Quantitative Modeling in Toxicology

Quantitative Modeling in Toxicology

Quantitative Modeling in Toxicology Editors KANNAN KRISHNAN D´epartement de sant´e environnementale et sant´e au travail, Ecole de sant´e publique & Facult´e de m´edecine, Universit´e de Montr´eal, Montr´eal, Canada MELVIN E. ANDERSEN Program in Chemical Safety Sciences, The Hamner Institutes for Health Sciences, Research Triangle Park, NC, USA

A John Wiley and Sons, Ltd., Publication

This edition first published 2010
C 2010 John Wiley & Sons Ltd Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com. The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. 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 or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. 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This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for every situation. In view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of experimental reagents, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each chemical, piece of equipment, reagent, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. The fact that an organization or Website is referred to in this work as a citation and/or a potential source of further information does not mean that the author or the publisher endorses the information the organization or Website may provide or recommendations it may make. Further, readers should be aware that Internet Websites listed in this work may have changed or disappeared between when this work was written and when it is read. No warranty may be created or extended by any promotional statements for this work. Neither the publisher nor the author shall be liable for any damages arising herefrom. Library of Congress Cataloging-in-Publication Data Quantitative modeling in toxicology / editors, Kannan Krishnan, Melvin E. Andersen. p. ; cm. Includes bibliographical references and index. Summary: “In Quantitative Modeling in Toxicology leading experts outline the current state of knowledge on the modeling of dose, tissue interactions and tissue responses. Each chapter describes the mathematical foundation, parameter estimation, challenges and perspectives for development, along with the presentation of a modeling template. Additionally, tools and approaches for conducting uncertainty, sensitivity and variability analyses in these models are described”–Provided by publisher. ISBN 978-0-470-99809-0 (cloth) 1. Toxicology–Mathematical models. I. Krishnan, Kannan, 1961- II. Andersen, Melvin E. [DNLM: 1. Toxicology–methods. 2. Environmental Exposure–adverse effects. 3. Hazardous Substances–toxicity. 4. Models, Biological. 5. Toxicity Tests–methods. QV 602 Q13 2010] RA1199.4.M37Q36 2010 615.9001 5118–dc22 2009045991 A catalogue record for this book is available from the British Library. ISBN 978-0-470-99809-0 Typeset in 10/12pt Times by Aptara Inc., New Delhi, India. Printed and bound in Great Britain by CPI Antony Rowe, Chippenham, Wiltshire. The figure on the front cover, showing the “cusp catastrophe surface” for a biological feedback loop, illustrates the dynamic behavior for different selections of binding affinities. Steady-state values for the interacting proteins are plotted against respective binding affinities. The arrow indicates those sets of affinities where an abrupt, discrete transition would be observed, as expected for processes such as cellular differentiation. The region of the surface “under the fold” represents the parameter range where the system is bistable. The reader is referred to Chapter 10 for further discussion of this behavior.

Contents

Preface About the Editors About the Book List of Contributors

ix xi xiii xv

SECTION 1 INTRODUCTION 1

Quantitative Modeling in Toxicology: An Introduction Melvin E. Andersen and Kannan Krishnan

3

SECTION 2 PHYSIOLOGICALLY-BASED TOXICOKINETIC AND PHARMACOKINETIC (PBPK) MODELING 2

PBPK Modeling: A Primer Kannan Krishnan, George D. Loizou, Martin Spendiff, John C. Lipscomb and Melvin E. Andersen

21

3

Pharmacokinetic Modeling of Manganese – An Essential Element Andy Nong, Michael D. Taylor, Miyoung Yoon, and Melvin E. Andersen

59

4

Physiologically Based Modeling of Pharmacokinetic Interactions in Chemical Mixtures Sami Haddad, Robert Tardif, Jonathan Boyd, and Kannan Krishnan

5

Physiological Parameters and Databases for PBPK Modeling Douglas O. Johns, Elizabeth Oesterling Owens, Chad M. Thompson, Babasaheb Sonawane, Dale Hattis and Kannan Krishnan

83

107

SECTION 3 MODELING TOXICANT-TARGET INTERACTIONS 6

Modeling Cholinesterase Inhibition Charles Timchalk, Paul M. Hinderliter, and Torka S. Poet

137

vi

Contents

7

Modeling of Protein Induction and Dose-Dependent Hepatic Sequestration Andy Nong and Melvin E. Andersen

167

8

Bistable Signaling Motifs and Cell Fate Decisions Sudin Bhattacharya, Qiang Zhang, and Melvin E. Andersen

181

9

Ultrasensitive Response Motifs in Biochemical Networks Qiang Zhang, Sudin Bhattacharya, Courtney G. Woods, and Melvin E. Andersen

199

10 Gene and Protein Expression – Modeling Nested Motifs in Cellular and Tissue Response Networks Melvin E. Andersen, Qiang Zhang, and Sudin Bhattacharya 11 Modeling Liver and Kidney Cytotoxicity Kai H. Liao, Yei M. Tan, Harvey J. Clewell III, and Melvin E. Andersen

219

235

SECTION 4 MODELING TISSUE AND ORGANISM RESPONSES 12 Computational Model for Iodide Economy and the HPT Axis in the Adult Rat Jeffrey W. Fisher and Eva D. McLanahan 13 Two-Stage Clonal Growth Modeling of Cancer Rory B. Conolly and Melvin E. Andersen 14 Statistical and Physiological Modeling of the Toxicity of Chemicals in Mixtures Hisham A. El-Masri, Michael A. Lyons, and Raymond S.H. Yang 15 (Q)SAR Models of Adverse Responses: Acute Systemic Toxicity Mark T.D. Cronin, Yana K. Koleva, and Judith C. Madden

253

269

283

299

SECTION 5 MODEL APPLICATION AND EVALUATION 16 Modeling Exposures to Chemicals From Multiple Sources and Routes Panos G. Georgopoulos, Sastry S. Isukapalli, and Kannan Krishnan 17 Probabilistic Reverse Dosimetry Modeling for Interpreting Biomonitoring Data Yu-Mei Tan and Harvey J. Clewell III

317

353

Contents

18

Quantitative Modeling in Noncancer Risk Assessment Q. Jay Zhao, Lynne Haber, Melissa Kohrman-Vincent, Patricia Nance, and Michael Dourson

19

Application of Physiologically Based Pharmacokinetic Modeling in Health Risk Assessment Harvey J. Clewell III

20

Uncertainty, Variability, and Sensitivity Analyses in Simulation Models Sastry S. Isukapalli, Martin Spendiff, Panos G. Georgopoulos and Kannan Krishnan

21

Evaluation of Quantitative Models in Toxicology: Progress and Challenges Kannan Krishnan and Melvin E. Andersen

Index

vii

371

399

429

459

477

Preface

The goal of most toxicology studies is to help reach some conclusion about likely risks posed to humans or to other species from chemical exposures. Test results, both from in vivo and in vitro studies, require various forms of extrapolation to make risk predictions for specific exposures and in specific populations. Over the past 50 to 60 years, a variety of modeling tools have emerged that help in describing toxicological processes quantitatively and in making these extrapolations. These quantitative models have substantially improved our understanding of human exposure, pharmacokinetics, mode of action and toxic responses associated with chemicals. In recent years, toxicology, as true for other biological disciplines, has also been enriched by the new tools from genomic biology and by the increasing emphasis on computational systems biology for describing cell and tissue function. The opportunity now exists for toxicology to transition from a qualitative science cataloging responses in various animal species to a discipline capable of quantitatively describing key mechanistic processes that determine dose-response behaviors for animal and human responses. Quantitative modeling in toxicology includes approaches that simulate (i) exposure and disposition of chemicals in the body, (ii) biochemical interaction between toxic moiety and target tissues, (iii) molecular and cellular alterations emanating from the initial interactions; and (iv) adverse responses at the organ or organism level. Properly developed, these quantitative mechanistic models can provide unambiguous, testable statements of working hypotheses regarding chemical uptake, biochemical interactions, and the initiation and progression of toxicity in the exposed organism. Integration of quantitative tools within experimental design, data collection and analysis as well as risk assessment applications is more important than ever. Specifically, these tools are important (i) for conducting scientifically sound extrapolations of dosimetry and responses for risk assessment purposes, (ii) for refining/reducing animal use in toxicology studies by facilitating the development of new, novel and efficient experiments, and (iii) for creating a framework with which to integrate the various observations (exposure, dose, mechanism, response) at a quantitative level. Despite the growth in interest in these quantitative models in toxicology, there are few resources to serve as a guide in learning more about these tools. The two of us, along with other colleagues, have taught modeling courses at our respective institutions through lectures and computer demonstrations. In these courses, we have also felt the need for a concise overview of quantitative modeling in toxicology and began discussions leading to this book. Quantitative Modeling in Toxicology now brings together contributions from key scientists on the modeling of exposure, tissue dose, tissue interaction and toxicological responses. Chapters 2-5 describe the quantitative models of pharmacokinetics of individual chemicals

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Preface

and mixtures. Chapters 6 through11 describe models for toxicant-target tissue interaction. Chapters 12 through 15 describe models for cellular, organ, and organism responses. The simulation models of toxic effects based on the toxicant-target interaction models and mode of action information are highlighted with specific examples. Finally, Chapters 16 through 21 present the approaches, tools and challenges regarding the application and evaluation of quantitative models for exposure and risk assessments. Based on the breadth of the material in these chapters, this book should serve as an initial reference for toxicologists and risk assessors who are interested in developing quantitative models for a better understanding of dose-response relationships. The process of simulation modeling requires writing computer code to represent the biological systems and the consequences of exposure. The models are written in a computer language and then solved by numerical integration. The examples throughout the book use a variety of commercial software, including ACSL
C , BERKELEY MADONNA
C , MATLAB
C , EXCEL
C and MEGen
C . We do not endorse any particular software and did not require our contributors to use any particular software. In general, the source code developed in one language can be easily recoded into alternative language. Code for running various models in the book have been included in specific chapters and made available for download from the publisher. The text files for these models are intended to assist the interested reader in developing models for their own use or for use for instruction. We would appreciate comments from our readers about the value of these models for learning more about quantitative modeling in toxicology. Needless to say, the completion of this work was in large part due to our group of talented authors. Thanks to all! We also thank Richard Davies of Wiley for his enthusiasm and cooperation throughout this project as well as Michelle Gagn´e and Mathieu Valcke of Universit´e de Montr´eal for editorial assistance. KK and MEA

About the Editors . . .

Kannan Krishnan, PhD, DABT, FATS is Professor of Occupational and Environmental Health at Universit´e de Montreal and Director of the Inter-University Toxicology Research Center (CIRTOX), Montreal, Canada. An expert in the areas of PBPK modeling, chemical mixture toxicology and health risk assessment methods, Dr. Krishnan has held visiting scientist/faculty appointments at the Karolinska Institutet, Sweden (2004), Toxicology Excellence for Risk Assessment (TERA, Cincinnati, OH) (2007) and Environmental & Occupational Health Sciences Institute of UMDNJ-Rutgers University, NJ (2007). He received the Veylian Henderson Award of the Society of Toxicology of Canada (2000) and the SOT Board of Publications Award for the best paper in Toxicological Sciences (2003) for a land-mark publication on the PBPK modeling of metabolic interactions and health risk assessment of chemical mixtures. He was a significant contributor to the U.S. EPA report “Approaches for the Application of Physiologically Based Pharmacokinetic (PBPK) Models and Supporting Data in Risk Assessment” (2006) and IPCS/WHO guidance document “Characterization and application of PBPK models in support of risk assessment” (2010). Melvin Ernest Andersen, PhD, DABT, CIH, FATS is Director, Program in Chemical Safety Sciences at The Hamner Institutes for Health Research, Research Triangle Park, NC, U.S.A. He is reknown for his career contributions in developing quantitative models of the dosimetry and effects of drugs and toxic chemicals as well as applying these models in safety assessments and quantitative health risk assessments, Through short-courses in quantitative modeling in toxicology, Dr Andersen has trained several hundred toxicologists and risk assessors in quantitative modeling. An author or a co-author of 325 papers and 60 book chapters, he has received several awards for professional contributions; including the Herbert Stokinger Award (American Conference of Industrial Hygienists, 1988), the

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About the Editors . . .

Kenneth Morgareidge Award (International Life Sciences Institute, 1989), the George Scott Award (Toxicology Forum, 1993), and the Frank R. Blood (1982), Achievement (1984), and Arnold J. Lehman (2004) Awards from the Society of Toxicology. Recognized as a ‘highly cited’ scientist by the Institute for Scientific Information (June 2002), Dr. Andersen co-edited a 2005 book, “Physiologically Based Pharmacokinetics: Science and Applications”.

About the Book . . .

Quantitative modeling in toxicology is a must-read for those interested in computer simulation of the biological fate and effects of chemicals. It brings together a diverse group of experts in this area to provide the reader with the current state of knowledge regarding the modeling of dose, tissue interactions and tissue responses. Additionally, tools and approaches for model evaluation and application are described. Access to an electronic MODEL LIBRARY containing the source code for several dosimetry, toxicant interaction and toxicity models is included with the book in order to allow the interested reader to reconstruct the examples in the various chapters. This book will be of particular interest to graduate students, practicing toxicologists and risk assessors who are fascinated by the application of quantitative modeling approaches to simulate perturbations of biological systems upon exposure to xenobiotics.

List of Contributors

Melvin E. Andersen Program in Chemical Safety Sciences, The Hamner Institutes for Health Sciences, Research Triangle Park, NC, USA Sudin Bhattacharya Division of Computational Biology, The Hamner Institutes for Health Sciences, Research Triangle Park, NC, USA Jonathan Boyd C Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, WV, USA Harvey J. Clewell III Center for Human Health Assessment, The Hamner Institutes for Health Sciences, Research Triangle Park, NC, USA Rory B. Conolly Integrated Systems Toxicology Division, National Health and Environmental Effects Research Laboratory, Office of Research and Development, US Environmental Protection Agency, Research Triangle Park, NC, USA Mark T.D. Cronin School of Pharmacy and Chemistry, Liverpool John Moores University, Byrom Street, Liverpool, England Michael L. Dourson

Toxicology Excellence for Risk Assessment, Cincinnati, OH, USA

Hisham A. El-Masri Integrated Systems Toxicology Division, National Health and Environmental Effects Research Laboratory, US EPA, Research Triangle Park, NC, USA Jeffrey W. Fisher

College of Public Health, University of Georgia, Athens, GA, USA

Panos G. Georgopoulos Computational Chemodynamics Laboratory, Environmental and Occupational Health Sciences Institute (EOHSI), Piscataway, NJ, USA Lynne T. Haber

Toxicology Excellence for Risk Assessment, Cincinnati, OH, USA

Sami Haddad D´epartement des sciences biologiques, Centre TOXEN, Universit´e du Qu´ebec a` Montr´eal, Montr´eal, Qu´ebec, Canada Dale Hattis Marsh Institute Center for Technology, Environment and Development, Clark University, Worcester, MA, USA

xvi

List of Contributors

Paul M. Hinderliter Center for Biological Monitoring and Modeling, Pacific Northwest National Laboratory, Richland, WA, USA Sastry S. Isukapalli Computational Chemodynamics Laboratory, Environmental and Occupational Health Sciences Institute (EOHSI), Piscataway, NJ, USA Douglas O. Johns National Center for Environmental Assessment, US Environmental Protection Agency, Research Triangle Park, NC, USA Melissa J. Kohrman-Vincent OH, USA

Toxicology Excellence for Risk Assessment, Cincinnati,

Yana K. Koleva School of Pharmacy and Chemistry, Liverpool John Moores University, Byrom Street, Liverpool, England Kannan Krishnan Groupe de recherche interdisciplinaire en sant´e et D´epartement de sant´e environnementale et sant´e au travail, Universit´e de Montr´eal, Montr´eal, Canada Kai H. Liao Drug Safety and Metabolism, Wyeth Research, Pearl River, NY, USA John Lipscomb National Center for Environmental Assessment, US Environmental Protection Agency, Cincinnati, OH, USA George Loizou Computational Toxicology Section, Health and Safety Laboratory, Buxton, United Kingdom Michael A Lyons Quantitative and Computational Toxicology Group, Colorado State University, Fort Collins, CO, USA Judith C. Madden School of Pharmacy and Chemistry, Liverpool John Moores University, Byrom Street, Liverpool, England Eva D. McLanahan Patricia M. Nance

College of Public Health, University of Georgia, Athens, GA, USA Toxicology Excellence for Risk Assessment, Cincinnati, OH, USA

Andy Nong The Hamner Institutes for Health Sciences, Research Triangle Park, NC, USA. Current address: Health Canada, Ottawa, Ontario, Canada Elizabeth Oesterling Owens Postdoctoral Fellow, Oak Ridge Institute for Science and Education, National Center for Environmental Assessment, US Environmental Protection Agency, Research Triangle Park, NC, USA Torka S. Poet Center for Biological Monitoring and Modeling, Pacific Northwest National Laboratory, Richland, WA, USA

List of Contributors

xvii

Babasaheb Sonawane National Center for Environmental Assessment, US Environmental Protection Agency, Washington, DC, USA Martin Spendiff Computational Toxicology Section, Health and Safety Laboratory, Buxton, United Kingdom Yu-Mei Tan Center for Human Health Assessment, The Hamner Institutes for Health Sciences, Research Triangle Park, NC, USA Robert Tardif Groupe de recherche interdisciplinaire en sant´e, D´epartement de sant´e environnementale et sant´e au travail, Universit´e de Montr´eal, Montr´eal Canada Michael D. Taylor

Environmental Science, Afton Chemical Corp., Richmond, VA, USA

Chad M. Thompson National Center for Environmental Assessment, U.S. Environmental Protection Agency, Washington, DC, USA; Present address: ToxStrategies, Houston, TX, USA Charles Timchalk Center for Biological Monitoring and Modeling, Pacific Northwest National Laboratory, Richland, WA, USA Courtney G. Woods Division of Computational Biology, The Hamner Institutes for Health Sciences, Research Triangle Park, NC, USA Raymond S. H. Yang Quantitative and Computational Toxicology Group, Colorado State University, Fort Collins, CO, USA Miyoung Yoon Division of Computational Biology, The Hamner Institutes for Health Sciences, Research Triangle Park, NC, USA Qiang Zhang Division of Computational Biology, The Hamner Institutes for Health Sciences, Research Triangle Park, NC, USA Q. Jay Zhao U.S. Environmental Protection Agency, Office of Research and Development, National Center for Environmental Assessment, Cincinnati, OH, USA

Section 1 Introduction

1 Quantitative Modeling in Toxicology: An Introduction Melvin E. Andersen1 and Kannan Krishnan2 1

2

The Hamner Institutes for Health Sciences, USA D´epartement de sant´e envrionnementale et sant´e au travail, University of Montreal, Canada

1.1 Introduction 1.1.1

Models and Modeling – Definitions

Models are simplified representations of a system with the intent of reproducing or simulating the structure, function or behavior of the system. Depending upon the goal, the models can be physical, conceptual, or mathematical. The mathematical models, also referred to as quantitative models, correspond to one or more equations whose solution provides the timespace evolution of the state variable (Bellomo and Preziosi, 1995). Quantitative modeling is, therefore, the process of developing mathematical descriptions of the interrelationships among input parameters in order to adequately simulate the system behavior (i.e., generate model output). The quantitative models can be classified in a number of ways. For example: r Discrete or continuous r Deterministic or stochastic r Empirical or mechanistic. A quantitative model is discrete if the state variable does not depend upon the time variable (Bellomo and Preziosi, 1995); the continuous or dynamic models describe the change in state variable over time. A model is deterministic if its outcome is a direct consequence of Quantitative Modeling in Toxicology
C 2010 John Wiley & Sons, Ltd

Edited by Kannan Krishnan and Melvin E. Andersen

4

Quantitative Modeling in Toxicology: An Introduction

the initial conditions, not influenced by any random factors; it is stochastic or probabilistic when some or all features of the model capture a random behavior. The empirical or data based models correspond to equations that emulate the observed data. These models require no prior knowledge of the system but require that both the input and output be known a priori. An example of this kind of models is the one-compartmental pharmacokinetic model, which describes the relationship between the blood concentration at any time t (Ct ) as a function of initial concentration (Co ) and elimination rate (k): Ct = Co e−kt The mechanistic models are based on “first principles” or key mechanisms of the process of interest. Here, the compartments mimic system elements and the equations describe the quantitative relationship among system elements or key parameters to generate predictions of system behavior. Many simulation models in practice, however, may consist of mechanistic and empirical components. The motivation for the use of quantitative simulation models in toxicology is related to one or more of the following needs (Andersen, Clewell, and Frederick, 1995): r r r r r r r r r

Organize and codify facts and beliefs. Expose contradictions in existing data/beliefs. Explore implications of beliefs about the system. Expose serious data gaps. Predict response under new conditions. Predict parameter values for “inaccessible” parameters. Identify essentials of system structure. Provide representation of current state of knowledge. Suggest and prioritize new research.

In the follow section, a short review of chemical risk assessment is provided to help understand the motivation for developing quantitative systems modeling in toxicology.

1.1.2 Evolution of Chemical Risk Assessment To a large extent, the development of quantitative modeling tools in toxicology parallels the increasingly sophisticated understanding of modes of action of toxic chemicals in the body and the desire to apply this information to improve quantitative chemical risk assessment. In this regard, mode of action represents the nature of the initial interactions between a toxic compound and the biological system, and the steps that ensue from this interaction leading to adverse downstream consequences for the organism. Initially, little information on modes of action was available. In safety assessments in the 1950s for instance, animal toxicity test results were used to determine No-Observed Effect Levels (NOELs). The US Food and Drug Administration (FDA) derived acceptable daily intakes (ADIs) by dividing animal NOELs by 100 (Lehman and Fitzhugh, 1954). The factor of 100 consisted of two safety factors of 10 each, intended in a general way to account for (1) differences in sensitivity of humans compared to animals and (2) variation in sensitivity of individuals in a heterogeneous human population compared to more homogeneous sensitivity in inbred

Introduction

5

animal stains. These ADIs were usually established based on organ or organism level responses that were clearly adverse to health. An underlying premise in this approach was the existence of a threshold dose, that is, the belief that there were concentrations or exposure levels below which the risk of adverse health effects was zero. The dose measure for these evaluations was administered dose, for example, ppm in air or food or mg/kg for orally administered materials. The 1970s brought a focus on the biology of cancer and a shift of testing and research resources in toxicology toward chemical carcinogenesis (Albert, Train, and Anderson, 1977). Animal studies provided information of the incidence of tumors at specific doses in test animals, usually rats and mice. Two extrapolations were introduced: one predicted the shape of the dose-response curve at low levels of response; the second adjusted the expected responses for different species. The low dose extrapolation used a mathematical model of carcinogenesis, the linearized multistage (LMS) model. This model predicted some probability of increased cancer incidence at every dose, no matter how small. Interspecies extrapolation was calculated on a surface area adjustment for dose. This body surface extrapolation regarded humans as more sensitive to toxic responses than the smaller rodent species. The concept of dose was initially refined by toxicologists who borrowed methods from the field of clinical pharmacokinetics (PK) to assess the relationship between exposure, sometimes called administered dose, and the concentrations of active chemical/metabolites at target tissues. The initial emphasis on pharmacokinetic modeling in toxicology arose mainly due to the high doses used in many animal tests, doses at which capacity limited processes, that is, metabolism, tubular excretion in kidney, and so on, became saturated. Work with vinyl chloride carcinogenesis showed a better relationship between metabolized dose of this compound and liver cancer rather than a correspondence with inhaled concentration (Watanabe and Gehring, 1976). The 1980s provided other important developments that would shape the need for quantitative modeling tools. Among them were increasing use of in vitro cell systems for assessing chemical interactions in living cells and the first applications of molecular techniques emerging from the new field of molecular biology. Receptor-mediated toxicity, such as dioxin interactions with the Ah receptor, gained prominence. Another advance was the increasing sophistication applied to assessing how chemicals caused their effects – the mode of action of chemicals in biological systems. These contributions provided pressure to apply this growing information in some manner to improve the scientific basis of chemical risk assessment.

