganisms showed similar variabilities, e.g. G ¼ 0:36 for Cu adsorption, 0.51 for Pb adsorption and 0.6 for Zn adsorption to the alga, S. capricornutum at pH 7.0. As discussed above, under the steady-state assumption, uptake fluxes can be employed to estimate complexation stability constants to carriers. In a similar manner, the carrier site capacity can be estimated from plots of J=Jmax against ½M [114], similar to the treatment of complexation capacity (Figures 3 and 4). Although the determination of saturated uptake rates, Jmax , at concentrations that are often no longer environmentally pertinent may not appear to have an immediate scientific interest, the plot of J=Jmax against the solute concentration corresponds with the rectangular hyperbola of the Langmuir adsorption isotherm [186]. Nonetheless, to ensure the validity of this data treatment, all binding sites must be identical and independent with a slope of 1 observed for concentrations below carrier saturation. Indeed, in the case of Pb uptake by C. kesslerii, no surface heterogeneity effects are required to explain either normalised uptake fluxes or carrier-bound metal, since the fraction of apparent occupied transport sites (ratio between occupied fPb
Rcell g and total fRt g transport sites) was well correlated (slope ¼ 1:01 and R2 ¼ 0:93) to the normalised uptake flux Jint =Jmax over three orders of magnitude [201]. On the other hand, for Zn uptake by the same alga [90], a slope significantly smaller than unity was observed for most of the concentration range examined. The lower than unity slope could be explained by the same charge (Section 4.2.1) or polyfunctionality (Section 4.2.2) arguments that were invoked previously for heterogeneous ligands in solution and the whole cell titrations. Nonetheless, this explanation is unlikely for carrier-mediated adsorption, since there is only limited quantitative information demonstrating the existence of multiple uptake sites and, in those cases, rarely more than two or three types of transporter sites have been identified (e.g. [209,217]). Furthermore, it is experimentally difficult to distinguish electric field effects [237] from a two (or more) carrier model. Depending upon the ratio of carrier numbers in each class, adjacent K values must be separated by 1–2 log units in order to be clearly resolved [105,163,238]. For smaller differences, statistical criteria [189,239] are required to decide whether the use of two or several carriers is superior to a one carrier model or whether improved fits are simply due to an increased number of fitting parameters. Another difference that is observed following binding to carriers that is not observed when measuring adsorption on an abiotic surface, is that adsorption can trigger a cooperativity [186] that includes both short-term responses (milliseconds to minutes) and long-term responses such as those requiring protein synthesis [114]. While the synthesis of significant concentrations of transporters can be avoided by working with short-term experiments, other examples of cooperativity include the clustering of carriers, binding of a single solute to several carriers and the binding of several solutes to a single carrier. Such events

K. J. WILKINSON AND J. BUFFLE

483

can trigger modifications in the apparent adsorption rate or stability constants. For example, Wiley et al. [240] have observed a three-fold increase in the adsorption rate constant and a slight (30%) decrease in the dissociation rate constant following pre-incubation with epidermal growth factor, EGF. In another example, Lin et al. [241] attributed a decrease in binding to the EGF receptor to its phosphorylation. As mentioned above, the lower than unity slope observed in the metal uptake experiments (Figure 6) is unlikely to be attributed to the same charge effect that

[Image not available in this electronic edition.]

Figure 6. (a) Variation of the uptake fluxes of the alga, Chlorella kesslerii, as a function of the free ion concentration for Pb (
) and Zn (?). (b) Carrier-bound Pb and Zn as a function of the free-ion concentration for the same alga. Ionic strength was 5 mmol dm
3 and pH was 6 for the Pb uptake experiments, while ionic strength was 1 mmol dm
3 and pH was 7 for Zn uptake. For both graphs, a slope of unity is given as the small solid line. Adapted with permission from: [201] Slaveykova, V. I. and Wilkinson, K. J. (2002). ‘Physicochemistry of Pb accumulation by Chlorella vulgaris’, Environ. Sci. Technol., 36, 969–975. Copyright SETAC, Pensacola, Florida, USA; also copyright (2002) American Chemical Society. See also [90,236]

484 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

was observed for ligands in solution (Section 4.2.1). Therefore, when working with living organisms, several other explanations must be examined including: (1) a non rate-limiting metal internalisation; (2) the existence of a significant metal efflux; and (3) other than first-order internalisation kinetics. The latter two explanations will be examined more thoroughly in Section 6. In Section 5.2.4, the conditions required for adsorption to be rate-limiting are examined. 5.2.4

Rate-Limiting Adsorption of Metal to Carriers

For undersaturated ([M] < KM ) systems with relatively fast internalisation kinetics (kint > kd ), the uptake of trace metals may be limited by their adsorption. Because the transfer of metal across the biological membrane is often quite slow, adsorption limitation would be predicted to occur for strong surface ligands (small values of kd ) with a corresponding value of KM (cf. equations (35) and (36)) that imposes an upper limit on the ambient concentration of the metal that can be present in order to avoid saturation of the surface ligands. More importantly, as pointed out by Hudson and Morel [7], this condition also imposes a lower limit on the carrier concentration. Since the complexation rate is proportional to the metal concentration and the total number of carriers, for very low ambient metal concentrations, a large number of carriers are required if cellular requirements are to be satisfied. Using a similar reasoning, it is possible to identify several metals (e.g. Cr(III), Fe, Ni, Zn, Al) that may exhibit slow enough reaction kinetics so as to be ratelimiting. Note that under the assumptions of a rate-limiting formation of the metal–carrier complex and the applicability of the Eigen–Wilkens mechanism, metal–ligand complexes in solution that are more stable than the metal–carrier complexes would not be available for uptake. This results from the fact that metal dissociation from the ligand in solution would be slower than its dissociation from the carrier. For uptake rates that are limited by the formation kinetics of a metal–carrier complex, the forward rate constants (and metal and carrier concentrations) would be the most indicative of uptake rates. Indeed, for ocean surface waters, nutrient concentrations appear to be better correlated with their kinetic lability rather than their complexation properties. Hudson and Morel [7] have suggested that this might be because the essential micronutrients (with presumably faster internalisation rates, cf. Figure 6) are controlled by mass transport as well as uptake kinetics, while nonessential metals (requiring a greater (thermodynamic) selectivity) could be thermodynamically controlled. Most laboratory measurements of trace metal uptake are performed by manipulation of the metal and chelator concentration, and therefore it is often impossible to distinguish between a thermodynamic and a kinetic dependence on the free-ion activity. In fact, only limited work has tested, in detail,

K. J. WILKINSON AND J. BUFFLE

485

whether adsorption at carrier sites could be rate-limiting. The most well-studied case is that of Hudson and Morel [192], who demonstrated quite convincingly that Fe uptake by Thalassiosira weissflogii cannot be explained by a simple thermodynamic control (the implications of these results are discussed in [7,8,92]). By performing transient uptake and pulse-chase experiments, these authors were able to show that the rate of formation of the surface complex and the rate of internalisation were nearly equal and much larger than the rate of complex dissociation. Pulse-chase experiments demonstrated quite clearly that internalisation occurred during the chase phase of the experiments, in the absence of radiolabelled iron. The observation that the formation and dissociation rates of the surface complex were not equal is unambiguous evidence that the carriers were not in equilibrium with the solution Fe. These results contrast quite clearly with the FIAM/ BLM steady-state models. Despite the intriguing results suggesting a kinetically limiting surface adsorption of Fe in oceanic surface waters [192], few other experiments have been performed that specifically examine the kinetics of the metal adsorption process. Among other complications, kinetic control of the transport would be expected to cause undersaturation of the carriers that could could produce a gradient of variable [metal]/[ligand] that would affect the overall flux. This would appear to be an area that is ripe for future research.

6 TRACE ELEMENT TRANSPORT ACROSS BIOLOGICAL MEMBRANES The simple adsorption of chemicals to the cell surface is rarely sufficient to induce a biological response. In most cases, a receptor or carrier protein must convey information to the cell interior to indicate that binding has taken place, resulting in the initiation of a number of processes including: catalysis, signal and energy transduction, cross-membrane transport and cellular defence mechanisms [114]. Because microorganisms do not have specific transport systems for the vast majority of compounds that are internalised by the cell, most compounds must borrow existing pathways designed for the essential elements: transport through ion channels, carrier-mediated transport, active transport and endocytosis [24,242]. In addition, passive diffusion through the cell membrane (hydrophobic compounds, e.g. [21]) and uptake by food (multicellular organisms, e.g. [243,244]) are important internalisation vectors in some cases. Despite a large body of literature examining the intracellular events that follow solute adsorption and precede cellular responses, in most cases, this remains an active area of research, especially with respect to the kinetics of the pathways that mediate the processes. It is known that most trace metals are moved down their electrochemical gradients by simple diffusion, diffusion

486 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

through channels or by facilitated diffusion (carrier-mediated transport). Once inside the cell, transition metals often play important roles as coenzymes or participate in catalytic processes, due to their ability to take on several redox states. In contrast, soft metals are often toxic, due to their ability to replace transition metals in biological structures. These and other biological mechanisms of the internalisation process have been discussed in much greater detail in Chapters 6 and 7 of this volume [24,245] and elsewhere (e.g. [242,246,247]). The main objective of this section is to examine the implications of the different transport mechanisms on the kinetics of the uptake process. Section 6.1 will examine the predicted kinetics of several of the more important transport mechanisms for trace elements: passive diffusion, transport through ion channels, carrier mediated transport and active transport. Endocytocis and the contribution of food to multicellular organisms will not be examined (see Chapter 8 in this volume, [248]). In Section 6.2, the limitations of the major techniques used for the measurement and interpretation of elemental internalisation fluxes will be discussed. As will be seen in the following sections, the kinetics of a large number of complicated systems are fortuitously simplified by the frequent observation of a single rate-limiting step for cellular transport. Although this observation greatly facilitates the modelling of cellular uptake processes by eliminating the consideration of transients, it is still uncertain whether such an assumption is valid in all cases. 6.1

KINETICS OF THE IMPORTANT TRANSPORT MECHANISMS

Depending upon the mechanism that is employed by the organism to accumulate the solute, internalisation fluxes can vary both in direction and order of magnitude. The kinetics of passive transport will be examined in Section 6.1.1. Trace element internalisation via ion channels or carrier-mediated transport, subsequent to the specific binding of a solute to a transport site, will be addressed in Section 6.1.2. Finally, since several substances (e.g. Naþ , Ca2þ , Zn2þ , some sugars and amino acids) can be concentrated in the cell against their electrochemical gradient (active transport systems), the kinetic implications of an active transport mechanism will be examined in Section 6.1.3. Further explanations of the mechanisms themselves can be obtained in Chapters 6 and 7 of this volume [24,245]. 6.1.1

Passive Transport

Nonpolar compounds, including the majority of xenobiotic chemicals and some metal complexes [249–252], generally diffuse passively through the lipid portions of the membrane by simple diffusion [21,246,253,254]. In this case, internalisation rates are reflected by compound permeability in the bilipid membrane [254,255] and can be predicted by Fick’s law [254,256]:

K. J. WILKINSON AND J. BUFFLE

Jint ¼

 Dm
Klw c
cin !

487

(42)

where ! is the thickness of the lipid component of the membrane, Dm is the molecular diffusivity of the nonpolar solute in the membrane, Klw is the lipid–water partition coefficient and cin is the concentration of compound inside the organism. In this case, the concentration of solute at the outer surface of the membrane, cm , is equal to Klw c . If cin is maintained low (cin  0) due to biodegradation or complexation, then the uptake rate will exhibit a first-order dependency on the concentration of compound in the bulk solution: Jint ¼ kint c

(43)

where kint is the rate constant of the reaction (in this case, DKlw !
1 ). For a given microorganism, relative uptake rates of a series of nonpolar compounds should therefore increase with an increasing value of DKlw . Schwarzenbach et al. [254] compiled kint values ranging from 0.005 to 1:8 min
1 and suggested that the observed variability was due to differences in surface structure among organisms, especially with respect to the proportion of hydrophilic surface area [21]. 6.1.2

Carrier-Mediated Transport and Ion Channels

Conceptual models that describe carrier-mediated transport generally include a loaded and unloaded carrier molecule that can each exist in two conformations, depending upon whether the binding sites are facing the inside or outside of the membrane. Changes in the conformation of the loaded carrier complex, M
Rcell , can bring about reorientation of the binding sites. Typically, carrier reorientation can occur hundreds to millions of times per second [7,246,257]. Conformational changes of the carrier, especially the unloaded carrier [258], or release of the metal from the transport ligand [7,259] would appear to be ratelimiting. Many experimental variations are possible when performing uptake studies [246]. In a simple experiment for which the cells are initially free of internalised compound, the initial rates of transmembrane transport may be determined as a function of the bulk solution concentrations. In such an experiment, hydrophilic compounds, such as sugars, amino acids, nucleotides, organic bases and trace metals including Cd, Cu, Fe, Mn, and Zn [260–262] have been observed to follow a saturable uptake kinetics that is consistent with a transport process mediated by the formation and translocation of a membrane imbedded complex (cf. Pb uptake, Figure 6; Mn uptake, Figure 7a). Saturable kinetics is in contrast to what would be expected for a simple diffusion-mediated process (Section 6.1.1). Note, however, that although such observations are consistent

488 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

with a carrier mediated transport, they are not mechanistic proof of this type of transport [263,264]. As discussed in Section 5.1, for saturable uptake of a trace metal, the steadystate process is most commonly described by Michaelis–Menten uptake kinetics [265]: M þ Rcell $ MRcell ! Mint þ Rcell

(5)

Jmax [M] KM þ [M]

(35)

For KM  [M] Jint ¼ k0int [M]

(35a)

and for KM  [M] Jint ¼ Jmax

(35b)

Jint ¼

where KM is the Michaelis–Menten constant corresponding to the concentration of M at which uptake is one-half the fastest possible rate, Jmax , and k0int (m s
1 ) is proportional to the internalisation rate constant. For low concentrations of (i.e. [M]  KM ), the internalisation flux is likely to be first-order
solute k0int ¼ Jmax =KM with respect to the solute concentration, whereas, for high solute concentrations (i.e. [M]  KM ), the flux will exhibit zero-order kinetics. Some of the more important assumptions of the Michaelis–Menten approach are given below [264]: (1) a single 1:1 binding site is involved and a single compound is transported. (2) the carrier molecule does not possess regulatory sites. (3) there is no significant modification of carrier numbers during the experiment (e.g. degradation, synthesis). (4) the carrier has a homogeneous distribution of charges. (5) mass transport to the biological surface can be neglected. (6) transients may be neglected, transport is assumed to take place under steady-state conditions (see also Chapter 4 where the Michaelis–Menten equation is derived as a steady-state limit of the rigorous transient flux expression, [266]). (7) the conformational changes of the carrier are rate-limiting. (8) the dissociation constant of the M
Rcell complex constant has the same value on both faces of the membrane. This final assumption only holds for non-ionised substances. When these assumptions hold, Thellier et al. [264] and others [267,268] have shown that the Michaelis–Menten equation (equation (35)) can be rigorously derived from the conservation equations for the various forms of the carrier. By

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489

modifying different simplifying assumptions (e.g. [269]), it is possible to derive other equations with a similar form (e.g. for competitive inhibition): Jint ¼

Jmax [M]KM [M]KM þ [N]KN þ [P]KP þ 1

(44)

where the overall reaction corresponds with the internalisation of M, and subscripts correspond with the reaction of solutes N and P with an identical site. If there is a net transport of charge across the membrane, the membrane potential will influence the solute transfer and also be affected by it, complicating the data treatment. The starting point for most descriptions of the internalisation flux of permeant ions, i, is the one-dimensional Nernst–Planck equation (cf. equation (10)) that combines a concentration gradient with the corresponding electric potential gradient [270]: Jint ¼ Dm, i

dci zi df þ ui c i dx jzi j dx

(45)

where Dm, i is the diffusion coefficient of the solute in the membrane and f is the electrostatic potential in the bulk solution at the edge of the channel protein. Note that the first term corresponds with Fick’s law of diffusion (equation (11)).
Rapidly accumulating ions (e.g. Naþ , Kþ , Ca2þ , Hþ , Cl
, HCO3 ) generally enter the cell via ion-selective channels [246]. In that case, the driving force for accumulation is the electrochemical gradient between the outside and inside of the cell [246]. The simplest expressions of flux through open ionic channels are obtained by combination of the Nernst–Planck equation with the Poisson equation. Unfortunately, analytical resolution of the Poisson–Nernst–Planck system of equations is rare [271]. An approximate analytical solution has been proposed by Gillespie and Eisenberg [272] for the special case of a channel with a spatially uniform charge density and a limiting resistance with respect to the bulk solution. In that case (other assumptions given in [272]): Jint ¼

z cm
cin expð
zcm Þ Dm cm ! 1
expð
zcm Þ

(46)

F  m f
fin RT

(47)

where: cm ¼

where fm and fin are the values of the electrostatic potential at the inner (in) and outer (m) edge of the membrane. This relationship suggests that a

490 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

first-order internalisation may indeed be observed for trace elements (that do not perturb the dimensionless transmembrane potential, cm ), under the assumption, cm ¼ 0, similar to the assumption that was used for the transport of hydrophobic compounds. Other resolutions of the Poisson–Nernst–Planck equations (i.e. using various simplifying assumptions) have been proposed that couple the adsorption, desorption and permeation of ions through a membrane (e.g. [273,274]) as might be observed for a carrier-mediated transport. For example, for a symmetrical membrane (identical electrolyte on both sides of the membrane) and variation in the electrical potential profile given by cm , Jint can be estimated from: Jint ¼ zcm ky fM
Rcell g

(48)

where ky is an exchange rate constant for the permeation (s
1 ). In this case, ion transfer again depends on the electric potential profile across the membrane, whereas the adsorption and desorption rate constants are functions of the potential difference between the membrane surface and the bulk solution. As observed previously (Section 6.1.1), for a constant transmembrane electrical potential (e.g. accumulation of trace elements or noncharged species), the coulombic term is constant and first-order internalisation can once again be predicted with a value of kint equal to zcm ky . 6.1.3

Active Transport

Two main types of systems exist in which transport is coupled to a source of energy other than that provided by the electrochemical gradient [275]. Primary active transport is directly linked to the consumption of metabolic energy (e.g. splitting of ATP), whereas in secondary active transport, the flows of two compounds are coupled so that the compound of interest is pumped against its electrochemical gradient while metabolic energy or an electrochemical potential gradient is used for the transport of the second compound. Because these systems allow the cell to concentrate solutes against their electrochemical gradients, the internalisation flux will not be a simple function of the solute concentration. For the internalisation of metals, many examples exist for which transport may be coupled to an energy-dependent process, of which only a few are described here. For example, the well-studied (e.g. [276]) Naþ =Kþ channel transports 3Naþ out and 2Kþ in for each ATP molecule that is hydrolysed [242]. Mg2þ influx (but likely not efflux) is highly regulated in eukaryotes [277]. ATPases have been implicated in certain cases of Fe [278] or Zn [90] uptake by phytoplankton. Finally, although Cd internalisation by a polychaete appeared to be energy independent, accumulation was increased rather than decreased in the presence of ATPase inhibitors, suggesting that the efflux system might depend upon ATP synthesis [279].

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491

6.2 POINTS OF CAUTION WHEN INTERPRETING UPTAKE KINETICS As shown above, trace solutes that are taken up by simple diffusion, diffusion through channels or carrier-facilitated diffusion should exhibit simple first-order kinetics at low concentrations. Nonetheless, active transport is only one example for which a simple first-order uptake should not be observed. Transport mechanisms through membranes are often complicated cascades of successive steps that are dependent both upon membrane and cell wall structure and upon the characteristics of the compound being internalised. In addition, transport sites are continually being recycled, degraded and synthesised at rates that can be modified by the cell. Indeed, once adsorbed to a carrier, a compound can activate numerous intracellular enzymes and entire cascades of intracellular reactions, triggering both short (milliseconds to minutes) and long-term (e.g. protein synthesis) modifications of the uptake process. Furthermore, internalisation mechanisms will differ greatly among different cell/organism types. For example, the internalisation of relatively large (> 500 g mol
1 ) hydrated or negatively charged chemicals are slowed significantly by the water-filled pores (porins) of the external membranes of Gram-negative bacteria [21,254]. In eukaryotic cells, internalisation processes are complicated, since transport occurs via membraneous systems connecting the outside of the cell with the double nuclear membrane [280]. In the case of multicellular organisms, not only are they motile, allowing them to search out desirable compounds, but they also possess circulatory, lymphatic and gastrointestinal systems that force the circulation of compounds through the organism. Furthermore, the organism might simply migrate into or away from a solute plume. These and other factors complicating the interpretation of uptake kinetics in real systems are discussed in the following sections. In Section 6.2.1, the limitations are primarily related to data interpretation, while in Sections 6.2.2–6.2.4, some of the fundamental characteristics of biological organisms that distinguish them from inorganic particles are discussed.