1.1.3

Risk Assessment Guidance

A seminal publication (NRC, 1983) proposed a set of consistent “inference guidelines” for use by federal regulatory agencies in the risk assessment process. Called “The Red Book,” because of the color of the cover, an emphasis was placed on the need to separate the scientific and the policy aspects of risk assessment. Risk assessment was defined as: “the use of the factual data base to define the health effects of exposures of individuals or populations to hazardous materials or situations.” It organized the risk assessment processes into four areas. Hazard identification is the determination of the effects of the chemical in

6

Quantitative Modeling in Toxicology: An Introduction

exposed animals or people. Dose-response assessment evaluates the exposure conditions under which these effects are observed. Exposure assessment estimates the amounts of the chemical present in the workplace, home, and general environment. The fourth component, risk characterization combines information on the exposure and dose-response assessment to estimate the risk level for specific individuals, groups, or populations. Various default methods are used in risk and safety assessments. These defaults are used to circumvent lack of detailed knowledge of the shape of the dose-response curve. In general, these policydriven defaults are designed to provide a conservative basis for estimating likely risks in exposed humans. This conservatism reflects an attempt to ensure adequate protection of members of the population in the absence of knowledge. The reliance on these defaults could be reduced by improved understanding of the shape of the dose-response curve in regions of low incidence. The major role of quantitative systems modeling in risk assessment is for enhancing dose-response assessment and in assisting in the various extrapolations, especially in understanding the biological factors that determine the shape of dose-response curves for adverse responses at low levels of incidence, that is, in regions of the dose-response curve where the probability of response in a population is small, and between animal species. The quantitative relationships among these biological factors are determinants of incidence-dose relationship for toxic responses. Mathematical models of various kinds can integrate this biological information to predict (calculate) incidence for various exposure situations. These models need to be developed in such a fashion to be concordant with biology and the chemistry of the compound in the biological system.

1.1.4

Quantitative Models in Risk Assessment

Both qualitative and quantitative inputs are required in the process of conducting safety/risk assessments. The qualitative studies are important for cataloging information about: (i) hazard, that is, the possible effects of a compound irrespective of exposure considerations; (ii) mode-of-action; (iii) progression, that is, the steps connecting initial interactions on to impaired function; and, (iv) susceptibility, that is, the inter-individual differences that may make any one person more affected by exposure than another (e.g., gender, age, genetics, pre-existing disease). Dose-response models were developed in the 1930s to assess responses in a population of animals treated with chemical, such as efforts to estimate the lethal dose in 50% of an exposed population (the LD50) or the effective dose for some response in 50% of the population, the ED50. Here a tolerance distribution depicted a quantal “either–or” response of individuals to chemical treatments. Incidence (number responding divided by number treated), either as a frequency distribution or as a cumulative response, was plotted against dose. In incidence-dose (ID) models, each member of the population has some dose sensitivity at which they respond to the test compound, and the “sensitivity” of individuals is considered to be distributed normally or log normally with tissue dose (Figure 1.1). In these analyses, the sensitivity of individuals and the variability in the population are estimated from the ID relationship, not from the underlying chemistry that describes delivery of chemical to target tissues or from the biology of the interactions of the chemical with specific cellular targets. This level of detail was unattainable in the 1930s; it is attainable in the twenty-first century.

Frequency

1.0

0.0

Cumulative

Frequency

7

Cumulative Probability

Introduction

Tissue Dose of Chemical

Figure 1.1 Biological responses were initially described by tolerance distributions within a population. Incidence-dose curves were generated by assuming that each individual in the population had some sensitivity or tolerance for expressing the biological responses. The frequency distribution for the response was the proportion of the population responding to a given tissue dose; the cumulative curve integrated the response from zero (no individual in the population had responded) to 1.0 (all members of the population had responded). In this figure, the distribution is represented as a log normal distribution, with skewing of the distribution towards high doses when plotted on a linear dose scale, as shown here. Andersen et al. (2005a), reprinted with permission from Elsevier. Copyright 2005.

Quantitative models have been developed to predict the relation between exposure and tissue dose (i.e., to describe the delivery of test molecule/metabolites to target tissues) and between tissue dose and tissue response (i.e., to describe the manner in which the molecular and cellular interactions of toxic compounds cause perturbations that are sufficiently large and sufficiently prolonged to lead to an adverse response). The broad categorization of these models breaks down into pharmacokinetic (PK) models for dosimetry and pharmacodynamic (PD) models for response. Pharmacokinetics has broadly been defined as what the body does to the compound; pharmacodynamics is what the compound does to the body. In order to be confident in the predictions/calculation from any model structure, these models themselves need to be as biologically realistic as possible without adding extraneous detail. Physiologically based (PB) models, such as physiologically based pharmacokinetic (PBPK) and physiologically based pharmacodynamic (PBPD) models, tend to be more firmly grounded in principles of biology and biochemistry (Reddy et al., 2005) than are conventional, compartmental models. Biologically based dose-response (BBDR) models predict expected incidence of adverse responses for varied exposure situations and, by their nature, combine PBPK and PBPD approaches. These model structures can provide important tools for improving risk and safety assessments. Starting in the 1980s there was considerable activity to create BBDR models for organism responses, including cancer and reproductive toxicity. These approaches had structures where dose led to alterations in cell growth, cell death, and mutation. Less detail was provided about the manner in which test chemicals altered cellular responses leading to the macroscopic changes in cell growth, differentiation, and mutation. Over the past decades with the growth of tools in cell and molecular biology, we now have the ability to query components of cellular, organ, and organism-level processes with exquisite detail, taking advantage of various new technologies, broadly referred to as “omics,” including components of genes, gene products, proteins, and various small molecules. This diverse

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Quantitative Modeling in Toxicology: An Introduction

array of data, however, needs to be organized quantitatively to create information, that is, to discover how the parts of the system are organized and controlled both in time and in space to provide biological functions, and how chemical exposures may perturb these functions. In this regard, “systems approaches” represent the attempt to quantitatively organize information across multiple levels of biological organization to unravel the manner in which biological functions are produced from simpler molecular, cellular, and organ interactions. 1.1.5 Systems Approaches in Pharmacokinetics Compartments in PBPK models correspond to discrete tissues or to groupings of tissues with appropriate volumes, blood flows, and pathways for metabolism of test chemicals (Bischoff and Brown, 1966; Leung, 1991). Pertinent biochemical and physicochemical constants for metabolism and solubility are included in each compartment with routes of dosing described maintaining the proper relationship between the dosing site and the overall physiology of the portal of entry. The time-course behaviors of chemical throughout the body are then accounted for by equations that form the basis of the PBPK model and permit introduction of multiple routes, if necessary, for specific exposure situations. PBPK models have developed for a wide variety of compounds, associated with diverse toxicological outcomes (Reddy et al., 2005). PBPK modeling is an example of a systems approach applied at the level of cells, organs, and organisms to integrate the mechanisms of distribution and interactions of environmental chemicals and drugs in the body. Two chemical engineers, Drs Kenneth Bischoff and Robert Dedrick, who first incorporated engineering principles, physiology, chemistry, and biochemistry into a computer modeling platform to predict kinetics (Bischoff et al., 1971; Dedrick, 1973) are generally credited with being the pioneers in use of contemporary PBPK modeling. These PBPK models do integrate information across multiple levels of organization, especially when describing the interactions of compounds with molecular targets, processes that include reversible binding of ligands to specific receptors, for example, methotrexate (Bischoff et al., 1971) or dioxin (Leung et al., 1990) and the adduction of proteins or DNA by reactive parent chemicals or their metabolites in various tissues, for example, ethylene oxide (Krishnan et al., 1992) or acrylonitrile (Gargas et al., 1995). The goal in PBPK modeling is to integrate molecular, cellular, organ level, and organism-level processes to account for the time-courses of chemicals, metabolites, and bound complexes within multiple organs in the body. To a large extent, the main emphasis with these PBPK models is to account for the major determinants of the distribution and elimination of compounds without describing every physical chemical process involved in transport and storage of chemical in every tissue. Following the law of parsimony, making the model only as complex as possible for its intended use requires purposeful simplification in model construction. Increasing levels of detail in specific tissues can always be included in these models as more information becomes available on chemical disposition from specific experiments. In the early application of PBPK modeling with environmental chemicals, for instance, many examples were quickly discovered where the kinetics were of necessity linked to dynamics. With methylene chloride, a metabolite, carbon monoxide, binds heme proteins and this interaction had to be taken into consideration (Andersen et al., 1991). Other examples included dioxin inducing a dioxin-binding protein in liver (Leung et al., 1990; Kohn et al.,

Linking Doses and Response

9

1993), ethylene dichloride depleting glutathione, thereby altering conjugation rates with the parent compound (D’Souza, Francis, and Andersen, 1988), and trans-dichloroethylene acting as a suicide inhibitor to reduce rates of oxidative metabolism (Lilly et al., 1998). While adding a degree of complication to the PBPK description for these individual materials, the PBPK modeling approach was sufficiently versatile to accommodate these biological interactions and provide good descriptions of dose to target tissues for parent compounds and key metabolites. These models support calculation of measures of the concentrations of test chemicals and metabolites reaching target tissues in the body during various exposures (Gentry et al., 2002). They have been applied for both chemicals not normally found in the body (xenobiotics) and for chemicals found in the body that are toxic in conditions of excess or deficiency, such as the essential element, manganese (Nong et al., 2009). Risk assessment application has also required development of tools for variability, uncertainty, and sensitivity analysis (Allen, Covington, and Clewell, 1996; Clewell and Andersen, 1996; Clewell, 1995), and new technologies associated with Bayesian methods and Markov Chain Monte Carlo tools have appeared to assist in estimating parameters in these PBPK models. In addition, dose metrics derived from PBPK modeling are also commonly used in deriving benchmark values (Barton et al., 2000). These methods involve fitting a variety of empirical mathematical models to dose-response data to estimate a dose, with attendant confidence intervals, that is associated with predetermined benchmark response (BMR), for example, a 10% alteration in the target response (Allen, Covington, and Clewell, 1996).

1.2

Linking Doses and Response

To link exposure and outcome for toxic compounds, toxicology and risk assessment have focused on the exposure-dose-response relationship for the past 25 years (Figure 1.2). PBPK models provide greater detail on the steps up to tissue interactions, including binding of reactive molecules with cellular macromolecules or recognition of chemical structures by reversible binding of the xenobiotic to cellular receptors that regulate key cell signaling pathways. The measures of tissue dose that are more closely aligned with tissue responses are called dose metrics (Andersen, 1987). These measures are preferred as the basis for the dose-response portion of chemical risk assessment. The steps linking these dose metrics to

Figure 1.2 The Linear Exposure-Dose-Response Paradigm for Organizing Toxicology Research and Testing for Risk Assessment Applications as defined in the 1980s. Andersen et al. (2005b), reprinted with permission from Elsevier. Copyright 2005.

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Quantitative Modeling in Toxicology: An Introduction

response are part of the pharmacodynamics (PD) of the response to chemical exposures. In this manner, dose metrics are the equivalent of a “biologically equivalent dose” (BED) and link active forms of the chemical at target tissues to the response of concern via the mode of action. Through the development of the PBPK modeling, tissue dose metrics have been linked with integrated cellular level responses, for example, cancer, cytotoxicity, and so on, to assist in risk assessments and guide various extrapolations (Clewell and Andersen, 1985). However, PD models have been more empirical, making use of simple effect compartments with responses correlated with blood or tissue concentrations of active chemical. Other PD approaches, called biologically based dose-response (BBDR) modeling, include two-stage clonal growth models for carcinogenesis and cell growth based models for developmental toxicology. These BBDR models were developed to assist with risk assessment (Moolgavkar and Luebeck, 1990; Leroux et al., 1996; Whitaker, Tran, and Portier, 2003). In these descriptions, adverse endpoints are a function of compound-related alterations in cell replication, apoptosis, and mutation rates. In general, the parameters in the BBDR models have not yet been described with respect to the effects of chemicals on specific cellular signaling pathways or the interactions among signaling pathways. 5-Fluorouracil (5-FU) is arguably the best example of a BBDR model for developmental toxicity where tissue concentrations are linked to enzyme inhibition, impaired nucleotide synthesis, altered DNA synthesis, and, finally, developmental anomalies (Lau et al., 2001; Setzer et al., 2001). As in all response models, a challenge with 5-FU is the difficulty in first providing an adequate description of the underlying biology that is being affected by the compound. The problem in describing biology is a particular issue for development where processes and structures are changing rapidly and consecutive developmental landmarks are critically dependent on completion of earlier steps.

1.2.1 Systems Biology and Dose-Response Assessment As noted earlier, PBPK models represent a “systems approach” to the physiological and biochemical levels. The ability to apply more integrated systems approaches to tissue response modeling has been seriously impeded by limited knowledge before the expansion of methods in cell molecular biology over the past two decades. These systems biology approaches integrate diverse data across various “omic” technologies and biological organization to understand how these various components lead to specific biological functions. Today, these high throughput, broad coverage technologies – such as, genomics, transcriptomics, proteomics, and metabonomics – are generating molecular “parts lists” for the components of cells, tissues, organs, and all the way to the organism level. In a perspective in Science at the turn of the millennium, Lander and Weinberg (2000) discussed the implications of the information generated by “genomics” technologies in providing a more complete understanding of biology: The long-term goal is to use this information to reconstruct the complex molecular circuitry that operates within the cell – to map out the network of interacting proteins that determines the underlying logic of various cellular biological functions including cell proliferation, responses to physiologic stresses, and acquisition and maintenance of tissue-specific differentiation functions. A longer term goal, whose feasibility remains unclear, is to create mathematical models of these biological circuits and thereby predict these various types of cell biological behavior.

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Current initiatives in computational systems toxicology emphasize an iterative process, with recurrent steps through laboratory experiments and computer modeling, to create an understanding of the manner in which the components of biological systems are organized in order to produce these circuit elements that regulate biological function. Perturbations of these biological processes by environmental stressors, including chemicals and drugs, can lead to adverse responses (toxicity), restoration of normal function to a compromised tissue (drug efficacy), or control of biological processes, such as occurs with use of hormonal therapies in post-menopausal women. Computational systems biology is now an intense area of activity providing key information for understanding cell behavior. Some of these approaches were highlighted in the focused series of papers in Nature in 2002 (Kitano, 2002; Surridge, 2002). More recent contributions outline contributions of computational systems biology to understanding the circuitry controlling biological responses and stress pathways (Alon, 2006, 2007). Toxicology and pharmacology are disciplines at the interface of chemistry/pharmacokinetics (primarily embedded in the vertical component from exposure to perturbation) and biology/pharmacodynamics (primarily captured by the horizontal chain from inputs to normal biological function – Figure 1.3). With the rapid advances in quantitative understanding of many biological processes and responses to perturbations, toxicology modeling can focus more directly on the underlying biology rather than simply the perturbations

Figure 1.3 The Maturing Exposure-Dose-Response Paradigm for Toxic Responses is related to Perturbations of the Normal Control Processes in the Cell by Toxicant Exposures. Low doses are largely without functional consequences; intermediate doses activate adaptive stress responses with attendant homeostatic controls; and, high enough doses lead to overt toxicity. Increasing dose leads to progress through several dose-dependent transitions. Andersen et al. (2005b), reprinted with permission from Elsevier. Copyright 2005.

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Quantitative Modeling in Toxicology: An Introduction

following chemical exposure. When the exposure-dose-response is recast with intersection of chemical perturbation with normal biology, toxicity and efficacy become situated at the intersection of chemical action with the underlying biology. We are now moving to a second-generation of systems approaches in PK and PD modeling. This new initiative will include simulation models with increasingly detailed descriptions of biology derived from new technologies coupled with the expansion of current modeling tools that focus on signaling pathways affected by chemical exposures and drug treatments.

1.2.2 Circuits, Networks and Signaling Motifs and Toxicity Cells consist of multiple interacting modules, with various feedback controllers. These control modules have been primarily examined through detailed experimental work prokaryote cell systems. These simplified signaling circuits have been described by mathematical models to capture the behavior of the control networks. Using the variety of tools from molecular biology, simple prokaryotic cells have in some cases been engineered with specific circuit elements, including, biological oscillators, switches, amplifiers, and so on. These artificial constructs then can be queried by laboratory experiments and the results used to construct detailed models for the underlying circuitry controlling these behaviors (Hasty, McMillen, and Collins, 2001, 2002; Guet et al., 2002; McMillen et al., 2002; Tyson et al., 2003). Computational models have evaluated the protein networks within cells, the control of these networks by the component circuitry, and uncovered the logic of cellular responses affected by these networks (Davidson et al., 2002; Ferrell, 2002; Alm and Arkin, 2003). Among these control processes are activation of latent networks, silencing of active networks, and modulation of network function. The circuitry is regulated by various input signals to the cells. Input signals, including endogenous compounds, such as hormones and various exogenous compounds, are capable of activating cell signaling networks to modulate both control circuitry and affect downstream genetic networks. Cell cycle control has been extensively modeled in eukaryotic organisms and represents a generic process that is common across biological organisms (Tyson, 1999; Tyson et al., 2003). Progress in understanding similar common signaling themes (Ray, Adler, and Gough, 2004; Schlessinger, 2004) has increased the appreciation of the manner in which modular components are used to achieve and control a host of cellular outputs/functions. Xenobiotics have effects on tissues in biological systems through two general processes – receptor-mediated recognition of the three-dimensional structure of the compound – or stress pathways, where the cells respond to chemical reactivity and stress through negative feedback control processes to maintain homeostasis. These interactions perturb cell circuits and modulate cellular functions. This classification of response pathways is especially relevant for so-called receptor-mediated toxicants that interact in the body with specific endogenous receptors. Receptor-mediated toxicants have the potential to cause toxicity by mimicking endogenous signaling molecules, leading to over-stimulation of natural circuits. Alternatively, compounds of this class may cause toxicity because they are competitive inhibitors of natural receptor-mediated functions. Competitive inhibitors can bind with endogenous receptors, but cause failure of activation of important circuits in the presence of normal signals. Inhibitory compounds with a receptor-mediated mode of action can lead to diseases associated with deficiencies of signaling molecules and circuit activation.

Linking Doses and Response

13

The report from the National Academy of Sciences, Scientific Frontiers of Developmental Toxicity and Risk Assessment (NRC, 2000), outlined the suite of known intercellular signaling motifs and their roles that these pathways play in development. This suite of signaling pathways represents potential targets that could lead to toxic responses if they are sufficiently perturbed by chemical exposures, that is, adverse responses could ensue if these pathways were inhibited or over-stimulated at times during development. 1.2.3

Modeling Cellular Response Pathways

Cell signaling pathway model code is similar to the sets of ordinary differential equations used in most PBPK models. There are some new challenges because the low copy number of genes, transcripts, and proteins may require stochastic simulation. Despite these difficulties, several mammalian signaling pathways have been modeled – including platelet derived growth factor (PDGF) pathway (Bhalla, Ram, and Iyengar, 2002) in mouse 3T3 cells and tumor necrosis factor-alpha (TNF-α) signaling through the nuclear factor kappa B (NF-κB) pathway in mouse fibroblasts (Hoffmann et al., 2002; Cho et al., 2003). The equations in these models represent groups of reactions within a cell and require estimation of multiple parameters in the biochemical steps embedded within the signaling networks. Models based on series of differential equations have also been augmented by Boolean approaches that use on-off logic to increase the model coverage on intracellular reactions, without necessarily increasing the numbers of parameters that have to be estimated for all the protein–protein interactions involved in the signaling networks (Bolouri and Davidson, 2002). The huge diversity of cellular responses and interactions can be broken down and categorized in a much smaller set of functional circuits – positive and negative feedback, feed-forward loops, and so on. While there are many discrete signaling modules within any cell, the process of careful modeling of prototype circuits that allows dissection and modeling of individual signaling modules should eventually encourage a modular approach to understanding more integrated biological pathways (Hartwell et al., 1999). Progress in applications of these modeling strategies in toxicology and risk assessment is likely to come from model development for a series of prototype compounds. These compounds would be selected based on knowledge of the key signaling pathways with which they interact. The computational systems biology models of the response pathway could then focus on the circuits giving rise to pathway function, allowing improved mechanistic understanding of the dose-response behavior of the circuit serving as a primary focus of model development. The increasing focus on cell response pathways for toxicity testing (NRC, 2007) is likely to spur greater interest in computational systems biology for evaluating the dose response for perturbations and for activation of adaptive responses. Along with a fairly large group of modern computational biologists, Alon (2006) has emphasized the pattern of recurring motifs and commonality of motif functions that are present in larger scale networks. Nonlinear processes associated with positive feedback, double negative feedback, negative feedback homeostasis, and coherent and incoherent feed-forward loops are increasingly being analyzed using engineering principles to understand cell function and how the intrinsic cell circuitry is designed to achieve specific functions (Alon, 2007). A course on computational systems biology and dose-response modeling at The Hamner Institutes for Health Sciences has outlined the key ideas and focused on both numerical simulation and on understanding the nonlinear dynamics that are the basis of complex

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Quantitative Modeling in Toxicology: An Introduction

Figure 1.4 The mitogen-activated protein kinase (MAPK)cascade generates nonlinear dose relationships for cellular responses. This signaling motif has three sequential kinase partners – MAP kinase kinase kinase (MAPKKK), MAP-kinase kinase (MAPKK), and MAP kinase (MAPK). The steepness of dose response increases through each component of the cascade. Reprinted with permission from Huang et al. Copyright 1996, National Academy of Sciences, USA.

cellular responses to chemical and environmental stressors (http://www.thehamner.org/ education-and-training/current-course-offerings.html). Cell response modeling, more than PBPK or PBPD simulation models, has created increasing attention on the characteristics of nonlinear dynamics rather than on numerical solution of series of differential equations (Strognatz, 1994). Key topics for cell signaling include ultrasensitivity (Ferrell and Machleder, 1998; Ferrell, 2002), bistability (Xiong and Ferrell, 2003), and the use stochastic differential equation solvers that account for noise and randomness in cellular reactions that involve small numbers of participating molecules (Kaern et al., 2005; Gillespie, 1976). One ubiquitous ultrasensitive motif in eukaryotes is the mitogen-activated protein kinase (MAPK) cascade (Johnson and Lapadat, 2002) that participates in a variety of cell response pathways (Figure 1.4). Through activation of the sequential kinase components, these motifs generate ultrasensitive behaviors, with equivalent for steepness for Hill-curves with n-values of greater than 5.0 for the MAPK itself (Huang and Ferrell, 1996). These ultrasensitive motifs coupled through positive feedback produce bistability, that is, true switches, in cellular response behaviors (Xiong and Ferrell, 2003). A common discussion among the community working on quantitative modeling of complex responses is whether the models should be built bottom-up (focusing on the initial interactions and going on to adverse responses) or top-down from the adverse consequences at the organism level and piecing the path back to uncover the key portions of the toxic response. Increasingly, it appears that real progress in quantitative modeling of toxic responses is likely to arise from a middle-out approach, where the primary responder is the cell, with model structures focusing on how cells respond to perturbations and how excessive perturbations cause cascades of cellular pathway activation, for example,

Acknowledgment

15

anti-oxidant stress, up-regulation of anti-oxidant response genes, inflammation, and, finally, apoptosis (Nel et al., 2006). The field of quantitative systems modeling for toxicology and risk assessment is emerging as a critical area for informing risk and safety assessment with environmental chemicals and drugs. Zhang et al. (2009), for instance, have examined dose-response relationships for reactive intermediates where liver concentration of reactive metabolites from Phase I enzymes is controlled by feed-forward activation of phase II and phase III enzymes. Feed-forward homeostatic control can produce complex, and in some cases, hormetic dose response. Integration of biomedical engineering concepts with the biology of cell signaling should provide theoretical justification for dose-response curves with a wide variety of shapes and allow consideration of dose-dependent transitions as key components of dose-response assessment strategies (Slikker et al., 2004).