6.2.1

Limitations of the Michaelis–Menten Approach

It is perhaps wise to begin by questioning the conceptual simplicity of the uptake process as described by equation (35) and the assumptions given in Section 6.1.2. As discussed above, the Michaelis constant, KM , is determined by steady-state methods and represents a complex function of many rate constants [114,186,281]. For example, in the presence of a diffusion boundary layer, the apparent Michaelis–Menten constant will be too large, due to the depletion of metal near the reactive surface [9,282,283]. In this case, a modified flux equation, taking into account a diffusion boundary layer and a first-order carrier-mediated uptake can be taken into account by the ‘Best’ equation [9] (see Chapter 4 for a discussion of the limitations) or by other similar derivations [282]:

492 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

ffi!   sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   D J d J d max max J¼  0:25 KM
c þ þ c  KM 0:5 KM þ c þ d D D

(49)

which, at low concentrations, c < KM , can be reduced to: J¼

c d KM þ D Jmax

(50)

where the denominator of equation (50) can be interpreted as transport resistance and includes the resistance of both the diffusion layer, d=D, and the carrier-mediated transport system, KM =Jmax . As was shown in Section 3, this equation demonstrates that for sufficiently large diffusion boundary layers (large d), slowly diffusing (small D) or rapidly accumulating (large Jmax ) solutes, or for large numbers of carriers (large Jmax ), permeability and therefore solute uptake may be limited by diffusion in solution. As mentioned above, the Michaelis–Menten treatment assumes that: (1) all of the active sites of the carriers are identical and independent; and (2) the solutes and/or carrier complexes do not act as inhibitors or activators. In that case, the inverse of the Michaelis constant is equivalent to the equilibrium formation constant, Kf , of the metal–carrier complex under the most restrictive assumptions of equation (35) (i.e. for kd  kint and a slower diffusion than dissociation of ML). In practice, experiments designed to determine the kinetics of the uptake process are performed in vivo under a steady-state assumption. Although several criteria are necessary to ensure the validity of the steady-state assumption [186], the observation of a constant concentration of accumulating solute, rather than the necessary condition of a constant concentration of the surface complex, fM
Rm g, is most often assumed sufficient. True kinetic constants can be determined from surface binding data only if the possibility of mass transport limitations can be reasonably excluded [284]. Additional useful and complementary experiments can be performed by: (1) careful restrictions of experimental time scales; (2) the use of pharmacological agents to block complicating processes; (3) the use of experimental protocols that distinguish among carrier states; or (4) the use of isolated membranes [114]. Of course, few real systems will possess such simplicity in vivo, since biological organisms are often able to influence their own uptake rates. 6.2.2

Cellular Responses Affecting Trace Element Internalisation

At the level of a single cell, bound carriers/receptors are known to trigger both short-term responses, such as the activation of various intracellular enzymes and long-term responses involving gene regulation, including the synthesis of

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493

proteins [114]. The diversity of adaptations with respect to protein production will depend upon a balance between the calorific payoff or reduction in toxicity on one hand, and the costs of maintaining and synthesising the carrier molecules on the other hand [28,285]. Ideally, in order to model cellular internalisation under the assumption of simple first-order kinetics (equation (6)), it is essential that neither the internalisation constant, kint , nor the total number of carriers, Rt , change significantly during the time course of the experiment. Of course, these conditions are not necessarily valid, since, for cells operating below the limits imposed by the maximal diffusive flux, changes in the physiology of the organism can have numerous repercussions on uptake, ranging from an increased affinity of the receptors for solute (equivalent to a lowering of KM ) to an increased number or increased turnover of cellular carriers (reflected by an increase of Jmax ) [9,28,29,286]. Rapid (< 1 min) apparent changes in the Michaelis–Menten derived value of Jmax [67,287,288] are well documented. For example, for planktonic algae, Jmax can increase under conditions of nutrient limitation [92,289]. In Chlamydomonas, the maximum uptake rate, Jmax , has been observed to increase by up to 30fold with decreases in the concentration of ionic Mn, in spite of the fact that the
1 remained constant (Figure 7b) [260]. In that case, Mn is affinity constant, KM taken up by a single high-affinity transport system under negative feedback regulation by the cell. The cell’s ability to regulate Jmax allows it to maintain internalised Mn concentrations at optimal levels for growth, in spite of variations in the external Mn concentration. On the other hand, for significant undersaturation of the cellular carriers at Mn < 10
8 mol dm
3 , the uptake rate again becomes directly proportional to [Mn2þ ] [92,260] (Figure 7a). A similar regulatory mechanism has been identified for iron [290] and zinc [209]. In many cases, it is unclear whether the changes in the maximal uptake flux, Jmax , are due to a physical increase in the turnover rate of the carriers, an increased production of carriers or an oversimplification in the interpretation of the Michaelis–Menten uptake kinetics. Because there are typically as few as 104
105 transport sites of a given type on a given microscopic cell [199], it is quite feasible to increase internalisation fluxes by increasing carrier numbers on the cell surface through the mutation of a regulatory gene or the duplication of a structural gene, genes or entire operon [41]. For example, in the case of Zn uptake by yeast, Zhao and Eide [291] have attributed feedback increases in Jmax to the production of membrane transport proteins regulated by Zn feedback on gene transcription. There are nonetheless limits to the capacity of the cell to respond via carrier production. Furthermore, it is not advantageous for the cell to respond too efficiently to a transient excess of solute, since too many carriers of any one type might crowd out other essential membrane components, or allow a toxic flux of an otherwise essential nutrient. In addition, there is an absolute limit to the number of carrier proteins that will fit into the membrane surface [292]. On the other hand, for very small concentrations of cell carriers,

494 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

log Jint (mol cm−2 min−1)

(a) −9

−10

−11 −8

log Jmax (mol cm−2 min−1)

(b)

−8.5

−9 −10

−9

−8 2+

−7 −3

log [Mn ] (mol dm )

Figure 7. Influence of cellular adaptation on short-term Mn uptake rates by exponentially growing cultures of Thalassiosira pseudonana. (a) Short-term uptake kinetics for cultures preacclimated to different [Mn2þ ]. Cells acclimated at 6:3  10
10 mol dm
3 [Mn2þ ] (
) exhibited higher uptake kinetics than those acclimated at 1:1  10
7 mol dm
3 [Mn2þ ] (!). (b) Maximum steady-state uptake rates as a function of [Mn2þ ]. Although the half-saturation constant (KM ¼ 7:9  10
8 mol dm
3 ; KS ¼ 1:3  107 dm3 mol
1 ) was constant across [Mn2þ ], maximum uptake fluxes decreased significantly at higher concentrations of [Mn2þ ]. Reprinted from: [92] Sci. Total Environ., 219, Sunda, W. G. and Huntsman, S. A. ‘Processes regulating cellular metal accumulation and physiological effects: phytoplankton as model systems’, pp. 165–181, Copyright (1998), with permission from Elsevier. See also, [206,211,216]

as the concentrations of carriers and environmental chemicals decrease, the magnitude of the stochastic variations should increase [293], since measurements of single cells may show relatively significant fluctuations with respect to population means. This effect may be especially important in experiments that measure the behaviour of single cells using intracellular amplification cascades. Few experiments have attempted to follow variations in the rate constant, kint . As discussed earlier, most experiments measure steady-state fluxes, and thus cannot distinguish a larger rate constant (kint ) from an increased number of carriers (fM
Rcell g). When metals compete for identical transport sites, it is possible to determine relative kint values from the ratio of the maximum uptake

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495

fluxes (e.g. [216]). The most clear evidence of a changing internalisation rate constant, kint , was given by Wiley and collaborators [294,295] who demonstrated that even though kint should be independent of receptor number, there was evidence of a lowering of the value of kint at high densities of occupied receptor. Using an approximation of transport sites based upon a chemical extraction technique [201], Hassler and collaborators have recently demonstrated apparent increases in kint for: increasing bulk concentrations of Zn [90]; decreasing concentrations of competing ion [296]; and increases in temperature [296]. For the most part, values of kint estimated from theoretical or experimental considerations vary between 1  10
4 s
1 and 1 s
1 (Table 4; [7,201,296]). These values are much smaller than the values of kint that can be estimated from the actual physical times for typical transport molecules to cross the biological membrane (typically < 10
3 s; kint > 1000 s
1 ; [7,246])

Table 4. Compilation of representative kint values for transport across the biological membrane Organism

Transported solute

Pleurochrysis carterae Thalassiosira weissflogii Thalassiosira weissflogii Thalassiosira weissflogii Thalassiosira weissflogii Thalassiosira weissflogii Chlorella kesslerii

Fe

kint =s
1

Fe

7  10
4 3
9  10
4 3  10
3 0:9
3  10
3 > 1  10
4

Mn

> 3  10
2

Ni

> 2  10
4

Zn

> 2  10
4

Zn

0:4
2  10
2

Chlorella kesslerii

Pb

4
7  10
4

Various

Various organic compounds

Fe

8  10
5
3  10
2

Determination

Ref.

Pulse-chase experiment and calculation based upon kd Pulse-chase experiment and calculation based upon kd Calculation based upon cellular requirementa Calculation based upon cellular requirementa Calculation based upon cellular requirementa Calculation based upon cellular requirementa Determination from estimated values of {M
Rcell } Determination from estimated values of {M
Rcell } Compilation of values determined for the transport of various organic compounds with low (8
15  10
5 s
1 ) to high (0:2
3  10
2 s
1 ) hydrophobic surface areas

[192] [192,290] [7] [7,290] [7,297] [7,209] [90,296]

[201]

[254]

a Minimum value of kint required to maintain a cellular metal quota that is sufficient for the microorganism to grow at 90% of its maximum rate

496 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

indicating that carrier reorientation or metal release from the carrier is most likely rate-limiting. For the normal environmental situation of multiple metals, the observation of a decreased uptake flux due to competition for binding sites (e.g. [194,216,298,299]) is the expected direct chemical response. Indeed, for Thalassiosira pseudonana, Cd internalisation rates have been postulated
 to decrease in the presence of low concentrations of Mn2þ < 10
8 mol dm
3 due to negative feedback decreases in Jmax and by a direct competition for binding to transport sites at higher concentrations ð[M] > KM Þ [217]. On the other hand, indirect stimulation of uptake fluxes due to a second metal have also been observed in several cases (e.g. [300]). For example, iron uptake fluxes by T. weissflogii have been shown to increase in the presence of Zn and Al [195], presumably due to the stimulation of Fe binding siderophores. Among other observations, an enhancement of Cu bioaccumulation was observed when Ni was added to solutions with a concurrent reduction of the respiratory rate and chlorophyll a contents of Scenedesmus quadricauda [301]. Finally, Cu and Mn have been shown to increase Cd biouptake fluxes to the Gram-negative, Rhodospirillum rubrum [302] and Cu has been shown to increase Pb and Zn uptake fluxes to C. kesslerii [296]. In the presence of Cd and Zn complexes of citrate, glycine and histidine (Cyprinus carpio, [303]), Mg, Ca, Co and Mn phosphate complexes (Escherichia coli, [304]), Ag thiosulfate complexes [305] and Cd citrate complexes (S. capricornutum, [306]), metal uptake fluxes have been observed to be larger than expected, based upon the concentration of free metal ion. In each case, it was demonstrated that the metals were transported using carriers meant for the ligands. On the other hand, no similar explanation can be put forward for the transport of highly hydrophilic (charged) complexes such as EDTA [307,308]. Indeed, in spite of the frequent use of EDTA as a ‘model’ ligand, metal–EDTA complexes can be degraded (15
275 mmol h
1 mg
1 protein, [309]) by mixed bacterial cultures and EDTA has been shown to increase the permeability of the outer membrane in Gram-negative bacteria [310]. Finally, a feedback mechanism has often been used to explain observed (negative and positive) deviations from the Scatchard type plots or nonunity slopes of the nonsaturated portion of the logarithmic Michaelis–Menten plots (e.g. [209]). When no artifacts are present (cf. [197,198]), deviations can indeed be interpreted to indicate that the intrinsic stability or dissociation rate constants vary with the number of occupied transport sites. Nonetheless, several other physical explanations, including multiple carriers, non 1:1 binding, carrier aggregation, etc. must also be considered. 6.2.3

Population Responses Affecting Trace Element Internalisation

When evaluating biouptake in long-term experiments, the rate of cell division will influence the uptake rate of the compound. In even longer-term

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experiments, genetic mutations or plasmid transfer are efficient responses to extreme levels of a compound. Indeed, the net steady-state cellular uptake rate is the product of the steady-state cellular metal concentration and the specific growth rate, implying that, for a constant growth rate, the cellular metal concentration can be employed to determine the uptake rate [92,311]. Similar considerations are used when describing the uptake kinetics of organic solutes, except that often the microorganism population increases in parallel to a depletion of solute concentration. In these cases, Monod kinetic expressions (e.g. equation (51)) are often better suited to describing the dependence of growth or solute depletion on the concentration of chemical in the bulk solution [254]. The overall biodegradation rate will be directly proportional to the rate of increase of the microbial population, and the resulting biouptake rate will have the same hyperbolic form as observed for the Michaelis–Menten equation (cf. equation (35) above): Jint ¼

mmax CY
1 c KMD þ c

(51)

where mmax is the fastest possible growth rate, C is the initial concentration of cells, Y is the yield of the conversion process and KMD is the Monod constant, which is equivalent to the concentration of solute for which growth is half maximal. At low concentrations of M ðc < KMD Þ, internalisation is directly proportional to the concentration of solute and the microbial abundance:   mmax Cc Jint ¼ (52) KMD Y and at c > KMD , internalisation becomes independent of solute concentration: Jint ¼

m max C Y

(53)

For limiting nutrients, cellular concentrations are constant under conditions of steady-state growth. To ensure that the limiting nutrient is not diluted in the microbial population, kint must be greater than the maximal growth rate, mmax . This limiting condition sets a minimum for the value of the Monod constant, KMD ¼ mmax =kf [7]. Note that while Monod kinetics are more applicable than first-order kinetics for many ecological uptake processes, solutions of the above equations require considerably more a priori information [48]. 6.2.4

Indirect Biological Responses Affecting Trace Element Internalisation

Most of the feedback control discussed previously resulted from a specific response of the organism to the solute in question. There are also several

498 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

cases for which indirect effects of the organism physiology induces modifications in the solution chemistry at the biological interface, that result in changes to the uptake fluxes. The most obvious of these are physicochemical modifications due to respiration/photosynthesis that can produce oxygen, carbon dioxide and pH gradients to and from the biological surface. For example, induced pH changes at the biological interface due the production and consumption of CO2 or Hþ can provoke significant modifications of the chemical speciation of several metals (e.g. Al(III), Cr(III), Fe(III), Pb(II)) due to hydrolysis or carbonate complexation. In addition, metabolic by-products such as ammonia are significant ligands in some cases (e.g. Cu, Ag). Although several authors have attempted to probe the solution chemistry in the immediate vicinity of the organism, using mainly optical techniques (e.g. [312,313]), it is extremely difficult, if not presently impossible, to perform accurate measurements in the area of greatest interest, i.e. in the reaction layer (few nm) immediately adjacent the biological surface. Furthermore, for certain organisms, both vertical (to and from the biological surface) and horizontal (along the surface) chemical gradients are present. For example, for fish, gaseous exchange at the gill surface is facilitated by increasing concentration gradients due to countercurrent flow (i.e. the cleanest water arrives at the front end of the gill lamellae which have the lowest ammonia concentrations, Figure 8). This creates a horizontal gradient of both pH and ½NH3 =½NH4 along the surface of the laminar gill channel. For a filter-feeding mollusc, Corbicula fluminae, animals that were subjected to different dissolved oxygen concentrations accumulated Cd according to the pumping rates of water across the gill rather than the ambient Cd2þ concentration [314]. Whilst such a result could be due in part to a decrease in the diffusion boundary layer, as was discussed earlier, it is more likely to be attributable to the dynamic transfer of much larger volumes of water through the gill. Microorganisms, especially bacteria, are quite responsive to the introduction of new stimuli such as the presence of previously unknown organic compounds. They have the capacity to produce enzymes that can degrade or complex the compound being accumulated. For example, Gram-negative bacteria are well known to excrete hydrolytic enzymes into the periplasmic space, either by constitutive or inducible means [18]. By reducing the local concentration of nutrients, they can increase the concentration gradient, potentially increasing the diffusive flux. On the other hand, some microorganisms have been shown to decrease uptake fluxes due to a decrease of chemically reactive solute in the bulk solution via complexation (e.g. [121,128]). Toxic intracellular metals may also be exported as metal chelates [125]. In bacteria, the efflux systems are often so rapidly induced that while the Jint determined using labelled solutes may not change, an overall apparent decrease in Jint may be observed [128,317–319]. Extracellular chelators are not only known for decreasing uptake fluxes. Under iron-limiting conditions, many organisms are known to release siderophores that strongly complex and solubilise iron (see Chapter 6 of this

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499

900 µm Lamella

25 µm 450 µm

Filament

Blood Water

Figure 8. Schematic diagram of gill filaments and lamellae. In this case, several mass transfer processes affect bioaccumulation of trace elements, including: (1) laminar water flow along the membrane; (2) counter current blood flow in the gill; (3) chemical exchange across the membrane; (4) binding and release from blood serum proteins and blood cells; and (5) transfer of chemical from blood to tissues by perfusion. Furthermore, due to the counter-current gaseous exchange at the gill surface, both horizontal and vertical chemical gradients are expected to occur. For further details, refer to [315] and [316]

volume; [24]). Internalisation of the iron chelates occurs by specific membrane transport proteins [259,320–322] followed by the recovery of the iron inside the cell via metal reduction or siderophore degradation reactions [320,323]. Interestingly, it has been shown that it is inefficient for an isolated (especially small) cell to use siderophores to increase iron availability [323] since strongly binding siderophores significantly increase the reaction layer thickness (see Section 7.2) and thus decrease the recovery efficiency. On the other hand, for sufficiently high densities of microorganism, siderophore concentrations may accumulate to the point where transport is increased. This specific example of biological modification of cellular transport was examined in much greater detail in Chapter 6 of this volume [24].

7

COUPLED DYNAMIC PROCESSES

As seen above, the processes leading to the biological internalisation of trace elements are complex and varied. Most often, they are studied as isolated steps,

500 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

either by assuming a single rate-limiting step or by attempting to isolate experimentally the important processes. Few experiments have been performed so as to allow distinction among diffusion-limited, reaction-limited or internalisation-limited situations. Such experiments are difficult to plan and control, due to the large number of biological, chemical and physical factors that must be taken into account in order to avoid ambiguous results. Although it is entirely artificial to consider the solute fluxes as independent from one another (as we have done thus far), it is beyond the scope of this chapter to quantitatively describe bioaccumulation in the absence of some simplifying concepts. Several authors, including contributors to this volume [32,266], have carefully examined the role of two or three coupled processes on the internalisation of trace elements. Mathematical modelling, in the presence of simple boundary conditions, has been used to solve reasonably complex transport problems by combining a limited number of important processes, including mass transfer and uptake (e.g. [48,282]); mass transfer, complexation/decomplexation and uptake (e.g. [69,323,324]); mass transfer, adsorption and biological uptake (e.g. [6,9]). Although these studies are helpful in identifying the important factors [167] influencing the biouptake process, they are most often limited by the use of the simplifying assumption of steady-state conditions. In the following section, several examples from the literature are re-examined, with the objective of giving the reader a feel for the complexity of the overall bioaccumulation process in real systems. 7.1. TIMESCALES AND LIMITING PERMEABILITIES RELATED TO THE VARIOUS PROCESSES In order to evaluate when steady-state conditions are relevant, as well as the relative importance of the various dynamic processes, it is useful to compare the characteristic timescale of each process (Table 5). It can be seen that the timescales of each of the main processes vary over several orders of magnitude, depending upon the precise nature of the solute, the accumulating surface and the physicochemistry and hydrodynamics of the medium. As discussed above, any of the major processes (i.e. diffusion (d), chemical dissociation (kin), adsorption (ad) and internalisation (int)) may limit the overall flux, J. Diffusion, adsorption and internalisation are sequential processes, such that when one of them is rate-limiting, (e.g. internalisation) then the overall flux, J, will be equal to the corresponding limiting flux (e.g. Jint ). On the other hand, chemical dissociation occurs in parallel to diffusion, giving it an overall different effect on the overall flux. In the following, the limiting lim lim ), chemical (Jkin ) and diffusional (Jdlim ) fluxes, values of the internalisation (Jint are discussed in greater detail. To this end, it is useful to introduce a corresponding limiting permeability, Plim , defined as Plim ¼ J lim =[M], where [M] is the free metal ion.

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501

Table 5. Characteristic timescales of several important processes involved in biouptake as estimated by their residence time (physical processes) or by their half-reaction time (chemical reactions). See also [2,165] Flux or reaction

Time/s a

(1) Linear diffusion of a 500 nm colloid through a diffusion boundary layer thickness of 50 mm (2) Advectionb of a compound over 50 mm for a velocity of 1 mm s
1 perpendicular to the plane of transfer (3) Predicted formation timesc of Cd, Pb, Zn complexes with EDTA (4) Observed formation times for Cd, Pb, Zn complexes with EDTA [2,178] (5) Complexation by second-order kinetics of 10
5
10
7 mol dm
3 Cu or Ni with typical aquatic ligand of similar concentration [167] (6) Dissociationc of a strong Fe(III) complex from a doubly charged ligand (K ¼ 1012 dm3 mol
1 ) (7) Dissociationc of a weak Ca complex with a singly charged ligand (K ¼ 106 dm3 mol
1 ) (8) Transport of an organic pollutant by passive diffusion across a biological membrane (kint ¼ 1 s
1 ) (9) Transport of a nonessential metal ion across a biological membrane (kint ¼ 10
4 s)

3  104 5  10
2 10
6
1 7  102
4  104 10
4
104 7  106 3:5  10
4 1 104

tdiff ¼ d2 =DM tad ¼ L=v c Times based on the assumption of an Eigen–Wilkens mechanism (see Section 4.3.1); for dissociation reactions, t1=2 ¼ ln 2=kd (see also Table 2) a b

7.1.1

Biological Uptake Limitation (J ¼ J int  J d , J ad , J kin )

When biological uptake does not perturb the external medium, then Jint can be given by equation (35). As discussed above, this limiting condition is assumed to occur in both the free-ion activity and biotic ligand models. When Ka [M]  1, then (cf. equation (7)): Plim int ¼ kint Ks {Rcell }

(54)

which demonstrates that the limiting permeability of the metal in the biological membrane, Plim int , is a parameter intrinsic to the microorganism and independent of the external medium. 7.1.2

Diffusion Limitation (J ¼ J d  J int )

In the case of a diffusion limitation, the free metal ion is largely consumed at the surface of the organism such that the concentration gradient of M in the external medium is strongly perturbed by biological uptake. The flux will depend on the concentration gradient of M that occurs between the bulk

502 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

solution and the surface of the organism (e.g. equation (14)). When uptake is very fast, the surface concentration of M approaches zero, and the limiting diffusive flux, Jdlim , is reached. Depending on the chemical dissociation rate and the mobility of the complexes ML, two extreme values of Jdlim are obtained: (1) inert complexes: For inert complexes, the dissociation of ML is so slow that there is no concentration gradient of ML and only free M will diffuse towards the surface. The corresponding minimum limiting flux, Jdlim ,min is obtained when the concentration of free metal at the biological surface is zero and the limiting permeability can be given by: Plim d,min

 ¼

 1 1 þ DM d r0

(55)

In this case, permeability depends only on factors that are outside the organism. Such a scenario might occur in an eutrophic lake where metal speciation is controlled by natural organic ligands forming inert complexes. (2) fully labile and mobile complexes: In the presence of labile complexes, if uptake is diffusion limited, internalised metal results from both the diffusion of M and the diffusion and rapid dissociation of ML. In this case, both [M] and [ML] approach 0 at the organism surface and all metal species contribute to diffusion. The bulk concentration of the metal that is given by c in equation (14), is replaced by the total concentration of all of the labile forms of the metal. In this case, D must be replaced by an average diffusion coefficient for all of the metal species [40]: D ¼ DM

[M] X [MLi ] þ DMLi [M]t [M]t i

(56)

When all complexes diffuse as quickly as free M, DMLi ¼ DM and the maximum obtainable limit for the permeability is: Plim d,max ¼



 1 1 [M]t [M]t þ DM ¼ Plim d,min d r0 [M] [M]

(57)

This situation would be typical of an eutrophic lake where only metal complexes with small inorganic ligands are formed. (3) fully labile but immobile complexes: For a diffusion limited situation, if complexes are immobile, then the concentration gradient approaches a maximum (c0 ¼ 0) but the average diffusion coefficient is reduced by the factor [M]t =[M] (equation (56)) and the permeability will take on the same value as was obtained for inert complexes, i.e. Plim d,min . This would be the expected case for a soil or sediment that contains no soluble metal complexes.

K. J. WILKINSON AND J. BUFFLE

7.2

503

LABILITY CRITERIA AND SEMI-LABILE COMPLEXES

A quantitative discrimination between labile and nonlabile complexes is made by comparing the diffusion timescale with those of the association/dissociation reactions (or alternatively, the reaction layer, m (equation (58)) and the diffusion layer, d, thicknesses (e.g. equations (15), (18) and (19)). sffiffiffiffiffiffiffiffiffiffi DM m¼ kf [L]

(58)

For complexation/dissociation reactions, m corresponds with the average distance that M can travel following dissociation of ML (and prior to reassociation) [40,46]. Complexes are dynamic when M frequently changes from its free to complexed state during its diffusion time to the membrane surface or, in other words, if the first-order dissociation rate constant, kd , and the pseudo first-order formation rate constant, kf [L], are much larger than their effective diffusion rate constants (D=d2 ) [325,326]. Thus, for conditions of planar diffusion, complexes are labile if: kd d Ld ¼ DML

sffiffiffiffiffiffiffiffiffiffi DM 1 kf [L]

(59)

while for conditions of radial diffusion [327]: kd r0 Lr0 ¼ pDML

sffiffiffiffiffiffiffiffiffiffi DM 1 kf [L]

(60)

For an excess of ligand over metal, [L] will be equal to the total concentration of ligand in the bulk solution ([L]t ), whereas d will depend on the hydrodynamic conditions (Section 3.2). It follows that the lability criterion (Ld or Lr0 ) is  1 for inert complexes and close to 1 for semi-labile complexes. In the case of semilabile complexes, the overall flux of M to the microorganism is larger than that given by the diffusion of inert complexes (cf. equation (55)), but smaller than that due to the diffusion of fully labile complexes (cf. equation (57)), due to partial dissociation of the complexes. The lack of precise measurements of environmentally relevant chemical rate constants limits the number of quantitative evaluations of the importance of complex dynamics on uptake fluxes. Nonetheless, examples involving bicarbonate–CO2 conversion [69,88] and trace metal complexation [8,46,325] have been examined theoretically in the literature. For example, comparison of the diffusional and reactional timescale allowed Riebesell and collaborators [69,88] to show that bicarbonate conversion to CO2 did not generally enhance the

504 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

diffusive supply of CO2 to algal cells in marine environments with respect to CO2 alone. In these studies, the authors calculated a diffusive timescale of ca. 0.05 s and a reaction timescale of ca. 100 s for a typical algal cell. Note, however, that for particularly large algal cells or under conditions for which mass transport is enhanced due to fluid motion, HCO
3 conversion to CO2 could become significant. Similarly, based upon the above considerations, Pinheiro and van Leeuwen [46] calculated a reaction layer thickness of 0:2 mm
1 for a Pb formation rate constant of 107 mol
1 m3 s [5], suggesting that Pb dissociation could be important for many microorganisms. On the other hand, Ni, which typically has slower complexation/dissociation kinetics, would probably be inert under the same conditions. 7.3

ROLE OF LIGAND EXCESS AND CHEMICAL HETEROGENEITY

Equations (60) and (61) are based upon the assumption that the degree of complexation, [M]=[M]t , is constant throughout the diffusion layer, implying that each ligand is in excess with respect to the total metal concentration. This assumption is not always valid under natural conditions, in particular for small concentrations of biogenic ligands or for chemically heterogeneous ligands containing small proportions of strongly complexing sites. In such cases, [M]=[M]t in the diffusion layer can decrease from the bulk solution to the organism surface (Figure 9) due to consumption of the free ion such that the remaining metal occupies stronger and stronger sites on the ligands (reflected by an increasing value of K  ). In a similar manner, kd (equation (30)) would be expected to decrease with decreasing distance from the organism to the point where the complexes can become non labile at the organism surface, even when they are labile in the bulk solution. For example, for metal complexes with HS, it has been shown that heterogeneity may strongly influence the transport flux to electrodes [142,326,328–331] and microorganisms [266,326], even when the complexes remain labile in the bulk solution. This observation is especially important when the internalisation flux is of the same order of magnitude as the limiting diffusion flux. In the case of a diffusion-limited, heterogeneous system, the maximum diffusive flux can be given by [326]: Jdlim ,max

  D[M]t DM [M]t w(1
G)=G þ eK  [L]t ¼ ¼ w(1
G)=G þ K  [L]t d d

(61)

where w is the ratio of local to bulk concentrations of the complex, e is the ratio of the diffusion coefficient of the complex to that of the free metal ion, and K  and G have their usual meanings (cf. equation (26)). In such a system, D and w will vary throughout the diffusion layer (Figure 9; [142,326,329]) and an increased chemical heterogeneity of the complexes will lead to an overall decrease in complex lability [326,332].

K. J. WILKINSON AND J. BUFFLE r0

505 d [ML]

[M] distance ML Jkin J int M

ML Jd

Mz+

Mz+

[ML]/[M] decreases K increases kd decreases _ D decreases

Figure 9. Schematic representation of concentration profiles at the biological surface in the case of a diffusion-limited uptake. Note that the ratio of bound metal to free metal is not drawn to scale; in reality, the ratio at the biological surface is always larger than that in solution. The figure assumes that the total concentration of ligand is much greater than the total concentration of metal. For further details, refer to [142,331,333]

7.4 NATURE OF THE RATE-LIMITING STEP FOR METAL BIOUPTAKE BY PHYTOPLANKTON Very few results are available to demonstrate unambiguously whether trace metal uptake is limited by diffusion, chemical dissociation, adsorption to the biological surface, transfer through the plasma membrane, or several of the processes simultaneously. A selection of the literature is given in Figure 10 which reports observed permeabilities (P ¼ Jobs =[M]) and the limiting values of lim Plim d,min and Pd,max calculated from equations (55) and (57), using the data reported in the papers. Figure 10 is based solely on reports where metal accumulation increased linearly with time (constant flux) for measurements that were made over a limited time span ( h), in order to minimise the potential secondary biological effects. Figure 10 shows that for the uptake of Pb(II) by C. kesslerii in an artificial freshwater, the observed permeability is four orders of magnitude lower than the value of the calculated minimum limiting diffusive flux, indicating that

506 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

Freshwater 0

Zn(II)

Chlorella kesslerii

Pb(II)

Chlorella kesslerii

Mn(II)

Chlamydomonas reinhardtii

Cd(II)

Chlorella pyrenoidosa

0

Chlamydomonas reinhardtii

0

Ag(I)

0

0

Seawater Mn(II)

Zn(II)

Zn(II)

Zn(II)

Thalassiosira pseudonana Phaeodactylum tricornutum

0 [M] = 10−7 10−8 mol dm−3

0 [M] = 7
10−7 7
10−8 mol dm−3

0

Thalassiosira pseudonana

[M] = 10−9 mol dm−3 0

Thalassiosira oceanica

Cd(II)

Emiliana huxleyi

Cd(II)

Thalassiosira oceanica

[M] = 10−9 mol dm−3 0

0

−6

−4

−2

0

2

log P (cm s−1)

Figure 10. Calculated and measured metal permeabilities for different microorganisms. Permeabilities have been calculated using data given in each of the original references: (P. tricornutum, Zn, [4]; T. pseudonana, Mn, [4]; C. kesslerii, Zn, [90]; C. kesslerii, Pb, [160]; C. pyrenoidosa, Cd, [205]; C. reinhardtii, Ag, Mn, [91]; T. oceanica, T. pseudonana, Zn, [311]; T. oceanica, E. huxleyi, Cd, [214]; T. pseudonana, Mn, [92]). The grey circles correspond with observed permeabilities, calculated by dividing the observed internalisation flux by the concentration of free ion (P ¼ Jint =[M]). The range of limiting lim diffusive permeabilities, Plim d,min and Pd,max , as calculated by equations (55) and (57), are given by the black rectangle

K. J. WILKINSON AND J. BUFFLE

507

Jobs ¼ Jint , and that Pb uptake is under thermodynamic (biological) control [201]. The same conclusion can be drawn from Mn(II) uptake data for C. reinhardtii (freshwater) and Phaeodactylum tricornutum (seawater). In these cases, steady-state models such as the FIAM or BLM (equations (6) and (7)) should be applicable. On the other hand, for the uptake of Cd(II) by Chlorella pyrenoidosa [205], Zn(II) and Cd(II) by Thalassiosira oceanica [214,311,334], Zn(II) by T. pseudonana [311] and Cd(II) by Emiliana huxleyi [214], Pobs is very close to the calculated value of Plim d,min . Furthermore, calculations appeared to indicate that Ag(I) uptake by C. reinhardtii in a synthetic freshwater was diffusion limited [91]. Finally, for Zn(II) uptake by C. kesslerii [90], internalisation fluxes were not directly proportional to [Zn2þ ], due to the active uptake of the metal. For this reason, permeability varied over several orders of magnitude, providing a clear demonstration of a failure of the FIAM. For [Zn2þ ] > 2  10
12 mol dm
3 , metal uptake was subjected to a biological limitation, while, at lower concentrations, a diffusion limitation was identified [90], similar to Zn uptake results obtained for several other species of phytoplankton [90,209,311]. The above results strongly suggested that uptake may, in some cases, be controlled by the diffusion of metal species in solution, rather than their biological transfer through the membrane. Interestingly, the cases of diffusion limitation occurred primarily for Zn or Cd uptake. Zn is an essential metal that tends to have high membrane permeabilities (cf. Section 3.5.1), especially at low [Zn2þ ] [90] whereas Cd(II) is known to borrow Zn(II) pathways [335]. Because Pint , and ultimately the nature of the rate-limiting process, depends on the prior conditioning of the organisms [90,209,211,298], different limiting steps might be observed in natural environments as opposed to laboratory conditions. For example, Mn(II) and Zn(II) permeabilities increased for T. pseudonana, P. tricornutum and C. kesslerii, when the algae were preconditioned in a culture medium containing low metal concentrations [90,92,311]. Similarly, large Zn(II) and Cd(II) permeabilities were obtained for T. pseudonana, T. oceanica, and E. huxleyi that were cultivated in natural seawater with very low trace metal concentrations [214,311,334]. The above results imply that: . steady-state models such as the FIAM or BLM cannot be applied to all conditions; . in some cases, the biouptake flux may be controlled by diffusion/dissociation in the external medium; and . metal permeabilities cannot always be considered constant for a given organism. This final point is important, since it implies that uptake by the same organism might be controlled by a diffusion limitation in one medium (e.g. unpolluted

508 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

water) and a biological limitation in another (e.g. polluted media). It should also be emphasised that while the lack of a linear relationship between the uptake flux and the concentrations of free metal ion (equation (6)) (or metal bound to carriers, equation (7)) indicates a failure of the steady-state models to predict uptake, a linear relationship is not sufficient proof of the applicability of the FIAM. A similar dependency on [Mzþ ] may also be observed when the uptake flux is controlled by the diffusion of inert complexes (equation (58)). Diffusion limitation of trace metal uptake might be particularly relevant in natural systems for which (1) diffusion coefficients of the metals are small due to the formation of colloidal complexes and/or (2) metal permeabilities are large due to the low environmental concentrations of the metals.

7.5 7.5.1

SOME IMPLICATIONS OF A RATE-LIMITING DIFFUSION Bioavailability of Colloidal Bound Metal

Based upon the above discussion, in the absence of separate uptake routes such as ingestion [336,337], complexation by colloidal ligands should decrease trace metal bioavailability to phytoplankton. For example, if uptake is limited by the internalisation flux, colloidal complexation will decrease uptake in direct proportion to the concentration of free metal ion, similar to what would be observed for simple ligands. On the other hand, for a given concentration of metal in the bulk solution under a diffusion limitation, uptake is predicted to be proportional to the average diffusion coefficient of the metal complexes. The transition between the internalisation and diffusion-limited regimes can be predicted from knowledge of the uptake fluxes in the absence of colloids and the diffusion coefficient of the colloidal complexes (equations (21) and (22)). For example, for the biologically limited uptake of Pb by C. kesslerii (Figures 6 and 10; [201]), uptake fluxes would need to be reduced by four orders of magnitude, corresponding to the complexation of Pb2þ by a ca: 2 mm particle, for diffusion to become limiting. Unfortunately, few authors have yet examined quantitatively the role of colloidal complexation on biological uptake fluxes. For example, although Cd and Zn uptake fluxes to T. pseudonana were significantly decreased when the metal was bound to colloidal (1 kDa
0:2 mm) organic carbon, limiting flux(es) and the role of colloidal heterogeneity were not evaluated [338]. Given the large proportion of colloidal bound metal in natural waters (e.g. [339,340]), this would appear to be a field that merits future studies. On the other hand, the uptake of colloidal iron has been studied in greater detail. For example, some bacteria have been demonstrated to reduce ferric oxide particles to increase iron bioavailability [341,342]. As was observed in Section 5.2.4, Fe reaction kinetics with metal carriers are thought to be ratelimiting. In the presence of colloidal iron, the thermodynamic stability or

K. J. WILKINSON AND J. BUFFLE

509

(photochemical) lability of the colloids has been shown to be the key factor determining their bioavailability [343–346]. In the presence of colloidal Fe, Fe uptake is highly correlated to the dissolution rate of the oxide phases: highly crystalline phases such as goethite dissolve too slowly to allow phytoplankton growth while amorphous iron is readily available [343,347]. Such results are consistent with a physicochemical rather than biological limitation of Fe uptake by phytoplankton. 7.5.2

Requirements of Trace Metal Carriers

Under steady-state conditions, the internalisation flux equals the rate of supply by diffusive transport and chemical reactions. As was shown earlier (cf. equations (12) and (13)), the maximum flux (rate) of solute internalisation by a microscopic cell under diffusion-limited conditions can be given by: Jint ¼ Jd ¼

Dc r0

Q ¼ 4pr0 Dc

(62) (63)

In this case, 4pr0 D is the Smoluchowski rate constant, which is useful for describing radial diffusion to a cell surface totally covered with transport sites. The rate corresponding with fractional surface coverages of carriers has been derived both analytically [35,237,348] and numerically [349] by assuming that the radius of the cell is large compared to the carrier radii, a, and that the NR carriers are sufficiently dispersed so as to be independent and noncompeting. The result: J¼

4pr0 DNR a  Jmax NR a c ¼ pr0 þ NR a pr0 þ NR a

(64)

is interesting, since it becomes apparent that cells can approach the physical limit of diffusion without requiring the entire surface to participate in the adsorption process. In fact, under conditions of diffusion limitation, the number of carriers that a cell can usefully employ is not much larger than the ratio of cell to carrier (or cluster) diameter [35]. Qualitatively, this can be explained by the onset of competition among the carriers for incoming solute with a resulting near-maximum efficiency even when only a small fraction of the cell surface is covered by transport sites. This effect is illustrated quantitatively in Figure 11 for a carrier radius of 1 nm and a cell radius of 1 mm [35]. In this case, carrier coverages of <0:1% are sufficient to ensure uptake at one-half the maximal rate (Jmax ). This result implies that under conditions of a diffusion limitation, hundreds of carrier systems could efficiently fit into the cell membrane. Furthermore, high surface area coverages that are typically estimated

510 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 1.0

J/Jmax

0.8 0.6 0.4 0.2 0.0 0

2000

4000 6000 Carrier number

8000

10000

Figure 11. Relative uptake rates as a function of carrier number in the diffusion-limited case. Calculations were performed according to the equations of Berg and Purcell [35] for a carrier radius of 1 nm on a cell with a radius of 1 mm

from trace metal quotas for nutrients with high affinities for the transporter [28] are probably not required to ensure cell viability. On the other hand, large carrier numbers will still be advantageous in cases for which internalisation or chemical reactivity is rate-limiting. Note finally that the preceding derivations assumed that the carriers were all uniformly reactive with no restrictions due to their spatial orientation. Although cases of receptor clustering have been documented in the literature [350], this would appear to have no advantage for the cell, since, in this case, the cluster will at best behave approximately as a single site with a larger area [281,349] and at worst compete to further reduce binding [351]. In that case, maximum uptake would occur for maximum carrier dispersion (equation (66); [281,349]). In reality, clustering may be a useful process for the cells [352], especially if the chemoreceptors are clustered at the leading pole of the cell or where a flagellum locally thins the boundary layer [114].

8

FUTURE PERSPECTIVES AND CONCLUSIONS

Bioaccumulation is a complicated process that couples numerous complex and interacting factors. In order to directly relate the chemical speciation of an element to its bioavailability in natural waters, it will be necessary to first improve our mechanistic understanding of the uptake process from mass transport reactions in solution to element transfer across the biological membrane. In addition, the role(s) of complex lability and mobility, the presence of competing metal concentrations and the role(s) of natural organic ligands will need to be examined quantitatively and mechanistically. The preceding chapter

K. J. WILKINSON AND J. BUFFLE

511

should also make it clear that the FIAM and BLM are oversimplifications that are unlikely to provide quantitative estimates of toxicity or uptake for a large number of conditions including: the transport of anionic metal complexes, the formation of ternary carrier complexes, cases where the ligand plays a direct role, active transport of the metal across biological membranes, cases where the (multicellular) organism is able to modify water flow over its surface, cases where uptake is primarily due to the food vector, etc. The large number of exceptions does not, in our view, suggest that a modelling approach is hopeless, rather that more complete, dynamic models are required. It is obvious that no model will be useful if the correct physicochemical processes are not known or if the data used to test the model are not valid. One of the goals of this chapter was to identify the parameters and processes that must be taken into account in the uptake process. Unfortunately, quantitative data required to test the various assumptions of the models are scarce, especially when relating uptake fluxes to both the chemical speciation in solution and to trace metal toxicity. Important temperature, pH and ionic strength dependencies that are extremely significant in the natural environment have been virtually ignored in the scientific literature to date. For example, experiments that distinguish the effect of the proton (surface complexation) from the effect of the hydroxy ion (complex formation) are rare for cations that form hydroxo complexes under environmentally relevant pH. As discussed above, the role of competing cations is also poorly understood. The similarity of the stability constants for the reaction with the carrier (Table 3) suggests that competition could play an important role in environmental systems by decreasing the concentration of free carrier. On the other hand, since most metals are present at sufficiently low concentrations in the natural environment, they should not significantly modify the concentration of free carrier. In this respect, a shift of emphasis from a solution chemistry (FIAM) to a surface complexation (BLM) approach could account for some of the important competition effects that must be implicitly taken into account in the FIAM. Unfortunately, few data are currently available to distinguish specific (physiologically active) adsorption to a biological ligand of interest (receptor, carrier, transporter) from the more prevalent (and less relevant; physiologically inactive) nonspecific adsorption (cell wall, cell membrane, etc.). For the biological limitation of trace metal internalisation, complex formation will invariably decrease the concentration of free metal ion and thus decrease the biouptake fluxes and carrier-bound metal (FIAM, BLM). In the case of a diffusion-limited internalisation, complex labilities and mobilities become much more pertinent when determining uptake fluxes. As shown earlier, few experiments have been designed to identify diffusion limitation of metal uptake fluxes, despite the fact that such a limitation is possible (Figure 10). Competition experiments that can distinguish a kinetic from a thermodynamic control are rare. In these areas, an important research focus is

512 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

required. Unfortunately, many of the ligands that form labile complexes are carboxylic acids or amino acids that may either be taken up or degraded by the organism. Even strongly bound, hydrophilic metal complexes such as those formed with EDTA can be taken up by plants in soil solutions. Other surprises should be expected, with even more heterogeneous ligands such as HS and microbial exudates. Finally, the ‘chemistry’ of the organism must be taken into account. Interrelationships among metals can rarely be explained on a purely chemical basis (i.e. inhibition of the uptake of the metal of interest and uptake of the competing metal). Even metals exhibiting the ‘expected’ chemical antagonisms, may also initiate a cellular feedback, alter the overall biological metabolism or modify membrane permeability or the cells’ capacity to deal with the metal of interest.

ACKNOWLEDGEMENTS This review was stimulated, in large part, by the work of the several collaborators in the group, both past and present: O. Caille, C. Hassler, H. Kola, M. Martin, N. Mirimanoff, A. Smiejan, V. Slaveykova, M. Tuveri and I. Worms. Their critical comments, results and discussions were extremely helpful in improving earlier drafts of the manuscript. We also greatly appreciate the critical reviews of J. Galceran, H. P. van Leeuwen and C. Rossier. This work was supported, in part, by the Swiss National Funds 2000-050529.971 and the European Union 5th framework BIOSPEC project (EVK1-CT-2001-00086).

GLOSSARY a aH A c c0 cin cm Cc D
D Dm F

Receptor or carrier radius Hydrodynamic radius of a molecule Surface area Concentration in the bulk solution Solute concentration at reactive surface Solute concentration inside the organism Solute concentration at the outer surface of the membrane Complexation capacity Diffusion coefficient Weighted average diffusion coefficient Diffusion coefficient of a solute in the membrane Faraday constant

m m m2 mol dm
3 mol dm
3 mol dm
3 mol dm
3 mol g
1 m2 s
1 m2 s
1 m2 s
1 As mol
1

K. J. WILKINSON AND J. BUFFLE

Jad Jd Jkin Jint J lim

Jmax Jnet Ki , Ks Klw KM KMD Kos ~ K K L Lv M, Mz+ ML N NA NR P Q R Rcell Rt

T Y gn kd , kf kd kint

Flux in the presence of advection Diffusive flux Limiting chemical flux Biological internalisation flux Limiting flux (generally with subscript to indicate whether it is a minimum or maximum limiting flux) Maximum uptake rate obtained from Michaelis–Menten kinetics Net flux to surface (adsorption flux – desorption flux) Thermodynamic equilibrium constants Lipid–water partition coefficient Michaelis–Menten half-saturation constant Monod constant: concentration of solute at which growth is half maximal Outer sphere stability constant Average stability constant for heterogeneous ligands Differential stability constant for heterogeneous ligands Free ligand Kolmogorov length scale Free metal Metal–ligand complex Number of moles Avogadro’s number Number of cellular metal carriers/transporters Permeability Area-integrated cellular flux Gas constant Free sensitive sites at the membrane surface, e.g. transporter, carrier Total number of sensitive sites (carriers, transporters, receptors, etc.) at the membrane surface Temperature Yield of a conversion process Gravitational acceleration constant Kinetic dissociation, formation rate constant Differential kinetic dissociation rate constant Internalisation rate constant

513

mol m
2 s
1 mol m
2 s
1 mol m
2 s
1 mol m
2 s
1 mol m
2 s
1 mol m
2 s
1 mol m
2 s
1 mol dm
3 mol dm
3

m

m s
1 mol s
1 J K
1 mol
1

K N m2 kg
2

s
1

514 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES

ky k
H2 O n r r0 t u v vint vsed x y z

Exchange rate constant for the permeation Water loss rate constant Cell number Radial distance from the centre of a cell Cell radius Time Ionic mobility Flow velocity of the bulk solution Uptake rate Sedimentation velocity Distance Distance from upstream edge Ion valency

b d G "

Mass transfer velocity Thickness of the diffusion boundary layer Heterogeneity parameter Ratio of the diffusion coefficient of the complex over the dissociated metal ion Turbulent kinetic energy dissipation rate Dynamic viscosity Spatial variable that relates the direction of the flow to the point of interest on the surface of the organism Double layer thickness Reaction layer thickness Maximum growth rate of a cellular population Kinematic viscosity Density Surface charge density Diffusion limited, reaction limited, advection limited or steady-state response times Electrostatic potential in the bulk solution at the edge of the channel protein Ratio of calculated maximal cellular flux by spherical diffusion to nutrient uptake flux Ratio of local to bulk concentrations of the metal–ligand complex Electrical surface potential Transmembrane potential Membrane thickness Concentration at a surface

e0 Z y k
1 m mmax
~ r s td , tr , tad , tss f j w c cm ! {}

m m s m2 s
1 V
1 mol
1 m s
1 mol s
1 m s
1 m m

m s
1 m

m2 s
3 g cm
1 s
1

m m m2 s
1 g m
3 mol m
2 s V

V V m mol m
2

K. J. WILKINSON AND J. BUFFLE

515

REFERENCES 1. 2. 3. 4.

5. 6. 7. 8. 9. 10. 11. 12.

13. 14. 15. 16. 17.

Stumm, W. and Morgan, J. J. (1981). Aquatic Chemistry. John Wiley and Sons, New York. Buffle, J. (1988). Complexation Reactions in Aquatic Systems: an Analytical Approach. Ellis Horwood, Chichester. Jackson, G. A. and Morgan, J. J. (1978). Trace metal–chelator interactions and phytoplankton, growth in seawater media: theoretical analysis and comparison with reported observations, Limnol. Oceanogr., 23, 268–282. Whitfield, M. and Turner, D. R. (1979). Critical assessment of the relationship between biological thermodynamic and electrochemical availability. In Chemical Modeling in Aqueous Systems. ed. E. A. Jenne, ACS Symposium Series, Vol. 93, American Chemical Society, Washington DC, pp. 657–680. Morel, F. M. M. and Hering, J. G. (1983). Principles and Applications of Aquatic Chemistry. Wiley Interscience, New York. Tessier, A., Buffle, J. and Campbell, P. G. C. (1994). Uptake of trace metals by aquatic organisms. In Chemical and Biological Regulation of Aquatic Systems. eds. Buffle, J. and De Vitre, R. R., CRC Press, Boca Raton, FL, pp. 199–232. Hudson, R. J. M. and Morel, F. M. M. (1993). Trace metal transport by marine microorganisms: implications of metal coordination kinetics, Deep-Sea Res., 40, 129–150. Hudson, R. J. M. (1998). Which aqueous species control the rates of trace metal uptake by aquatic biota? Observations and predictions of non-equilibrium effects, Sci. Total Environ., 219, 95–115. Best, J. B. (1955). The inference of intracellular enzymatic properties from kinetic data obtained on living cells, J. Cell Comp. Physiol., 46, 1–27. Wang, W.-X. and Fisher, N. S. (1999). Assimilation efficiencies of chemical contaminants in aquatic invertebrates: a synthesis, Environ. Toxicol. Chem., 18, 2034–2045. Sunda, W. G. and Guillard, R. L. L. (1976). The relationship between cupric ion activity and the toxicity of copper to phytoplankton, J. Mar. Res., 34, 511–529. Campbell, P. G. C. (1995). Interactions between trace metals and aquatic organisms: a critique of the free-ion activity model. In Metal Speciation and Bioavailability in Aquatic Systems. eds. Tessier, A. and Turner, D. R., Vol. 3, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Ltd, Chichester, pp. 45–102. Playle, R. C. (1998). Modelling metal interactions at fish gills, Sci. Total Environ., 219, 147–163. Campbell, P. G. C., Erre´calde, O., Fortin, C., Hiriart-Baer, V. P. and Vigneault, B. (2002). Metal bioavailability to phytoplankton – applicability of the biotic ligand model, Comp. Biochem. Physiol. C, 133, 185–202. Richards, J. G. and Playle, R. C. (1998). Cobalt binding to gills of rainbow trout (Oncorhynchus mykiss): an equilibrium model, Comp. Biochem. Physiol. C, 119, 185–197. Wood, C. M., Playle, R. C. and Hogstrand, C. (1999). Physiology and modelling of mechanisms of silver uptake and toxicity in fish, Environ. Toxicol. Chem., 18, 71–83. Playle, R. C., Dixon, D. G. and Burnison, K. (1993). Copper and cadmium binding to fish gills: estimates of metal–gill stability constants and modelling of metal accumulation, Can. J. Fish. Aquat. Sci., 50, 2678–2687.