1.3

Summary

Quantitative modeling in toxicology dates back to the development of dose-response methods for estimating effective doses using probit analyses for quantal responses. Major advances increased our ability to understand dose to tissues through pharmacokinetic (PK), and, especially, physiologically based pharmacokinetic (PBPK) modeling. PBPK models have spurred growth of sensitivity, variability, and uncertainty analysis; they forced development of statistical tools for assessing goodness-of-fit of models to diverse data sets; and they instigated strategies for using measures of internal dose in risk assessment through linkage with benchmark dose (BMD) models. Response modeling matured more slowly due to lack of detailed understanding of the biological processes leading to organism level responses. Response models for cytotoxicity, cancer, and developmental toxicity have focused on cell level responses and relied on admixtures of mechanistic and empirical structures. Models for precursor responses related to chemical adduction of protein and DNA and enzyme inhibition retained more fidelity with the chemistry of test compounds and the biology of the precursor interactions. Looking forward, rapid development are expected in continued expansion of PBPK models at the organism, organ, and cell levels, and in computational systems biology modeling of intra- and intercellular signaling, leading to more biologically relevant dose-response models for cell and tissue level responses. Other advances in bioinformatics and high data content methodologies will drive new dose-response modeling approaches that organize genomic results on the basis of the classification of gene families affected by chemical treatment (see for example, Thomas et al., 2007; Andersen et al., 2008) that are more difficult to predict. It is hoped that the chapters and examples in this volume will spur further development of quantitative modeling in toxicology and continue the improvement of chemical risk assessment by encouraging quantitative, biological modeling approaches for toxicology and for risk assessment decision making.

1.4

Acknowledgment

This chapter draws heavily from two other contributions by the senior author: Andersen, Conolly, Gaido, and Thomas (2005b) and Andersen and Hanneman (2002).

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Quantitative Modeling in Toxicology: An Introduction

NRC (National Research Council) (1983) Risk Assessment in the Federal Government: Managing the Process, National Academies Press, Washington, DC. NRC (National Research Council) (2000) Scientific Frontiers in Developmental Toxicology and Risk Assessment, National Academies Press, Washington, DC. NRC (National Research Council) (2007) Toxicity Testing in the 21st Century. A Vision and a Strategy, National Academies Press, Washington, DC. Ray, L.B., Adler, E.M., and Gough, N.R. (2004) Common signaling pathways. Science, 306, 1505 Reddy, M.B., Yang, R.S.H., Clewell, H.J. III and Andersen, M.E. (eds) (2005) Physiologically Based Pharmacokinetics: Science and Applications, John Wiley & Sons, Inc., Hoboken, NJ. Schlessinger, J. (2004) Common and distinct elements in cellular signaling via EGF and FGF receptors. Science, 306, 1506–1507. Setzer, R.W., Lau, C., Mole, M.L., et al. (2001) Toward a biologically based doe-response model for developmental toxicity of 5-fluorouracil in the rat: a mathematical construct. Toxicol. Sci., 59, 49–58. Slikker, W. Jr., Andersen, M.E., Bogdanffy, M.S., et al. (2004) Dose-dependent transitions in mechanisms of toxicity. Toxicol. Appl. Pharmacol. 201, 203–225. Strognatz, S. (1994) Nonlinear Dynamics and Chaos: With Application to Physics, Biology, Chemistry, and Engineering, Westview Press, Boulder, CO. Surridge, C. (2002) Nature insight: computational biology. Nature, 420, 205. Thomas, R.S., Allen, B.C., Nong, A., et al. (2007) A method to integrate benchmark dose estimate with genomic data to assess the functional effects of chemical exposure. Toxicol. Sci., 98, 240–248. Tyson, J.J. (1999) Models of cell cycle control. J. Biotechnol., 71, 239–244. Tyson, J.J., Chen, K.C., and Novak, B. (2003) Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell. Curr. Opin. Cell Biol., 15, 221–231. Watanabe, P.G. and Gehring, P.J. (1976) Dose-dependent fate of vinyl chloride and its possible relationship to oncogenicity in rats. Environ. Health Perspect., 17, 145–152. Whitaker, S.Y., Tran, H.T., and Portier, C.J. (2003) Development of a biologicallybased controlled growth and differentiation model for developmental toxicology. J. Math. Biol., 46, 1–16. Xiong, W. and Ferrell, J.E. Jr. (2003) A positive-feedback-based bistable ‘memory module’ that governs a cell fate decision. Nature, 426, 460–465. Zhang, Q., Pi, J., Woods, C.G., and Andersen, M.E. (2009) Phase I to II cross-induction of metabolizing enzymes: a feed forward control mechanism for potential hormetic responses. Toxicol. Appl. Pharmacol., 237, 345–356.

Section 2 Physiologically-based toxicokinetic and pharmacokinetic (PBPK) modeling

2 PBPK Modeling: A Primer Kannan Krishnan1 , George D. Loizou2 , Martin Spendiff 2 , John C. Lipscomb3 , and Melvin E. Andersen4 1

D´epartement de sant´e environnementale et sant´e au travail, Groupe de recherche interdisciplinaire en sant´e (GRIS), Universit´e de Montr´eal, Canada 2 Computational Toxicology Section, Health and Safety Laboratory, United Kingdom 3 National Center for Environmental Assessment, US Environmental Protection Agency, USA 4 Division of Computational Biology, The Hamner Institutes for Health Research, USA

2.1 Introduction Pharmacokinetic models are quantitative descriptions of the time-course behavior of chemicals in biological matrices (e.g., blood, urine, exhaled air, tissues). The pharmacokinetic models can be developed either based on fitting to the experimental data (often referred to as “data based” or compartmental models) or based on the critical determinants of absorption, distribution, metabolism, and excretion (ADME). The later is the basis of physiologically based pharmacokinetic (PBPK) (alternatively referred to as physiologically based toxicokinetic) models. The mathematical formulation and implementation of “data based” pharmacokinetic models have been described in detail in several monographs (e.g., Notari, 1987; Heinzel, Woloszczak, and Thomann, 1993; Rowland and Tozer, 1995; Kwon, 2001). PBPK models, the focus of this chapter, refer to mathematical descriptions of the uptake and disposition of chemicals based on quantitative interrelations among the critical determinants of these processes (i.e., physiological processes, metabolic and excretory processes, absorption, and tissue solubility phenomena). The literature on PBPK models dates back to the research works of Haggard (1924), Teorell (1937a, 1937b), Kety (1951), Mapleson (1963), Riggs (1970) and Fiserova-Bergerova (1975) on antineoplastics, anesthetics, and other pharmaceuticals. Since the early 1980s, PBPK models have been developed for a Quantitative Modeling in Toxicology
C 2010 John Wiley & Sons, Ltd

Edited by Kannan Krishnan and Melvin E. Andersen

22

PBPK Modeling: A Primer

number of environmental chemicals of toxicological interest and are being increasingly explored for use in improving the dose-response relationships (reviewed in Krishnan and Andersen, 2001, 2007; Clewell, Andersen, and Barton, 2002; Reddy et al., 2005; Lipscomb and Ohanian, 2006; USEPA, 2006). This chapter provides a beginner-level description of the quantitative aspects of PBPK models and their implementation. The role of in silico and in vitro methods for developing PBPK models in data-poor situations is also discussed.

2.2

Model Structure and Purpose

The development of PBPK models typically starts with a definition of the problem such that the capability and complexity of the resulting model can be determined appropriately. The intended use of a PBPK model may be for the conduct of in vitro to in vivo extrapolation, high dose to low dose extrapolation, animal to human extrapolation or route to route extrapolation of the tissue dose of a chemical. The level of detail relates not only to the compartments (e.g., whole body, target tissue, or intracellular concentrations) but also to the chemical forms that are tracked within the model (e.g., parent chemical and/or metabolite(s)). Accordingly, a conceptual representation, that is, a diagrammatic description of the compartments and interconnections among them, is developed. The conceptual model requires an understanding of the anatomical and physiological characteristics of the species, as well as the pathways of ADME of the chemicals and/or its metabolite(s). Lumping or splitting approaches can be used to identify those tissues that need to be represented individually in the PBPK models (Clewell and Clewell, 2008). Here, statistical approaches for evaluation of model structure may be of relevance, in addition to the fundamental considerations of biology and mode of action (see Chapter 20, this volume). Generally, the approach to PBPK model building is one of striking the balance between model parsimony and biological plausibility. In this regard, parsimony refers to the choice of a model structure that has minimal but necessary elements that together adequately describe the pharmacokinetics of a chemical (Krishnan and Andersen, 1994). In other words, model complexity is increased only when it is required for explaining the behavior contained in the data. In PBPK models, increments in complexity generally involve the addition of mathematical representations of mechanisms that are thought to represent the system behavior. The necessity for representing a particular organ or tissue as a separate compartment is determined by its relevance to toxicity, mode-of-action, uptake, and pharmacokinetics of the chemical under study. The most common criteria for the selection and definition of a compartment are related to significant role of: (a) relevant metabolizing enzyme activities within an organ or tissue, and (b) the solubility of a chemical within an organ or tissue. The liver is an example of the former and the adipose compartment for lipophilic chemicals is an example of the latter. Figure 2.1 shows the conceptual representations of the PBPK models for selected chemicals. In these particular examples, the model compartments together represent ≈91% of body mass, with the remaining 9% corresponding to the mass of the skeletal/structural components. The slowly and rapidly perfused compartments are assumed to be “kinetically homogeneous” since a chemical would be well mixed, assuming venous equilibration (i.e., the free tissue concentration and the venous concentration exiting the tissue are equal), and

Model Structure and Purpose (a)

23

(b) Exhaled Chemical

Inhaled Chemical

Alveolar Space Lung Blood

Inhaled Chemical

Exhaled Chemical

Lungs

Fat

Fat Binding

Poorly Perfused Tissues

Poorly Perfused Tissues

Venous blood

Liver

Brain Metabolism and Binding

Testes

Arterial blood

Metabolism and Binding

Richly Perfused Tissues

Metabolism and Binding

Metabolism

Other Richly Perfused Tissues Metabolism and Binding

Liver

(c)

Metabolism and Binding

I.V.

Blood

(d)

Fat

Inhalation

TCDD

Exhalation

Lungs & arterial blood

TCDD

Biotransformation

Poorly perfused Tissues

Rapidly perfused tissue

TCDD

TCDD

Perirenal fat Richly perfused Tissues

Subcutaneous fat

TCDD

TCDD

Working muscle

Liver Ah-TCDD Ah

Pr-TCDD

Resting muscle

Pr TCDD

TCDD

Metabolism

Liver Biotransformation

Figure 2.1 (a) Conceptual representation of a PBPK model for (a) styrene, (b) ethylene oxide, (c) 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD; Pr, protein; Ah, Ah receptor) and (d) toluene. Adapted with permission from Ramsey and Andersen (1984), Krishnan et al. (1992), Andersen, Mills, and Gargas (1993), and Jonsson and Johanson (2001). ((a) and (d) reprinted with permission from Elsevier, (b) reprinted with permission from SAGE Publications Ltd, (c) reprinted with permission from Wiley-Blackwell.

24

PBPK Modeling: A Primer

have a similar disposition or “time constant” (i.e., blood flow rate divided by the product of partition coefficient and tissue mass) within each individual compartment (Krishnan and Andersen 1994). It is also very common for fat depots such as perirenal, epididymal, and omental fat to be grouped and represented as a single “fat” compartment. This simplification is justified in cases of small molecular weight compounds, which predominately exhibit perfusion-limited kinetics. While lumping or splitting the compartments, the following fundamental tenets should be observed: 1. The sum total of tissue and organ compartment masses should be within the body mass of the organism; and 2. the total blood flow (i.e., cardiac output) in the model should be equal to the sum of the flows to the tissue compartments of the model in order to maintain the mass balance of the chemical at all times.

2.3

Mathematical Representation

A summary of frequently used mathematical representations in PBPK models is provided in Table 2.1, along with the symbols and abbreviations used in equations presented in this chapter. A list of some fundamental measures and units relevant to PBPK modeling is provided in Table 2.2. 2.3.1 Calculating the Rate of Change in the Compartments The rate of change in the amount of chemical in tissues is essentially proportional to the concentration difference, as defined by Fick’s first law: dAt/dt ∝ ∆C

(2.1)

In the above equation, ∆C refers to the input-output difference in chemical concentration (i.e., Cin – Cout ). Replacing the ∝ sign in the above equation with the = sign necessitates the introduction of a proportionality constant, k. Therefore, Equation 2.1 becomes: dAt/dt = k(Cin − Cout )

(2.2)

The constant, k, corresponds to the membrane permeability coefficient, which can be represented as PAQt /(PA + Qt ), where PA = permeation area cross product and Qt = tissue blood flow rate. Accordingly, when the PA of a chemical is very large compared to Qt , k approximates to Qt . On the other hand, when the PA is small compared to Qt (i.e., membrane diffusion is the factor limiting chemical movement into and out of the tissue compartment), then k ≈ PA. For small molecular weight compounds, blood flow rather than the membrane diffusion is the limiting factor (Figure 2.2a), such that: dAt (2.3) = Qt(Ca − Cvt ) dt However, for high molecular weight compounds dAt/dt is frequently calculated as a function of the rate of change in the tissue blood (vascular) subcompartment and cellular matrix subcompartment (Figure 2.2b). The rate of change in the amount of chemical in

Mathematical Representation

25

Table 2.1 Mathematical representation of ADME in PBPK models. Toxicokinetic process

Examples of PBPK mathematical descriptions

1. Absorption Pulmonary Dermal Oral Intravenous 2. Distribution Protein binding Diffusion limited tissue distribution Perfusion limited tissue distribution

Ca =

Qp · Ci nh + Qc · Cv 
Qc + Qp/Pb     Csk Csk = K p · S Cai r − + Qsk · Ca − Ps:a Ps:b

dAsk dt dAo = K o · Do · e−ko ·t dt   Cv =

K z+

n  t

Qt ·Cvt

Qc

n · β · Kd · C f  Cb =
1 + Kd · C f   Ct dAt = P At · Cvt − dt Pt dAt = Qt · (Ca − Cvt ) dt

3. Metabolism First order Second order Saturable process 4. Excretion Urinary Pulmonary

dAmet = K f · Cvt · Vt = C L int · Cvt dt dAmet = K s · Cvt · Vt · Ccf dt Vmax · Cvt dAmet = dt K m + Cvt   Tm dAr c = GF R · Cp dt Kt + Cp   Ca + (0.3 · Ci nh ) C x = 0.7 · Pb

Abreviations: Qc , cardiac output (liters.h−1 ); Qp , alveolar ventilation rate (liters.h−1 ); Qt , blood flow to tissue “t” (liters.h−1 ); Qf , blood flow to fat (liters.h−1 ); Ql , blood flow to liver (liters.h−1 ); Qp , blood flow to poorly perfused tissues (liters.h−1 ); Qr , blood flow to richly perfused tissues or rest of body (liters.h−1 ); C, Concentration (mg/l). Subscripts: a, arterial blood; alv, alveolar air; b, bound; cf., cofactor in tissue “t”; f , free; inh, inhaled air; p, plasma; pr, binding protein; sk, skin; t, tissue “t”; v, mixed venous blood; vf , venous blood leaving fat; vl, venous blood leaving liver; vp, venous blood leaving poorly perfused tissues; vr, venous blood leaving richly perfused tissues (or rest of body); vt, venous blood leaving tissue “t”; x, exhaled air; V, Volume (liters); A, Quantity. Subscripts: rc, renal compartment; met, metabolized; o, oral absorption; CLint , Intrinsic clearance (liters.h−1 ); GFR, Glomerular filtration rate (liters.h−1 ); Kd , dissociation constant (mg/liter); Kf , first-order metabolism rate constant (h−1 ); Km , Michaelis constant (mg/l); Ko , oral absorption rate constant (h−1 ); Kp , skin permeability coefficient rate constant (cm × 10−2 .h−1 ); Ks , second-order metabolism rate constant (liters·mg−1 h−1 ); Kt , Apparent Michaelis–Menten constant with respect to secretary carrier (mg/l); Kz , Input via intravenous dosing; nβ, binding maximum; PAt , Permeation area cross product for tissue “t” (liters.h−1 ); Pb , blood : air partition coefficient; Pl , liver: blood partition coefficient; Pr , richly perfused (or rest of body):blood partition coefficient; Ps : a , skin : air partition coefficient; Ps : b , skin : blood partition coefficient; Pt , tissue : blood partition coefficient; S, Exposed skin surface area (cm.h−1 × 10−2 ); t, Elapsed time (h); Tm , Apparent maximum transport of the carrier system (mg.h−1 ); V max , Maximal velocity of enzymatic reaction (mg.h−1 ).

26

PBPK Modeling: A Primer Table 2.2 Some measures and units of relevance to PBPK modeling. Measures

Units

Quantity Volume Weight Area Concentration Time Administered (applied) dose Area under the curve (AUC)

µg, mg, kg ml, l g, kg cm2 , m2 µg/ml, mg/la , ppm min, h, day mg/kg mg/l × hr

a

mg/l (air) = ppm × molecular weight/24 450

cellular matrix is equal to the product of the diffusion constant and the net flux from the vascular compartment:   Ct dAcm = PAt Cvt − (2.4) dt Pt The rate of change in the vascular (i.e., tissue blood) sub-compartment equals the sum of the net flux from blood flow plus the net flux from cellular matrix:   Ct dAtb − Cvt = Q t (Ca − Cvt ) + PAt (2.5) dt Pt So, if diffusion from the vascular compartment to cellular matrix is slow with respect to total tissue blood flow, then Equations 2.4 and 2.5 are necessary. However, if the blood flow is slow compared to diffusion, then tissues are described as homogeneous, well mixed compartments, such that the rate of change is described using a single equation (Equation 2.3) (i.e., cellular matrix + tissue blood or Equations 2.4 + 2.5). When there is metabolism and other clearance processes operative in a given tissue, additional terms are included within Equations 2.3–2.5. The rate of change as per Equations 2.3–2.5 is calculated in terms of amount per unit time (e.g., mg/h); therefore, the next step is to determine the amount of chemical in the tissue at any time, t. The differential equations presented above are all ordinary differential equations, that is, they consist of differentials of dependent variables with respect to an independent variable. Here the dependent variable is the amount and the independent variable is the time. The time-dependent incremental change in the resulting value of the dependent variable at the end of a simulation period should be added to the initial or starting value, such that the new value of the dependent variable at the end of each time interval can be obtained. Obviously, the computer then needs to track and maintain a record of the solved values of the dependent variable during a simulation exercise. The general principle underlying the solution for the first order ordinary differential equations used in PBPK models is reflected by the following strategy: Current value = Previous value + (slope × dt)

(2.6)

Mathematical Representation

27

(a) Qt · Cvt Out

Qt · Ca In

Tissue

(b) Cell + interstitial fluid Qt ·Cvt Out

Qt · Ca Vascular

In

Figure 2.2 Schematic of a tissue compartment. Qt is tissue blood flow rate, Ca is arterial blood concentration, Cvt is the concentration of the chemical in the venous blood leaving tissue.