516 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 18. 19. 20. 21. 22. 23. 24.

25. 26. 27. 28. 29. 30. 31.

32.

33. 34.

Koch, A. L. (1990). Diffusion. The crucial process in many aspects of the biology of bacteria. In Advances in Microbial Ecology. Vol. 11, ed. Marshall, K. C., Plenum, New York, pp. 37–70. Geesy, G. G., Bremer, P. J., Smith, J. J., Muegge, M. and Jang, L. K. (1992). Twophase model for describing the interactions between copper ions and exopolymers from Alteromonas atlantica, Can. J. Microbiol., 38, 785–793. Hudson, R. J. M. (1998). Modeling the fate of metals in aquatic systems: the mechanistic basis of particle–water partitioning models, Crit. Rev. Anal. Chem., 28, 19–26. Nikaido, H. (1979). Nonspecific transport through the outer membrane. In Bacterial Outer Membranes. Biogenesis and Functions. ed. Inouye, M., John Wiley & Sons, New York, pp. 361–407. Meador, J. P., Stein, J. E., Reichert, W. L. and Varanasi, U. (1995). Bioaccumulation of polycyclic aromatic hydrocarbons by marine organisms, Rev. Environ. Contam. Toxicol., 143, 79–165. Di Toro, D. M., Allen, H. E., Bergman, H. L., Meyer, J. S., Paquin, P. R. and Santore, R. C. (2001). Biotic ligand model of the acute toxicity of metals. 1. Technical basis, Environ. Toxicol. Chem., 20, 2383–2396. Ko¨ster, W. (2004). Transport of solutes across biological membranes: prokaryotes. In Physicochemical Kinetics and Transport at Biointerfaces. eds. van Leeuwen, H. P. and Ko¨ster, W., Vol. 9, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle J. and van Leeuwen, H. P., John Wiley & Sons, Ltd, Chichester, pp. 271–335. Lazier, J. R. N. and Mann, K. H. (1989). Turbulence and diffusive layers around small organisms, Deep-Sea Res., 11, 1721–1733. Kiorboe, T. (1993). Turbulence, phytoplankton cell size, and the structure of pelagic food webs, Adv. Mar. Biol., 29, 1–72. Karp-Boss, L., Boss, E. and Jumars, P. A. (1996). Nutrient fluxes to planktonic osmotrophs in the presence of fluid motion, Oceanogr. Mar. Biol., 34, 71–107. Jumars, P. A., Deming, J. W., Hill, P. S., Karp-Boss, L., Yager, P. L. and Dade, W. B. (1993). Physical constraints on marine osmostrophy in an optimal foraging context, Mar. Microb. Food Web., 7, 121–159. Pasciak, W. J. and Gavis, J. (1974). Transport limitation of nutrient uptake in phytoplankton, Limnol. Oceanogr., 19, 881–888. Pasciak, W. J. and Gavis, J. (1975). Transport limited nutrient uptake rates in Ditylum brightwellii, Limnol. Oceanogr., 20, 604–617. Ko¨ster, W. and van Leeuwen, H. P. (2004). Physicochemical kinetics and transport at the biointerface: setting the stage. In Physicochemical Kinetics and Transport at Biointerfaces. eds. van Leeuwen, H. P. and Ko¨ster, W., Vol. 9, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Ltd, Chichester, pp. 1–14. van Leeuwen, H. P. and Galceran, J. (2004). Biointerfaces and mass transfer. In Physicochemical Kinetics and Transport at Biointerfaces. eds. van Leeuwen, H. P. and Ko¨ster, W., Vol. 9, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Ltd, Chichester, pp. 113–146. Bard, A. J. and Faulkner, L. R. (1980). Electrochemical Methods: Fundamentals and Applications. John Wiley & Sons, New York. Gavis, J. (1976). Munk and Riley revisited: nutrient diffusion transport and rates of phytoplankton growth, J. Mar. Res., 34, 161–179.

K. J. WILKINSON AND J. BUFFLE 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57.

517

Berg, H. C. and Purcell, E. M. (1977). Physics of chemoreception, Biophys. J., 20, 193–219. Roberts, A. M. (1981). Hydrodynamics of protozoan swimming. In Biochemistry and Physiology of Protozoa. eds. Levandowsky, M. and Hunter, S. H., Academic Press, New York, pp. 5–66. Jumars, P. A. (1993). Concepts in Biological Oceanography: an Interdisciplinary Primer. Oxford University Press, New York. Fick, A. E. (1855). Uber diffusion, Poggend. Annel. Phys. Chem., 94, 59–86. Crank, J. (1975). The Mathematics of Diffusion. Oxford University Press, New York. Heyrovsky´, J. and Ku˚ta, J. (1966). Principles of Polarography. Publishing House of the Czechoslovak Academy of Sciences, Praha, and Academic Press, New York. Koch, A. L. (1971). The adaptive responses of Escherichia coli to a feast and famine existence, Adv. Microb. Physiol., 6, 147–217. Koch, A. L. and Wang, C. H. (1982). How close to the theoretical diffusion limit do bacterial uptake systems function? Arch. Microbiol., 131, 36–42. Levich, V. G. (1962). Physicochemical Hydrodynamics. Prentice-Hall, Englewood Cliffs, NJ. Kariuki, S. and Dewald, H. D. (1996). Evaluation of diffusion coefficients of metallic ions in aqueous solutions, Electroanalysis, 8, 307–313. Delahay, P. (1954). New Instrumental Methods in Electrochemistry. Interscience, New York. Pinheiro, J. P. and van Leeuwen, H. P. (2001). Metal speciation dynamics and bioavailability. 2. Radial diffusion effects in the microorganism range, Environ. Sci. Technol., 35, 894–900. Gavis, J. and Ferguson, J. F. (1975). Kinetics of carbon dioxide uptake by phytoplankton at high pH, Limnol. Oceanogr., 20, 211–221. Sanford, L. P. and Crawford, S. M. (2000). Mass transfer versus kinetic control of uptake across solid–water boundaries, Limnol. Oceanogr., 45, 1180–1186. Frank-Kamenetskii, D. A. (1969). Diffusion and Heat Transfer in Chemical Kinetics. Plenum Press, New York. Ploug, H., Stolte, W., Epping, E. H. G. and Jorgensen, B. B. (1999). Diffusive boundary layers, photosynthesis, and respiration of the colony-forming plankton algae, Phaeocystis sp., Limnol. Oceanogr., 44, 1949–1958. Ploug, H., Stolte, W. and Jorgensen, B. B. (1999). Diffusive boundary layers of the colony-forming plankton alga Phaeocystis sp. – implications for nutrient uptake and cellular growth, Limnol. Oceanogr., 44, 1959–1967. Thomas, F. I. M. and Atkinson, M. J. (1997). Ammonium uptake by coral reefs: effects of water velocity and surface roughness on mass transfer, Limnol. Oceanogr., 42, 81–88. Baird, M. E. and Atkinson, M. J. (1997). Measurement and prediction of mass transfer to experimental coral reef communities, Limnol. Oceanogr., 42, 1685–1693. Wheeler, W. N. (1980). Effect of boundary layer transport on the fixation of carbon by the giant kelp Macrocystis pyrifera, Mar. Biol., 56, 103–110. Logan, B. E. and Kirchman, D. L. (1991). Uptake of dissolved organics by marine bacteria as a function of fluid motion, Mar. Biol., 111, 175–181. Logan, B. E. and Dettmer, J. W. (1990). Increased mass transfer to microoganisms with fluid motion, Biotechnol. Bioeng., 35, 1135–1144. Kelly, F. X., Dapsis, K. J. and Lauffenburger, D. A. (1988). Effect of bacterial chemotaxis on dynamics of microbial competition, Microb. Ecol., 14, 115–131.

518 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70.

71. 72. 73.

74. 75.

Buffle, J., Bernhard, J. P. and Tercier, M. L. (1987). Extension of the sensitivity limit of amalgam electrodes in dilute aquatic media, based on the study of their oxidation process, J. Electroanal. Chem., 236, 67–86. van Ierland, E. T. and Peperzak, L. (1984). Separation of marine seston and density determination of marine diatoms by density gradient centrifugation, J. Plankton Res., 6, 29–44. Mullin, M. M., Sloan, P. R. and Eppley, R. W. (1966). Relationship between carbon content, cell volume, and area in phytoplankton, Limnol. Oceanogr., 11, 307–311. Culver, M. E. and Smith, W. O. (1989). Effects of environmental variation on sinking rates of marine phytoplankton, J. Phycol., 25, 262–270. Eppley, R. W., Holmes, R. W. and Strickland, D. H. (1967). Sinking rates of marine phytoplankton measured with a fluorometer, J. Exper. Mar. Biol. Ecol., 1, 191–208. Smayda, T. J. (1970). The suspension and sinking of phytoplankton in the sea, Oceanogr. Mar. Biol. Ann. Rev., 8, 353–414. Purcell, E. M. (1978). The effect of fluid motions on the absorption of molecules by suspended particles, J. Fluid Mech., 84, 551–559. Throndsen, J. (1973). Motility in some marine nanoplankton flagellates, Norweg. J. Zool., 21, 193–200. Sournia, A. (1982). Form and function in marine phytoplankton, Biol. Rev. Cambridge Phil. Soc., 57, 347–394. Pahlow, M., Riebesell, U. and Wolf–Gladrow, D. A. (1997). Impact of cell shape and chain formation on nutrient acquisition by marine diatoms, Limnol. Oceanogr., 42, 1660–1672. Soloviev, A. V., Vershishy, N. V. and Bezverchnii, B. A. (1988). Small scale turbulence measurements in the thin surface layer of the ocean, Deep-Sea Res., 35, 1859–1879. Wolf-Gladrow, E. and Riebesell, U. (1997). Diffusion and reactions in the vicinity of plankton: a refined model for inorganic carbon transport, Mar. Chem., 59, 17–34. Leermakers, F. A. M. and Kleijn, J. M. (2004). Molecular modelling of biological membranes. Structure and permeation properties. In Physicochemical Kinetics and Transport at Biointerfaces. eds. van Leeuwen, H. P. and Ko¨ster, W., Vol. 9, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Ltd, Chichester, pp. 15–111. Guillard, R. R. L. and Hellbust, J. A. (1971). Growth and the production of extracellular substances by two strains of Phaeocystis pouchetii, J. Phycol., 7, 330–338. Myklestad, S. and Haug, A. (1972). Production of carbohydrates by the marine diatom Chaetorceros affinis var. willei (Gran) Hustedt. I. Effect of the concentration of nutrients in the culture medium, J. Exp. Mar. Biol. Ecol., 9, 125–136. Christensen, B. E. (1999). Physical and chemical properties of extracellular polysaccharides associated with biofilms and related systems. In Microbial Extracellular Polymeric Substances. Characterization, Structure and Function. eds. Wingender, J., Neu, T. R. and Flemming, H.-C., Springer-Verlag, Berlin, pp. 143–154. Sutherland, I. W. (1999). Biofilm exopolysaccharides. In Microbial Extracellular Polymeric Substances. Characterization, Structure and Function. eds. Wingender, J., Neu, T. R. and Flemming, H.-C., Springer-Verlag, Berlin, pp. 73–92 Norberg, A. B. and Persson, H. (1984). Accumulation of heavy metals by Zoogloea ramigera, Biotechnol. Bioeng., 26, 239–246.

K. J. WILKINSON AND J. BUFFLE 76. 77. 78.

79. 80. 81.

82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94.

519

Kuhn, S. P. and Pfister, R. M. (1989). Adsorption of mixed metals and cadmium by calcium alginate immobilised Zoogloea ramigera, Appl. Microbiol., 31, 613–618. Tanford, C. (1961). Physical Chemistry of Macromolecules. John Wiley & Sons Ltd, New York. Buffle, J. and Tercier-Waeber, M.-L. (2000). In situ voltammetry: concepts and practice for trace analysis and speciation. In In Situ Monitoring of Aquatic Systems: Chemical Analysis and Speciation. eds. Buffle, J. and Horvai, G., Vol. 6, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Ltd, Chichester, pp. 279–405. Lerman, A. (1979). Geochemical Processes. Wiley Interscience, New York. Robinson, R. A. and Stokes, R. H. (1970). Electrolyte Solutions. Butterworths, London. Lead, J. R., Wilkinson, K. J., Starchev, K., Canonica, S. and Buffle, J. (2000). Diffusion coefficients of humic substances as determined by fluorescence correlation spectroscopy: role of solution conditions, Environ. Sci. Technol., 34, 1365–1369. Lerman, A. (1971). Nonequilibrium Systems in Natural Water Chemistry. American Chemical Society, Washington, DC. Meunier, F. and Wilkinson, K. J. (2002). Non-perturbing fluorescent labeling of polysaccharides, Biomacromolecules, 3, 857–864. Confer, D. R. and Logan, B. E. (1991). Increased bacterial uptake of macromolecular substrates with fluid shear, Appl. Environ. Microbiol., 57, 3093–3100. Riber, H. H. and Wetzel, R. G. (1987). Boundary layer and internal diffusion effects on phosphorus fluxes in lake periphyton, Limnol. Oceanogr., 32, 1181–1194. Harms, H. and Zehnder, A. J. B. (1994). Influence of substrate diffusion on degradation of dibenzofuran and 3-chlorodibenzofuran by attached and suspended bacteria, Appl. Environ. Microbiol., 60, 2736–2745. Mierle, G. (1985). Kinetics of phosphate transport by Synchococcus leopoliensis (Cyanophyta): evidence for diffusion limitation of phosphate uptake, J. Phycol., 21, 177–185. Riebesell, U., Wolf-Gladrow, D. A. and Smetacek, V. (1993). Carbon dioxide limitation of marine phytoplankton growth rates, Nature, 361, 249–251. Koch, E. W. (1994). Hydrodynamics, diffusion-boundary layers and photosynthesis of the seagrasses, Thalassia testudinum and Cymodocea nodosa, Mar. Biol., 118, 767–776. Hassler, C. S. and Wilkinson, K. J. (2003). Failure of the biotic ligand and free-ion activity models to explain zinc bioaccumulation by Chlorella kesslerii, Environ. Toxicol. Chem., 22, 620–626. Fortin, C. and Campbell, P. G. C. (2000). Silver uptake by the green alga, Chlamydomonas reinhardtii, in relation to chemical speciation: influence of chloride, Environ. Toxicol. Chem., 19, 2769–2778. Sunda, W. G. and Huntsman, S. A. (1998). Processes regulating cellular metal accumulation and physiological effects: phytoplankton as model systems, Sci. Total Environ., 219, 165–181. Paerl, H. W. and Merkel, S. M. (1982). Differential phosphorus assimilation in attached vs. unattached microorganisms, Arch. Hydrobiol., 93, 125–134. Jeffery, W. H. and Paul, J. H. (1986). Activity measurements of planktonic microbial and microfouling communities in a eutrophic estuary, Appl. Environ. Microbiol., 51, 157–162.

520 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 95. 96. 97. 98. 99. 100. 101. 102. 103. 104.

105.

106. 107. 108. 109. 110. 111. 112.

Iriberri, J., Unanue, M., Barcina, I. and Egea, L. (1987). Seasonal variation in population density and heterotrophic activity of attached and free-living bacteria in coastal waters, Appl. Environ. Microbiol., 53, 2308–2314. Kirchman, D. (1983). The production of bacteria attached to particles suspended in a freshwater pond, Limnol. Oceanogr., 28, 858–872. Simon, M. (1987). Biomass and production of small and large free-living and attached bacteria in Lake Constance, Limnol. Oceanogr., 32, 591–607. Logan, B. E. and Hunt, J. R. (1987). Advantages to microbes of growth in permeable aggregates in marine systems, Limnol. Oceanogr., 32, 1034–1048. Rittman, B. E., McCarty, P. L. and Roberts, P. V. (1980). Trace-organics biodegradation in aquifer recharge, Ground Water, 18, 326–343. Wanner, O. and Gujer, W. (1986). A multispecies biofilm model, Biotechnol. Bioeng., 28, 314–328. Bosma, T. N. P., Middeldorp, P. J. M., Schraa, G. and Zehnder, A. J. B. (1997). Mass transfer limitation of biotransformation: quantifying bioavailability, Environ. Sci. Technol., 31, 248–252. Ploug, H. and Jorgensen, B. B. (1999). A net-jet flow system for mass transfer and microsensor studies of sinking aggregates, Mar. Ecol. Prog. Ser., 176, 279–290. Lubbers, G. W., Gieskes, W. W., Del Castillo, P., Salomons, W. and Brill, J. (1990). Manganese accumulation in the high pH microenvironment of Phaeocystis sp. (Haptophyceae) colonies from the North Sea, Mar. Ecol. Prog. Ser., 59, 285–293. Escher, B. and Sigg, L. (2004). Chemical speciation of organics and metals at biological interphases. In Physicochemical Kinetics and Transport at Biointerfaces. eds. van Leeuwen, H. P. and Ko¨ster, W., Vol. 9, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons Ltd, Chichester, pp. 205–269. Buffle, J. and Altmann, R. S. (1987). Interpretation of metal complexation by heterogeneous complexants. In Aquatic Surface Chemistry: Chemical Processes at the Particle–Water Interface. ed. Stumm, W., John Wiley & Sons, New York, pp. 351–383. Stumm, W. (1992). Chemistry of the Solid–Water Interface. John Wiley & Sons Ltd, New York. Preston, R. D. (1974). The Physical Biology of Plant Cell Walls. John Wiley & Sons Ltd., New York. Adhiya, J., Cai, X., Sayre, R. T. and Traina, S. J. (2002). Binding of aqueous cadmium by the lyophilized biomass of Chlamydomonas reinhardtii, Coll. Surf. A. Physicochem. Eng. Aspects, 210, 1–11. Crist, R. H., Oberholser, K., Schwartz, D., Marzoff, J., Ryder, D. and Christ, D. R. (1988). Interactions of metals and protons with algae, Environ. Sci. Technol., 22, 755–760. Plette, A. C. C., Benedetti, M. F. and van Riemsdijk, W. H. (1996). Competitive binding of protons, calcium, cadmium, and zinc to isolated cell walls of a grampositive soil bacterium, Environ. Sci. Technol., 30, 1902–1910. Pinheiro, J. P., Mota, A. M., d’Oliverira, J. M. R. and Martinho, J. M. G. (1996). Dynamic properties of humic matter by dynamic light scattering and voltammetry, Anal. Chim. Acta, 329, 15–24. Dixon, A. M. and Larive, C. K. (1997). Modified pulsed-field gradient NMR experiments for improved selectivity in the measurement of diffusion coefficients in complex mixtures: application to the analysis of the Suwannee River fulvic acid, Anal. Chem., 69, 2122–2128.

K. J. WILKINSON AND J. BUFFLE

521

113. Beckett, R., Jue, Z. and Giddings, J. C. (1987). Determination of molecular weight distributions of fulvic and humic acids using flow field-flow fractionation, Environ. Sci. Technol., 21, 289–295. 114. Lauffenburger, D. A. and Linderman, J. J. (1993). Receptors. Models for Binding, Trafficking, and Signaling. Oxford University Press, New York. 115. Schulten, H.-R. and Schnitzer, M. (1993). A state of the art structural concept for humic substances, Naturwissenschaften, 80, 29–30. 116. Thurman, E. M. (1985). Organic Geochemistry of Natural Waters. Martinus Nijhoff/Dr W. Junk, Boston. 117. Kinniburgh, D. G., Milne, C. J., Benedetti, M. F., Pinheiro, J. P., Filius, J., Koopal, L. K. and van Riemsdijk, W. H. (1996). Metal ion binding by humic acid: application of the NICA-Donnan model, Environ. Sci. Technol., 30, 1687–1698. 118. Moffett, J. W., Zika, R. G. and Brand, L. E. (1990). Distribution and potential sources and sinks of copper chelators in the Sargasso Sea, Deep-Sea Res., 37, 27–36. 119. Xue, H.-B. and Sigg, L. (1998). Cadmium speciation and complexation by natural organic ligands in fresh water, Anal. Chim. Acta, 363, 249–259. 120. Xue, H.-B. and Sigg, L. (1993). Free cupric ion concentration and Cu(II) speciation in a eutrophic lake, Limnol. Oceanogr., 38, 1200–1213. 121. Moffett, J. W. and Brand, L. E. (1996). Production of strong, extracellular Cu chelators by marine cyanobacteria in response to Cu stress, Limnol. Oceanogr., 41, 388–395. 122. Xue, H.-B., Kistler, D. and Sigg, L. (1995). Competition of copper and zinc for strong ligands in a eutrophic lake, Limnol. Oceanogr., 40, 1142–1152. 123. Rue, E. L. and Bruland, K. W. (1995). Complexation of iron(III) by natural organic ligands in the Central North Pacific as determined by a new competitive ligand equilibration/adsorptive cathodic stripping voltammetric method, Mar. Chem., 50, 117–138. 124. Leal, M. F. C. and van den Berg, C. M. G. (1998). Evidence for strong copper(I) complexation by organic ligands in seawater, Aquat. Geochem., 4, 49–75. 125. Lee, J. G., Ahner, B. A. and Morel, F. M. M. (1996). Export of cadmium and phytochelatin by the marine diatom Thalassiosira weissflogii, Environ. Sci. Technol., 30, 1814–1821. 126. Ahner, B. A. and Morel, F. M. M. (1995). Phytochelatin production in marine algae. 2. Induction by various metals, Limnol. Oceanogr., 40, 658–665. 127. Ahner, B. A., Morel, F. M. M. and Moffett, J. W. (1997). Trace metal control of phytochelatin production in coastal waters, Limnol. Oceanogr., 42, 601–608. 128. Mirimanoff, N. and Wilkinson, K. J. (2000). Regulation of Zn accumulation by a freshwater Gram-positive bacterium (Rhodococcus opacus), Environ. Sci. Technol., 34, 616–622. 129. Smith, R. M. and Martell, A. E. (1976). Critical Stability Constants, Vol. 4: Inorganic Complexes. Plenum Press, New York. 130. Gordon, A. S. (1998). Microbial control of trace metals in the oceans, ASM News, 64, 79–83. 131. Town, R. M. and Filella, M. (2000). Dispelling the myths: is the existence of L1 and L2 ligands necessary to explain metal ion speciation in natural waters? Limnol. Oceanogr., 45, 1341–1357. 132. McKnight, D. M. and Morel, F. M. M. (1979). Release of weak and strong copper-complexing agents by algae, Limnol. Oceanogr., 24, 823–837.

522 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 133. van den Berg, C. M. G., Merks, A. G. A. and Dursma, E. K. (1987). Organic complexation and its control of the dissolved concentration of copper and zinc in the Scheldt estuary, Estuar. Coast. Shelf Sci., 24, 785–797. 134. Coale, K. H. and Bruland, K. W. (1988). Copper complexation in the northeast Pacific, Limnol. Oceanogr., 33, 1184–1101. 135. Gledhill, M. and van den Berg, C. M. G. (1994). Determination of complexation of iron(III) with natural organic complexing ligands in seawater using cathodic stripping voltammetry, Mar. Chem., 47, 41–54. 136. Capodaglio, G., Coale, K. H. and Bruland, K. W. (1990). Lead speciation in surface waters of the eastern North Pacific, Mar. Chem., 29, 221–223. 137. Wells, M. L., Kozelka, P. B. and Bruland, K. W. (1998). The complexation of ‘dissolved’ Cu, Zn, Cd and Pb by soluble and colloidal organic matter in Narragansett Bay, RI, Mar. Chem., 62, 203–217. 138. Kozelka, P. B., San˜udo-Wilhelmy, S., Flegal, A. R. and Bruland, K. W. (1997). Physicochemical speciation of lead in South San Francisco Bay, Estuar. Coast. Shelf Sci., 44, 267–282. 139. Bruland, K. W. (1989). Complexation of zinc by natural organic ligands in the central North Pacific, Limnol. Oceanogr., 34, 269–285. 140. Filella, M., Town, R. M. and Buffle, J. (1995). Speciation in fresh waters. In Chemical Speciation in the Environment. eds. Ure, A. M. and Davidson, C. M., Chapman and Hall, New York, pp. 169–200. 141. Buffle, J. (1984). Natural organic matter and metal–organic interactions in aquatic systems. In Metal Ions in Biological Systems. Vol. 18, Circulation of Metals in the Environment, ed. Sigel, H., Marcel Dekker, New York, pp. 165–221. 142. Filella, M., Buffle, J. and van Leeuwen, H. P. (1990). Effect of physico-chemical heterogeneity of natural complexants Part I. Voltammetry of labile metal–fulvic complexes, Anal. Chim. Acta, 232, 209–223. 143. Buffle, J., Altmann, R. S., Filella, M. and Tessier, A. (1990). Complexation by natural heterogeneous compounds: site occupation distribution functions, a normalized description of metal complexation, Geochim. Cosmochim. Acta, 54, 1535–1553. 144. Milne, C. J., Kinniburgh, D. G., De Wit, J. C. M., van Riemsdijk, W. H. and Koopal, L. K. (1995). Analysis of proton binding by a peat humic acid using a simple electrostatic model, Geochim. Cosmochim. Acta, 59, 1101–1112. 145. Pinheiro, J. P., Mota, A. M. and Simo˜es Gonc¸alves, M. L. (1994). Complexation study of humic acids with cadmium (II) and lead(II), Anal. Chim. Acta, 284, 525–537. 146. Dzombak, D. A. and Morel, F. M. M. (1990). Surface Complexation Modeling: Hydrous Ferric Oxide. John Wiley & Sons, New York. 147. Loeb, A. L., Overbeek, J. Th. G. and Wiersema, P. H. (1961). The Electrical Double Layer Around a Spherical Colloid Particle. MIT Press, Cambridge, MA. 148. Cleven, R. F. M. J. (1984). Heavy Metal/Polyacid Interaction. An Electrochemical Study of the Binding of Cd(II), Pb(II) and Zn(II) to Polycarboxylic and Humic Acids. Ph.D. Thesis, Wageningen Agricultural University, Netherlands. 149. Hosse, M. and Wilkinson, K. J. (2002). Determination of electrophoretic mobilities and hydrodynamic radii of three humic substances as a function of pH and ionic strength, Environ. Sci. Technol., 35, 4301–4306. 150. Balnois, E., Wilkinson, K. J., Lead, J. and Buffle, J. (1999). Atomic force microscopy study of humic substances adsorbed on mica surfaces: effects of pH and ionic strength, Environ. Sci. Technol., 33, 3911–3917.

K. J. WILKINSON AND J. BUFFLE

523

151. Warwick, P., Hall, A., Pashley, V. and Bryan, N. (2001). Investigation of the permeability of humic molecules using zeta potential measurements, Chemosphere, 45, 303–307. 152. Buffle, J., Tessier, A. and Haerdi, W. (1984). Interpretation of trace metal complexation by aquatic organic matter. In Complexation of Trace Metals in Natural Waters. eds. Kramer, C. J. M. and Duinker, J. C., Martinus Nijhoff/Dr W. Junk, The Hague, pp. 301–316. 153. Bartschat, B. M., Cabaniss, S. E. and Morel, F. M. M. (1992). Oligoelectrolyte model for cation binding by humic substances, Environ. Sci. Technol., 26, 284–294. 154. Cernik, M., Borkovec, M. and Westall, J. C. (1995). Regularized least-squares methods for the calculation of discrete and continuous affinity distributions for heterogeneous sorbents, Environ. Sci. Technol., 29, 413–425. 155. Gamble, D. S. and Schnitzer, M. (1973). The chemistry of fulvic acid and its reactions with metal ions. In Trace Metals and Metal–Organic Interactions in Natural Waters. ed. Singer, P. C., Ann Arbor Science, Ann Arbor, pp. 265–302. 156. Gamble, D. S., Underdown, A. W. and Langford, C. H. (1982). Copper(II) titration of fulvic acid ligand sites with theoretical, potentiometric and spectrophotometric analysis, Anal. Chem., 52, 1901–1908. 157. Buffle, J., Altmann, R. S. and Filella, M. (1990). Effect of physico-chemical heterogeneity of natural complexants. Part II. Buffering action and role of their background sites, Anal. Chim. Acta, 232, 225–237. 158. Buffle, J. (1990). The ecological role of aquatic organic and inorganic components, deduced from their nature, circulation and interactions. In Metal Speciation in the Environment. eds. Broeckaert, J. A. C., Guc¸er, S. and Adams, F., SpringerVerlag, Berlin, pp. 469–501. 159. Filella, M. and Town, R. M. (2001). Heterogeneity and lability of Pb(II) complexation by humic substances: practical interpretation tools, Fresenius J. Anal. Chem., 370, 413–418. 160. Slaveykova, V., Wilkinson, K. J., Ceresa, A. and Pretsch, E. (2003). Role of fulvic acid on lead bioaccumulation to Chlorella kessleri, Environ. Sci. Technol., 37, 1114–1121. 161. Lofts, S. and Tipping, E. (1998). An assemblage model for cation-binding by natural particulate matter, Geochim. Cosmochim. Acta, 62, 2609–2625. 162. Tipping, E. (1998). Humic Ion-Binding Model VI: an improved description of ionbinding by humic substances, Aquatic Geochem., 4, 3–48. 163. Altmann, R. S. and Buffle, J. (1988). The use of differential equilibrium functions for the interpretation of metal binding in complex ligand systems: its relation to site occupation and site affinity distributions, Geochim. Cosmochim. Acta, 52, 1505–1519. 164. Basolo, F. and Pearson, R. G. (1967). Mechanisms of Inorganic Reactions: A Study of Metal Complexes in Solution. Wiley-Interscience, New York. 165. Wilkins, R. (1991). Kinetics and Mechanism of Reactions of Transition Metal Complexes. VCH, Weinheim. 166. Stumm, W. ed. (1990). Aquatic Chemical Kinetics: Reaction Rates of Processes in Natural Waters, Environmental Science and Technology. John Wiley & Sons Ltd, New York. 167. Hoffman, M. R. (1981). Thermodynamic, kinetic, and extrathermodynamic considerations in the development of equilibrium models from aquatic systems, Environ. Sci. Technol., 15, 345–353.

524 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 168. Pankow, J. F. and Morgan, J. J. (1981). Kinetics for the aquatic environment, Environ. Sci. Technol., 15, 1155–1164. 169. Pankow, J. F. and Morgan, J. J. (1981). Kinetics for the aquatic environment, Environ. Sci. Technol., 15, 1306–1313. 170. Hering, J. G. and Morel, F. M. M. (1990). Kinetics of trace metal complexation: ligand-exchange reactions, Environ. Sci. Technol., 24, 242–252. 171. Burgess, J. (1978). Metal Ions in Solution. Halsted Press, New York. 172. Margerum, D. W., Cayley, G. R., Weatherburn, D. C. and Pagenkopf, G. K. (1978). Kinetics and mechanisms of complex formation and ligand exchange. In Coordination Chemistry. Vol. 2, ed. Martell, A. E., ACS Monograph 174, American Chemical Society, Washington DC, pp. 1–220. 173. Crumbliss, A. L. and Garrison, J. M. (1988). A comparison of some aspects of the aqueous coordination chemistry of aluminum(III) and iron(III), Comments Inorg. Chem., 8, 1–26. 174. Grant, M. and Jordan, R. B. (1981). Kinetics of solvent water exchange on iron (III), Inorg. Chem., 20, 55–60. 175. Monzyk, B. and Crumbliss, A. L. (1982). Kinetics and mechanisms of stepwise dissociation of iron(III) from ferrioxamine B in aqueous acid, J. Am. Chem. Soc., 104, 4921–4929. 176. Pohlmeier, A. and Knoche, W. (1996). Kinetics of the complexation of Al3þ with aminoacids, IDA and NTA, Intern. J. Chem. Kinet., 28, 125–136. 177. Hering, J. G. and Morel, F. M. M. (1988). Kinetics of trace metal complexation: role of alkaline-earth metals, Environ. Sci. Technol., 22, 1469–1478. 178. Raspor, B., Nu¨rnberg, H. W., Valenta, P. and Branica, M. (1980) Kinetics and mechanism of trace metal chelation in sea water, J. Electroanal. Chem., 115, 293–308. 179. Lion, L. W., Altmann, R. S. and Leckie, J. O. (1982). Trace-metal adsorption characteristics of estuarine particulate matter: evaluation of contributions of iron/ manganese oxide and organic surface coatings, Environ. Sci. Technol., 16, 660–666. 180. Davis, J. A., James, R. O. and Leckie, J. O. (1978). Surface ionization and complexation at the oxide/water interface. I. Computation of electrical double layer properties in simple electrolytes, J. Coll. Interf. Sci., 63, 480–499. 181. Benjamin, M. M. and Leckie, J. O. (1981). Multiple-site adsorption of cadmium, copper, zinc, and lead on amorphous iron oxyhydroxide, J. Coll. Interf. Sci., 79, 209–221. 182. Pei, J., Tercier-Waeber, M.-L. and Buffle, J. (2000). Simultaneous determination and speciation of zinc, cadmium, lead and copper in natural waters with minimum handling and artefacts by voltammetry on gel-integrated microelectrode arrays, Anal. Chem., 72, 161–171. 183. Talibudeen, O. (1981). Precipitation. In The Chemistry of Soil Processes. eds. Greenland, D. J. and Hayes, M. H. B., John Wiley & Sons, Ltd, Chichester, pp. 81–114. 184. Schuman, M. S., Collins, B. J., Fitzgerald, P. J. and Olson, D. L. (1983). Spectrum analysis of ion-selective electrode and photometric data. In Aquatic and Terrestrial Humic Materials. eds. Christman, R. F. and Gjessing, E. T., Ann Arbor Science, Michigan, pp. 349–370. 185. Warwick, P., Carlsen, L., Randall, A., Zhao, R. and Lassen, P. (1993). 14 C and 125 I labelling of humic material for use in environmental studies, Chem. Ecol., 8, 65–80.

K. J. WILKINSON AND J. BUFFLE

525

186. Gutfreund, H. (1995). Kinetics for the Life Sciences. Receptors, Transmitters and Catalysts. Cambridge University Press, Cambridge. 187. Munson, P. J. and Rodbard, D. (1983). Number of receptor sites from Scatchard and Klotz graphs: a constructive critique, Science, 220, 979–981. 188. Munson, P. J. (1983). Experimental artifacts and the analysis of ligand binding data: results of a computer simulation, J. Receptor Res., 3, 249–259. 189. Munson, P. J. and Rodbard, D. (1980). Ligand: a versatile computerized approach for characterization of ligand-binding systems, Anal. Biochem., 107, 220–239. 190. Bates, S. S., Tessier, A., Campbell, P. G. C. and Buffle, J. (1982). Zinc adsorption and transport by Chlamydomonas variabilis, J. Phycol., 18, 521–529. 191. Hudson, R. J. M. and Morel, F. M. M. (1989). Distinguishing between extra- and intracellular iron in marine phytoplankton, Limnol. Oceanogr., 34, 1113–1120. 192. Hudson, R. J. M. and Morel, F. M. M. (1990). Iron transport in marine phytoplankton: kinetics of cellular and medium coordination reactions, Limnol. Oceanogr., 35, 1002–1020. 193. Ting, Y. P., Lawson, F. and Prince, I. G. (1989). Uptake of cadmium and zinc by the alga Chlorella vulgaris: Part I. Individual ion species, Biotechnol. Bioeng., 34, 990–999. 194. Ting, Y. P., Lawson, F. and Prince, I. G. (1991). Uptake of cadmium and zinc by the alga Chlorella vulgaris: Part II. Multi-ion situation, Biotechnol. Bioeng., 37, 445–455. 195. Santana-Casiano, J. M., Gonza´lez-Da´vila, M., Laglera, L. M., Pe´rez-Pen˜a, J., Brand, L. and Millero, F. J. (1997). The influence of zinc, aluminum and cadmium on the uptake kinetics of iron by algae, Mar. Chem., 59, 95–111. 196. Roberts, S. B., Lane, T. W. and Morel, F. M. M. (1997). Carbonic anhydrase in the marine diatom Thalassiosira weissfloggii, J. Phycol., 33, 845–850. 197. Klotz, I. M. (1985). Ligand–receptor interactions: facts and fantasies, Q. Rev. Biophys., 18, 227–259. 198. Limbird, L. E. (1986). Cell Surface Receptors: a Short Course on Theory and Methods. Martinus Nijhoff, Boston. 199. Park, L. S., Gillis, S. and Urdal, D. L. (1990). Hematopoietic growth-factor receptors. In Colony-Stimulating Factors. Molecular and Cellular Biology. eds. Dexter, T. M., Garland, J. M. and Testa, N. G., Marcel Dekker, New York, pp. 39–75. 200. Sunda, W. G. and Huntsman, S. A. (1995). Iron uptake and growth limitation in oceanic and coastal phytoplankton, Mar. Chem., 50, 189–206. 201. Slaveykova, V. I. and Wilkinson, K. J. (2002). Physicochemistry of Pb accumulation by Chlorella vulgaris, Environ. Sci. Technol., 36, 969–975. 202. Watt, R. K. and Ludden, P. W. (1999). Ni2þ transport and accumulation in Rhodospirillum rubrum, J. Bacteriol., 181, 4554–4560. 203. Gadd, G. M. and White, C. (1985). Copper uptake by Penicillium ochro-chloron: influence of pH on toxicity and demonstration of energy-dependent copper influx using protoplasts, J. Gen. Microbiol., 131, 1875–1879. 204. Gadd, G. M. and Laurence, O. S. (1996). Demonstration of high-affinity Mn2þ uptake in Saccharomyces cerevisiae: specificity and kinetics, Microbiol., 142, 1159–1167. 205. Hart, B. A., Bertram, P. E. and Scaife, B. D. (1979). Cadmium transport by Chlorella pyrenoidosa, Environ. Res., 18, 327–335. 206. Sunda, W. G. and Huntsman, S. A. (1998). Interactions among Cu2þ , Zn2þ , and Mn2þ in controlling cellular Mn, Zn, and growth rate in the coastal alga Chlamydomonas, Limnol. Oceanogr., 43, 1055–1064.

526 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 207. White, C. and Gadd, G. M. (1995). Determination of metals and metal fluxes in algae and fungi, Sci. Total Environ., 176, 107–115. 208. Garnham, G. W., Codd, G. A. and Gadd, G. M. (1992). Kinetics of uptake and intracellular location of cobalt, manganese and zinc in the estuarine green alga Chlorella salina, Appl. Microbiol. Biotechnol., 37, 270–276. 209. Sunda, W. G. and Huntsman, S. A. (1992). Feedback interactions between zinc and phytoplankton in seawater, Limnol. Oceanogr., 37, 25–40. 210. Wolterbeek, H.Th., Viragh, A., Sloof, J. E., Bolier, G., van der Veer, B. and de Kok, J. (1995). On the uptake and release of zinc (65 Zn) in the growing alga Selenastrum capricornutum Printz, Environ. Poll., 88, 85–90. 211. Sunda, W. G. and Huntsman, S. A. (1986). Relationships among growth rate, cellular manganese concentrations and manganese transport kinetics in estuarine and oceanic species of the diatom Thalassiosira, J. Phycol., 22, 259–270. 212. Alsop, D. H. and Wood, C. M. (2000). Kinetic analysis of zinc accumulation in the gills of juvenile rainbow trout: effects of zinc acclimatation and implications for biotic ligand modeling, Environ. Toxicol. Chem., 19, 1911–1918. 213. Sunda, W. G. and Huntsman, S. A. (1983). Effect of competitive interactions between manganese and copper on cellular manganese and growth in estuarine and oceanic species of the diatom Thalassiosira, Limnol. Oceanogr., 28, 924–934. 214. Sunda, W. G. and Huntsman, S. A. (2000). Effect of Zn, Mn, and Fe on Cd accumulation in phytoplankton: implications for oceanic Cd cycling, Limnol. Oceanogr., 45, 1501–1516. 215. Maeda, S., Mizoguchi, M., Ohki, A. and Takeshita, T. (1990) Bioaccumulation of zinc and cadmium in freshwater alga, Chlorella vulgaris. Part I. Toxicity and accumulation, Chemosphere, 21, 953–963. 216. Sunda, W. G. and Huntsman, S. A. (1996). Antagonisms between cadmium and zinc toxicity and manganese limitation in a coastal diatom, Limnol. Oceanogr., 41, 373–387. 217. Sunda, W. G. and Huntsman, S. A. (1998). Control of Cd concentrations in a coastal diatom by interactions among free ionic Cd, Zn, and Mn in seawater, Environ. Sci. Technol., 32, 2961–2968. 218. Ke, H.-Y. D. and Rayson, G. D. (1992). Characterization of cadmium binding sites on Datura innoxia using cadmium-113 NMR spectrometry, Environ. Sci. Technol., 26, 1202–1205. 219. Carrilho, E. N. V. M., Ferreira, A. G. and Gilbert, T. R. (2002). Characterization of sorption sites on Pilayella littoralis and metal binding assessment using 113 Cd and 27 Al nuclear magnetic resonance, Environ. Sci. Technol., 36, 2003–2007. 220. Bertsch, P. M. and Hunter, D. B. (2001). Applications of synchrotron-based X-ray microprobes, Chem. Rev., 101, 1809–1842. 221. Wilkinson, K. J., Bertsch, P. M., Jagoe, C. H. and Campbell, P. G. C. (1993). Surface complexation of Al on isolated fish gill cells, Environ. Sci. Technol., 27, 1132–1138. 222. Wilkinson, K. J., Campbell, P. G. C. and Couture, P. (1990). The effect of fluoride complexation on aluminum toxicity towards juvenile Atlantic salmon (Salmo salar L.), Can. J. Fish. Aquat. Sci., 47, 1446–1452. 223. Wilkinson, K. J. and Campbell, P. G. C. (1993). Aluminum bioconcentration at the gill surface of juvenile Atlantic salmon in acidic media, Environ. Toxicol. Chem., 12, 2083–2095. 224. Gensemer, R. W. and Playle, R. C. (1999). The bioavailability and toxicity of aluminum in aquatic environments, Crit. Rev. Environ. Sci. Technol., 29, 315–450.

K. J. WILKINSON AND J. BUFFLE

527

225. Parker, D. R., Kinraide, T. B. and Zelazny, L. W. (1988). Al speciation and phytotoxicity in dilute hydroxy-Al solutions, Soil Sci. Soc. Amer. J., 52, 438–444. 226. Kinraide, T. B. and Parker, D. R. (1989). Assessing the phytotoxicity of mononuclear hydroxy-aluminum, Plant Cell Environ., 12, 479–487. 227. Neville, C. M. and Campbell, P. G. C. (1988). Possible mechanisms of aluminum toxicity in a dilute, acidic environment to fingerlings and older life stages of salmonids, Water, Air, Soil Poll., 42, 311–327. 228. Campbell, P. G. C., Twiss, M. R. and Wilkinson, K. J. (1997). Accumulation of natural organic matter on the surfaces of living cells: implications for the interaction of toxic solutes with aquatic biota, Can. J. Fish. Aquat. Sci., 54, 2543–2554. 229. Knauer, K. and Buffle, J. (2001). Adsorption of fulvic acid on algal surfaces and its effect on carbon uptake, J. Phycol., 37, 47–51. 230. Buffle, J. and Cominoli, A. (1981). Voltammetric study of humic and fulvic substances. Part IV. Behaviour of fulvic substances at the mercury–water interface, J. Electroanal. Chem., 121, 273–299. 231. Buffle, J., Mota, A. M. and Simo˜es Gonc¸alves, M. L. S. (1987). Adsorption of fulvic-like organic ligands and their Cd and Pb complexes at a mercury electrode, J. Electroanal. Chem., 223, 235–262. 232. Vigneault, B., Percot, A., Lafleur, M. and Campbell, P. G. C. (2000). Permeability changes in model and phytoplankton membranes in the presence of aquatic humic substances, Environ. Sci. Technol., 34, 3907–3913. 233. Parent, L., Twiss, M. R. and Campbell, P. G. C. (1996). Influences of natural dissolved organic matter on the interaction of aluminum with the microalga Chlorella: a test of the free-ion model of trace metal toxicity, Environ. Sci. Technol., 30, 1713–1720. 234. Gonc¸alves, M. L. S. and da Conceic¸ao, A. C. L. (1991). Interaction of heavy metals with organisms and proteins, Sci. Total Environ., 103, 185–198. 235. Gonc¸alves, M. L. S., Sigg, L., Reutlinger, M. and Stumm, W. (1987). Metal ion binding by biological surfaces: voltammetric assessment in the presence of bacteria, Sci. Total Environ., 60, 105–119. 236. Wilkinson, K. J., Slaveykova, V. I., Hassler, C. S. and Rossier, C. (2002). Physicochemical mechanisms of trace metal bioaccumulation by microorganisms, Chimia, 56, 681–684. 237. DeLisi, C. and Wiegel, F. W. (1981). Effect of nonspecific forces and finite receptor number on rate constants of ligand cell-bound receptor interactions, Proc. Natl Acad. Sci. USA, 78, 5569–5572. 238. De Lean, A., Hancock, A. A. and Lefkowitz, R. J. (1982). Validation and statistical analysis of a computer modeling method for quantitative analysis of radioligand binding data for mixtures of pharmacological receptor subtypes, Mol. Pharmacol., 21, 5–16. 239. Lipkin, E. W., Teller, D. C. and de Haen, C. (1986). Kinetics of insulin binding to rat white fat cells at 15 8C, J. Biol. Chem., 261, 1702–1711. 240. Wiley, H. S., Walsh, B. J. and Lund, K. A. (1989). Global modulation of the epidermal growth factor is triggered by occupancy of only a few receptors: evidence for a binary regulation system in normal human fibroblasts, J. Biol. Chem., 264, 18 912–18 920. 241. Lin, C. R., Chen, W. S., Lazar, C. S., Carpenter, C. D., Gill, G. N., Evans, R. M. and Rosenfeld, M. G. (1986). Protein kinase C phosphorylation at Thr 654 of the unoccupied EGF receptor and EGF binding regulate functional receptor loss by independent mechanisms, Cell, 44, 839–848.

528 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 242. Simkiss, K. and Taylor, M. G. (1995). Transport of metals across membranes. In Metal Speciation and Bioavailability in Aquatic Systems. eds. Tessier, A. and Turner, D. R., Vol. 3, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Ltd, Chichester, pp. 1–44. 243. Munger, C., Hare, L. and Tessier, A. (1999). Cadmium sources and exchange rates for Chaoborus larvae in nature, Limnol. Oceanogr., 44, 1763–1771. 244. Roy, I. and Hare, L. (1999). Relative importance of water and food as cadmium sources to the predatory insect Sialis velata (Magaloptera), Can. J. Fish. Aquat. Sci., 56, 1143–1149. 245. Handy, R. D. and Eddy, F. B. (2004). Transport of solutes across biological membranes in eukaryotes: sodium and copper homeostasis in gill epithelial cells, In Physicochemical Kinetics and Transport at Biointerfaces. eds. van Leeuwen, H. P. and Ko¨ster, W., Vol. 9, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley & Sons, Ltd, Chichester, pp. 337–356. 246. Stein, W. D. (1990). Channels, Carriers and Pumps. An Introduction to Membrane Transport. Academic Press, San Diego, CA. 247. Gadd, G. M. (1988). Accumulation of metals by microorganisms and algae. In Biotechnology. eds. Rehm, H. J. and Reed, G., VCH, Weinheim, pp. 401–433. 248. Taylor, M. G. and Simkiss, K. (2004). Transport of colloids and particles across biological membranes. In Physicochemical Kinetics and Transport at Biointerfaces, eds. van Leeuwen, H. P. and Ko¨ster, W., Vol. 9, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle J. and van Leeuwen, H. P., John Wiley & Sons, Ltd., Chichester, pp. 357–400. 249. Stauber, J. L. and Florence, T. M. (1987). Mechanism of toxicity of ionic copper and copper complexes to algae, Mar. Biol., 94, 511–519. 250. Phinney, J. T. and Bruland, K. W. (1997). Trace metal exchange in solution by the fungicides Ziram and Mandeb (dithiocarbamates) and subsequent uptake of lipophilic organic zinc, coper and lead complexes into phytoplankton cells, Environ. Toxicol. Chem., 16, 2046–2053. 251. Mason, R. P., Reinfelder, J. R. and Morel, F. M. M. (1996). Uptake, toxicity and trophic transfer of mercury in a coastal diatom, Environ. Sci. Technol., 30, 1835–1845. 252. Phinney, J. T. and Bruland, K. W. (1994). Uptake of lipophilic organic Cu, Cd, and Pb complexes in the coastal diatom Thalassiosira weissflogii, Environ. Sci. Technol., 28, 1781–1790. 253. Collander, R. (1954). The permeability of Nitella cells to non-electrolytes, Physiol. Plant., 7, 420–445. 254. Schwarzenbach, R. P., Gschwend, P. M. and Imboden, D. M. (1993). Environmental Organic Chemistry. John Wiley & Sons, Ltd, New York. 255. Castro, C. E., Wade, R. S. and Belser, N. O. (1985). Biodehalogenation. Reactions of cytochrome P-450 with polyhalomethanes, Biochem., 24, 204–210. 256. Konings, W. N., Hellingwerf, K. J. and Robillard, G. T. (1981). Transport across bacterial membranes, In Membrane Transport. eds. Bonting, S. L. and dePont, J. J. H. H. M., Elsevier, New York, pp. 257–283. 257. Stryer, L. (1995). Biochemistry. 4th edn, W. H. Freeman, San Francisco. 258. Theorell, H. and Chance, B. (1951). Studies on liver alcohol dehydrogenase, Acta Chem. Scand., 5, 1127–1144. 259. Raymond, K. N. and Carrano, C. J. (1979). Coordination chemistry and microbial iron transport, Acc. Chem. Res., 12, 183–190.