Consider a situation where arterial blood with a concentration of 5 µg/l enters an adipose tissue compartment at the flow rate of 0.4 l/unit time. The influx here would be 5 µg/l × 0.4 l/unit time = 2 µg/unit time. The blood, flowing out at the same rate, let’s say contains a concentration of 0.05 µg/l. The output here equals 0.05 µg/l × 0.4 l/ unit time = 0.2 µg/ unit time. The rate of change in the adipose tissue compartment (dAt/dt) then equals: Input (2 µg/unit time) – Output (0.2 µg/unit time) = 1.8 µg/unit time. The calculation of the rate of change should be done for very small units of time or simulation period (alternatively referred to as the integration interval, dt). At the beginning of a simulation period, say the amount of chemical in the compartment is zero. In that case, the amount in the tissue would become 0 µg + [(1.8 µg/unit time) × dt] = 1.8 µg at the end of one unit time or one integration interval. This process yields the amount in tissue, which is divided by the volume of the tissue compartment to obtain the concentration in the tissue, which in turn is used as the basis to derive the free concentration of chemical leaving the tissue. The integration, or the determination of numerical solution, for the differential equations used in PBPK models can be obtained using different algorithms (i.e., step-by-step procedures). For a generic differential equation of the following form: dy = f(t, y) dt

(2.7)

at any time t = t0 , y = y0 , the derivative is f (t0 , y0 ); the true solution (value) of the y at t = t0 + ∆t can be expressed by an infinite series as follows: f (t0 + ∆t) = f (t0 ) + f  (t0 ) ∆t +

1 1   1  f (t0 ) ∆t 2 + f  (t0 ) ∆t 3 + f (t0 ) ∆t 4 + · · · 2 6 24 (2.8)

A number of algorithms are useful for solving the differential equations used in PBPK models (e.g., Euler, Gear, Runge–Kutta routines, and predictor-corrector methods) (Gear 1971; Rideout 1991; Haddad, Pelekis, and Krishnan, 1996). Of the commonly used

28

PBPK Modeling: A Primer Ca =

QpCi + QcCv Q Qc + p Pb:a

V C dAt = Ql (Ca − Ccl ) − max vl dt K m + Cvl

dAr = Qr (C a − Cvr ) dt

t

Al = ∫ dAl

t

Ar = ∫ dAr

0

0

Cl =

Al Vl

Cr =

C vl =

Cl Pl

Ar Vr

C vr =

Cr Pr

Cv =

Qr Cvr + Ql Cvl Qc

Figure 2.3 Illustration of the calculation of mixed venous blood concentration in PBPK models (abbreviations defined in Table 2.1).

algorithms, the Euler method takes the first term of the derivatives (Equation 2.8) for the increments in integration, and therefore the error associated with Euler method arises from the negligence of the rest of the terms and is proportional to ∆t2 . The Runge–Kutta method, on the other hand, takes four terms in approximating the integration update. The associated error then is proportional to or of the same order as ∆t5 . In other words, the higher the order of the error, the more accurate would the integration method be. Let’s examine the derivation of solution and the integration mechanics, using a simple PBPK model. Figure 2.3 shows the equations and interconnections in a two compartmental PBPK model (liver and rest of body). Here, to compute the mixed venous concentration, Cv , the venous blood concentration leaving the two compartments is needed (Cvl , Cvr ). To compute Cvl and Cvr , in turn, the concentrations in the respective tissues are required (Cl , Cr ) in addition to the knowledge of the tissue: blood partition coefficients. The tissue concentrations in turn can be calculated knowing the amount in tissues, Al and Ar , which result from the integration of the differential equations in each of these tissues (dAt/dt). In order to solve the two differential equations (one for each compartment), we need the arterial blood concentration, Ca , as well as the tissue blood flow rate (Ql , Qr ). Ca , in turn, can be calculated with knowledge of several input parameters along with that of mixed venous concentration, Cv , thus establishing a loop-type calculation within the PBPK model (Haddad, Pelekis, and Krishnan, 1996). The solution to the differential equations then becomes key to the computational implementation of these models. In this example, for initial conditions of n = 0, f = 0, Cl = 0, Cr = 0 and Ci = 45 µg/l, the differential equations can be written as follows (Note that the simplification is the result of the use of all the numerical values of constants in the equations): fl (Cl , Cr ) =

1.0301Cl dCl = −114.270Cl − + 81.1640Cr + 128.629Ci dt 1.10713Cl + 59.04 (2.9)

Mathematical Representation

fr (Cl , Cr ) =

dCr = 4.7517Cl − 4.9145Cr + 17.1419Ci dt

29

(2.10)

For the above problem, the solution based on Euler method is obtained as follows:
 (2.11) Cln+1 = Cln + fln Cln , Crn ∗ ∆t Crn+1 = Crn + frn (Cln , Crn ) ∗ ∆t

(2.12)

For the fourth-order Runge–Kutta integration method, the updates are calculated as follows: k1 = fl (Cln , Crn ) ∗ ∆t

(2.13)

l1 = fr (Cln , Crn ) ∗ ∆t

(2.14)

  1 1 k2 = fl Cln + k1 , Crn + l1 ∗ ∆t 2 2

(2.15)

  1 1 l2 = fr Cln + k1 , Crn + l1 ∗ ∆t 2 2

(2.16)

  1 1 n n k3 = fl Cl + k2 , Cr + l2 ∗ ∆t 2 2

(2.17)

  1 1 n n l3 = fr Cl + k2 , Cr + l2 ∗ ∆t 2 2

(2.18)


 k4 = fl Cln + k3 , Crn + l3 ∗ ∆t

(2.19)


 l4 = fr Cln + k3 , Crn + l3 ∗ ∆t

(2.20)

and updates at each iteration using the Runge–Kutta method are obtained as follows: Cln+1 = Cln +

1 (k1 + 2k2 + 2k3 + k4 ) 6

(2.21)

1 (l1 + 2l2 + 2l3 + l4 ) 6

(2.22)

Crn+1 = Crn +

The solution obtained with Euler integration is presented in Box 2.1, while the step-bystep solution obtained with Runge–Kutta procedure is depicted in Box 2.2, for the first two integration intervals. The results of integration obtained with these two methods, for this particular case, are very close to each other as summarized in Table 2.3.

30

PBPK Modeling: A Primer

Box 2.1: Solution by Euler method At n = 1, t = n∗ dT = 0.001 fl(0, 0) = - 114.270∗ 0 + 81.1640∗ 0 - 1.0301∗ 0(1.0713∗ 0 + 59.04) + 128.629∗ 45 = 5788.3 Cl(n=1) = Cl(n=0) + dT∗ fl = 0 + 0.001 ∗ 5788.3 = 5.7883 fr(0, 0) = 4.7517∗ 0 - 4.9145∗ 0 + 17.7419∗ 45 = 798.386 Cr(n=1) = Cr(n=0) + dT∗ fr = 0 + 0.001 ∗ 798.386 = 0.7984 n = 2, t = n∗ dT = 0.002 fl(5.7883, 0.7984) = - 114.270∗ 5.7883 + 81.1640∗ 0.7984 - 1.0301∗ 5.7883/(1.0713∗ 5.7883 + 59.04) + 128.629∗ 45 = 5191.59 Cl(n=2) = Cl(n=1) + dT∗ fl = 5.7883 + 0.001 ∗ 5191.59 = 10.9799 fr(5.7883, 0.7984) = 4.7517∗ 5.7883 - 4.9145∗ 0.7984 + 17.7419∗ 45 = 821.966 Cr(n=2) = Cr(n=1) + dT∗ fr = 0.7984 + 0.001 ∗ 821.966 = 1.6204

Box 2.2: Solution by Runge–Kutta method n = 1, n∗ dT = 0.001 kl = fl(Cl, Cr)∗ dT = fl(0,0)∗ 0.001 = 5.7883 l1 = fr(Cl, Cr)∗ dT = fr(0,0)∗ 0.001 = 0.798386 fl(0,0)=-114.270∗ 0 + 81.1640∗ 0 - 1.0301∗ 0/(1.0713∗ 0 + 59.04) + 128.629∗ 45 =5788.3 fr(0,0)=4.7517∗ 0 - 4.9145∗ 0 + 17.7419∗ 45 = 798.386 k2 = fl(Cl+k1/2, Crl1/2)∗ dT = fl(0+5.7883/2, 0+0.798386/2) = 5.48994 l2 = fr(Cl+k1/2, Cr+l1/2)∗ dT = fr(0+5.7883/2, 0+0.798386/2 = 0.810176 fl(2.89415, 0.399193)=-114.270∗ 2.89415 + 81.1640∗ 0.399193 - 1.0301∗ 2.89415/(1.0713∗ 2.89415 + 59.04) + 128.629∗ 45 =5489.94 fr(2.89415, 0.399193)=4.7517∗ 2.89415 - 4.9145∗ 0.399193 + 17.7419∗ 45 = 810.176 k3 = fl(Cl+k2/2, Crl2/2)∗ dT = fl(0+5.48994/2, 0+0.810176/2) = 5.50747 l3 = fr(Cl+k2/2, Cr+l2/2)∗ dT = fr(0+5.48994/2, 0+0.810176/2) = 0.809438 fl(2.74497, 0.405088)=-114.270∗ 2.74497 + 81.1640∗ 0.405088 1.0301∗ 2.74497/(1.0713∗ 2.74497 + 59.04) + 128.629∗ 45 =5507.47 fr(2.74497, 0.405088)=4.7517∗ 2.74497- 4.9145∗ 0.405088+ 17.7419∗ 45 = 809.438 k4 = fl(Cl+k3, Crl3)∗ dT = fl(0+5.50747, 0+0.809438) = 5.22458 l4 = fr(Cl+k3, Cr+l3)∗ dT = fr(0+5.50747, 0+0.809438) = 0.820577

Mathematical Representation

31

fl(5.50747, 0.809438)=-114.270∗ 5.50747+ 81.1640∗ 0.8094381.0301∗ 5.50747/(1.0713∗ 5.50747+ 59.04) + 128.629∗ 45 =5224.58 fr(5.50747, 0.809438)=4.7517∗ 5.50747- 4.9145∗ 0.809438+ 17.7419∗ 45 = 820.577 Cl(n=1) = Cl(0)+(k1+2∗ k2+2∗ k3+k4)/6 = 0 + (5.7883 + 2∗ 5.48994 + 2∗ 5.50747 + 5.22458)/6 = 0 + 5.50128 = 5.50128 Cr(n=1) = Cr(0)+(l1+2∗ l2+2∗ l3+l4)/6 = 0 + (0.798386 + 2∗ 0.810176 + 2∗ 0.809438 + 0.820577)/6 = 0 + 0.809698 = 0.809698 n = 2, n∗ dT = 0.002 kl = fl(Cl, Cr)∗ dT = fl(5.50128,0.809698)∗ 0.001 = 5.2253 l1 = fr(Cl, Cr)∗ dT = fr(5.50128,0.809698)∗ 0.001 = 0.820547 fl(5.50128,0.809698)=-114.270∗ 5.50128 + 81.1640∗ 0.809698 - 1.0301∗ 5.50128/(1.0713∗ 5.50128 + 59.04) + 128.629∗ 45 =5225.3 fr(5.50128,0.809698)=4.7517∗ 5.50128 - 4.9145∗ 0.809698 + 17.7419∗ 45 = 820.547 k2 = fl(Cl+k1/2, Crl1/2)∗ dT = fl(5.50128+5.2253/2, 0.809698+ 0.820547/2) = 4.96002 l2 = fr(Cl+k1/2, Cr+l1/2)∗ dT = fr(5.50128+5.2253/2, 0.809698+ 0.820547/2= 0.830945 fl(8.11394, 1.21997)=-114.270∗ 8.11394 + 81.1640∗ 1.21997 1.0301∗ 8.11394 /(1.0713∗ 8.11394 + 59.04) + 128.629∗ 45 = 4960.02 fr(8.11394, 1.21997)= 4.7517∗ 8.11394 - 4.9145∗ 1.21997 + 17.7419∗ 45 = 830.945 k3 = fl(Cl+k2/2, Crl2/2)∗ dT = fl(5.50128+4.96002/2, 0.809698+ 0.830945/2) = 4.9756 l3 = fr(Cl+k2/2, Cr+l2/2)∗ dT = fr(5.50128+4.96002/2, 0.809698+ 0.830945/2) = 0.830289 fl(7.98129, 1.22517)=-114.270∗ 7.98129+ 81.1640∗ 1.225171.0301∗ 7.98129/(1.0713∗ 7.98129+ 59.04) + 128.629∗ 45 =4957.6 fr(7.98129, 1.22517)=4.7517∗ 7.98129- 4.9145∗ 1.22517 + 17.7419∗ 45 = 830.289 k4 = fl(Cl+k3, Crl3)∗ dT = fl(5.50128+4.9756, 0.809698+0.830289) = 4.72407 l4 = fr(Cl+k3, Cr+l3)∗ dT = fr(5.50128+4.9756, 0.809698+ 0.830289) = 0.840109 fl(10.4769, 1.63999)=-114.270∗ 10.4769+ 81.1640∗ 1.639991.0301∗ 10.4769/(1.0713∗ 10.4769+ 59.04) + 128.629∗ 45 =4724.07 fr(10.4769, 1.63999)=4.7517∗ 10.4769- 4.9145∗ 1.63999+ 17.7419∗ 45 = 840.109 Cl(n=2) = Cl(1)+(k1+2∗ k2+2∗ k3+k4)/6 = 5.50128 + (5.2253 + 2∗ 4.96002 + 2∗ 4.9756 + 4.72407)/6 = 5.50128 + 4.9701 = 10.4714 Cr(n=2) = Cr(1)+(l1+2∗ l2+2∗ l3+l4)/6 = 0.809698 + (0.820547 + 2∗ 0.830945 + 2∗ 0.830289 + 0.840109)/6 = 0.809698 + 0.830521 = 1.64022

32

PBPK Modeling: A Primer

Table 2.3 Summary of integration results obtained for Equations (2.9) and (2.10), using Euler and fourth order Runge–Kutta algorithms. Time

Cl (µg/l) Euler

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01

0 5.788 10.979 15.644 19.845 23.635 27.063 30.172 32.998 35.576 37.934

Cr (µg/l)

Runge–Kutta

Euler

Runge–Kutta

0 5.501 10.471 14.969 19.047 22.751 26.123 29.200 32.014 34.595 36.968

0 0.798 1.620 2.463 3.323 4.2 5.090 5.992 6.904 7.825 8.754

0 0.809 1.640 2.489 3.354 4.233 5.124 6.027 6.939 7.859 8.787

2.3.2 Calculating the Concentration of Chemical Leaving the Tissues In the “venous equilibration-type” PBPK models, the chemical concentration in venous blood leaving the tissue is considered to be in equilibrium with the chemical in tissue. In this case then, if the tissue:blood partition coefficient (Pt ) is 10, it would imply that the affinity of the chemical towards the tissue is 10 times greater than that for the blood. In other words, the concentration of chemical leaving the tissue compartment to enter the venous blood pool, that is, Cvt , will be equal to one tenth of the tissue concentration. Notationally, Cvt = Ct /Pt . So the greater the tissue:blood partition coefficient, the greater the concentration in a given tissue and the smaller the contribution of the tissue to the mixed venous pool. In calculating Cvt , binding to tissue proteins and blood proteins should be accounted for, as applicable (Chapter 7). 2.3.3 Calculating the Arterial and Venous Blood Concentrations The arterial blood concentration, following inhalation exposures, has been calculated based on the mass balance equation for the combined lung tissue-alveolar air compartments as shown in Box 2.3. The algebraic equation for computing arterial blood concentration shown in Box 2.3 is based on the specification that the loss of chemical from the air is balanced by an identical gain in the pulmonary (arterial) blood (Ramsey and Andersen, 1984). Box 2.3: Calculation of Arterial Blood Concentration During Inhalation Exposures (Parameters and Variables are Defined in Table 2.1) Conceptual model: Qp · Cinh Qc · Cv v

Qp · Calv Qc · Ca

Mathematical Representation

33

Quantitative descriptions leading to computation of arterial blood concentration: Q p Cinh + Q c Cv = Q p Calv + Q c Ca Q c Ca − Q c Cv = Q p Cinh − Q p Calv Calv =

Ca Pb

Q c Ca − Q c Cv = Q p Cinh − Q p

Ca Pb

Ca = Q p Cinh + Q c Cv Pb   Qp Ca Q c+ = Q p Cinh + Q c Cv Pb

Q c Ca + Q p

Ca =

Q p Cinh + Q c Cv   Q Q c + Pbp

The mixed venous blood concentration, resulting from the pooling of the venous blood exiting various tissue compartments (Figure 2.4), is not a simple, arithmetic average of the Cvt of the various tissues. Rather, it is a weighted average of the free concentrations of chemicals originating from the tissues. This is due to the fact that the fraction of cardiac output flowing through the tissues differs from one tissue to another (e.g., liver = 0.25, fat = 0.09, slowly perfused tissues = 0.15, and richly perfused tissues = 0.51 in the rat); therefore, the weighted average is calculated as follows: Cven = (0.25 × Cvl ) + (0.09 × Cvf ) + (0.15 × Cvs ) + (0.51 × Cvr )

2.3.4

(2.23)

Calculating the Rate of Metabolism

The rate of the amount of chemical metabolized in liver or other metabolizing tissues can be computed as per the nature of the metabolic reaction. Accordingly, it may be calculated using the first order, second order or saturable descriptions as shown below: dAmet = K f Cvt Vt dt dAmet = K s Cvt Vt Ccf dt Vmax Cvt dAmet = dt K m + Cvt

(2.24) (2.25) (2.26)

In all the above cases, dAmet /dt has units of mg/h (or quantity per time). Whereas the first order reaction suggests that the amount metabolized per unit time increases (or decreases)

34

PBPK Modeling: A Primer Ql · Cvl (Liver)

Qf · Cvf (Fat)

Qc · Cv

Qr · Cvr (Richly perfused tissues)

Qp · Cvp (Poorly perfused tissues) n

∑Q ⋅C t

Cv =

vt

t =1

Qc

Figure 2.4 Functional representation of a two-compartmental PBPK model for a volatile organic chemical. All symbols and abbreviations are defined in Table 2.1.

in direct relation to the input variable (i.e., free concentration of chemical), the second order reaction suggests that it is a function of both cofactor as well as the substrate. The saturable reaction, on the other hand, implies that the reaction is essentially first order at low concentrations of the substrates, and it approaches zero order after a certain high concentration (which exceeds the K m for the reaction). Box 2.4 depicts the relationship between the metabolism rate and hepatic clearance, on the basis of the venous equilibration model. Other types of physiological descriptions of liver metabolism, such as the parallel tube model and the distributed sinusoidal perfusion model, may also be used, depending upon the objective of the study (Liu and Pang, 2006). Conjugation reactions are often described as a second order process (Equation 2.25) with respect to the concentration of the cofactor and the chemical (D’Souza, Francis, and Andersen, 1988; Krishnan et al., 1992). Alternatively, descriptions based on a ping-pong mechanism have also been used successfully (Csanady et al., 1996).

Box 2.4: Quantitative Description of Hepatic Clearance for a Well-Stirred Model of Liver (Refer to Table 2.1 for the Definition of Parameters and Variables) Conceptual model: Ql Cvl

Liver

CLint

Cvl

Ql Ca

Computer Implementation

35

Quantitative description of hepatic clearance: Amount in = amount out + amount metabolized   Vmax · Cvl Q l · Ca = Q l · Cvl + Km  As CLh = Q l · ⎡

⎛

Ca − Cvl Ca

 and Cvl =

Q l · Ca Ql +

Vmax Km

⎞⎤

⎜ Q l · Ca ⎟ ⎥ ⎢ ⎟⎥ ⎢ Ca − ⎜ ⎝ ⎢ Vmax ⎠ ⎥ ⎢ ⎥ Ql + ⎢ Km ⎥ ⎥. CLh = Q l · ⎢ ⎢ ⎥ Ca ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦

⎛ Simplifying,

⎜ CLh =Q l · ⎜ ⎝1 −

⎛

⎞ Vmax + − Q Q l⎟ ⎜ l Km ⎟ Rewriting, CLh = Q l · ⎜ ⎝ Vmax ⎠ Ql + Km since

⎞ ⎟ Ql ⎟ Vmax ⎠ Ql + Km

Vmax Km CLh = Vmax Ql + Km Ql ·

or

Vmax Q l · CLint = CLint , CLh = , Km Q l + CLint

For high clearance (CLint  Q l ) CLint ≈ Ql CLh = Q l · Q l + CLint

For low clearance (CLint  Q l ) CLint CLh = Q l · ≈ CLint Q l + CLint

2.4 Computer Implementation This section describes the implementation of PBPK models using an open-source model equation generator, MEGen. The following description is based on MEGen Version 0.3.0.16788 (http://xnet.hsl.gov.uk/megen/). However, it is emphasized that MEGen captures just one approach to the computational representation and implementation of the model building process. MEGen comprises two main components: an electronic database of species-specific anatomical and physiological parameters for the most commonly used species in toxicological research, and a PBPK model equation generator (Figure 2.5). MEGen enables a user to describe physiology, biology, and toxicology in order to output a set of mathematical equations that emulate the information supplied by the user and which

36

PBPK Modeling: A Primer MATLAB®

Database acslXtreme®

Equation Generator

XML MCSim

Berkeley Madonna®

Figure 2.5

Overview of MEGen and the model generation process.

constitute a PBPK model. Collation and storage of the most commonly used species-specific anatomical and physiological parameters, such as organ and tissue masses and blood flow rates, into an electronic database provide a means of readily and rapidly accessing these data. Further, by merging the database with the equation generator it would be possible for the software to interrogate and retrieve pertinent data for use within the model during the model building process. The PBPK functional forms are merged, in the form of mathematical markup language (MathML), into an extensible markup language (XML) document. The resulting mathematics can be translated and imported into a number of modeling packages where the equations can be solved and the output visualized (Figure 2.5). The current version of MEGen can generate code for Berkerley Madonna (www.berkeleymadonna.com), acslXtreme version 2.4 (www.acslXtreme.com), and MATLAB (www.mathworks.com), which are commercial available packages, and MCSim (http://fredomatic.free.fr/), which is freely available. In addition, MEGen provides a schematic diagram of a built model along with a corresponding table listing the value, units, source, origin, and reference for each parameter specified (Figure 2.6). The diagrams and tables can be exported directly into documents prepared in standard word processors, providing a clear, transparent, and auditable trail as well as error-free, auditable numerical code. Generated code is designed to be robust to modification outside of MEGen due to the presence of a number of check functions. One example of this is an expression to ensure that mass balance is preserved. Manual alterations to code can create inconsistencies in the equations, leading to predictions that do not correspond to the modeling assumptions. By inserting a check function that calculates the quotient of mass delivered and amount present in the compartments as well as the amount excreted, it is possible to plot this function over time. The mass balance check function should be used after every manual alteration made to the model code. Building such check functions into code generated using MEGen increases the chances of trapping errors in the code that may subsequently be manually adjusted. In the Berkeley Madonna code this function is expressed as: rel = IF(dose > 0)THEN mass/dose ELSE 1

Computer Implementation

Figure 2.6

37

Model documentation by MEGen.