K. J. WILKINSON AND J. BUFFLE

529

260. Sunda, W. G. and Huntsman, S. A. (1985). Regulation of cellular manganese and manganese transport rates in the unicellular alga Chlamydomonas, Limnol. Oceanogr., 30, 71–80. 261. Knauer, K., Behra, R. and Sigg, L. (1997). Adsorption and uptake of copper by the green alga Scenedesmus subspicatus (chlorophyta), J. Phycol., 33, 596–601. 262. Lee, J. G., Roberts, S. B. and Morel, F. M. M. (1995). Cadmium: a nutrient for the marine diatom Thalassiosira weissflogii, Limnol. Oceanogr., 40, 1056–1063. 263. Vincent, J. C. and Thellier, M. (1983). Theoretical analysis of the significance of whether or not enyzmes or transport systems in structured media follow Michaelis–Menten kinetics, Biophys. J., 41, 23–28. 264. Thellier, M., Ripoll, C., Vincent, J.-C. and Mikulecky, D. (1993). Interpretation of the fluxes of substances exchanged by cellular systems with their external medium. In Some Physicochemical and Mathematical Tools for Understanding of Living Systems. eds. Greppin, H., Bonzon, M. and Degli Agosti, R., RochatBaumann Imprimerie nationale, Geneva, pp. 221–277. 265. Michaelis, L. and Menten, M. L. (1913). Die kinetic der invertinwirkung, Biochem. Z., 49, 333–369. 266. Galceran, J. and van Leeuwen, H. P. (2004). Dynamics of biouptake processes. The role of transport, adsorption and internalisation. In Physicochemical Kinetics and Transport at Biointerfaces. eds. van Leeuwen, H. P. and Ko¨ster, W., Vol. 9, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle J. and van Leeuwen, H. P., John Wiley & Sons, Ltd, Chichester, pp. 147–203. 267. Schachter, H. (1972). The use of the steady-state assumption to derive kinetic formulations for the transport of a solute across a membrane. In Metabolic Transport. ed. Hokin, L. E., Metabolic Pathways. Vol. 6, Series ed. Greenberg, D. M., Academic Press, New York, pp. 1–15. 268. Epstein, E. and Hagen, C. E. (1952). A kinetic study of the absorption of alkali cations by barley roots, Plant Physiol., 27, 457–474. 269. Briggs, G. E. and Haldane, J. B. S. (1925). A note on the kinetics of enzyme action, Biochem. J., 19, 338–339. 270. Eisenberg, B. (1998). Ionic channels in biological membranes: natural nanotubules, Acc. Chem. Res., 31, 117–123. 271. Barcilon, V., Chen, D. P., Eisenberg, R. S. and Jerome, J. W. (1997). Quantitative properties of steady-state Poisson–Nernst–Plank systems: perturbation and simulation study, SIAM J. Appl. Math., 57, 631–648. 272. Gillespie, D. and Eisenberg, R. S. (2002). Physical descriptions of experimental selectivity measurements in ion channels, Eur. Biophys. J., 31, 454–466. 273. van Leeuwen, H. P. and Kleijn, J. M. (2000). Electrostatic and electrodynamic properties of biological interphases. In Physical Chemistry of Biological Interfaces. eds. Baszkin, A. and Norde, W., Marcel Dekker, New York, pp. 49–84. 274. Aguilella, V., Belaya, M. and Levadny, V. (1996). Ion permeability of a membrane with soft polar interfaces. 1. The hydrophobic layer as the rate-determining step, Langmuir, 12, 4817–4827. 275. Tanford, C. (1983). Mechanism of free energy coupling in active transport, Ann. Rev. Biochem., 52, 379–409. 276. Skou, J. C. (1988). Overview: the Na, K pump, Methods Enzymol., 156, 1–25. 277. Gunther, T. and Ebel, H. (1990). Membrane transport of magnesium. In Metal Ions in Biological Systems. Vol. 26, Compendium on Magnesium and its Role in Biology, Nutrition, and Physiology. eds. Sigel, H. and A. Sigel, A., Marcel Dekker, New York, pp. 215–225.

530 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 278. Sunda, W. G. (1988/9). Trace metal interactions with marine phytoplankton, Biol. Oceanogr., 6, 411–442. 279. Mason, A. Z., Jenkins, K. D. and Sullivan, P. A. (1988). Mechanisms of trace metal accumulation in the polychaete Neanthes areanoceodentata, J. Mar. Biol. Assoc. UK, 68, 61–80. 280. Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, M. and Walter, P. (2002). Molecular Biology of the Cell. 4th edn, Garland Science, New York. 281. Goldstein, B. (1989). Diffusion limited effects of receptor clustering, Comm. Theor. Biol., 1, 109–127. 282. Winne, D. (1973). Unstirred layer, source of biased Michaelis constant in membrane transport, Biochim. Biophys. Acta, 298, 27–31. 283. Lieb, W. R. and Stein, W. D. (1972). The influence of unstirred layers on the kinetics of carrier-mediated transport, J. Theor. Biol., 36, 641–645. 284. Glaser, R. W. (1993). Antigen–antibody binding and mass transport by convection and diffusion to a surface: a two-dimensional computer model of binding and dissociation kinetics, Anal. Biochem., 213, 152–161. 285. Azam, F. and Hodson, R. E. (1981). Multiphasic kinetics for D-glucose uptake by assemblages of natural marine bacteria, Mar. Ecol. Prog. Ser., 6, 213–222. 286. Koch, A. L. and Coffman, R. (1970). Diffusion, permeation, or enzyme limitation: a probe for the kinetics of enzyme induction, Biotechnol. Bioeng., 12, 651–677. 287. McCarthy, J. J. (1981). The kinetics of nutrient utilization. In Physiological Bases of Phytoplankton Ecology. ed. Platt, T., Department of Fisheries and Oceans, Ottawa, Canada. 288. Wheeler, P. A., Gilbert, P. M. and McCarthy. J. J. (1982). Ammonium uptake and incorporation by Chesapeake Bay phytoplankton: short term uptake kinetics, Limnol. Oceanogr., 27, 1113–1128. 289. Zevenboom, W. A., De Vaate, A. B. and Mur, L. R. (1982). Assessment of factors limiting growth rate of Oscillatoria agardhii in hypertrophic Lake Wolder wijd, 1978, by use of physiological indicators, Limnol. Oceanogr., 27, 39–52. 290. Harrison, G. I. and Morel, F. M. M. (1986). Response of the marine diatom Thalassiosira weissflogii to iron stress, Limnol. Oceanogr., 31, 989–997. 291. Zhao, H. and Eide, D. (1996). The yeast ZRT1 gene encodes the zinc transporter protein of a high-affinity uptake system induced by zinc limitation, Proc. Natl Acad. Sci., 93, 2454–2458. 292. Morel, F. M. M., Hudson, R. J. M. and Price, N. M. (1991). Limitation of productivity by trace metals in the sea, Limnol. Oceanogr., 36, 1742–1755. 293. McQuarrie, D. A. (1963). Kinetics of small systems. I, J. Chem. Phys., 38, 433–436. 294. Wiley, H. S. (1988). Anomalous binding of epidermal growth factor to A431 cells is due to the effect of high receptor densities and a saturable endocytic system, J. Cell Biol., 107, 801–810. 295. Starbuck, C., Wiley, H. S. and Lauffenburger, D. A. (1990). Epidermal growth factor binding and trafficking dynamics in fibroblasts: relationship to cell proliferation, Chem. Eng. Sci., 45, 2367–2373. 296. Hassler, C. S., Slaveykova, V. I. and Wilkinson, K. J. (2004). Some fundamental (and often overlooked) considerations underlying the free ion activity and biotic ligand models, Environ. Toxicol. Chem., in press. 297. Price, N. M. and Morel, F. M. M. (1991). Colimitation of phytoplankton growth by nickel and nitrogen, Limnol. Oceanogr., 36, 1071–1077.

K. J. WILKINSON AND J. BUFFLE

531

298. Harrison, G. I. and Morel, F. M. M. (1983). Antagonism between cadmium and iron in the marine diatom Thalassiosira weissflogii, J. Phycol., 19, 495–507. 299. Price, N. M. and Morel, F. M. M. (1990). Cadmium and cobalt substitution for zinc in a marine diatom, Nature, 344, 658–660. 300. Babich, H. and Stotzky, G. (1983). Influence of chemical speciation on the toxicity of heavy metals to the microbiota, Adv. Environ. Sci. Technol., 13, 1–46. 301. Fargasova, A. (1998). Accumulation and toxic effects of Cu2þ , Cuþ , Mn2þ , 2þ VO3
and MoO2
4 and their associations: influence on respiratory rate and 4 , Ni chlorophyll a content of the green alga Scenedesmus quadricauda, J. Trace Micro. Tech., 16, 481–490. 302. Smiejan, A., Wilkinson, K. J. and Rossier, C. (2003). Cd bioaccumulation by a freshwater bacterium, Rhodospirillum rubrum, Environ. Sci. Technol., 37, 701–706. 303. van Ginneken, L., Chowdhury, M. J. and Blust, R. (1999). Bioavailability of cadmium and zinc to the common carp, Cyprinus carpio, in complexing environments: a test for the validity of the free ion activity model, Environ. Toxicol. Chem., 18, 2295–2304. 304. van Veen, H. W., Abee, T. , Kortstee, G. J., Konings, W. N. and Zehnder, A. J. B. (1994). Translocation of metal phosphate via the phosphate inorganic transport system of Escherichia coli, Biochemistry, 33, 1766–1770. 305. Fortin, C. and Campbell, P. G. C. (2001). Thiosulphate enhances silver uptake by a green alga: role of anion tranporters in metal uptake, Environ. Sci. Technol., 35, 2214–2218. 306. Erre´calde, O., Seidl, M. and Campbell, P. G. C. (1998). Influence of a low molecular weight metabolite (citrate) on the toxicity of cadmium and zinc to the unicellular green alga Selenastrum capricornutum: an exception to the free-ion model, Water Res., 32, 419–429. 307. Vassil, A. D., Kapulnik, Y., Raskin, I. and Salt, D. E. (1998). The role of EDTA in lead transport and accumulation by Indian mustard, Plant Physiol., 117, 447–453. 308. Epstein, A., Gussman, C., Blaylock, M., Yeriyahu, U., Huang, J., Kapulnik, Y. and Orser, C. (1999). EDTA and Pb–EDTA accumulation in Brassica juncea grown in Pb-amended soil, Plant Soil, 208, 87–94. 309. Thomas, R. A. P., Lawlor. K., Bailey, M. and Macaskie, L. E. (1998). Biodegradation of metal–EDTA complexes by an enriched microbial population, Appl. Environ. Microbiol., 64, 1319–1322. 310. Vaara, M. (1992). Agents that increase the permeability of the outer membrane, Microbiol. Rev., 56, 395–411. 311. Sunda, W. G. and Huntsman, S. A. (1995). Cobalt and zinc interreplacement in marine phytoplankton: biological and geochemical implications, Limnol. Oceanogr., 40, 1404–1417. 312. Slavik, J. and Smetana, K. (1997). Intracellular pH of macrophages and foreign body giant cells colonising an implant surface, J. Fluores., 7, 203S–205S. 313. Flemstroem, G. and Kivilaakso, E. (1983). Demonstration of a pH gradient at the luminal surface of rat duodenum in vivo and its dependence on mucosal alkaline secretion, Gastroenterology, 84, 787–794. 314. Tran, D., Boudou, A. and Massabuau, J. C. (2001). How water oxygenation level influence [sic.] cadmium accumulation pattern in the Asiatic clam Corbicula fluminea: a laboratory and field study, Environ. Toxicol. Chem., 20, 2073–2080. 315. Scheid, P. and Piiper, J. (1971). Theoretical analysis of respiratory gas equilibration in water passing through fish gills, Respir. Physiol., 13, 305–318.

532 PHYSICOCHEMICAL KINETICS AND TRANSPORT AT BIOINTERFACES 316. Spacie, A., McCarty, L. S. and Rand, G. M. (1995). Bioaccumulation and bioavailability in multiphase systems. In Fundamentals of Aquatic Toxicology. Effects, Environmental Fate and Risk Assessment. ed. Rand, G. M., Taylor and Francis, Washington DC, pp. 493–522. 317. Silver, S. and Misra, T. K. (1988). Plasmid-mediated heavy metal resistances, Ann. Rev. Microbiol., 42, 717–743. 318. Silver, S. and Phung, L. T. (1996). Bacterial heavy metal resistance: new surprises, Ann. Rev. Microbiol., 50, 753–789. 319. Nies, D. H. and Silver, S. (1995). Ion efflux systems involved in bacterial metal resistances, J. Ind. Microbiol., 14, 186–199. 320. Neilands, J. B. (1981). Iron absorption and transport in microorganisms, Ann. Rev. Nutr., 1, 27–46. 321. Neilands, J. B. (1984). Methodology of siderophores, Struct. Bonding, 58, 1–24. 322. Neilands, J. B. (1982). Microbial envelope proteins related to iron, Ann. Rev. Microbiol., 36, 285–309. 323. Volker, C. and Wolf-Gladrow, D. A. (1999). Physical limits on iron uptake mediated by siderophores or surface reductases, Mar. Chem., 65, 227–244. 324. van Leeuwen, H. P. (1999). Metal speciation dynamics and bioavailability: inert and labile complexes, Environ. Sci. Technol., 33, 3743–3748. 325. De Jong, H. G., van Leeuwen, H. P. and Holub, K. (1987). Voltammetry of metal complex systems with different diffusion coefficients of the species involved. Part I. Analytical approaches to the limiting current for the general case including association/dissociation kinetics, J. Electroanal. Chem., 234, 1–16. 326. Pinheiro, J. P., Mota, A. M. and van Leeuwen, H. P. (1999). On lability of chemically heterogeneous systems. Complexes between trace metals and humic matter, Coll. Surf. A. Physicochem. Eng. Aspects, 151, 181–187. 327. Galceran, J., Puy, J., Salvador, J., Cecı´lia, J. and van Leeuwen, H. P. (2001). Voltammetric lability of metal complexes at spherical microelectrodes with various radii, J. Electroanal. Chem., 505, 85–94. 328. van Leeuwen, H. P. and Buffle, J. (1990). Voltammetry of heterogeneous metal complex systems. Theoretical analysis of the effects of association/ dissociation kinetics and the ensuing lability criteria, J. Electroanal. Chem., 296, 359–370. 329. Pinheiro, J. P., Mota, A. M. and Simo˜es Gonc¸alves, M. L. S. (1996). Voltammetry of labile heterogeneous complexes with low diffusion coefficients, J. Electroanal. Chem., 402, 47–55. 330. Filella, M., van Leeuwen, H. P., Buffle, J. and Holub, K. (2000). Voltammetry of chemically heterogeneous metal complex systems. Part II. Simulation of the kinetic effects induced on polarographic waves, J. Electroanal. Chem., 485, 144–153. 331. Garce´s, J. L., Mas, F., Cecı´lia, J., Puy, J., Galceran, J. and Salvador, J. (2000). Voltammetry of heterogeneous labile metal–macromolecular systems for any ligand-to-metal ratio. Part I. Approximate voltammetric expressions for the limiting current to obtain complexation information, J. Electroanal. Chem., 484, 107–119. 332. van Leeuwen, H. P. and Pinheiro, J. P. (1999) Lability criteria for metal complexes in micro-electrode voltammetry, J. Electroanal. Chem., 471, 55–61. 333. van Leeuwen, H. P., Puy, J., Galceran, J. and Cecı´lia, J. (2002). Evaluation of the Koutecky´–Koryta approximation for voltammetric currents generated by metal complex systems with various labilities, J. Electroanal. Chem., 526, 10–18.

K. J. WILKINSON AND J. BUFFLE

533

334. Sunda, W. G. and Huntsman, S. A. (2000). Effect of Zn, Mn, and Fe on Cd accumulation in phytoplankton: implications for oceanic Cd cycling, Limnol. Oceanogr., 45, 1501–1516. 335. Bloss, T., Clemens, S. and Nies, D. H. (2002). Characterization of the ZAT1p zinc transporter from Arabidopsis thaliana in microbial model organisms and reconstituted proteoliposomes, Planta, 214, 783–791. 336. Maranger, R. D., Bird, D. and Price, N. M. (1998). Iron acquisition by photosynthetic marine phytoplankton from ingested bacteria, Nature, 396, 248–251. 337. Nodwell, L. M. and Price, N. M. (2001). Direct use of inorganic colloidal iron by marine mixotrophic phytoplankton, Limnol. Oceanogr., 46, 765–777. 338. Wang, W.-X. and Guo, L. (2000). Bioavailability of colloid-bound Cd, Cr, and Zn to marine plankton, Mar. Ecol. Prog. Ser., 202, 41–49. 339. Honeyman, B. D. and Santschi, P. H. (1992). The role of particles and colloids in the transport of radionuclides and trace metals in the oceans. In Environmental Particles. Vol. 1, eds. Buffle, J. and van Leeuwen, H. P., IUPAC Series on Environmental, Analytical and Physical Chemistry, Lewis Publishers, Chelsea, MI, pp. 379–423. 340. Martin, J.-M., Dai, M.-H. and Cauwet, G. (1995). Significance of colloids in the biogeochemical cycling of organic carbon and trace metals in the Venice Lagoon (Italy), Limnol. Oceanogr., 40, 119–131. 341. Straub, K. L., Hanzlik, M. and Buchholz-Cleven, B. E. E. (1998). The use of biologically produced ferrihydrite for the isolation of novel iron-reducing bacteria, Syst. Appl. Microbiol., 21, 442–449. 342. Urrutia, M. M., Roden, E. E. and Zachara, J. M. (1999). Influence of aqueous and solid-phase Fe(II) complexants on microbial reduction of crystalline iron(III) oxides, Environ. Sci. Technol., 33, 4022–4028. 343. Rich, H. W. and Morel, F. M. M. (1990). Availability of well-defined iron colloids to the marine diatom Thalassiosira weissflogii, Limnol. Oceanogr., 35, 652–662. 344. Chen, M. and Wang, W.-X. (2001). Bioavailability of natural colloid-bound iron to marine plankton: influences of colloidal size and aging, Limnol. Oceanogr., 46, 1956–1967. 345. Wells, M. L., Mayer, L.M, Donard, O. F. X., de Souza Sierra, M. M. and Ackelson, S. G. (1991). The photolysis of colloidal iron in the oceans, Nature, 353, 248–250. 346. Kuma, K., Tanaka, J. and Matsunaga, K. (1999). Effect of natural and synthetic organic–Fe(III) complexes in estuarine mixing model on iron uptake and growth of coastal marine diatom Chaetoceros sociale, Mar. Biol., 134, 761–769. 347. Kuma, K. and Matsunaga, K. (1995). Availability of colloidal ferric oxides to coastal marine phytoplankton, Mar. Biol., 122, 1–11. 348. Shoup, D. and Szabo, A. (1982). Role of diffusion in ligand binding to macromolecules and cell-bound receptors, Biophys. J., 40, 33–39. 349. Northrup, S. H. (1988). Diffusion-controlled ligand binding to multiple competing cell-bound receptors, J. Phys. Chem., 92, 5847–5850. 350. Maddock, J. R. and Shapiro, L. (1993). Polar location of the chemoreceptor complex in the Escherichia coli cell, Science, 259, 1717–1723. 351. Zwanzig, R. (1990). Diffusion-controlled ligand binding to spheres partially covered by receptors: an effective medium treatment, Proc. Natl. Acad. Sci. USA, 87, 5856–5857. 352. Berg, O. and von Hippel, P. H. (1985). Diffusion-controlled macromolecular interactions, Ann. Rev. Biophys. Chem., 14, 131–160.

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Index Note: references to Figures and Tables are indicated by italic page numbers ABC (ATP binding cassette) transporters 298–300 binding protein dependent uptake systems 298–299 of ferric iron type 317–318 systems without autonomous binding protein 300 for uptake of haem 311–317 iron and other metals 318–319 siderophores 311–317, 433 vitamin B12 313–314 absorption isotherms, alkanes in DPPC membranes 91–92, 92 acidity constant, listed for various HIOCs 210–211, 234 actin-driven phagocytosis 375, 376, 379 active mobilisation of substrate, mechanisms 402–403, 415–433 active transport 7, 280, 351, 490 kinetics 490 see also primary active transporters; secondary active transporters activity coefficients, in membrane–water partitioning 223–224 adaptation 1, 114 adhesion, role in substrate mobilisation 411, 413–414 adsorbed substrates compared with solid substrates 423 microbial uptake from 422–423 adsorption to carrier sites 478–485 chemical heterogeneity effects 481–484 and competition among metals 478, 480 rate-limiting adsorption 484–485 ternary complexes and ligand adsorption 480–481

cooperativity in 482–483 equilibrium and rate constants 474–476 Langmuirian, diffusional steady-state approach 175–178, 476 linear (Henry), diffusional steady-state approach 172–175 in transport mechanism for eukaryote membranes 339, 341–344 adsorption processes, and biouptake modelling 193 adsorption/desorption at biological interphases 473–485 kinetics 193 limitations in determination and interpretation of equilibrium and kinetic data 474–478 advection effects on mass transport 459 typical timescale 501 aggregates, mass transfer/transport to cells in 462–463 airborne particles 358 endocytosis of 388–391 sources 388 algae, uptake of metal species by 244, 245 alkane–octanol–chloroform–dibutylether system, as membrane model 218 AlnA protein 427, 429 aluminium, bioaccumulation of 480 amoebocytes, digestion by 382, 384 amoeboid protozoa, assimilation of particles by 379 amphiphiles 21 effect on lipid bilayers 91, 229 anaesthetics effect on lipid bilayers 91, 236 interaction site(s) for 236, 237 anammoxosome 275–276 aniline 209, 210 animal cell membranes 5

Page links created automatically - some may be erroneous 536 anthracene aqueous solubility 419 dissolution by Mycobacterium sp. 419 antibiotics as environmental pollutants 209 as HIOCs 209, 211 antifouling agents 215–216, 370 see also tributyltin antiport 280 antiport systems, secondary active transport by 295–296 antiporter(s) 351 counter-transport on 346–347 solute export from epithelial cells to blood via 348–349 aquaporins 289–290 aquatic complexes classification of 464–465 dissociation kinetics 469–473 thermodynamic stability 466–469 aquatic environment contaminants in 365–371 endocytotic uptake of 379–391 mass-transfer limitations 460–463 separation of dissolved and colloidal fractions 366–367 aquatic invertebrates, endocytosis by 382–388 archaeal (bacterial) species 277 binding proteins 299 uptake of carbohydrates by 284 arrested phase separation 21 asbestos fibres 388–389 assimilation efficiency of cadmium 386 of chromium 386 meaning of term 384 models 383–386 of silver 369 of zinc 386 atomic force microscopy (AFM), erythrocyte membrane 5 ATP binding cassette transporters see ABC transporters ATP synthetase, inhibition of 240, 251 ATPases 297–298, 316–317 solute export from epithelial cells to blood via 349 availability of chemical species 1, 114 factors affecting 3, 114

INDEX bacteria growth kinetics 409 membranes 6, 274–278 specific affinity of substrate uptake, listed 408 surfactants produced by 364, 423, 426, 427, 429 uptake of environmental chemicals 416 from liquid substrates 420–422 from solid substrates 419–420 from sorbed substrates 422–423 without cell wall peptidoglycans 277–278 see also Gram-negative bacteria; Grampositive bacteria; mycobacteria bacterial adhesion parameter 414 role in substrate mobilisation 411, 413–414 bacterial cell membranes 6, 274–278 cytoplasmic membranes 274–275 substrate transport across 289–302 iron transport across 302–321 substrate transport across 278–321 cytoplasmic membranes 289–302 future research 321 iron species 302–321 mycobacterial cell walls 288–289 outer membrane of Gram-negative bacteria 285–288 various approaches 278–285 bacterial cell wall(s) charge on 116 thickness 116 water-dissolved state for uptake by 417 Best equation 9, 156, 184, 411, 491 binding protein dependent ABC-type importers 298–299 binding protein dependent secondary transporters 296–297 binding proteins interactions with integral membrane proteins 299 structures 299 bioaccumulation of aluminium 480 of cadmium 386 of chromium 386 of HIOCs 239 kinetic approach 385 meaning of term 384

Page links created automatically - some may be erroneous INDEX of metals as colloidal complexes 367–368 of polonium-210 386–387 of silver 368 of tributyltin 251, 370–371, 387 of zinc 386 see also assimilation efficiency bioaffinity parameter 151, 156, 182 bioavailability effect of speciation 8–9, 370 iron, factors affecting 8–9, 178, 216, 244, 302, 303 physicochemical processes affecting 449 terms used for 384 bioconcentration factor (BCF) 239 organotin compounds 251 silver 369 bioemulsifiers 423, 427–429 biofilms, mass transfer/transport to cells in 462–463 biological interactions, metal speciation and 207–208 biological interphases adsorption/desorption at 473–485 electrodynamics at 120–122 interaction with HIOCs 220–241 effects of speciation of HIOCs 238–241 partitioning and sorption models 220–226 pH dependence of membrane–water partitioning 227–231 sites of interactions 236–238 sorption of HIOCs to charged membranes 233–236 speciation in membrane 232–233 thermodynamics of membrane–water partitioning 226–227 interaction of hydrophobic metal complexes 245–247 interaction with metal species 241–245 binding to biological ligands 241–244 and free ion activity model 242, 243 uptake of specific complexes 244–245 interaction with organometallic compounds 248–251 ionic distributions at 117–119 biological membranes

537 complexity 30–31 components 3–4 models 7, 17 sorption of HIOCs to 233–236 thickness (average) 3 trace element transport across 485–499 biosurfactants 364, 423 applications 427 mobilisation of hydrophobic organic substrates using 423–429 production by microbes 364, 423, 426, 427, 429 biotic ligand model (BLM) 9, 244, 449 applicability 450–451, 501 basis 450, 473 biouptake, physicochemical processes leading to 448–452 biouptake modelling 147–195 future research areas 190–194 mass transfer coupled with chemical reaction 178–190 refinements based on adsorption processes adsorption isotherm and kinetics 193 competition 193 refinements based on internalisation factors efflux 194 kinetics 194 refinements based on mass transfer factors complex media 192–193 finite media 190–192 nonstagnant media 192 uncomplicated mass transfer 150–178 bivalves, feeding and digestion in 380, 381, 382–383 Blasius solution (for velocity profile) 131 borderline metals (complexation classification) 465 boundary conditions, in mass transfer 124, 151–152 boundary value problem 124 Bragg–Williams approach 52 Brownian dynamics (BD) simulation 45 BtuC2 D2 complex 314 crystal structure 316, 317 BtuF protein 313–314

Page links created automatically - some may be erroneous 538 cadmium uptake by aquatic invertebrates 386 uptake by particles 366 canonical ensemble 32 carbohydrates 4 uptake by bacteria 284 carbon fixation at leaf surfaces, mass transfer coefficients for 141 carcinogens asbestos fibres 389 nickel compounds 390 carrier-mediated transport 280 kinetics 487–490 carriers adsorption to 478–485 affinity constants listed 479 chemical heterogeneity effects 481–484 and competitive uptake of metals 478, 480 rate-determining adsorption 484–485 for ternary complexes 480–481 numbers/concentration 476–478 rate-determining adsorption of metal to 484–485 rate-limiting adsorption of metals to 484–485 requirements in diffusion-limited uptake 509–510 cation–chloride co-transporters 346 caveolae 378 cavities in membranes, and permeation of small molecules 94–95 cell membrane 1–2 factors affecting transport through 4–5, 371–372 see also bacterial cell membranes cell surface hydrophobicity 414 cell wall(s) 2–3, 115 charge on 116 Donnan partition characteristics 3, 115 Gram-positive bacteria 6, 276–277 iron transport across 308–309 cellular drinking see pinocytosis cellular eating see phagocytosis channelled laminarly flowing liquid, convective diffusion from 135–137 channels in cytoplasmic membranes of bacteria 289–292 gas channels 292

INDEX mechanosensitive channels 291–292 MIP channels 289–291 hydrophilic 95 ion-selective 97–99 transmembrane 97–99 see also ion channels chaperones 278, 340, 347 chemical heterogeneity effects 472, 481–484, 504 chemical potential 223 chemical speciation biouptake affected by 205–252 meaning of term 207, 463 see also speciation chemoattractants 415 chemotaxis 415 to poorly bioavailable substrates 415–416 chlorocatechols 215 chlorophenols, bioconcentration in fish 239, 240 chloroplasts 10, 11 cholesterol, effect on lipid bilayers 90–91 chromatophores 275 chromium in airborne particles 390–391 speciation 216 uptake by aquatic invertebrates 383, 386 ciprofloxacin 209, 211 classification of transport systems 280–281, 282 clathrin-coated pits/vesicles (in endocytosis) 374, 378 clathrin-dependent pinocytosis 377, 378 clay colloids, properties 461 clofibric acid 209, 210 cluster size distribution, factors affecting 56 coarse graining (in molecular modelling) 45, 53 colloidal bound metals 216, 242, 244 bioavailability 508–509 colloidal complexes, bioaccumulation of metals as 367–368 colloidal fraction 366 separation from dissolved fraction 366–367 colloidal particles, binding to cell membrane 376

Page links created automatically - some may be erroneous INDEX colloidal suspensions, properties 361 colloids as absorbents 362 binding of metals to 216, 242, 244 coagulation and precipitation of 362 measurement of particle size 360–361 size range 216, 360 competition among metals adsorption to carriers 478, 480 for same ligand, Eigen–Wilkens mechanism not applicable 471 complexation 463–469 interpretation of metal complexation data 468–469 kinetics 217 typical timescales 501 complexes aquatic classification of 464–465 dissociation kinetics 469–473 thermodynamic stability 466–469 fully labile, mass transfer coupled with chemical reaction 180–182 inert limiting permeability 502 mass transfer coupled with chemical reaction 180 labile, limiting permeability 502 partially labile, mass transfer coupled with chemical reaction 182–186 see also metal complexes; organic complexes composite media, diffusion in 127–129 concentration factor in aquatic environment 367–368 see also bioconcentration factor conservation of mass 122 conservation of momentum 122 constant-capacitance model 225 constant-pressure/surface-tension ensemble 32 contamination soils, remediation of 365 continuous affinity spectrum, complexation data interpreted using 468 convective diffusion 129–141 from channelled laminarly flowing liquid 135–137

539 from liquid to moving spherical body 137–141 from unbounded laminarly flowing liquid to plane surface 130–135 in nonstagnant media 192 velocity profile derivation 130–131 cooperativity, in adsorption 482–483 copper, speciation 214–215, 242 copper complexes, interactions with biological interphases 246–247 copper–fulvic acid complexes, dissociation of 472, 473 coral-reef supply of nutrients, mass transfer coefficients for 141 Corynebacterium cells, electrophoretic mobility 121, 122 co-transport 280, 345–346 Coulombic interactions 36 coupled diffusion of metal and complex 180 coupled systems, Eigen–Wilkens mechanism not applicable 471 creeping flow around a sphere 137, 138 critical micellisation concentration (c.m.c.) 22, 424 cross-flow filtration (CFF) technique 360 curvature energy, as function of ionic strength 80, 82 curvature-induced membrane-structural changes 78–79 curved interface, surface tension calculation 27 curved membrane systems 27–28 cytoplasmic membrane see cell membrane; intracytoplasmic membrane cytoplasmic membrane, bacterial 274–275 architecture 274–275 channels in 289–292 functions 274 group translocators 300–302 primary active transporters 297–300 secondary active transporters 292–297 siderophore transport across 433 transport across 289–302 Damko¨hler number 124, 183 Davies equation 223–224 DCT1 (divalent cation/metal ion transporter) 379 Debye length 117

Page links created automatically - some may be erroneous 540 dictyosomes 10 diesel exhaust particles 389–390 differential equilibrium factor (DEF), complexation data interpreted using 468–469 diffuse double layer 115–116, 225, 361 diffusion in composite media 127–129 convective 129–141 Fick’s law(s) 87, 413, 452–453, 486–487 role in substrate mobilisation 410–411, 412, 501–502, 505 typical timescale 501 diffusion layer distinction from hydrodynamic boundary layer 132 thickness calculations 134, 137, 139, 453–454 diffusion-limited uptake concentration profiles at biological interphase 505 implications 508–510 bioavailability of colloidal bound metal 508–509 carrier requirements 509–510 in phytoplankton 507 research required 511–512 diffusional steady-state (dSS) approach 157, 170–178 advantage 171–172 basis 170–172 Langmuirian adsorption 175–178 linear adsorption 172–175 diffusive mass transfer/transport 452–455 kinetics 486–487 radius effects 162–163, 185, 453 specific affinity as driving force for 409–410 digestion, by aquatic invertebrates 380–388 3,4-dimethylaniline, lipophilicity profile 221 dinitro-o-cresol, lipophilicity profile 221 dinoseb 209, 210 dipalmitoylphosphatidylcholine (DPPC) bilayer DPD simulation results 46 MD simulation 40–44

INDEX as substrate for polyelectrolyte brush 84–86 dipole potentials, of biomembranes 43, 96, 116 dissipative particle dynamics (DPD) method 45–46 dissociation kinetics aquatic complexes 469–473 with simple ligands 469–470 typical timescales 501 distribution ratio see membrane–water distribution ratio dithiocarbamate metal complexes 215, 246 DMPC bilayer membrane–membrane interactions 83 SCF simulation 63–65, 66 Donnan layer 117–118 Donnan partition characteristics, cell wall(s) 3, 115 Donnan potential 118, 343, 351 DPPC bilayer see dipalmitoylphosphatidylcholine bilayer dynamin 372, 375 EAA motif 299 Eigen–Wilkens mechanism 469–470 application to aquatic complexes 470–472 conditions to which not applicable 470–471 for heterogeneous ligands 472, 473 electric double layer 2–3, 115, 361 Gouy–Chapman model 56, 68, 117, 225, 361 insignificance in some transport processes 121 time constant for 120 electrochemical gradient destruction of 240–241 as driving force in ion channels 489 electrochemical potential 6 electrodynamics, at biological interphases 120–122 electrostatic potential profiles DMPC bilayer 67 DPPC bilayer 44 lipid bilayers 43, 44, 67–68, 67 polyelectrolyte-modified lipid 85

Page links created automatically - some may be erroneous INDEX emulgating agents 427 emulsan 428 emulsification compared with micellar solubilisation 428 mobilisation of liquid substrates by 427–429 see also bioemulsifiers endocytosis 10, 14, 359, 372–379 by aquatic invertebrates 382–388 criteria required in future 392 receptor-mediated 373, 378–379 by terrestrial invertebrates 388 endocytotic pathways 373–375 endoplasmatic reticulum (ER) 10 endosomes 373 ensembles 32–33 enterobactin receptor 287, 305 EntS protein 303 enzymes, extracellular, substrate mobilisation by 9, 429–430, 498 epithelial cells 338 co-transport in 345–346 counter-transport in 346–347 intracellular trafficking 347–348 solute export from 348–349 solute import into 344–347 solute transfer across 339–341 equilibrium dialysis 219 Escherichia coli iron(II) transport system 309 outer membrane transport proteins 287, 303, 305, 306, 311–317 symport systems 293, 294 ethylenediaminetetraacetate (EDTA) complexes 212–213 eukaryote cells intracellular environment 347 intracellular membranes 10 intracellular trafficking in 347–348 phagocytosis in 375 see also epithelial cells eukaryote epithelium 339–341 eukaryote membranes, solute transport across 337–352 adsorption step 339, 341–344 export step 339, 348–349 fundamental processes 338–341 import step 339, 344–347 intracellular trafficking 347–348 evolutionary adaptations 1, 114, 434

541 Ewald method 38 excess-of-ligand approximation 180 exocytosis 10, 373, 374 exo-enzymes 9, 429, 498 exopolymers 363, 459 extended single point charge (SPC/E) model 38 external surface area of organisms, ways of achieving 404 extracellular chelators 244, 303, 431, 498–499 see also siderophores extracellular digestion 380 extracellular enzymes 9 substrate mobilisation by 429–430, 498 facilitated diffusion see carrier-mediated transport; uniport FAs see fulvic acids FbpA (ferrin-binding protein) 318 FecA (ferric citrate transporter) 306–307 feo type transport systems 309–310 FeoB protein 309 FepA enterobactin receptor 287, 305 crystal structure 288 ferrichrome structure 307 transporter for 287, 305, 306 FhuA protein 287, 305, 306 FhuB protein 314–315 interaction with FhuC protein 317 interaction with FhuD protein 314 transmembrane arrangement in cytoplasmic membrane 315–316 FhuC protein 316–317 interaction with FhuB protein 317 FhuD protein 312–314 compared with other binding proteins 313 crystal structure of complex with gallichrome 312, 313 interaction with FhuB protein 314 Fick’s law(s) of diffusion 87, 413, 452–453, 486–487 field flow fractionation (FFF) technique 360 film diffusion 418 fish accumulation of HIOCs in 239, 240 accumulation of methylmercury in 248 copper toxicity 246, 247

Page links created automatically - some may be erroneous 542 fish gills mass transfer processes 342, 343, 498, 499 rapid solution dipping experiments 342–344 see also gill microenvironment flocs formation of 192 mass transfer/transport to cells in 462–463 Flory–Huggins (FH) interaction parameters 57, 58 listed 62 fluid motion, mass transfer/transport affected by 455–459 laminar flow 130–137, 456–458 convective diffusion from channelled liquid 135–137 convective diffusion from unbounded liquid to planar surface 130–135 steady, uniform flow 456–458 turbulent flow 458–459 fly-ash 389 free-ion activity model (FIAM) 9, 187, 449 applicability 450–451, 501 basis 450 exceptions/limitations 189, 507, 511 and mass transfer coupled with chemical reaction 186–190 metal species interacting with biological interphases 242, 243 and toxicity of silver 369 fulvic acid(s) 213 dissociation of copper–fulvic acid complexes 472, 473 interactions with biological interphases 245 fungicides 209, 210, 215 gas channels, in cytoplasmic membranes of bacteria 292 Gaussian bending modulus, curved membrane 28, 80, 81 gel-state membrane 76–77 MD modelling of 77 SCF modelling of 77 gel-to-liquid phase transition, lipid bilayers 18–19 gel-to-liquid phase transition temperature, lipid bilayers, factors affecting 73–74 gill epithelial cells 338

INDEX gill microenvironment 342, 351 GlpF protein 290–291 glucose, uptake by bacteria 283–284 glycerol channels 290–291 glycerol-3-phosphate transporter (GlpT) 295 glyceryl trioleate–water system, as membrane model 218 Goldman–Hodgkin–Katz equation 6 Golgi vesicles 10 Gouy–Chapman model 56, 68, 117, 225, 361–362 gradient operator(s), listed for various geometries 126 Gram-negative bacteria binding proteins 298–299 inner membrane 274 outer membrane 6, 274, 276 iron transport across 303–308, 432 proteins 278–279 transport across 285–288 periplasm 274–275 uptake of ferric siderophores by 312 Gram-positive bacteria binding proteins 299 cell walls 6, 276–277 iron transport across 308–309 uptake of ferric siderophores by 312 gramicidine 97 grand canonical ensemble 32 group translocators 300–302 GTPases 372, 375 haem, ABC transporters for 311–317 haemocytes, in invertebrates 381 haemoglobin 303, 304 haemopexin 303, 304 Haemophilus influenzae, iron uptake by 320 haemophores 303, 304, 304 half-saturation constant 151 hard metals (complexation classification) 465 HAs see humic acids HbpA and HbpB proteins 319 Helfrich analysis, for charged bilayer systems 79–80, 81 Helicobacter pylori, iron uptake by 309–310 Henderson–Hasselbalch equation 228 Henry adsorption coefficient 160

Page links created automatically - some may be erroneous INDEX heterogeneity parameter, variabilities 481–482 HitA protein 318 hopanoids 4 humic acids 213, 362–363 interactions with biological interphases 245 humic substances adsorption of 481 as ligands in complexes 464 properties 461 hydrocarbon chains 20 hydrocarbon–water interface 20–21 hydrocarbon–water repulsion 55, 62–63 hydrodynamic boundary layer/ region 131–132 distinction from diffusion layer 132 hydrophilic channels 95 hydrophilic organic complexes 212–215 hydrophilic particles, charging of 361 hydrophobic anions, membrane-binding capability compared with cations 229 hydrophobic cell walls, adhesion to 414 hydrophobic colloids 361 hydrophobic effect 19–20 hydrophobic ionogenic organic compounds (HIOCs) 208–209 bioaccumulation of 239 bioavailability 207 examples of environmentally relevant HIOCs 209–211 interactions with biological interphases 220–241 effectsofspeciationofHIOCs 238–241 future research 251–252 sites of interactions 236–238 and ion trapping 238 meaning of term 208 membrane–water partitioning of 230 redox speciation of 211 site of interaction with membranes 236–238 sorption to charged membranes/ vesicles/biological membranes 233–236 speciation 207, 232–233 toxicity 207, 239–241 see also amphiphiles hydrophobic metal complexes 215 interaction with biological interphases 245–247

543 hydrophobic organic substrates, mobilisation using biosurfactants 423–429 hydrophobicity cell surface 414 octanol–water partition coefficient as descriptor 217, 220 ibuprofen 209, 210 IhtA and IhtB proteins 320 imposex 370 inert complexes, limiting permeability 502 inorganic complexes, speciation 212 instantaneous steady-state approximation (ISSA) method 169, 191 integral membrane proteins (IMPs) 298 interactions with binding proteins 299, 315 integrated approach to transport studies 12–13 interaction sites of HIOCs with membranes 236–238 dielectric properties 237–238 SCF modelling 237 interdigitation in lipid bilayers 23, 24, 66 interfacial acidity constant 232–233 derivation from lipophilicity profiles 232, 233 internal dipole moment, of lipid bilayer 229 internal membrane potentials 116 internalisation of trace elements cellular responses affecting 492–496 coupled dynamic processes 499–510 indirect biological responses affecting 497–499 population responses affecting 496–497 internalisation kinetics, effect on biouptake modelling 194 internalisation mechanisms, dependence on organism types 491 internalisation rate constant 160 determination methods 495 factors affecting 494–496 typical values 495

Page links created automatically - some may be erroneous 544 internalisation routes with one adsorption-only route 155–156 two parallel steady-state limit for 156–159 transient model for 150–156 typical results 153–155 internalisation sites 150 intracellular digestion 380 intracytoplasmic membranes 275–276 invertebrates aquatic body fluid osmotic pressure 338 endocytosis by 382–388 haemocytes in 381 toxicity of tributyltin 370 terrestrial, endocytosis by 388 ion channels 95, 97–99 in cytoplasmic membranes of bacteria 289–292 driving force for 489 in eukaryote membranes 345 kinetics of transport in 489–490 molecular dynamics modelling of 97–99 solute export from epithelial cells to blood via 348 ion pair formation at membrane interphases 228, 231–232 partitioning affected by 220 ion pair partitioning 220 ion-selective transmembrane protein channels 97 ion trapping, HIOCs 238 ionic distributions at biological interphases 117–119 in phosphatidylcholine bilayers 68 ionic pumps 7 ions, partitioning in bilayers, SCF calculations 56, 91 IraA and IraB proteins 319 iron bioavailability, factors affecting 8–9, 178, 216, 244, 302, 303 endocytosis of airborne particles affected by 389 as essential element 302, 303 mobilisation by siderophores 178, 244, 303, 430–433 redox reactions 216 role in bacteria 302–303 transport in bacteria 302–321

INDEX across cell walls of Gram-positive bacteria 308–309 across outer membranes of Gramnegative bacteria 303–308 as model systems 321 outlook 320–321 phlogenetic aspects 320 translocation across cytoplasmic membrane 309–319 iron(III) binding sites on siderophores 244, 432 colloids 216, 244 in ocean surface waters 431 solubility 430 iron transferrin receptor complex (in endocytosis) 374, 379 IsdA protein 309 Kþ channels 98–99 KcsA (potassium channel) 98–99, 99 kinetics adsorption/desorption 193 dissociation of complexes 469–473 ligand-exchange reactions 217 of transport processes 281, 486–490 caution in interpretation 491–499 Kolmogorov length 458 labile but immobile complexes, limiting permeability 502 labile complexes, mass transfer coupled with chemical reaction 180–182 labile and mobile complexes, limiting permeability 502 lability criteria 183–184, 503 radial diffusion 185, 503 Lactobacillus plantarum 431 lactoferrins 303, 304 sequestration of iron from 308, 318 lactose permease 293–294 LacY protein 293 ladderanes 276 lakewater, organic complexes in 214, 215 LamB porin 286 laminarly flowing fluids, mass transfer/ transport in 130–137, 456–458 landfill leachates 246–247 Langmuirian adsorption 150–151, 155, 226 diffusional steady-state approach 175–178

Page links created automatically - some may be erroneous INDEX one site adsorbing and internalising 175, 176 two sites 176–178 in phagocytosis 377 Laplacian operator(s) 125 listed for various geometries 126 large unilamellar vesicles (LUVs) 28 lateral compressibility, lipid bilayers 74–75 lateral pressure profile, in bilayers 69–70 lateral tension, membranes under 83 lattice-fluid models 56–57 lattice-gas models 56–57 lead(II), biouptake of, factors affecting 185–186 lead chromate particles, endocytosis of 390–391 Legionella pneumophilia, iron uptake by 319 Lennard–Jones interaction energy 36 Le´veˆque approximation 136, 137 ligand excess, effect on uptake 504 ligand-exchange reactions, kinetics 217 ligands, properties 461 limiting conditions for uptake processes 500–502 biological uptake limitation 501 diffusion limitation 501–502 limiting flux ratios 156, 182, 500 limiting permeability 500 biological uptake limitation 501 diffusion limitation 502 linear adsorption, diffusional steady-state approach 172–175 linear adsorption coefficient 160 linear adsorption limit 160–170 lipid bilayer membranes, conductivities 120, 121 lipid bilayers 2, 3 assumptions made in surfactant parameter approach 23 head-group orientation 66–67 interdigitation in 23, 24, 66 internal dipole potentials 43, 96, 116 mechanical parameters 78–82 models 31–86 moleculardynamicssimulation 17,18,35 phase transition 18–19 self-consistent-field simulation 63–69 size-dependency of small-molecule permeation 90, 95

545 surface tension calculations 28 thickness 65 see also dipalmitoylphosphatidylcholine bilayer; DMPC bilayer; phosphatidylcholine (PC) bilayer; phospholipid bilayers lipids 4 charged, in bilayers 75–76 phase behaviour 30, 100 SCF simulation 54–55 lipophilicity profiles 221 propranolol in various liposomes 235 lipopolysaccharides 276 liposomes 26, 218–219 separation of 219 uptake affected by 426 see also vesicles liquid phases/substrates, uptake of 420–422 local friction coefficient 94 relationship to local diffusion coefficient 94 lysosomal membrane fragility 380–381 lysosomes 373 Macoma balthica (clam), bioaccumulation of metals by 369, 384 macrophages, endocytotic action 380 Major Facilitator Superfamily (MFS) transporters 292–293, 296 major intrinsic protein (MIP) channels 289–291 manganese, uptake of, effects of cellular adaptation 493, 494 ˇ elja bilayer membrane model 60 MarC ‘marine snow’ 363–364 Markov processes 54, 61 mass transfer/transport 113–141, 452–463 boundary conditions 124 conservation laws 122, 123 coupled with chemical reaction 178–190 and free ion activity model 186–190 fully labile complexes 180–182 inert complexes 180 labile complexes 180–186 mathematical formulation 178–180 partially labile complexes 182–186 diffusional steady-state approach 157, 170–178