The IF statement prevents division by zero when dose = 0. In practice, this is only likely to occur before exposure (usually at time = 0). 2.4.1

A PBPK Model for β-Chloroprene

Implementation is illustrated in this section, which includes a selection of screenshots taken from MEGen during the construction of a male Syrian Golden hamster model for simulation of exposure to β-chloroprene. The physiological, biochemical, and physicochemical parameters were taken from the paper by Himmelstein et al. (2004). It is not a comprehensive step-by-step guide, although the selection of screenshots should convey the intuitive nature of the approach. Table 2.4 lists the parameters used to build the model; they were either determined experimentally by Himmelstein et al. (2004), taken by Himmelstein et al. from Brown et al. (1997), or are default assumptions in MEGen. Clicking “database” or “model” menu options on the home page provides access to the PBPK database and model equation generator, respectively. Clicking on “model” and then “load” leads to a page where the model builder wizard can be run. In addition to obtaining help by clicking “Help” on the drop down menu, assistance and information text is available on various pages. The left-hand pane contains links to different steps of the model building process. The transparent box is a “floating menu” which allows models to be saved at various stages of the model building process, initiation of the building process, editing, and verification of a model structure (validation) and the generation of model code for export. Model building is initiated by clicking “Begin” at the bottom right-hand corner; alternatively, clicking “Labeling” in the left-hand pane of the model builder wizard home page

38

PBPK Modeling: A Primer

Table 2.4 Parameters used to build model for β-chlorpyrene in MEGen. Parameter

Symbol

Value

Molecular mass (g/mol) Body mass (kg) Proportion of vascularized tissue (body mass) Cardiac allometric constant (l/h/kg) Cardiac allometric exponent Respiratory allometric exponent Blood:air partition coefficient

RMM BW VT QCC CAE RAE Pba

88.53 0.11 0.91 30 0.75 0.75 9.3

Metabolism (Oxidative, Liver) Michaelis constant (mg/l) Maximum rate of metabolism (scaled to body mass) (mg/h)

KM V max C

Gas exchange Proportion of dead space (not involved in gas exchange) Respiratory allometric constant (l/h/kg)

DS QPC

0.3 30

c

Partition coefficient Slowly perfused Richly perfused Adipose Liver

Pspda Prpda Pfaa Plia

5 8.2 130.1 10.5

a

Tissue blood flow as a fraction of cardiac output Slowly perfused blood flow Richly perfused blood flow Adipose blood flow Liver blood flow

QspdC Qrpd QfaC QliC

0.15 0.07 0.183

Tissue volume as a fraction of body mass Slowly perfused mass Richly perfused mass Adipose mass Liver mass

V spdC V rpd V faC V liC

0.75 — 0.07 0.04

0.118 4.28

Reference c b c a c c a

a a

a

a a a

a d a a

b d b b

a

Himmelstein et al. (2004). Brown et al. (1997). Default assumption in MEGen. d Calculated by difference by MEGen. b c

opens the labeling page. A title and description of the model can be entered here. A simple PBPK model comprising a slowly and richly perfused compartment, represented by the schematic on the right-hand side, is the starting point of the model building process. As organs and tissue compartments are defined discretely they are removed from the aggregated compartments and the schematic diagram is updated accordingly. The aggregated compartments are reduced by the same mass and blood perfusion rate as the newly defined discrete compartment in order to maintain mass and blood flow balance. Clicking on “Exposure routes” or “next” in the bottom right-hand corner links to the “Exposure Routes” page (Figure 2.7). At the time of writing, MEGen had dermal, inhalation, and intravenous routes available. An example of how the schematic diagram is updated to include a gas exchange

Figure 2.7

Configuration of exposure routes in MEGen.

40

PBPK Modeling: A Primer

compartment when the inhalation route is enabled is illustrated in Figure 2.7. Clicking “Next” in the bottom right-hand corner or “Metabolism” in the left-hand panel links to the page where metabolism can be ascribed to, and enabled for, any chosen organ or tissue compartment. The schematic is updated to include a compartment in which metabolism can take place. In this example the diagram displays the liver compartment. Any number of enzymes, which contribute to metabolism, can be described. Clicking on “Functions” in the left-hand pane links to the “Functions” page. The appropriate form or “dose metric” of the chemical leading to a biological response is selected on this page. For example, the “peak” value or “areaunder-the-curve” of the venous or exhaled concentration of chemical or the rate or amount metabolized may be selected. Clicking “Compartments” in the left-hand pane or “Next” at the bottom right hand corner loads the compartments page (Figure 2.8). More compartments may be defined discretely by enabling the required compartment. In the example shown in Figure 2.8 adipose, stomach, and gut compartments have been enabled. Another example of an in-built check function is demonstrated in Figure 2.8. The correct anatomical location of organs and tissues such as the stomach and gut, which send blood to the liver by pouring blood into the hepatic portal vein, are enforced in MEGen. Likewise, when enabled the lung would appear separately from the gas exchange compartment and have the same configuration of arterial input and venous output as seen for liver, adipose, richly perfused, and so on. This is because the lung has two circulations, the pulmonary circulation that perfuses the alveoli, and the bronchial circulation that provides nutrients and gas exchange for the conducting airways. The bronchial circulation is part of the systemic circulation and receives about 2% of the cardiac output from the left side of the heart. Many PBPK models published in the literature, which describe a lung compartment for the estimation of tissue dosimetry, do not separate the bronchial and pulmonary circulations (e.g., Csanady et al., 2003; Himmelstein et al., 2004). Clicking on “Animal” in the left-hand pane links to the animal selection page. The anatomical and physiological parameters for a number of animal species and their gender are available in the database. Selection of an animal species imposes a filter during interrogation and retrieval of model parameters from the database, so that only those parameters corresponding to that animal species can be selected. Clicking on “Chemical” in the left-hand pane links to the chemical selection page. Chemical specific data such as partition coefficients can also be stored in the database. The specification of a chemical imposes an additional filter to further limit the interrogation and retrieval of chemical-specific data from the database. Clicking on “Configuration” links to the “Configuration” page where on–off time points for exposure may be configured. Each enzyme that contributes to the metabolism of the chemical is named on this page. In the case of β-chloroprene a general name such as “oxidative” may be entered to describe cytochrome P450 enzyme mediated oxidative metabolism. In addition, an abbreviation may be entered such as “2E1” if the specific isoenzyme catalyzing the metabolism of the chemical is known. This information provides labels that will appear in the code that is generated once the model is completed and also provides the name “Oxidative metabolism,” in this case, for the header on the data entry page for metabolism (Figure 2.9). Clicking on “Data” in the left-hand pane links to the page where model parameters can be selected (Figure 2.9). Model parameters such as body mass, organ and tissue masses, blood perfusion rates, partition coefficients, and metabolic rate constants are entered on the “Data” page. Clicking

Figure 2.8

Additional compartment selection in MEGen.

Figure 2.9

Model parameter input in MEGen.

Computer Implementation

43

the “Root” header allows entry of the molecular mass of the chemical, the body mass of the animal, proportion of vascularized tissue, and blood:air partition coefficients. If allometric equations are used to estimate cardiac output then the cardiac allometric constant and exponent may be entered. The default allometric exponents for biological flow rates are 0.75 (Ings, 1990). The respiratory allometric constant or alveolar ventilation rate is entered under the “Gas exchange” header (Figure 2.9). Clicking on “Edit” allows selection of a datum (Figure 2.10). An “Edit datum” dialog box appears. Clicking the cylinder symbol initiates a search of the PBPK database. If the datum does not appear in the database the datum may be entered manually by clicking the fountain pen nib symbol. Clicking the cylinder brings up another dialog box with a datum selected from the database. In this example, the blood:air partition coefficient for β-chloroprene in the Golden Syrian Hamster is available (Figure 2.11). In addition to the parameter value, the animal species, sex, chemical, and source of the datum are displayed. Also, the ticked boxes indicate that filters for animal species and chemical are enabled. Clicking “Select” retrieves the datum, which is then incorporated into the model. A summary information page, for the selected datum, appears by clicking the information button, “i” to the left of the “Select” button in the dialog box. The partition coefficient, organ mass, and perfusion rate are retrieved by interrogating the database or entering the value directly as described for each compartment. The appropriate units for the metabolic rate constants, K M and V max may be selected from a drop down menu obtained after clicking the “Oxidative” header. Clicking “Finish” in the left-hand pane links to the “Build Complete” page. The model is considered “valid,” which, in this specific context, implies that all the required parameters and configurations have been successfully entered (Figure 2.12). A validation report on model structure may be viewed by clicking “View validation report.” The validation report provides an overview of the model. It lists the compartments, exposure, and elimination routes. When a datum is missing from a specific compartment it is highlighted along with instructions to rectify the problem. When clicking “generate code” an XML document is created, which is populated by the built model. The PBPK functional forms are merged, in the form of MathML, into the XML document (see the folder entitled LOIZOU in the QMT Model Library). For the computer codes of PBPK models written in Bekeley Madonna and Microsoft Excel, ACSL, and MATLAB the reader is referred to the MODEL LIBRARY folders for Chapters 3, 4, 5, 7, and 11 (e.g., manganese, 2,3,7,8-TCDD, chloroform and mixtures of volatile aromatic hydrocarbons). A list of toxicologically important chemicals for which PBPK models have been developed in one or more species is provided in Table 2.5. For further mathematical treatment of PBPK models, parameter estimation methods, as well as their evaluation and use in risk assessment, the reader is referred to Gerlowski and Jain (1983), Clark, Setzer, and Barton (2004), Reddy et al. (2005), Lipscomb and Ohanian (2006), Chiu, Barton, and Dewoskin (2007), Krishnan and Andersen (2007) and Chapter 21. Whereas Chapter 5 of this volume discusses physiological parameters and databases for PBPK modeling, the following sections highlight current progress and challenges regarding the integration of in vitro and in silico approaches within PBPK models, to facilitate their rapid development in data-poor situations.

Parameter selection in MEGen.

Cylinder

Figure 2.10

Fountain pen nib

Figure 2.11

Searching the database in MEGen.

Figure 2.12

MEGen model completion screenshot.

Computer Implementation

47

Table 2.5 List of environmental chemicals for which PBPK models have been developed in one or more speciesa . Acetone Acrylamide Acrylic acid Acrylonitrile & cyanoethylene oxide Aldicarb Allyl chloride Amyl methyl ether (tert) & tert-amyl alcohol Arsenic

Dichloroethane (1,2-) Dichloroethylene (1,1-; 1,2) Dichloromethane Dichlorophenoxyacetic acid (2,4-) Dieldrin Diethylether Difluoromethane

Methyl mercury Methyl tertiary-butyl ether Methylene chloride Methylene dianiline (4,4 -)

Diisopropylfluorophosphate

Benzene Benzo(a)pyrene Benzoic acid Bisphenol A Bromide Bromochloromethane Bromodichloromethane Bromoform Bromotrifluoromethane

Dimethyl sulfate Dioxane (1,4-) Dioxins Ethanol Ethyl acrylic acid Ethylbenzene Ethylene dibromide Ethylene dichloride Ethylene glycol and its metabolite Ethylene glycol mono butyl ether & intermediates Ethylene oxide Fluazifop-butyl Fluoride

Naphthalene & naphthalene oxide n-Hexane n-Hexane Nickel Nicotine Nitropyrene Octamethylcyclotetrasiloxane Paraoxon Parathion PCBs

Butadiene (1,3-) and metabolites Butanol (tertiary) Butoxyacetic acid (2-) Butoxyethanol (2-) and metabolites Butyl compounds (n-butyl acetate, n-butanol, n-butyraldehyde, n-butyric acid) Carbon tetrachloride

Chlordecone Chlorfenvinphos Chloride Chloro(1-)-1,1difluoroethane Chloro(2-)-1,1,1,2tetrafluoroethane Chlorobenzene Chloroethane Chlorofluorohydrocarbons

Formaldehyde

Furans

Methylethylketone Methylmetacrylate Mirex

p-chlorobenzotrifluoride Pentachloroethane Pentafluoroethane Phthalates (diethylhexyl-; dibutyl-; monobutyl-) Polychlorotrifluoroethylene

Glycol ethyl ether acetate Glycol monomethyl ether Heptafluoropropane Hexachlorobenzene

Propylene glycol methyl ether & propylene glycol methyl ether acetate Pyrene Styrene Tetrachloroethane (1,1,1,2-) Tetrachloroethane (1,1,2,2-)

Hexachlorobutadiene

Tetrachloroethylene

Hexachloroethane Hexanedione (2,5-) Hexanemethyldisiloxane

Tetrachorobenzyltoluene Toluene Toluene diamine (Contined)

48

PBPK Modeling: A Primer

Table 2.5 (Continued) Chloroform

Hydroquinone

Chloromethane Chloropentafluorobenzene Chloroprene (β-) Chlorpyrifos Chromium Cyclohexane DDE Decane Diazinon Dibromochloromethane Dibromoethane (1,2-) Dibromomethane Dichloro(1,1-)-1fluoroethane Dichlorodiphenylsulfone (p-p -)

Iodide Iron Isofenphos Isoflurane Isopropanol Isopropene Lead Lindane Malathion Manganese Methanol Methoxyacetic acid (2-) Methoxyethanol (2-)

a

Trichloroethylene and its metabolites Trichlorofluoromethane Trichloropropane (1,2,3-) Trifluoroethane Trifluoroiodomethane Trifluralin Trimethyl-2-pentanol (2,4,4-) Trimethylbenzene (1,2,4-) Vinyl acetate Vinyl chloride Vinyl fluoride Xylene Zinc

Methyl chloroform

Based on compilations by Krishnan and Andersen (2008).

2.5 In silico Methods for PBPK Modeling Limited advances have been made regarding the development of in silico methods, particularly qualitative and quantitative structure–activity relationship (QSAR) models for parameterizing PBPK models (B´eliveau and Krishnan 2003). An advantage of QSARs is that the impact of number and nature of the molecular fragments on the pharmacokinetics of chemicals (within the valid application domain) under untested scenarios can be generated. As such, these could be useful as a tool for screening-level evaluation and for planning limited key pharmacokinetic studies in vivo. The in silico approaches for estimating tissue:air, blood:air and tissue:blood partition coefficients may be one of the following types: empirical, mechanistic, and semi-empirical (B´eliveau and Krishnan, 2003). The empirical methods relate the partition coefficients to structural features or physicochemical properties of chemicals through a mathematical function, whereas the mechanistic approaches allow the use of information on the mechanisms (i.e., solubility and binding) in computing the parameters. In this regard, the tissue:blood PCs of volatile organic chemicals, for which macromolecular binding in tissue and blood is negligible, have been estimated from n-octanol:water PCs or vegetable oil:water PCs (Po : w ) as follows (Poulin and Krishnan, 1995):

Pt =

(Po:w × Fnlet ) + Fwet (Po:w × Fnleb ) + Fweb

(2.27)

In silico Methods for PBPK Modeling

49

Table 2.6 The content (volume/volume) of neutral lipid and water equivalents of major tissues in humans and rats (Poulin, Beliveau, and Krishnan, 1999). Water equivalent

Neutral lipid equivalent

Tissues

Rat

Human

Rat

Human

Blood Fat Liver Muscle

0.842 0.121 0.717 0.747

0.821 0.151 0.740 0.757

0.002 0.853 0.042 0.011

0.004 0.798 0.047 0.037

where Fnlet = fractional volume of neutral lipid equivalents in tissue, calculated as the sum of neutral lipids plus 0.3 × phospholipid content, Fwet = fractional volume of water equivalents in tissue, calculated as the sum of tissue water content plus 0.7 × phospholipid content, Fnleb = fractional volume of neutral lipid equivalents in blood, calculated as the sum of neutral lipids plus 0.3 × phospholipid content, and Fweb = fractional volume of water equivalents in blood, calculated as the sum of tissue water content plus 0.7 × phospholipid content. The physicochemical properties in the above equation, in turn, can be obtained with the use of QSARs, and integrated with tissue-specific water and lipid composition data (Table 2.6). Poulin and Theil (2000, 2002) demonstrated the applicability of the above algorithm to predict the tissue:plasma partition coefficients and volumes of distribution of pharmaceuticals, with the consideration of protein binding, as follows: 

Pvow · Vnlt + 0.3 · V plt + 1 · Vwt + 0.7 · V plt f up 
·
f ut Pvow · Vnlp + 0.3 · V plp + 1 · Vwp + 0.7 · V plp

(2.28)

where: Pvow = vegetable oil:water PC; V = total volume fraction; nl = neutral lipids; pl = phospholipids; t = tissue; p = plasma; fup = unbound fraction in plasma; and fut = unbound fraction in tissue. More recent re-formulations of this algorithm, accounting for the differential behavior in acidic and neutral phospholipids, have been published (Box 2.5). Such in silico approaches for predicting maximal velocity and the Michaelis constant for metabolic reactions in animals and humans are not available yet (B´eliveau and Krishnan, 2003). The limited QSARs developed to date have characterized the fragment-specific values related to intrinsic clearance of volatile organic chemicals (e.g., Table 2.7). The in silico approaches, or algorithms, have been integrated within PBPK models to automatically generate pharmacokinetic predictions based on molecular structure information (B´eliveau et al., 2005; B´eliveau and Krishnan, 2005; Kamgang, Peyret, and Krishnan, 2008).

50

PBPK Modeling: A Primer

Table 2.7 Fragment Specific Contributions toward Po : a and Pw : a as well as Intrinsic Clearance [CLint (l/h/µmol P450)]. Fragments

Log Po : a

Log Pw : a

Log CLint

CH3 CH2 CH C C C H (on ) Br Cl F AC H AC

0.354 0.441 0.377 −0.354 0.197 0.134 0.174 0.776 0.136 3.729 −0.19.0

−3.76E–2 −0.223 −0.477 −1.49 −1.94 0.555 0.622 0.468 0.229 0.650 −0.062 4

1.552 0.514 7.83E–2 −0.871 0.591 0.383 1.00 0.522 −7.646 1.535

From B´eliveau et al. (2005).

Box 2.5: Algorithms for Calculation of Tissue:Plasma Partition Coefficients for Pharmaceuticals (Rodgers, Leahy, and Rowland, 2005; Rodgers and Rowland, 2006) Tissue:plasma PC for weak bases

  Ka AP− T · 10 pK a− p HI W 1 + 10 pK a− p HIW · fIW + Ptp = f EW + 1 + 10 pK a− p H p 1 + 10 pK a− p H p Pow · f NL + (0.3 · Pow + 0.7) · f NP + . 1 + 10pKa−pHp Tissue:plasma PC for acids, neutrals, and zwitterions Ptp = f EW +

X · f IW Pow · f NL + (0.3 · Pow + 0.7) · f NP + + KaPR · [PR]T Y Y

where: f = fractional tissue volume; EW = extracellular water; IW = intracellular water; NL = neutral lipids; NP = neutral phospholipids; PR = dominant binding protein; AP= acidic phospholipids; T = tissue; Ka = association constant; pKa = acid dissociation constant; X = 1 for neutrals; (1 + 10pKa – pHIW for monoprotic bases; 1 + 10pHIW-pKa for monoprotic acids; 1 + 10pHIW-pKaACID +10pKABASE-pHIW for zwitterions); Y = 1 for neutrals; (1 + 10pKa-pHp for monoprotic bases; 1 + 10pHp+pKa for monoprotic bases; 1 + 10pHIW-pKaACID + 10pKABASE-pHIW for zwitterions).

2.6 In vitro-Derived Metabolic Parameters for PBPK Models The development of PBPK models, especially those for the human, is complicated by many factors. For humans, ethical constraints limit the exposure to known or suspected toxicants.

In vitro-Derived Metabolic Parameters for PBPK Models

51

Substance availability for scarce and otherwise untested and expensive products may limit the amount of substance available for in vivo testing. Especially in these circumstances, in vitro test systems offer an alternative means of characterizing metabolism. In vitro systems have been used to develop and extrapolate clearance values useful in designing pharmacokinetic and toxicologic studies with test animals, and similar studies with human preparations have been used to develop data considered when estimating safe “first in human” doses for testing of drugs in development. In vitro test systems offer several distinct advantages over in vivo systems in metabolic studies. There are several methodological considerations that must be undertaken when designing, conducting and evaluating data from in vitro systems for the purpose of extrapolating metabolic rate constants. Among these are the choice of the in vitro test system, the methods to quantify metabolic rate constants, data and methods to quantify the amount of enzyme in the intact liver, data to extrapolate in vitro metabolic rate constants to the intact liver, and allometric scaling of extrapolated metabolic rate constants for use in parameterizing PBPK models. 2.6.1

Choosing the In Vitro System

The choice of system and method require careful consideration, with advantages and drawbacks inherent in each. Choosing the in vitro test system requires some basic considerations. Some of the available test systems include tissue slices, isolated cells in primary suspension culture, isolated and plated cells, subcellular fractions (cytosol, microsomal protein, etc.), purified enzymes, recombinantly expressed enzymes, and so on. If characterizing the metabolites without regard to metabolism rate constants, tissue slices may be acceptable; for determining the enzymes responsible for metabolism, recombinant systems represent a good choice. However, to get results best suited to the species of interest, the isolated hepatocyte in suspension culture may represent the best option. When the metabolism of the compound has not been determined (it is not known which enzyme is responsible), the use of plated cells should be avoided, due to the shift in enzymology (selective down-regulation of some enzymes). Further, distribution of substance in an inhomogeneous system may complicate the understanding of substrate availability in the cell. To the extent possible, binding of the substrate to components of the system other than the enzyme or metabolic system should be taken into account. For example, protein binding in vitro may be different from that in vivo, resulting in differential availability to the metabolic systems studied in vitro and for which predictions will be made in vivo. The use of recombinantly expressed enzymes presents some often under-appreciated complications. These systems typically use an expression vector such as bacteria to express a cloned and inserted human gene encoding a drug metabolizing enzyme. When isolated in microsomal protein (especially), these enzymes reside in a lipid matrix that is different in composition and physicochemical properties from that of the human. Further, differences in co-enzymes, such as oxidoreductases, between the two species may also result in different observed catalytic properties of the enzyme (Remmel and Burchell, 1993), although amino acid sequence may be identical. When the enzymology is known, then subcellular preparations offer a cost effective and readily available consideration. These preparations can be easily made in the laboratory or procured from commercial services. The availability of samples from multiple human organ donors offers a means to estimate population variability, within some constraints.