Page links created automatically - some may be erroneous 546 mass transfer/transport (contd.) diffusive 452–455 effects of fluid motion 455–459 general equations 122–129 geometry effects 125 limitation in aquatic systems 460–463 for cells in aggregarates, biofilms, and flocs 462–463 for rapidly accumulating compounds 460–462 for slowly diffusing compounds 462 linear adsorption limit 160–170 analytical solution for steady state 160–161 analytical solution for transient 161–162 approach to steady state after maximum 163–165 cumulative plot 168–170 impact of radius 162–163 model formulation 160 time to reach steady state 165–167 size effects organism size 459 solute size 460 steady-state conditions 125, 127 transient conditions 125, 127 uncomplicated 150–178 diffusional steady-state approach 170–178 linear adsorption limit 160–170 steady-state limit 156–159 transient model 150–156 Mayer–Saupe interactions 60 MC see Monte Carlo simulation technique MD see molecular dynamics mean bending modulus, curved membrane 80, 81 mean-field approximation 51 see also self-consistent-field method mean-field potential 51 mechanosensitive ion channels 291–292 mecoprop 209, 210 mediated transport processes 11 molecular dynamics modelling of 97–99 MelB symporter 294 membrane interphases, ion pair formation at 231–232 membrane–membrane interactions, SCF modelling of 83–84

INDEX membrane models biological membranes 219 liposomes 218–219 octanol–water system 217 solvent–water systems 218 membrane phase, speciation in 232–233 membrane potentials 6 membrane tension 24–26 effect of undulation entropy 26 membrane transport processes 371–372 membrane–water distribution ratio 227–228 and ion-pair formation 231 membrane–water partition coefficient 224 thermodynamics 226–227 membrane–water partitioning general derivation of partition coefficients 223–226 pH dependence 227–231 thermodynamics 226–227 membranes meaning of term 21 role 273 site of interaction of HIOCs 236–238 mercury species uptake of 246, 249 see also organomercury compounds metal complexes classification 464–465 interaction with biological interphases 245–247 properties 461 thermodynamic stability 466–469 uptake of specific complexes by microorganisms 244–245 metal oxides, as ligands in complexes 464 metal speciation 211–217 and biological interactions 207–208 metal species binding to biological ligands 241–244 interaction with biological interphases 241–245 metallothioneins 461, 465 metals, classification by complexation properties 465 methylmercury 215 bioaccumulation of 248, 249 Metropolis scheme 47 MFS (Major Facilitator Superfamily) transporters 292–293, 296

Page links created automatically - some may be erroneous INDEX micellar solubilisation compared with emulsification 428 substrate mobilisation by 424–427 micelles 21, 364–365 substrate mobilisation in 424–426 Michaelis–Menten coefficient 151, 476, 491 Michaelis–Menten equation 409, 476 Michaelis–Menten kinetics 151, 406, 409, 476, 488 assumptions 488 compared with Monod kinetics 409, 497 limitations 491–492 mineral oils extraction from rock 427 microbial uptake from 421–422 MIP (major intrinsic protein) channels 289–291 mitochondria 10 MntH co-transporter 310–311 mobilisation of organic compounds, reasons for studying 403–404 mobilisation of substrate see substrate mobilisation molecular dynamics (MD) simulation method advantage 34 box 34–35 coarse-grained 44–46 compared with SCF simulation, for SOPC bilayers 70–74 dipalmitoylphosphatidylcholine bilayers 40–44 force field 35–39 hybrid MC/MD approaches 48 limitations 39 lipid bilayers 17, 18, 33–46 mediated membrane transport modelling by 97–99 molecular structure representation 35, 36 permeation processes investigated by indirect technique 94, 95 strategy 33–34 time and length scales 39–40 molecular modelling ensembles 32–33 of lipid bilayers 31–86 molecules, transport across membranes 11

547 molluscs, digestion by 380, 381, 382–383 Monod kinetics, compared with Michaelis–Menten kinetics 409, 497 monodispersed liquid substrate, uptake from 422 Monte Carlo (MC) simulation technique 46–51 box 47–48 hybrid MC/MD approaches 48 molecular model 47–48 pragmatic approximations 48 strategy 46–47 typical results 49–51 MscL channel 291–292 MscS channel 292 MspA porin 288–289 multiplicity of ligands, Eigen– Wilkens mechanism not applicable 471 murein sacculus 6, 275 mycobacterial cell walls 277 transport through 288–289 Mycobacterium sp. LB501T biofilm development on 418–419 factors affecting adhesion 414 specific affinity for substrate uptake 408 substrate uptake driven diffusive transfer data 412 mycolic acids 414 Mycoplasma (bacterial) species 277 Mytilus edulis (common mussel), bioaccumulation of metals by 369, 383, 385, 386, 387 Naþ channels 97 Naþ =H þ transporters 295–296 Naþ =Kþ channel 490 Naþ /proline transporter 294 natural ligands adsorption of 480–481 dissociation kinetics of complexes 472 Nernst diffusion layer concept 134–135 Nernst distribution coefficient 127 Nernst layer approximation 181 Nernst–Planck equation 6–7, 87, 114, 123, 451–452, 489 combined with Poisson equation 489, 490 diffusive term 127–128 without conduction term 129

Page links created automatically - some may be erroneous 548 Neutral Red (dye) retention time 380 NhaA antiporters 295–296 nickel compounds, endocytosis of 390 nisin 279 nitrilotriacetate (NTA) 212–213 noble gases, distribution in bilayers 89, 90 nonaqueous liquids, uptake by bacteria 420–422 nonmediated transport processes pore mechanism 95–97 solubility–diffusion mechanism 86–95 Nramp proteins 310–311, 379 nuclear envelope 10 octadecane, microbial uptake of 426 octanol 217 octanol–water partition coefficent 217, 220 listed for various HIOCs 210–211 octanol–water partitioning 220–222 octanol–water system, as membrane model 217 Ohshima–Kondo model 118–119, 119 oil droplets, microbial uptake from 422 oil extraction applications 427 OmpF porin 285, 286 one-gradient self-consistent-field (1DSCF) theory 53 Onsager reciprocal relation 47 optimised parameters for liquid systems (OPLS) method 38 order parameter for lipid bilayers 42–43, 49–50, 68–69 MC simulation 49, 50 MD simulation 43 SCF simulation 69 organic complexes hydrophilic 212–215 hydrophobic 215 organic compounds speciation of 207, 208–211 see also hydrophobic ionogenic organic compounds (HIOCs) organism–medium interphase 1–3, 115–122 dimensions of various layers 2 ionic distributions 117–119 physicochemical characteristics 115–117

INDEX organolead compounds, interactions with biological interphases 248 organomercury compounds 215 interactions with biological interphases 248 organometallic compounds 215–216 interactions with biological interphases 248–251 organotin compounds 215–216 interactions with biological interphases 248–251 outer membrane (in Gram-negative bacteria) 6, 274, 276 iron transport across 303–308 proteins 278–279 TonB-dependent receptors 287 transport across 285–288 Overton rule 87 oxalinic acid 209, 211 particles hydrophilic 361 larger 363–364 organic coatings 362–363 size measurement of 360–361 partition coefficient as function of molecular weight 91 and molecular structure 93–94 partitioning in bilayers 88–94 membrane–water 223–231 models 220–226 octanol–water 220–222 passive mechanisms of substrate mobilisation 405–414 passive transport 7, 280 kinetics 486–487 pathogenic bacteria, factors affecting virulence 303, 304, 318, 319 Pe´clet number 129 pentachlorophenol 209, 210 pentachlorophenoxide interaction site 238 ion pair 220 peptides, properties 461 peptidoglycans 6, 275 bacteria devoid of 277–278 as ligands in complexes 464 periphyton uptake, mass transfer coefficients for 141

Page links created automatically - some may be erroneous INDEX permeabilities values for various phytoplankton 506 see also limiting permeability permeability of membranes 238, 239 permeation of molecules across membranes dynamic aspects 94–95 equilibrium aspects 88–94 persistence length hydrocarbon chains 20 membrane 29 pesticides as environmental pollutants 209 as HIOCs 209, 210 pH dependence, membrane–water partitioning, with HIOCs 227–231 phagocytosis 372, 373, 375–377, 419 phase separation, arrested 21 phase transition, lipid bilayers 18–19 PhoE porin 285, 286 phosphatidylcholine (PC) bilayer acidity constant of lipid 234 effect of tail lengths 74–75 electrostatic potential profiles 44, 67 head-group orientation 66–67, 72, 238 interdigitation in 66 ion distributions 68 molecular dynamics simulation 35 self-consistent-field simulation 63–69 sorption of HIOCs to 233–236 see also dipalmitoylphosphatidylcholine bilayer; DMPC bilayer phosphatidylethanolamine, in microbial membranes 279 phosphatidylserine (PS) lipids 75–76, 234 phosphoenolpyruvate (PEP), in carbohydrate uptake 301 phospholipid bilayer, as surrogate for biological membrane 219 phospholipids 4 acidity constants listed 234 phosphotransferase systems (PTS) 280, 300–302 photosynthesis, trace-element uptake affected by 498 phototrophic bacteria, intracytoplasmic membranes 275 physicochemical processes, conceptual model for 449, 480 phytochelatins 461, 465

549 phytoplankton, uptake by effect of fulvic and humic acids 245 mass transfer coefficients for 141 rate-limiting step 505–508 pinocytosis 373, 374, 377–378, 420 clathrin-dependent pathway 377 plant cell membranes 5–6 plasma membrane 371 see also cell membrane plastids 10 pneumococci, uptake of iron by 308 Poisseuille velocity profile 135–136 Poisson–Boltzmann equation 56, 58 Poisson equation 59 combined with Nernst–Planck equation 489, 490 for Donnan layer 118 polonium-210, bioaccumulation by aquatic invertebrates 386–387 polyelectrolyte brush, substrate for 84–86 polyelectrolytic effect 467–468 polyfunctionality effect 468 polymer brush theory 84, 92 polymers, transport across membranes 11 polysaccharides in exopolymers 363 as ligands in complexes 464 as membrane components 4, 6 properties 461 population response, trace element internalisation affected by 496–497 pore mechanism, for nonmediated transmembrane transport 95–97 porins general, as channels 285–286, 429 selective 286 porphyrins 461, 465 potassium channels 98–99 Prandtl layer 131 pre-lysosomes 373 primary active transport 280, 351, 490 primary active transporters 297–300 ABC transporters 298–300 ATPases 297–298 decarboxylation-driven 300 light absorption-driven 300 methyltransfer-driven 300 oxidoreduction-driven 300

Page links created automatically - some may be erroneous 550 prokaryote membranes 10–11, 274–278 nutrient acquisition 283–284 solute transport across 271–321 transporters control of number of active molecules 284–285 examples 283–284, 283 propranolol interaction site 237 lipophilicity profiles in various liposomes 235 proteins as membrane components 4, 278 properties 461 transport of 278–279 protonophoric shuttle mechanism 240–241 PsaA protein 314, 319 PspA protein 308 PutP transporter 294 pyoverdin 432 quantitative structure–activity relationships (QSARs), hydrophobicity in 217 r-strategists 433 radius effects, on diffusive mass transfer 162–163, 185, 453 rate constants, adsorption at membrane surface 475 rate-limiting adsorption of metals to carriers 484–485 rate-limiting diffusion implications 508–510 bioavailability of colloidal bound metal 508–509 carrier requirements 509–510 phytoplankton 507 reaction layer thickness 503 receptor-mediated endocytosis (RME) 373, 378–379 redox conditions, effects on organic compounds 211 redox reactions, metal species 216 relaxation time constant, electric double layer 120, 121 respiration processes, trace-element uptake affected by 498 retention efficiency, meaning of term 384

INDEX rhamnolipids 364, 426–427 rotational isomeric state (RIS) schemes 54, 61 sacculus (around bacterium) 6, 275 saddle-shaped membranes 82 scaled-particle theory 90 Scatchard data treatment, complexation data interpreted using 468 SCF see self-consistent-field method Schultze–Hardy rule 361 ScrY porin 286, 287 secondary active transport 280, 351, 490 secondary active transporters 292–297 antiport systems 295–296 binding protein dependent 296–297 symport systems 293–294 uniport systems 293 sediment-quality guidelines 391 sediments effect on uptake of TBT 387 factors affecting toxicity 365–366, 369 silver species in 369 segment potentials, SCF method 57–61 self-assembling systems, thermodynamics 25 self-assembly 21 self-consistent anisotropic field (SCAF) theory 61, 77 self-consistent-field (SCF) method 51–86 advantages 51, 100 box 53–54 case studies 74–86 charge lipids in bilayers 75–76 effect of hydrocarbon tail lengths 74–75 gel-phase of DPPC bilayers 76–77 mechanical parameters of lipid bilayers 78–82 membrane–membrane interactions 83–84 substrate for polyelectrolyte brush 84–86 compared with MD simulation, for SOPC bilayers 70–74 computation time compared with MD simulation 51 dynamics incorporated in calculations on lipid bilayers 100

Page links created automatically - some may be erroneous INDEX equilibrium properties predicted by 89, 100 force-field parameters 62 interaction sites studied by 237 lateral pressure profile 69–70 molecules 54–57 ions 56 lattice models 56–57 lipids 54–55 water 55–56 phosphatidylcholine bilayers 63–69 segment potentials 57–61 solution 61–63 strategy 52–53 semi-labile complexes, lability criterion 503–504 Sfu systems 317–318 shape of organism, effects on mass transport 459 Sherwood number 129 Shp protein 309 siderophores 178, 244–245, 303, 430–433 ABC transporters for 311–317, 433 binding sites on 244, 432 properties 461 structural types 244–245, 303, 432 synthesis of 431–432 transport though outer membrane of Gram-negative bacteria 303, 432–433 signal transduction cascade 11 silver bioaccumulation of 368–370 diffusion-limited uptake of 462 Singer–Nicholson fluid mosaic model 7, 17 compared with surfactant parameter approach 24 single point charge (SPC) model 38, 39 single-chain mean-field theory 61 slime layers 6, 84 synthesis of 84 small unilamellar vesicles (SUVs) 28 Smf proteins 310 Smoluchowski rate constant 509 sodium channels 97 sodium–substrate cotransport carriers 294 soft metals (complexation classification) 465

551 soil bacteria, chemotaxis 415 soils, contaminated soils, remediation of 365 solid phases/substrates compared with adsorbed substrates 423 solubility 216 uptake of 372–379, 419–420 solubility–diffusion mechanism for nonmediated transmembrane transport 86–95 limitations 96 solute transport eukaryotes 337–352 prokaryotes 271–321 solvent–water systems, as membrane models 218 sophorolipid 427 sorbed substrates, uptake of 422–423 speciation bioavailability affected by 8–9, 207 biouptake affected by 205–252 HIOCs, at biological interphases 238–241 in membranes 232–233 metal 211–217 organic compounds 207, 208–211 specific affinity of substrate uptake 405–409 definition 407 as driving force for diffusive transfer 409–410 listed for various bacteria 408 spherical body, moving, convective diffusion to 137–141 spontaneous curvature 27 square-well potential 55 staphylococci, uptake of iron by 308–309 statistical mechanics/thermodynamics 32 StbA protein 309 steady-state conditions, for mass transfer 125, 127 steady-state diffusion layer, thickness 3, 115 steady-state limit, for two parallel internalisation routes 156–159 1-stearoyl-2-oleoyl-sn-glycero-3phosphatidycholine (SOPC) representation of molecular structure in MD simulation 36 in SCF simulation 64

Page links created automatically - some may be erroneous 552 1-stearoyl-2-oleoyl-sn-glycero-3phosphatidylcholine (SOPC) bilayer conformational properties of acyl chains 72–73 ionic profile 72 molecular dynamics simulation 17, 18 molecular modelling of, MD compared with SCF methods 70–74 orientation of PC head-group 72 Stern layer 56, 361 Stern model 225 sterols 4 Stokes–Einstein equation 460 streptococci, iron uptake by 308, 309 stress-induced adhesion 84 strong ligands, in complexes 465 substrate cotransport 280, 293–294 see also symport substrate diffusion, role in substrate mobilisation 410–411, 412 substrate mobilisation active mechanisms 415–433 biosurfactants used 423–429 chemotaxis 415–416 extracellular enzymes used 429–430 iron 429–433 various physical states 416–423 active vs passive mechanisms 402–403 limits 433–434 mechanisms and principles 404–405 passive mechanisms 405–414 adhesion, role of 411, 413–414 diffusion, role of 410–411 specific affinity 405–410 physical factors affecting substrate uptake 416–423 purpose 404 sugar–phosphate/anion antiporters 295 sugar-specific porins 286, 287 sugars as membrane components 4, 6 uptake via PEP-dependent PTS mechanism 301–302 surface charge density 224–225 dependence on surface potential 225 surface freezing 20 surface potential, of biomembrane 43 surface tension curved interface 27 hydrocarbon/water interface 21 lipid bilayers 74, 75

INDEX surfactant packing parameter 22 surfactant parameter approach 22 assumptions made 22–24 compared with Singer–Nicholson fluid mosaic model 24 surfactants 21, 364, 423 effect on lipid bilayers 91 surfactin 425 surrogate membranes 217–219 symport 280 symport systems, secondary active transport by 293–294 symporter(s) 352 co-transport on 345–346 TBT see tributyltin teichoic acids 6, 276 terrestrial invertebrates, endocytosis by 388 tetracaine (local anaesthetic), interaction site for 236, 237 tetraethyllead 248 tetraphenylborate ions, binding sites in lipid bilayers 236 thermodynamics membrane–water partitioning, with HIOCs 226–227 solute transfer across eukaryote cell 341 Thiele modulus 124 thylakoid membranes 10, 11 time constant, for electric double layer 120 timescales, of various uptake processes 501 timolol, site of interaction 237 TonB, activation of 307–308 TonB-dependent outer-membrane proteins/receptors 287, 288, 305–307 role in utilisation of iron 304 tonoplasts 10 toxicity HIOCs 207, 239–241 hydrophobic metal complexes 246–247 Tpn protein 308–309 trace element internalisation cellular responses affecting 492–496 coupled dynamic processes 499–510 indirect biological responses affecting 497–499

Page links created automatically - some may be erroneous INDEX

553

population responses affecting 496–497 trace elements, transport across biological membranes 485–499 transferrin 303, 304 transferrin receptor 308 transition metals role in cells 486 transport of 310–311 transmembrane channels 97–99 transmembrane potential(s) 116–117 ‘transport commission’ (classification) system 281, 282 transport processes mediated 11 molecular modelling of 97–99 nonmediated pore mechanism 95–97 solubility–diffusion mechanism 86–95 prokaryotic membranes 271–322 classification of 280–281 driving forces 280 energy-coupling modes 280 regulation of 285 types 11–12 typical timescales 501 transport proteins 278–279 Treponema denticola, iron uptake by 319 tributyltin (TBT) 215–216, 248–249, 251 bioaccumulation of 251, 370–371, 387 triclosan 209, 210 triolein–water system, as membrane model 218 triphenyltin (TPT) 215–216, 248–249, 250–251 TroA protein 314, 319 turbulent flow, mass transfer/transport in 458–459 uncoupling effect 239–241 undersaturated systems, uptake of trace metals in 484 undulation entropy, membrane tension affected by 26 undulations, in vesicles 29 uniport 280 uniport systems, secondary active transport by 293

unsaturated lipids, effects on biomembranes 73–74 unstirred layer at fish gill epithelium 342, 343 see also steady-state diffusion layer vacuoles 10 valinomycin 98 vertebrates, body fluid osmotic pressure 338 vesicles 26–30, 275 preparation of 28, 218 SCF analysis of 78–82 sorption of HIOCs to 233–236 thermodynamics stability 83 vitamin B12 ABC transporters for 313–314 receptors in outer membrane of Gram-negative bacteria 303 Volmer isotherm 226 Volta potential 117 von Heijne’s ‘positive inside’ rule 279 Walker A and Walker B motifs 299, 316, 317 water H-bonds 19, 48 in MD simulation 35 in SCF simulation 55–56 segregation of hydrocarbons 19–20, 55 as solvent 19 unique properties 19 water-dissolved substrates, uptake by bacteria 416–419 water ‘wires’, proton transport along 96–97 whole-cell Michaelis–Menten equation 406, 407, 408 xenobiotics, binding site(s) for 236, 237 zeta-potentials 116 zinc diffusion-limited uptake of 462 uptake by aquatic invertebrates 386 zwitterionic compounds, lipophilicity profiles 222, 222

With kind thanks to Paul Nash for creation of this index.

Plate 1 (Figure 1, Chapter 2, p. 18).MA molecular view of a small section of a flat lipid bilayer generated by molecular dynamics simulations. The bilayers are composed of 1-stearoyl-2docosahexaenoyl-sn-glycero-3-phosphatidylcholine lipids, i.e. the sn1 chain is 18 C atoms long and the sn2 chain has 22 carbons including 6 cis double bonds. The hydrophobic core is in the centre of the picture and the hydrated head-group regions are both on top and bottom of the view graph. The head group is zwitter-ionic and no salt has been added. From [102]. Reproduced by permission of the American Physical Society. Copyright (2003)

Plate 2 (Figure 3, Chapter 2, p. 36).MRepresentation of molecular structure in MD simulations. Shown here is the SOPC lipid, discussed in the text. The numbers at each atom indicate the partial charge on the atom. The space-filling picture on the left gives insight into the van der Waals radii of the various groups and thus into the shape of the molecule

Plate 3 (Figure 4, Chapter 2, p. 37).MTypical snapshot of a start configuration in MD simulation. Plate 1 resulted after equilibration of this initial guess. From [102]. Reproduced by permission of the American Physical Society. Copyright (2003)

Plate 4 (Figure 8, Chapter 2, p. 46).MTypical snapshot of DPD simulation results [64]. The hydrophobic part of mixed bilayers of DPPC-like lipids and up to 0.8 mole-fraction of the nonion surfactant C12E6 (left) and 0.9 (right). The surfactant C12 chains are represented by green curves, the lipid C15 chains are black. The hole in the left conformation is transient, at the right they are stable. Reproduced by permission of the Biophysical Society

Plate 5 (Figure 4, Chapter 6, p. 287).MAtomic structure of the sucrose specific selective porin ScrY isolated from the outer membrane. Longer loops are directed to the outside, shorter turns are facing the periplasm. Monomer and assembled homotrimer in side view (left and middle); top view of assembled trimer (right). (Reproduced by permission of W. Welte and A. Brosig)

Plate 6 (Figure 5, Chapter 6, p. 288).MCrystal structure of FepA, the TonB dependent receptor for ferric-enterochelin. (Reproduced by permission of D. van der Helm and L. Esser)

(a)

(b)

(c) Plate 7 (Figure 8, Chapter 6, p. 306).MStructure of the Escherichia coli FhuA protein serving as receptor for ferrichrome and the antibiotic albomycin. (a), side view; (b), side aspect with partly removed barrel to allow the view on the “cork” domain; (c), top view. A single lipopolysaccharide molecule is tightly associated with the transmembrane region of FhuA (reproduced by permission of W. Welte and A. Brosig)

Plate 8 (Figure 12, Chapter 6, p. 315).MTransmembrane arrangement of the polytopic FhuB protein in the cytoplasmic membrane as determined by the analysis of ß-lactamase proteins Cterminally fused to various portions of FhuB. The FhuB protein is composed of two times 10 membrane spanning regions connected by loops contacting the periplasm or the cytoplasm. These loops were predicted to entirely or partly fold back into the overall structure. The conserved regions (CR) typical of all prokaryotic importers belonging to the ABC transporter family are shown in red. They are important for the interaction with the FhuC protein—the ATPase supplying energy for the siderophore translocation process

Plate 9 (Figure 13, Chapter 6, p. 316).MCrystal structure of the BtuC2D2 complex involved in the uptake of vitamin B12. Two copies of the polytopic integral membrane protein BtuC are shown in blue and green. The two copies of the ATPase subunit BtuD are coloured orange and yellow. Bound ATP is presented in pink (reproduced by permission of K. Locher). For more details see the text