52

PBPK Modeling: A Primer

2.6.2 Quantifying Metabolic Rate Constants PBPK models are populated with values for metabolic rate constants, typically expressed as units of mg/h. The expression of in vitro-derived metabolic rate constants is typically in units of pmol/min/mg subcellular fraction (e.g., microsomal protein; MSP), pmol/min/pmol of a given enzyme, or pmol/min/106 hepatocytes. It is important to consider the expression of enzyme in the in vitro system. Up until recently, metabolic rate constants have usually been expressed as rate per time per milligram MSP, most often without regard to considerations such as inter and intraspecies differences in the MSP content of the responsible enzyme (e.g., pmol CYP2E1/mg MSP). This is a primary concern when extrapolating metabolic rate constants for substrates metabolized by a specific (single) form of an enzyme. Recent advances in quantitative models adapted to 96-well plate reading quantitation have enabled near high-throughput quantitation of CYP forms (Snawder and Lipscomb, 2000). These methods have also been applied to MSP from other species, increasing the reliability of interspecies comparisons of metabolic rate constants derived in vitro. Species differences in enzyme expression have been demonstrated to be one basis for quantitative metabolic differences between species. The combination of well-controlled in vitro metabolic rate constant determination and determination of the responsible enzyme concentration in subcellular preparations can result in increased understanding of interspecies differences in chemical metabolism. Recently, in vitro studies to determine metabolic rate constants for the CYP2E1-mediated metabolism of chloroform in rats and humans demonstrated remarkable species similarity in the specific activity of CYP2E1 for chloroform (pmol/min/pmol CYP2E1) between rats and humans (Lipscomb et al., 2003, 2004). The determination of metabolic rate constants for CYP enzymes usually assumes saturable metabolism, but exceptions have been noted for some forms (e.g., CYP3A forms). For saturable reactions, K m and V max values are derived via conventional methods. The extrapolation of V max values is a relatively straightforward process, whereas the extrapolation of K m values is somewhat more challenging. 2.6.3 Enzyme Quantitation Studies Because the ultimate mediator of xenobiotic biotransformation is the enzyme, the extrapolation of data (i.e., metabolic rate constants) derived in vitro requires quantitative data on enzyme distribution. Regardless of the preparation involved, the goal is the same – to determine the amount of enzyme present per individual (organism). Because most PBPK models are constructed around the assumption that metabolism occurs primarily, if not solely, in the liver, then this is the initial target for extrapolation of enzyme quantity. This is of more direct importance for studies conducted with subcellular preparations than with isolated hepatocytes. Studies with MSP are typical of studies with cytosol and will be used here as an example. The units of expression of original metabolic rate constants determine the methods and data required for extrapolation. When V max is expressed only per milligram MSP, and there are no data to determine the identity of the enzymes involved, or when the substrate is metabolized by multiple enzymes (e.g., multiple CYP forms), then optimal units of measurement may be those expressed per milligram MSP. Here, the most important laboratory measurement may

In vitro-Derived Metabolic Parameters for PBPK Models

53

Table 2.8 Physiologic and biochemical parameters important for scaling in vitro clearance valuesa . Parameter

Parameter value

Scaling factor

0.25 kg 4.5 g/kg BW 1.35 × 108 cells/g liver 45 mg/g liver

11 g 1.5 × 109 cells 500 mg MSP

70 kg 2.6 g/kg BW 99 × 106 cells/g livere 34 mg/g livere

1 820 g 1.8 × 1011 cells 61,880 mg MSP

b

RAT Body Weight Liver Weight Hepatocellularity MSP Yield HUMANc, d Body Weight Liver Weight Hepatocellularity MSP Yield a

Adapted from Lipscomb and Poet (2008). Source: Houston (1994); presented for a Standard Rat Weight (SRW) of 250 grams; values from published literature. c Human values adapted from typical PBPK values. d Cardiac output = 5200 ml/min, liver blood flow = 25% cardiac output; Body weight = 70 kg; liver mass = 0.026 BW (Brown et al., 1997). e Source: Barter et al. (2007). b

be that describing the amount of MSP per gram liver. Barter et al. (2007) have presented the results of a meta analysis of laboratory data demonstrating that a general consensus value for the amount of MSP per gram human liver might be 32 mg/gram. Biological values for the amount of human liver per body mass are available and are already used in PBPK modeling for the purpose of predicting liver dosimetry. For example, if liver comprises 0.026 of body mass, then a 70 kg human will have a liver mass of 1800 grams. Values for mice are not readily available, but Houston and colleagues have developed a value of 55 mg MSP/gram rat liver, and this value has been widely used in the in vitro to in vivo extrapolation of clearance values in drug development. However, when the enzymology or a reaction is known, especially when the reaction is catalyzed by a single form (e.g., CYP2E1), then data on the MSP content of that enzyme become important. There are multiple studies that have presented the distribution of CYP forms to human MSP (e.g., Shimada et al., 1994; Snawder and Lipscomb, 2000). To extrapolate metabolic rate constants expressed per unit enzyme (e.g., pmol/min/pmol CYP2E1), then combining data sets describing the distribution of enzyme to MSP and describing the distribution of MSP to intact liver can and have been combined. This approach was employed by Lipscomb et al. (2004) to examine the population variability of metabolic rate constants for trichloroethylene oxidation in humans, and more recently to examine the age and population variability of chloroform oxidation in humans (USEPA, 2005). Mathematically, these approaches are demonstrated below. Table 2.8 provides some quantitative data useful in the IVIVE of V max values for application in PBPK modeling. 2.6.4

Extrapolation of V max values

Once V max has been determined and appropriate protein (enzyme) recovery data are located, extrapolation to the intact organism is accomplished, followed by scaling for incorporation

54

PBPK Modeling: A Primer

into PBPK models. When V max is determined and expressed as specific activity (turnover number), for example, pmol/min/pmol microsomal enzyme, then the extrapolation to intact liver is constructed as: pmol/min/pmol enzyme × pmol enzyme/mg MSP × mg MSP/gram liver × gram liver/organism = pmol/min/liver (2.29) When V max is determined and expressed as pmol/min/ mg MSP, then the extrapolation to intact liver is constructed as: pmol/min/mg MSP × mg MSP/gram × gram liver/organism = pmol/min/liver When V max is determined and expressed as pmol/min/106 hepatocytes, then the extrapolation to intact liver is constructed as: pmol/min/106 hepatocytes × hepatocellularity (e.g. 99 × 106 cells/gram human liver) × gram liver/organism = pmol/min/liver (2.30) The final step in extrapolation of in vitro-derived metabolic rate constants is scaling for inclusion in the model code for the PBPK model. Once extrapolated to units of “pmol/min/liver,” this is equivalent to pmol/min/animal; this value is then adjusted by formula weight and by scaled body weight, as demonstrated below. Because PBPK models include V max as a value scaled to body weight, typically body weight raised to the 0.75 power, this must also be taken into account. Once V max is expressed per whole body (e.g., mg/hour), body weight (not the V max value) is raised to the exponential power. Using an in vitro-derived metabolic rate of 175 mg/h (per 70-kg human) as an example, the following demonstrates the scaling for incorporation in PBPK modeling. While other exponential powers of body weight may be used, this example is typical, in that it uses body weight raised to the 0.75 power. (70 kg)0.75 = 24.2 kg 175 mg/h/24.2 kg = 7.23 mg/h/kg

(2.31) (2.32)

The V max C value would be 7.23 mg/h/kg 2.6.5 Extrapolation of K m Values The extrapolation of V max values has been accomplished for several compounds, but the extrapolation of K m values has not received so much attention. Most often, PBPK models are constructed so that K m values (as substrate concentration) are expressed as concentration in venous blood at equilibrium with liver. This construction seems to be based on reasoning that substrate in the aqueous phase of liver will be at equilibrium with the concentration of substrate in blood. The implicit assumption seems to be that these concentrations will be not only in equilibrium, but will be equivalent. There are other considerations and approaches to the extrapolation of K m values derived in vitro, and these differ for volatile and non-volatile compounds, and for lipophilic and hydrophilic compounds. For volatile compounds for which K m values are reported as concentration in headspace, these concentrations may be adjusted to represent concentration in either the biological component (i.e., hepatocytes) of the incubation system or concentration in the incubation system. The

References

55

latter is appropriate when the incubation system can be deemed a valid representation of the functional characteristics of the intact liver. Once this has been accomplished, the concentration in the representative phase of the incubation system can be multiplied by the value of the liver:blood partition coefficient used in the model to adjust the concentration so that it is expressed in units of concentration in venous blood at equilibrium with liver tissue (Mazur et al., 2007). The same considerations, except for consideration of partitioning from headspace into incubation system, apply to non-volatile compounds. It may be reasoned that for hydrophilic compounds little, if any, adjustment from in vitro K m values may be necessary when incorporating those values into PBPK models. For lipophilic compounds, some accounting for partitioning into the enzymatic fraction of the incubation system should be considered. Finally, differences between protein binding in the in vitro system and in vivo should be taken into account. Differential protein binding can significantly affect the free fraction of substrate available for metabolism (Lipscomb and Poet, 2008). While protein binding can affect metabolic rates, when V max values are derived in vitro under saturating conditions, it may be reasoned that protein binding may have a greater impact on K m values than on V max values. Clearly, the extrapolation of K m values has received far less attention that the extrapolation of V max values.

2.7

Concluding Remarks

This chapter provided a beginner-level description of the mathematical representation and computation implementation of PBPK models. The model codes in the QMT Model Library should facilitate structured learning of PBPK modeling. Other chapters in this book provide ample examples and model codes for describing protein binding and induction, diffusion-limited uptake, hepatic sequestration, metabolite kinetics, metabolic interactions, GSH depletion by reactive metabolites, and so on. Also, examples in this volume describe the role of probabilitic analyses and Bayesian approaches in PBPK modeling as well the tools and approaches for the conduct of specialized analyses (variability, uncertainty, and sensitivity) (Chapters 17 and 20). Progress to-date and challenges associated with the documentation, evaluation, and validation of PBPK models and other quantitative models in toxicology are discussed in Chapter 21.

Acknowledgements The authors thank Thomas Peyret and Katia Sokoloff of Universit´e de Montr´eal for their assistance with the preparation of this chapter.

References Andersen, M.E., Mills, J.J., and Gargas, M.L. (1993) Modeling receptor-mediated processes with dioxin: Implications for pharmacokinetics and risk assessment. Risk Anal., 13, 25–36. Barter, Z.E., Bayliss, M.K., Beaune, P.H., et al. (2007) Scaling factors for the extrapolation of in vivo metabolic drug clearance from in vitro data: Reaching a consensus on values of human microsomal protein and hepatocellularity per gram of liver. Current Drug Metabolism, 8 (1), 33–45.

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B´eliveau, M. and Krishnan, K. (2003) In silico approaches for developing physiologically based pharmacokinetic (PBPK) models, in Alernative Toxicology Methods (eds H. Salem and S. Katz), CRC Press, NY, pp. 479–532. B´eliveau, M. and Krishnan, K. (2005) A spreadsheet program for modeling quantitative structurepharmacokinetic relationships for inhaled volatile organics in humans. SAR QSAR Environ. Res., 16, 63–77. B´eliveau, M., Lipscomb, J., Tardif, R., and Krishnan, K. (2005) Quantitative structure-property relationships for interspecies extrapolation of the inhalation pharmaconkinetics of organic chemicals. Chem. Res. Toxicol., 18, 475–485. Brown, R.P., Delp, M.D., Lindstedt, S.L., et al. (1997) Physiological parameter values for physiologically based pharmacokinetic models. Toxicol. Ind. Health, 13, 407–484. Chiu, W.A., Barton, H.A., and Dewoskin, R.S. (2007) Evaluation of physiologically based pharmacokinetic models for use in risk assessment. Journal of Applied Toxicology, 27, 218–237. Clark, L.H., Setzer, R.W., and Barton, H.A. (2004) Framework for evaluation of physiologically-based pharmacokinetic models for use in safety or risk assessment. Risk Anal., 24, 1697–1717. Clewell, H.J., Andersen, M.E., and Barton, H.A. (2002) A consistent approach for the application of pharmacokinetic modeling in cancer and noncancer risk assessment. Environmental Health Perspectives, 110, 85–93. Clewell, R.A., Clewell, H.J. 3rd (2008) Development and specification of physiologically based pharmacokinetic models for use in risk assessment. Regulatory Toxicology and Pharmacology, 50 (1), 129–143. Csanady, G.A., Kessler, W., Hoffmann H.D., and Filser, J.G. (2003) A toxicokinetic model for styrene and its metabolite styrene-7,8-oxide in mouse, rat and human with special emphasis on the lung. Toxicol. Lett., 138, 75–102. Csanady, G.A., Kreuzer, P.E., Baur, C., and Filser, J.G. (1996) A physiological toxicokinetic model for 1,3-butadiene in rodents and man: blood concentrations of 1,3-butadiene, its metabolically formed epoxides, and of haemoglobin adducts - relevance of glutathione depletion. Toxicology, 113, 300–305. D’Souza, R.W., Francis, W.R., and Andersen, M.W. (1988) Physiological model for tissue glutathione depletion and decreased resynthesis after ethylene dichloride exposures. J. Pharmacol. Exp. Ther., 245, 563–568. Fiserova-Bergerova, V. (1975) Mathematical modeling of inhalation exposure. J. Combust. Toxicol., 32, 201–210. Gear, C.W. (1971) Numerical Initial Value Problems in Ordinary Differential Equations, PrenticeHall, Englewoods Cliffs, NJ. Gerlowski, L.E. and Jain, R.K. (1983) Physiologically based pharmacokinetic modeling: principles and applications. Journal of Pharmaceutical Sciences, 72, 1103–1127. Haddad, S., Pelekis, M., and Krishnan, K. (1996) A methodology for solving physiologically based pharmacokinetic models without the use of simulation softwares. Toxicol. Lett., 85, 113–126. Haggard, H.W. (1924) The absorption, distribution and elimination of ethyl ether. Analysis of the mechanism of the absorption and elimination of such a gas or vapor as ethyl ether. J. Biol. Chem., 59, 753–770. Heinzel, G., Woloszczak, R., and Thomann, P. (1993) TopFit, Version 2.0 : Pharmacokinetic and Pharmacodynamic Data Analysis System for the PC (ed. G. Fischer), VCH Publishers, Stuttgart/New York. Himmelstein, M.W., Carpenter, S.C., Evans, M.V., et al. (2004) Kinetic modeling of beta-chloroprene metabolism: II. The application of physiologically based modeling for cancer dose response analysis. Toxicol. Sci., 79, 28–37. Houston, J.B. (1994) Utility of in vitro drug metabolism data in predicting in vivo metabolic clearance. Biochem. Pharmacol., 47, 1469–1479. Ings, R.M.J. (1990) Interspecies scaling and comparisons in drug development and toxicokinetics. Xenobiotica, 20, 1201–1231. Jonsson, F. and Johanson, G. (2001) Bayesian estimation of variability in adipose tissue blood flow in man by physiologically based pharmacokinetic modeling of inhalation exposure to toluene. Toxicology, 157, 177–193.

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3 Pharmacokinetic Modeling of Manganese – An Essential Element Andy Nong1 , Michael D. Taylor2 , Miyoung Yoon1 , and Melvin E. Andersen1 1

The Hamner Institutes for Health Sciences, USA 2 Afton Chemical Corp., USA

3.1 Introduction The past 20 years have witnessed the expansion of PBPK modeling for many compounds and the use of these models to support extrapolations required in risk assessment, including extrapolations from high to low doses, across routes of exposure and for different animal species, from the test animal to humans (Reddy et al., 2005; Chapter 19). Most of these successes were with exogenous compounds that lack active processes for controlling uptake, retention, and elimination. Essential elements participate in multiple biological pathways that conserve concentrations at low levels and may enhance their elimination at higher intake levels. Manganese is an essential metal that is obtained from the diet. Recommended dietary intakes are about 3 mg/day in an adult, but only a small percentage of the ingested manganese is taken into the body systemically. Manganese deficiency leads to a failure to thrive, congenital abnormalities, impaired reproductive performance, ataxia, and defects in lipid and carbohydrate metabolism. Despite its essentiality, inhalation of high levels of manganese dust and fumes in occupational settings, the intake of drinking water with high concentrations of manganese, or the inability to adequately excrete manganese via the bile lead to neurotoxicity in humans. The target tissues for manganese neurotoxicity are mid-brain structures such as the striatum and globus pallidus, which influence motor control, and which accumulate manganese in conditions where intake chronically exceeds elimination. Neurotoxicity generally arises Quantitative Modeling in Toxicology
C 2010 John Wiley & Sons, Ltd

Edited by Kannan Krishnan and Melvin E. Andersen

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Pharmacokinetic Modeling of Manganese – An Essential Element

over a prolonged period and results from accumulation of excess manganese in these tissues and impairment of function of dopaminergic and γ -aminobutyric acid (GABA)-containing structures. A Parkinson’s Disease-like condition known as manganism has been observed after prolonged (>2 years) inhalation of high concentrations (>1 mg/m3 ) of manganesecontaining dusts in occupational settings such as mining. More subtle neurological effects, such as subclinical deficits in fine motor control, have been reported in workers with chronic inhalation to lower concentrations (0.5–1 mg/m3 ) of manganese in other occupational settings such as smelting. Neurological effects have also been reported in human populations that consumed water or food with total manganese intakes by these routes of more than 10 mg/day, received manganese intravenously as a constituent in total parenteral nutrition (TPN) solutions, or in individuals with impaired clearance of manganese because of liver disease (Aschner and Aschner, 2005). The finding of similar neurological effects following high dose oral, inhalation, or parenteral exposure to manganese, or when hepatobiliary clearance of this metal is impaired, indicates that the dose to target tissue in the central nervous system is the critical determinant for manganese toxicity, regardless of route. Thus, the risk assessment challenge with manganese is to identify inhaled and ingested doses that do not alter target tissue concentrations to levels associated with neurotoxicity while ensuring adequate intake for normal function, including adequacy during critical times of manganese incorporation into tissues during early life-stage growth and development (Andersen et al., 2010). To do this, an understanding of the biological processes that control manganese movement to brain and its retention in brain and other target tissues is necessary. The integration of these characteristics for manganese uptake and persistence was possible with the PBPK models described in this chapter. Previous essential element models were developed for zinc (Foster et al., 1979; Miller, Krebs, and Hambidge, 2000) and copper (Cartwright and Wintrobe, 1964; Harvey et al., 2005). These models captured the control of these essential elements under normal and deficient dietary conditions. Compartmental (or mammillary) structure and linear exchange models distribute the elements to different tissues and cellular components. With manganese, a linear PK model was adapted to describe decreased gastrointestinal manganese uptake and increased hepatobiliary elimination seen with rising manganese dietary levels (Teeguarden et al., 2007a, 2007b, 2007c). However, linear compartmental exchange rates were unable to capture the kinetic data for inhalation exposure to manganese in which tissue concentrations at higher inhaled manganese increased within weeks to steady state and decreased rapidly to basal levels after cessation of exposure (Nong et al., 2008). A different model structure was required that had limited tissue stores of manganese capable of avidly binding manganese at low dietary intake that filled quickly on higher concentration exposures (Nong et al., 2009). Key components of the current model structure include: (1) saturable tissue binding, (2) variable percentage uptake from diet depending on daily manganese intake, (3) inducible biliary excretion, and (4) asymmetric tissue diffusion behaviors in tissue that have proportionately higher than average tissue manganese, such as mid-brain targets. With these processes included in the PBPK description, it is possible to examine the relative role of different processes in controlling tissue manganese concentrations over a broad range of intake concentrations from levels of deficiency to levels that can lead to toxicity. This chapter provides background on the development of the PBPK model for manganese, shows several examples of using main elements of the published model for examining PK

Processes Included In the PBPK Model for Manganese

61

behaviors for different exposure conditions, discusses extension of the modeling from the adult to other life stages, and outlines the risk assessment challenges in applying the PBPK model to assist in setting reference concentrations (RfCs) or references doses (RfDs) for this essential element.

3.2 3.2.1

Processes Included In the PBPK Model for Manganese Tissue Binding

The overall PBPK model schematic for manganese is made up of tissues with some maximal binding capacity for manganese (Figure 3.1). The manganese concentrations in various tissues represent a combination of free manganese and manganese bound to tissue

Inhaled Mn QP Lung & Nose

QC

Olfactory ka

B + Mnf

Mnb kd

kout

QBrn

Brain Blood kin

kin

kout

Striatum

kout Cerebellum

ka

B + Mnf

Arterial blood

Venous blood

kin

ka

Mnb

B + Mnf

kd

Mnb kd

Rest of body

Qbody

ka

B + Mnf

Mnb kd

Liver

QLiv

ka

B + Mnf

Mnb kd

Diet

Bile

Figure 3.1 Final manganese PBPK model structure (adapted from Nong et al., 2009). Tissue storage is based on binding rate constants (ka, kd) and regional brain manganese sequestration is determined by influx/efflux diffusional constants (kin, kout).

62

Pharmacokinetic Modeling of Manganese – An Essential Element

constituents. Tissue binding likely represents incorporation of manganese into various cytosolic macromolecules and into constituents within subcellular organelles, including mitochondria. While the binding sites are diverse, representing various intracellular pools, the binding is described with a maximal binding capacity per tissue and a single dissociation constant. The amount bound in a tissue is determined by association and dissociation processes between free manganese and the pool of binding sites, as noted in Equation 3.1. Mnfree + Bfree,tissue ← → Mnbound

(3.1)

The provision of a maximal binding capacity in each tissue allows a limited ability of each tissue to sequester manganese; saturation of the binding capacity with increasing exposure concentrations leads to differential increases of free manganese in certain tissues depending on this capacity. Free manganese is likely to be the form more closely associated with toxicity. The tissue binding processes are described by association and dissociation rate constants, ka and kd. The tissue dissociation constant (Kd) would be the ratio of the dissociation and association rate constants, that is, Kd = kd/ka. The change of amount of free manganese in the liver with time (dAliver / dt) includes loss due to binding and increased dissociation of bound manganese: dAliver = Q liv (Cart − Cvl ) + kdliver × ABliver − kaliver × Bliv dt ×Aliver − R Abile + kDiet

(3.2)

In addition to the binding between manganese and the tissue constituents (Bliv ), there is also uptake from the diet (kDiet), elimination to bile (RAbile ), and terms for manganese entering and leaving the liver in blood. The venous effluent concentration depends on the free manganese concentration in tissue divided by the tissue partition coefficient. The rate of change of the amount of bound manganese in liver (ABliver ) over time is then calculated as the difference in the rates of binding and the rates of dissociation from the bound complex: dABliver (3.3) = −kdliver × ABliver + kaliver × Bliv × Afree dt The rate constants for the association and dissociation processes are the main driving components for the exchange between free and bound forms of manganese. The maximal binding capacity (Bmax ) in each tissue regulates the storage capacity of the tissue for bound manganese: Bliv = Bmax,liv − Abound

(3.4)

The rate constants for these dissociation processes are small, indicating relatively slow exchange of manganese between bound and free pools (Figure 3.1). 3.2.2 Tissue Uptake/Accumulation Preferential increases of manganese in some brain regions compared to other tissues such as the liver were observed in several studies where rats were exposed to manganese by inhalation (Dorman et al., 2006a). Preferential tissue accumulation was achieved in the

Processes Included In the PBPK Model for Manganese

63

model by including asymmetric diffusion from tissue blood into tissue and back. Such asymmetries could arise from the presence of metal transporters with differential activity for efflux and intake in specific cells. With diffusion-limited tissue uptake, tissues have to be described with two compartments – tissue itself and tissue blood. Uptake from striatal blood to striatal tissue is described with a diffusional clearance (kin); the reverse direction from striatum to striatal blood was also described with a diffusional clearance (kout), but the two-diffusional clearances, kin and kout, have different values. Thus, the rate of change in amount of free manganese in the brain blood compartment with time (dABrBd / dt) depends on blood flow and diffusion from blood to brain and from brain back to blood, as shown in Equation 3.5. dABrBd = Q brn (Cart − Cvbr ) + koutstr × Astr − kinstr × ABrBd dt

(3.5)

In the striatal tissue (str), the rate of change of free manganese over time depends on the diffusion of manganese into and out of the tissues and the binding and release of manganese from the tissue binding capacity, as shown in Equation 3.6. dAstr = −koutstr × Astr + kinstr × ABrBd + kdstr × ABstr − kastr × Bstr × Astr dt

(3.6)

The diffusional clearance terms are likely to account for manganese movement across the blood–brain barrier into brain tissue (Moos and Morgan, 2000; Crossgrove et al., 2003; Yokel, Crossgrove, and Bukaveckas, 2003). Equations describing the binding of manganese to saturable tissue stores are similar to those for the liver. Simulated brain concentrations include amounts in tissue (free plus bound) and the contribution of blood in the brain compartment, assumed to be 3% of the tissue by weight (Brown et al., 1997). Basal tissue concentrations were used to provide initial estimates for tissue Bmax . 3.2.3

Calibrating Dietary Uptake and Biliary Elimination

Dorman and colleagues (2001a, 2001b, 2004) have collected extensive data on tissue concentrations in rats and monkeys exposed to manganese by diet and inhalation, and have evaluated the relationship between dietary manganese and increases in tissue manganese concentrations following inhalation exposures. Several studies were conducted with rats receiving diets containing 2, 10, or 100 ppm manganese. After maintenance on the diet for 13 weeks, analyses included both steady-state tissue manganese concentrations and elimination kinetics for an intravenous tracer dose of 54 MnCl2 (Dorman et al., 2001a). These studies were critical for setting dietary uptake and biliary excretion parameters. Initial calibration of the PBPK model consisted of adjusting daily manganese dietary intake (F DietUp ) and biliary elimination (kelim ) to correspond with the observed steadystate tissue concentrations in rats fed defined daily diets containing 2, 10, or 100 ppm manganese (Dorman et al., 2001a). Initial calibration also consisted of adjusting fractional gastrointestinal absorption (fdietup) and biliary manganese excretion (kbile ) rate based on the dietary levels. Since the processes controlling uptake and elimination of manganese are dose dependent (Teeguarden et al., 2007a), specific model parameters were defined for each diet. The biliary manganese excretion rate was fitted to be consistent with the tracer elimination kinetics following an intravenous (iv) injection of 54 Mn (Figure 3.2). These

64

Pharmacokinetic Modeling of Manganese – An Essential Element (a)

Total 54Mn Radioactivity (kBq)

30 25 20 15 10 5 0 0

20

40

60

80

100

60

80

100

60

80

100

Days

(b)

Total 54Mn Radioactivity (kBq)

30 25 20 15 10 5 0 0

20

40 Days

(c)

Total 54Mn Radioactivity (kBq)

30 25 20 15 10 5 0 0

20

40 Days

Figure 3.2 Simulation of the whole body 54 Mn elimination at different dietary concentrations: (a) 2, (b) 10, and (c) 100 ppm. Manganese dietary uptake and biliary excretion are calibrated to data from Dorman et al., 2001a. The curves represent model predictions and the symbols with standard errors represent data (8 rats/diet). Reprinted with permission from supplementary materials of Nong et al., 2009.

Processes Included In the PBPK Model for Manganese

65

biphasic tracer curves indicate that the relative amount of free manganese in the body increases slightly with increasing dietary intake and this increase is adequately captured by the manganese model with saturable binding within all the tissues in the body. Fractional gastrointestinal absorption was then determined in correspondence with the steady-state tissue manganese concentrations for each dietary level (Figure 3.3). Preliminary fits were (a) 5

Concentration (µg/g))

4

3

2

1

0 10

30

50

70

90

70

90

Days

(b)

Concentration (µg/g)

2.0

1.5

1.0 ` 0.5

0.0 10

30

50 Days

Figure 3.3 Manganese tissue binding capacity of the (a) liver and (b) striatum is calibrated to steady-state tissue concentrations (Dorman et al., 2001a). Dietary concentration of 2, 10, and 100 ppm were simulated. The curves represent model predictions and the symbols with standard errors represent data (8 rats/diet). Reprinted with permission from supplementary materials of Nong et al., 2009.

66

Pharmacokinetic Modeling of Manganese – An Essential Element

obtained for the tissue steady-state manganese concentrations in rats fed on each diet by adjusting tissue binding constants (ka, kd) and maximal capacity (Bmax ). Model fits to the dietary studies indicate that, as the dietary manganese level increases, the biliary manganese excretion increases and fractional dietary uptake decreases. These results are consistent with the rise in bile manganese concentration from increasing manganese dietary intake observed from several rodent studies (Teeguarden et al., 2007b). These changes in kinetic constants with dietary manipulations are essential for maintaining steady-state manganese levels in the body over a range of dietary manganese intakes. With increasing dietary intake of manganese, coordinate changes occur to restrict uptake percentage and enhance elimination.

3.2.4 Calibrating the Inhalation Exposures in Rats The second aspect of model fitting was the extension to describe inhalation. Studies were conducted with rats fed a 100 ppm diet that were exposed by inhalation to soluble MnSO4 at 0.03, 0.3, or 3 mg manganese/m3 for six hours per day for 14 consecutive days. This data set provided tissue concentrations of manganese in rats at the end of the exposure as well as tracer kinetics beyond the 14-day exposure period (Dorman et al., 2001b). A study was also conducted with rats fed a 10 ppm manganese diet exposed to MnSO4 at 0.1 and 0.5 mg/m3 for six hours per day, five days per week over a 90-day period (Dorman et al., 2004). This study included evaluation of tissue manganese concentrations of some cohorts midway through the inhalation exposure (i.e., day 45), at the end of the 90-day exposure, and at 45 and 90 days after the cessation of exposure, and included 54 Mn tracer clearance measurements immediately after the 90-day inhalation. Intake by inhalation was estimated from a particle deposition model that calculated the percentage of inhaled manganese that would be deposited in various regions of the respiratory tract. Soluble forms of manganese (MnSO4 and MnCl2 ) were modeled as rapidly dissolving after deposition on the respiratory epithelial surfaces and rapidly transferred into tissue and on to the blood. To represent the olfactory transport of manganese directly to the olfactory bulb along olfactory nerves observed in rodent studies, manganese deposited on the olfactory epithelium in the nose was modeled as being transported directly into the olfactory bulb, where it diffused into tissues within the olfactory tract in the central nervous system. Model simulations of the 14-day inhalation study (Dorman et al., 2001b) produced tissue concentrations consistent with the measured concentration-dependent increases in tissue concentrations (Figure 3.4). The ability to recapitulate the greater uptake of the striatum compared to liver tissue with increasing inhalation exposure to manganese was related to the inclusion of diffusion-limited permeability constants that had larger input than efflux clearance from tissue (kin and kout). Biliary elimination parameters did not have to be changed appreciably at high inhalation exposure of manganese (3 mg/m3 ) in these 14-day studies (Figure 3.4; 3 mg Mn/m3 ). As the inhaled exposure is increased from 0.03 to 3 mg Mn/m3 , the increases in tissue manganese estimated from the model were likely primarily increases in free manganese, since the available binding sites become filled. With the inclusion of saturable tissue manganese binding and differential transport, model predictions for liver and striatum were consistent with the data from the 14-day inhalation studies in rats. The model then predicted the more rapid approach to steady state and rapid

Processes Included In the PBPK Model for Manganese

67

Concentration (µ g/g)

Cerebellum 7

3 mg/m3

6

0.3 mg/m3 0.03 mg/m3

5 4 3 2 1 0 0

2

4

6

8

10

12

14

8

10

12

14

8

10

12

Days

Concentration (µ g/g)

Striatum 7

3 mg/m3

6

0.3 mg/m3 0.03 mg/m3

5 4 3 2 1 0 0

2

4

6 Days

Concentration (µg/g)

Olfactory Bulb 7

3 mg/m3

6

0.3 mg/m3 0.03 mg/m3

5 4 3 2 1 0 0

2

4

6

14

Days

Figure 3.4 Comparison of simulated manganese brain concentrations at various inhaled manganese concentrations during a 14-day exposure versus data collected in Dorman et al., 2001b. It is important to distinguish between data from experiments (symbols with error bars) and modelled results (curves) since they are different entities. Reprinted with permission from supplementary materials of Nong et al., 2009.

68

Pharmacokinetic Modeling of Manganese – An Essential Element

return to basal tissue levels like those observed in experimental studies than it would have if it were only consistent with low intake tracer rate constants. Thus, the characteristics of manganese tissue accumulation over different durations and exposure concentrations were achieved using tissue binding to regulate the daily tissue concentration excursions caused by manganese inhalation. The tissue binding capacity was a major factor in determining tissue manganese accumulation and slow release of tracer manganese. Maximal bound manganese tissue levels are reached once the binding capacities are saturated. The 14-day exposure model was then extrapolated to predict tissue levels following longer duration exposures (Figure 3.5). The simulated liver and striatal manganese concentrations were more consistent with measured levels after slight adjustments of dietary uptake and biliary excretion for the 10 ppm diet (F DietUp = 0.02, kBileC = 0.60 /h/kg). Nonetheless, the parameter set successful in simulating the 14-day studies produced extremely good predictions of the 90-day study, with only a slight over-prediction. A mammillary model lacking saturable tissue binding was not capable of making this extrapolation between these times of exposure and concentrations (Nong et al., 2008; Model A). With overexposure via inhalation, compensatory mechanisms exist to enhance biliary elimination – an observation also seen in the monkey (Dorman et al., 2006b; Nong et al., 2009). However, the gastrointestinal uptake of dietary manganese remains similar at higher inhaled concentrations as at lower inhaled concentrations. 3.2.5 Sensitivity Analysis of Model Parameters The sensitivity coefficients for the parameters controlling total manganese concentration in liver and striatum were generated to determine the influence of tissue binding constants on the tissue manganese concentration at low and high inhaled manganese exposure (Figure 3.6). Parameters related to the tissue binding capacity and tissue clearance were evaluated (i.e., kd, ka, Ptissue:blood , kin, kout, Bmax , Qtissue ). These sensitivity coefficients were estimated for 0.0, 0.03, or 3 mg Mn/m3 concentration exposure scenarios (until near steady-state concentrations were reached) and found to be highly dose dependent. As the inhaled manganese concentration increases, the liver binding capacity saturates and, consequently, the sensitivity of the tissue binding parameters (ka and kd) towards change in liver tissue concentration decreases. Liver free manganese concentration is highly sensitive to the liver partition coefficient and biliary excretion, while bound manganese concentrations are more sensitive to liver binding capacity (not shown). Changes in striatal manganese concentrations are sensitive to changes in brain influx and efflux permeability rate constants (kin, kout) at all manganese concentrations. Sensitivity of brain manganese concentration to binding parameters was high for dietary intake with and without low inhalation exposures and decreased sharply at high inhaled concentrations (Figure 3.6).

3.3

Model Results

3.3.1 Excursions of Free Manganese in Tissues Computer codes for running the manganese model in Berkeley Madonna are provided in the QMT library (Folder: NONG1). This model is adapted from Model B from Nong et al.

Model Results

69

Cerebellum Tissue concentration (µg/g)

4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.001 control

0.01 Inhaled Mn concentration

0.1

1

(mg/m3 )

Striatum Tissue concentration (µg/g)

4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 control 0.001

0.01 0.1 Inhaled Mn concentration (mg/m3 )

1

0.01 0.1 Inhaled Mn concentration (mg/m3 )

1

Liver Tissue concentration (µg/g)

4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 control 0.001

Figure 3.5 Comparison of simulated end of exposure manganese brain concentrations at various inhaled manganese concentration during a 90-day exposure versus data collected in Dorman et al., 2004. It is important to distinguish between data from experiments (symbols with error bars) and modelled results (curves) since they are different entities. Long-term changes in hepatobiliary excretion was needed to refine the model results (solid vs dotted lines). Reprinted with permission from supplementary materials of Nong et al., 2009.

70

Pharmacokinetic Modeling of Manganese – An Essential Element Cerebellum 1.00

Normalized sensitivity ratio

0.75 0.50 0.25 0.00 -0.25 -0.50 -0.75 -1.00 Bmax

ka

kd

kin

kout

Qbrn

kbile

fdietup

Bmax

ka

kd

kin

kout

Qbrn

kbile

fdietup

Striatum 1.00

Normalized sensitivity ratio

0.75 0.50 0.25 0.00 -0.25 -0.50 -0.75 -1.00

Liver 1.00

0 mg/m3 0.3 mg/m3 3 mg/m3

Normalized sensitivity ratio

0.75 0.50 0.25 0.00 -0.25 -0.50 -0.75 -1.00 Bmax

ka

kd

kin

kout

Qliv

kbile

fdietup

Figure 3.6 Sensitivity analysis of manganese concentration in the cerebellum, striatum, and liver at 0, 0.3, or 3 mg Mn/m3 for various model parameters. The model parameters analyzed in each tissue are maximal binding capacity (Bmax ), association and dissociation rate constants (ka, kd), influx and efflux permeability diffusion rate constants (kin, kout), tissue blood flow (Qtissue ), biliary elimination rate (kbile), and dietary absorption fraction (fdietup). The tissue with asymmetric diffusion has a more diverse group of factors affecting tissue accumulation. Reprinted with permission from supplementary materials of Nong et al., 2009.

Model Results

71

(2008) and includes saturable binding stores for tissue manganese. In this adaptation, the brain is divided into two equally sized regions. In region I, there is asymmetrical diffusion; in region II diffusional clearances are comparable for intake and efflux. The first exercise examines the alteration in tissue stores of manganese in the rats exposed to 3 mg Mn/m3 for six hours per day, every day for 14-days. The model calculates increases in tissue concentration during inhalation exposures and calculates the percentage of manganese in brain and liver that is free. PCFTissue = 100∗ (Afree, tissue/Atotal, tissue)

(3.7)

The distribution between bound and free manganese in each tissue is mainly determined by the dissociation binding ratio (i.e., kd/ka), binding maximum, and the total amount of manganese at any given time. Tissue levels of bound manganese are constrained by the maximal binding capacity (Bmax ). Model simulation of the 14-day exposure study by Dorman et al. (2001b) after fitting to this revised model was still consistent with the dataset (Figure 3.7). In this example, kbilec and Fdietup were based on values in Table 3.1 for rats fed a 125 ppm manganese diet. Each diffusion influx rate (kinBRx) was adjusted to its respective data (kinBR1 = 14; kinBR2 = 2.1). The simulation was generated for a 14-day exposure (dstop = 14, dstart = 0) at six hours per day (tlen = 6) and seven days per week

90

4

80

3.5

70

PCFBR1

3

3

mg/m3

data 60

2.5 50 2 40 1.5 30 1

Percent Free Mn

Mn Concentration (µg/g)

CTOTBR1

20

0.5

10

0

0 0

8

16

24

32

40

Days

Figure 3.7 Simulation of total manganese concentration in brain region I (CTOTBR1) from a 14-day exposure at 3 mg/m3 for 6 hours/day, 7 days/week. Percentage of manganese in tissue as free manganese capacity (PCFBR1) is also plotted versus time. The simulation for brain region I concentration is compared to a single data point from Dorman et al. (2001b). In this example, kbilec and fdietup were based from values in Table 3.1 for rats fed a 125 ppm manganese diet.

72

Pharmacokinetic Modeling of Manganese – An Essential Element

Table 3.1 Model parameters regulating background manganese levels in rats. Parameter (abbreviation) Manganese diet Daily dietary intakea Fractional gut absorptionb Biliary excretionc

Values Ddiet inFac Fdietup kbilec

2 10 0.05 0.05 0.13 0.040 0.001 6 0.002 2

100 0.05 0.005 8 0.003 6

Units 125 ppm 0.05 kg/day/kg BW 0.005 0 0.010 l/h/kg

a

Dietary intake of manganese is from USEPA, 1986. Daily dose is calculated as Ddiet × inFac × fdietup × BW. c kbilec is allometrically scaled (kbile = kbile × BW). Values were fitted to data from Dorman et al., 2001a, 2001b. b

(dayson = 7). With increasing numbers of inhalation days and increasing tissue manganese concentration, the percentage of free manganese rises after all tissue binding capacity is occupied. Excursions of free manganese above the maximal binding capacity cause proportionately greater rises in free manganese in tissues compared to basal conditions where tissue manganese is mostly in the bound form. The increase in percentage of free manganese is greater in brain region I, the portion of the brain with asymmetric diffusion, compared to region II (Figure 3.7). A parameter plot of the end of exposure brain manganese concentration shows the rapid increase expected after exposure to about 0.1 mg Mn/m3 (Figure 3.8), where the free manganese also begins to increase disproportionately. The incorporation of tissue binding capacity not only allows for a rapid rise of free manganese when the binding maximum is exceeded, but is responsible for the rapid return to the initial basal level of manganese following exposure. 3.3.2 Influence of Diet on Tracer Kinetics and Basal Manganese Levels Initial calibration of the PBPK model consisted of adjusting daily manganese dietary intake (Fdietup) and biliary elimination (kbilec) to correspond with the observed steady-state tissue concentrations in the dietary study by Dorman et al. (2001a). Further refinements of the tissue-specific parameters (e.g., kin, kout, kd, or ka) for each model were determined by fitting each model structure to the 14-day inhalation dataset. The next exercise consists of modeling long-term kinetic data by changing dietary controls from the 100 ppm manganese diet of a 14-day inhalation exposure study to a 10 ppm manganese diet in a 90-day study. The daily dietary dose (ddiet) was first changed to 10 ppm and the exposure conditions were adjusted for a 90-day exposure (dstop = 90, dstart = 0) at six hours per day (tlen = 6) and five days per week (dayson = 5). Afterwards, fractional intake (Fdietup) and biliary elimination (kbilec) were changed according to the values in Table 3.1. The PBPK model parameters were established with the steady-state tissue concentrations and tracer kinetic data in rats fed a defined daily diets containing 2, 10, or 100 ppm manganese (Dorman et al., 2001a). Fractional gastrointestinal absorption (Fdietup) and biliary manganese excretion (kbilec) rate constants were estimated for tracer elimination fitted to the model for each dietary level (Table 3.1). After maintenance on the diet for 13 weeks, kinetic analyses included both tissue steady-state manganese concentrations and elimination kinetics from the iv tracer dose of 54 MnCl2 . In this manner, these kinetic

Model Results

73

3.5

Mn Concentration (µg/g)

3

CTOTBR1 CTOTBR2

2.5

2

1.5

1

0.5 0.01

0.01

0.1 Inhaled Concentration (mg/m3)

1

10

Figure 3.8 Parameter plot of the brain manganese concentration in regions I and II following 14-day exposure over a range of inhaled manganese concentration. In this example, the end of exposure brain regional manganese concentrations were plotted (dstop = stoptime = 14). The brain region with the asymmetric diffusional properties (I) accumulates a larger concentration of manganese than does the second region (II) with all other parameters similar, except kin and kout from the tissue.

data served for calibration of the model estimates of daily manganese dietary intake and manganese elimination by biliary excretion. The biliary manganese excretion rate was consistent with the tracer elimination kinetics following an iv injection (Figure 3.9a). Fractional gastrointestinal absorption was then determined to correspond with the steady-state tissue manganese concentration for each dietary level (Figure 3.9b). Preliminary fits were obtained for tissue steady-state manganese concentrations in rats fed on each diet by adjusting tissue binding constants (ka, kd) and maximal capacity (Bmax ). Model fits to the dietary studies indicated that, as the dietary manganese level rises, the manganese biliary rate constant for excretion increases and fractional dietary uptake decreases. The results are consistent with the increases in bile manganese concentration from increasing manganese diet observed from several rodent studies (Teeguarden et al., 2007b). These small changes in kinetic constants with dietary manipulations are important for maintaining steady-state manganese levels in the body from gradual changes of dietary manganese intake. Model simulations for liver manganese concentrations from the 90-day inhalation data (Figure 3.10) were predicted from the 14-day study parameters. This simulation overestimated the tissue manganese levels. A better fit was obtained by adjusting the kbilec (0.0022 l/h/kg) and fdietup (0.040) to the 10 ppm diet and making small changes in

74

(a)

Pharmacokinetic Modeling of Manganese – An Essential Element 25

2 ppm diat 10 ppm diat 100 ppm diat 54 Mn tracer data

54Mn Radioactivity (kBq)

20

15

10

5

0 0

20

40

60

80

100

Days

(b)

4 3.5

Mn Concentration (µg/g)

3 2.5 2

CTOTLIV CTOTBR1 100 ppm diet data

1.5 1 0.5 0 0

20

40

60

80

100

Days

Figure 3.9 (a) Simulation of the whole body 54 Mn elimination (AtotMn54) at different dietary manganese concentrations: (from top to bottom) 2, 10, and 100 ppm. (b) Manganese tissue binding capacity of the liver (top) and brain (bottom) from a dietary concentration of 100 ppm were also compared. Steady-state manganese dietary uptake and biliary excretion is calibrated to data from Dorman et al., 2001a.

Model Results

75

3 2.8

Mn Concentration (µg/g)

2.6

CTOTLIV default CTOTLIV high kbilec 0.5 mg/m3 data

2.4 2.2 2 1.8 1.6 1.4 –10 0

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Days

Figure 3.10 Simulation of liver manganese concentration (CTOTLIV) from 90-day exposure at 0.5 mg/m3 for 6 hours/day and 5 days/week. The rats were fed a 10 ppm manganese diet during the study. The lower plot was obtained by increasing the biliary excretion rate constant (kbilec) from 0.0022 to 0.005. The simulation curve is compared to data from Dorman et al., 2004.

the initial condition values for Bmax (1800 µg/kg) and Cliv0 (1600 µg/kg) in liver. The simulation results were more consistent with measured levels after the adjustment of biliary excretion for the long-term exposure (from 0.0022 to 0.005 l/h/kg). The projected increase in biliary excretion with longer-term exposures suggests that the dose dependencies of the hepatobiliary excretion of manganese for inhalation are similar to those seen for dietary uptake of this element. 3.3.3

Asymmetrical Diffusion in Target Tissues

The ability to recapitulate the greater uptake of the striatum compared to liver tissue concentrations at higher inhalation exposure of manganese was related to diffusion-limited permeability constants where influx is larger than efflux in striatal tissue (kin/kout). This next exercise demonstrates regional distribution of manganese in the brain by preferential influx in areas with larger rises of manganese concentration upon inhaled exposure (Figure 3.11). The two brain regions (I and II) in the model represent distinct areas of manganese sequestration. Due to greater affinity of transport in region I, kinBR1 (14) is over five times greater than kinBR2 (2.1). All other constants are equivalent for brain regions and are kept the same in this example. Differences in uptake in different tissues could be due to preferential barrier characteristics or to the presence of specific metal transporters in different tissues.

76

Pharmacokinetic Modeling of Manganese – An Essential Element 4 3.5 CTOTBR1 CTOTBR2 3 mg/m3 data

Mn Concentration (µg/g)

3 2.5 2 1.5 1 0.5 0 0

5

10

15

20 Days

25

30

35

40

Figure 3.11 Simulations of manganese concentrations in different brain regions from 14-day repeated exposure at 3 mg/m3 for 6 hours/day. The high manganese concentration brain region I has a five time greater influx to efflux diffusion ratio than the brain region II with lower manganese levels. The simulation curve for the 14-day study is compared to data from Dorman et al., 2001b.

3.4 Extrapolations to Other Life Stages and Species 3.4.1 Extension of the Adult Rat Model to Pregnancy, Lactation, Fetal, and Neonatal Life Stages The adult rat PBPK model has been extended to describe manganese uptake and tissue distribution in pregnant and lactating dams, fetuses, and neonates during dietary and inhalation exposures (Yoon et al., 2009a; 2009b). This extension incorporated key physiological processes controlling manganese pharmacokinetics during pregnancy/lactation and fetal/neonatal development. After calibration against a variety of studies showing tissue manganese concentrations during inhalation exposures, the model accurately simulated manganese tissue distribution in the dam and fetus following both diet and inhalation exposures to the pregnant rat. Maternal to fetal transfer of manganese through placenta was described using two pathways, a saturable active transport process with high affinity and a simple diffusion process. The active transport dominates under normal dietary and low to moderate inhaled manganese exposure conditions; at higher manganese exposures, the relative contribution of the diffusion pathway increases. To simulate fetal tissue manganese concentrations, tissue binding parameters and preferential influx/efflux rates in the fetal brain were adjusted from the adult model based on differential developmental processes and varying tissue demands for

Extrapolations to Other Life Stages and Species

77

manganese in early life. Model simulations were consistent with observed tissue manganese concentrations in fetal tissues, including brain, for diet alone and for combined diet and inhalation exposure. Simulations of manganese in placenta and other maternal tissues in late gestation correlated well with measured tissue concentrations. The conditions modeled at the end of gestation were then transposed to the early postnatal stage for dams and pups. The adult model was extended to lactating dams and pups by including differential tissue binding capacities in developing pups, increased absorption of dietary manganese in lactating dams, and more efficient gastrointestinal absorption and lower basal biliary excretion in pups. Enhancement of biliary excretion in pups was also required to accurately simulate tissue manganese during early postnatal inhalation. Overall, these changes were concordant with the behavior of manganese and other essential metals during development. The resulting model simulations match a variety of published studies on maternal manganese homeostasis during lactation, milk manganese levels, and changing patterns of neonatal tissue manganese for normal dietary intake and with manganese inhalation. The successful description of manganese kinetics across these life stages suggests that the present model can help describe the relationship between exposure dose and target tissue manganese concentrations across different developmental stages and assist in assessing whether infants and children should be regarded as susceptible populations for manganese inhalation.

3.4.2

Extension of the Rat Models to Primates and Humans

The PBPK model for manganese in rats was scaled to describe manganese tissue accumulation in nonhuman primates exposed to manganese by inhalation and diet (Nong et al., 2009). The extent of manganese accumulation in rat and monkey tissues differs because of a few key physiological and biochemical differences in these species, such as tissue volumes and blood flows between the rat and monkey. The interspecies scaling was based on typical allometric expectations for flows (BW 0.75 ) and volumes (BW). The permeability rate constants (kkin , kout ) were scaled as BW −0.25 because they represent rate constants comprised of a clearance term divided by a tissue volume. Because tissue binding capacity (Bmax ) terms account for observed tissues manganese concentrations in each species, they were simply scaled to the tissue volumes. The tissue binding rate constants (ka and kd) terms represent presumed association and dissociation processes that are likely related to incorporation and degradation of specific macromolecular manganese stores. These parameters were kept essentially constant from the rat to the monkey. After accounting for these physiological differences between rat and monkey, the monkey model parameters were calibrated using steady-state tissue manganese concentration from rhesus monkeys fed a diet containing 133 ppm manganese. The model was then applied to simulate 65 exposure days of weekly (6 h/d; 5 d/wk) inhalation exposures to soluble MnSO4 at 0.03–1.5 mg Mn/m3 (Dorman et al., 2006b). A few additional adjustments were required besides the generic scaling approaches. These changes included dose dependencies in brain uptake rate constants and in biliary elimination of free manganese. While inducible biliary excretion of manganese was suggested by the results in long-term exposure in rats, the need to incorporate dose-dependent uptake mechanisms in the monkey brain is likely indicative of a more complex control of brain

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Pharmacokinetic Modeling of Manganese – An Essential Element

manganese concentrations in monkeys than in rats. Another significant difference is the 20-fold difference in nasal olfactory surface area between the rat and monkey, with the rat having a much larger nasal olfactory surface area. The difference in surface area of the nasal epithelium influences the amount of manganese delivered to olfactory bulb through the olfactory pathway, which is relatively less in monkeys. Recognition of the differences in factors which control manganese uptake into target tissues between rat and monkey is important since the monkey, with selective increases in mid-brain regions and toxic responses to manganese more like those in humans, appears to be the better animal model for predicting expected behaviors in humans. 3.4.3 Extension of the Animal Models to Humans Sensitivity analyses show that manganese tissue concentrations in the rat and monkey models have dose dependencies in (1) biliary excretion of free manganese from liver, (2) saturable tissue binding in all tissues, and (3) differential influx/efflux rates for tissues that preferentially accumulate manganese. These PBPK models are consistent with the available experimental kinetic data, indicating preferential increases in some brain regions with exposures above 0.2 mg/m3 and fairly rapid return to steady state levels (within several weeks rather than months) after cessation of exposure. The models can now be extended to humans by incorporating human physiological values into the models and comparing the model output with human tissue manganese data. This data will include both direct measurements of human brain manganese levels and the determination of brain manganese content from magnetic resonance imaging (MRI) data of people following various overexposure scenarios, such as occupational cohorts exposed by inhalation or people exposed to high manganese levels in TPN or drinking water. Human PBPK models that account for preferential manganese tissue accumulation from both oral and inhalation exposures will be central to support efforts of tissue dosimetry-based human risk assessments for manganese, described below.

3.5

Discussion and Conclusion

3.5.1 Insights Gained During the Modeling Process for Manganese Manganese is both essential and toxic, and, unlike exogenous compounds typically examined with PBPK models, biological process exist to both ensure adequate tissue concentrations in times of low intake and enhance elimination to prevent toxicity during times of excess intake. The modeling process for manganese revealed insights regarding this control of manganese that were not readily apparent from the data the models were constructed from, such as the importance of tissue binding and free vs bound manganese to the regulation of tissue manganese levels. Initial attempts to construct a mammillary model of manganese based on tracer kinetics failed to reproduce the rapid tissue increases due to inhalation and the rapid return to baseline manganese levels after the cessation of exposure. This deficiency was rectified by the addition of tissue binding that served to maintain tissue levels during normal dietary exposures and low to moderate inhalation exposures but allowed rapid tissue accumulation

Discussion and Conclusion

79

(and subsequent rapid clearance) once a dose-dependent threshold for inhalation exposure was reached. The modeling process highlighted the importance of tissue binding in maintaining relatively constant tissue manganese concentrations across a wide range of low to moderate inhaled concentrations. Only with saturation of these binding capacities do tissue concentrations throughout the body increase in closer proportion to the rate of intake. The elevation occurs preferentially in free manganese that would be more available for excretion, transport, and toxic interactions. The challenge in describing the observed tissue manganese after inhalation is to distinguish those tissues that show relative consistent tissue manganese levels across a wide range of inhalation exposures and those that show some preferential dose-related increases, such as the striatum. The discrepancies between predictions of the earlier mammillary PBPK model (Teeguarden et al., 2007a) and the observed data led to the incorporation of processes that were required in the model to gain consistency with both dietary and inhalation studies, specifically the use of tissue binding that is capacity limited with association and dissociation rate constants that are unusually small. Small dissociation rate constants were also necessary because the terminal phase in tracer studies is correspondingly small. These small association and dissociation rate constants probably reflect processes other than simple bimolecular manganese binding and may be related to organellar storage of manganese.

3.5.2

The Use of PBPK Models in Manganese Risk Assessment

PBPK models reduce uncertainty and improve the scientific basis for determining the relationship among: (a) exposure to the substance of interest; (b) dose to target tissues; and (c) toxicity and other biological responses (USEPA, 2006). PBPK models are typically used for inter-species extrapolation, estimating intra-species variability, route-to-route extrapolation, high-to-low dose extrapolation, and duration of exposure adjustment in the risk assessment of exogenous chemicals. However, for as essential element such as manganese, the PBPK models will allow for a more sophisticated analysis of normal tissue levels, dietary intake, and homeostatic controls of inhaled manganese than was possible before they were constructed. Previous to the development of PBPK models for manganese, risk assessments for inhaled environmental manganese relied upon extrapolation from occupational studies of workers exposed to relatively high concentrations of manganese. To determine a lifetime exposure level that is likely to be without risk of deleterious effects to a population (including sensitive subgroups), such as a RfC or Tolerable Daily Intake (TDI), regulators used the traditional risk assessment approach of determining a point of departure, that is, a no (or lowest) observed adverse effect level (i.e., NOAEL or LOAEL) or benchmark concentration (BMC) based on subclinical changes in motor function in workers, and applying uncertainty factors to extrapolate to the entire population. PBPK models may be used in these types of traditional risk assessments to incorporate chemical specific adjustment factors (CSAFs) instead of traditional uncertainty factors (WHO IPCS, 2005; USEPA, 2006). PBPK models allow for a multi-media risk assessment of essential elements such as manganese that simultaneously considers ingestion and inhalation, along with their homeostatic controls, in the derivation of RfCs by quantifying the relative risk of adverse effects from each route. PBPK models quantitatively consider factors which affect the accumulation and excretion

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Pharmacokinetic Modeling of Manganese – An Essential Element

of manganese and estimate a range of possible internal levels associated with a given exposure for a population. Specifically, the models describe variation in tissue manganese levels during early development or other potentially susceptible life stages. Because rich data sets were used to build and validate the PBPK models, including animal exposures of different durations to different forms of manganese, the models for manganese have the capability to compare the effects of potential differences in bioavailability of different manganese forms due to differing solubilities, the duration of exposure, and other PK factors to aid in setting appropriately protective CSAFs. The ability of PBPK modeling to use numerous studies and evaluate internal doses to target tissues will produce more robust manganese risk assessments. Another key application of PBPK models to risk assessment involved their ability to extrapolate beyond the exposure conditions that were used to establish and validate the model. Thus, the PBPK models may be used to determine air manganese concentrations that do or do not lead to target tissue (i.e., globus pallidus) accumulation during chronic or lifetime exposures. This attribute allows PBPK models to be used in an alternative risk assessment strategy for essential elements such as manganese based on dose to target tissue. An upper safe exposure value might be based on an air concentration that changes brain tissue levels by no more than some fraction of the normal variability within a population (Andersen, Gearhart, and Clewell, 1999; Andersen et al., 2010). This approach requires a PBPK model and some level of confidence in the model across species and dose routes. The current PBPK model recapitulates (1) elevation in tissue manganese with increasing doses, (2) the long half-life of tracer manganese with normal dietary exposures and the shorter half-lives with high concentration inhalation, (3) the preferential increases in specific brain regions, and (4) combined uptake by both oral and inhalation exposures. While the underlying biological processes, especially those determining the capacity of tissues to maintain bound stores of manganese and asymmetric tissue diffusion, remain only partially understood, the consistency of the processes across species and the consistency with expected behavior for a biologically controlled essential element indicate that the important elements of the kinetics of manganese are captured by this PK model. The asymmetry in diffusion likely represents behavior of specific metal ion transporters. In fact, the tissues that show larger increases in manganese in high concentration inhalation exposures – for example, mid-brain, heart, hypothalamus – may have asymmetric transport to ensure maintenance of adequate manganese in times of deficiency. Their ability to preserve manganese at low concentrations may render them at greater risk in conditions of excess once exposures are sufficiently high to overwhelm the body’s homeostatic mechanisms that attempt to regulate tissue levels. With a more complete evaluation of monkey toxicity results using the now-available monkey manganese PBPK model to assess dosimetry, and with applications of the model to human datasets, the current PBPK model (and subsequent human model) should be an important component of future tissue-dose-based approaches for manganese risk assessment. Similar PK model-based dosimetry approaches could also be considered for risk assessments with other essential metals.

References Andersen, M.E., Gearhart, J., and Clewell, H.J. III (1999) The role of pharmacokinetics and tissue dosimetry in risk assessments for inhaled and ingested Manganese. Neurotoxicology, 20, 161–172.

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Andersen, M.E., Dorman, D.C., Clewell, H.J. III, et al. (2010) Multi-dose-route, multi-species pharmacokinetic models for manganese and their use in risk assessment. J. Toxicol. Environ. Health A, 73, 217–234. Aschner, J.L. and Aschner, M. (2005) Nutritional aspects of manganese homeostasis. Mol. Aspects Med., 26, 353–362. Brown, R.P., Delp, M.D., Lindstedt, S.L., et al. (1997) Physiological parameter values for physiologically based pharmacokinetic models. Toxicol. Ind. Health, 13, 407–484. Cartwright, G.E. and Wintrobe, M.M. (1964) Copper metabolism in normal subjects. Am. J. Clin. Nutr., 14, 224–232. Crossgrove, J.S., Allen, D.D., Bukaveckas, B.L., et al. (2003) Manganese distribution across the blood–brain barrier. I. Evidence for carrier-mediated influx of manganese citrate as well as manganese and manganese transferrin. Neurotoxicology, 24, 3–13. Dorman, D.C., Struve M.F., James, A.R., et al. (2001a) Influence of dietary manganese on the pharmacokinetics of inhaled manganese sulfate in male CD Rats. Toxicol. Sci., 60, 242–251. Dorman, D.C., Struve, M.F., James, A.R., et al. (2001b) Influence of particle solubility on the delivery of inhaled manganese to the rat brain: manganese sulfate and manganese tetroxide pharmacokinetics following repeated (14-Day) exposure. Toxicol. Appl. Pharmacol., 170, 79–87. Dorman, D.C., McManus, B.E., Marshall, M.W., et al. (2004) Old age and gender influence the pharmacokinetics of inhaled manganese sulfate and manganese phosphate in rats. Toxicol. Appl. Pharmacol., 197, 113–124. Dorman, D.C., Struve, M.F., Clewell, H.J. III, and Andersen, M.E. (2006a) Application of pharmacokinetic data to the risk assessment of inhaled manganese. Neurotoxicology, 27, 752–764. Dorman, D.C., Struve, M.F., Marshall, M.W., et al. (2006b) Tissue manganese concentrations in young male Rhesus monkeys following subchronic manganese sulfate inhalation. Toxicol. Sci., 92, 201–210. Foster, D.M., Aamodt, R.L., Henkin, R.I., and Berman, M. (1979) Zinc metabolism in humans: a kinetic model. Amer. J. Physiol., 237 (5), R340–R349. Harvey, L.J., Dainty, J.R., Hollands, W.J., et al. (2005). Use of mathematical modeling to study copper metabolism in humans. Am. J. Clin. Nutr., 81, 807–813. Miller, L.V., Krebs, N.F., and Hambidge, K.M. (2000) Development of a compartmental model of human zinc metabolism: identifiability and multiple studies analyses. Am. J. Physiol. Regul. Integr. Comp. Physiol., 279, R1671–R1684. Moos, T. and Morgan, E.H. (2000) Transferrin and transferrin receptor function in brain barrier systems. Cell. Mol. Neurobiol., 20, 77–95. Nong, A., Teeguarden, J.G., Clewell, H.J. III, et al. (2008) Pharmacokinetic modeling of manganese in the rat IV: Assessing factors that contribute to brain accumulation during inhalation exposure. J. Toxicol. Environ. Health A, 71, 413–426. Nong, A., Taylor, M.D., Clewell, H.J. III, et al. (2009) Manganese tissue dosimetry in rats and monkeys: accounting for dietary and inhaled Mn with physiologically based pharmacokinetic modeling. Toxicol. Sci., 108, 22–34. Reddy, M.B., Yang, R.S.H., Andersen, M.E., and Clewell, H.J. III (2005) Physiologically Based Pharmacokinetic Modeling: Science and Applications, John Wiley & Sons, Inc., Hoboken, NJ. Teeguarden, J.G., Dorman, D.C., Covington, T.R., et al. (2007a) Pharmacokinetic modeling of manganese. I. Dose dependencies of uptake and elimination. J. Toxicol. Environ. Health A, 70, 1493–1504. Teeguarden, J.G., Dorman, D.C., Nong, A., et al. (2007b) Pharmacokinetic modeling of manganese. II. Hepatic processing after ingestion and inhalation. J. Toxicol. Environ. Health A, 70, 1505–1514. Teeguarden, J.G., Gearhart, J., Clewell, H.J. III, et al. (2007c) Pharmacokinetic modeling of manganese. III. Physiological approaches accounting for background and tracer kinetics. J. Toxicol. Environ. Health A, 70, 1515–1526. USEPA (US Environmental Protection Agency) (2006) Approaches for the Application of Physiologically Based Pharmacokinetic (PBPK) Models and Supporting Data in Risk Assessment, National Center for Environmental Assessment, Washington, DC; EPA/600/R-05/043F. Available from: National Technical Information Service, Springfield, VA, and at http://epa.gov/ncea (accessed 1 May 2009).

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WHO IPCS (World Health Organization and International Programme on Chemical Safety) (2005) Chemical-specific adjustment factors for Interspecies differences and human variability: Guidance document for use of data in dose/concentration-response assessment. Available at http://www.who.int/ipcs/methods/harmonization/areas/uncertainty/en/index.html (accessed 1 May 2009). Yokel, R.A., Crossgrove, J.S., and Bukaveckas, B.L. (2003) Manganese distribution across the blood–brain barrier. II. Manganese efflux from the brain does not appear to be carrier mediated. Neurotoxicology, 24, 15–22. Yoon, M., Nong, A., Clewell, H.J. III, et al. (2009a) Lactational transfer of manganese in rats: Predicting manganese tissue concentration in the dam and pups from inhalation exposure with a pharmacokinetic model. Toxicol. Sci., 112, 23–43. Yoon, M., Nong, A., Clewell, H.J. III, et al. (2009b). Evaluating placental transfer and tissue concentrations of manganese in the pregnant rat and fetuses after inhalation exposures with a PBPK model. Toxicol. Sci., 112, 44–58.

4 Physiologically Based Modeling of Pharmacokinetic Interactions in Chemical Mixtures Sami Haddad1 , Robert Tardif 2 , Jonathan Boyd3 and Kannan Krishnan2 1

D´epartement des sciences biologiques, Center TOXEN, Universit´e du Qu´ebec a` Montr´eal, Canada 2 Groupe de recherche interdisciplinaire en sant´e et D´epartement de sant´e environnementale et sant´e au travail, Universit´e de Montr´eal, Canada 3 C Eugene Bennett Department of Chemistry, West Virginia University, USA

4.1 Introduction Guideline values for chemicals are developed based on data from toxicity studies of individual chemicals. However, human exposure in occupational and general environments often occurs to a multitude of chemical stressors, concurrently or sequentially. Several chemicals can interact with each other by various mechanisms and, of the many reports on chemical–chemical and drug–drug interactions, the vast majority of these occur at the pharmacokinetic level (Krishnan and Brodeur, 1991). These interactions occur through various mechanisms that are dependent on the dose, dosing regimen (i.e., single or repeated exposure), exposure pattern (i.e., pretreatment, co-administration, or postadministration), and/or exposure route of one or both chemicals (Krishnan and Brodeur, 1991). Most of the interaction studies reported to date have been conducted in laboratory animals by administering high doses of one or both chemicals by routes and scenarios often different from anticipated human exposures (Calabrese, 1991; Krishnan and Brodeur, 1994). Further, information on the toxicological consequences of low-level or chronic exposures to binary Quantitative Modeling in Toxicology
C 2010 John Wiley & Sons, Ltd

Edited by Kannan Krishnan and Melvin E. Andersen

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Physiologically Based Modeling of Pharmacokinetic Interactions in Chemical Mixtures

chemical mixtures, which show significant interactions when administered acutely, is often unavailable (Krishnan and Brodeur, 1991). In order to account for interactions in risk assessment of mixtures, there is a need for tools that can describe and predict the impact of co-exposure on the pharmacokinetics and pharmacodynamics of mixture constituents as well as allow all necessary extrapolations related to differences between toxicity studies and human exposure (i.e., high dose to low dose, route to route, species to species, scenario to scenario, and binary to more complex mixtures). These concerns can be addressed with the use of a physiologically based modeling approach. Physiologically based modeling refers to the process of reconstructing mathematically the anatomic-physiological characteristics of the organism of interest and describing the complex interplay among the critical determinants of pharmacokinetics and pharmacodynamics.

4.2

Pharmacokinetic Interactions and Mathematical Descriptions

Pharmacokinetic interactions occur when a compound alters determinants of absorption, distribution, metabolism or excretion of another chemical. These determinants belong to one of the three types of parameters: physiological, physicochemical, and biochemical. 4.2.1 Interactions Due to Physiological Effects Physiological changes altering the pharmacokinetics of one chemical by another have been characterized largely for binary chemical mixtures. For example, cyanide and hydrogen sulfide at low concentrations increase alveolar ventilation rates (Qalv), and hence change inhalation/exhalation rates of other volatile chemicals (Dreisbach 1977). Cardiac output and tissue blood flows can also be influenced by chemicals which can thereby affect the distribution or the metabolic rates of coexposed chemicals. Ethanol and phenobarbital increase hepatic blood flow, which can increase the extraction ratio of highly metabolized compounds during co-exposure (Krishnan, Clewell, and Andersen 1994). Vasodilators and vasoconstricors may influence the distribution of other chemicals by modifying regional blood flows. Glomerular filtration rates (GFR), an important factor for renally excreted chemicals, can be modified by certain compounds. Chronic exposure to cadmium leads to accumulation of metallothionin-cadmium complexes in kidneys which diminish GFR (Webb, 1986; Goyer et al., 1989; Shigematsu et al., 1989). Some chemicals can modify skin structure or composition, leading to changes in the rate of dermal absorption of other chemicals. An interaction due to skin composition changes is exemplified by the reduction of absorption of m-xylene due to skin dehydration by isobutanol (Riihim¨aki 1979). Dimethyl sulfoxide (DMSO) causes swelling of basal cells of the stratum corneum as well as a disruption of keratin matrices in skin (Kurihara-Bergstrom, Flynn, and Higuchi, 1987; Qiao et al., 1996). This has been shown to positively influence the dermal permeability of coexposed lipophilic compounds (Hayes and Pearce, 1953; Jacob, Bischel, and Herschler 1964; Choi, Flynn, and Amidon, 1990). To date, there are no published pharmacokinetic models incorporating changes in physiological parameters caused by co-exposures.

Pharmacokinetic Interactions and Mathematical Descriptions

4.2.2

85

Physicochemical Interactions

Co-exposures can lead to modification of a chemical’s solubility in lipid or water or even in its permeability across biological membranes, resulting in changes in distribution or rates of absorption. For example, some chemicals, such as antacids, can alter the pH of gastric or intestinal regions and, therefore, influence the ionization state of other acidic or basic chemicals, leading to altered absorption rates. For some chemicals, their presence together leads to formation of complexes which are more lipophilic than either chemical itself, resulting in an increase in their permeability across membranes (e.g., increased permeability across blood–brain barrier of lead-dithiocarbamate complexes (Oskarsson and Lind, 1985)). Much like interactions due to physiological alterations, interactions at the physicochemical level have not yet been described in PBPK models. 4.2.3

Interactions at the Biochemical Level

Interactions at the metabolic and transporter levels are by far the most frequently reported pharmacokinetic interactions. They occur when a chemical alters the binding, the biotransformation or the active transport of another chemical. These types of modifications are either the result of changes in the affinity or maximal velocity. 4.2.3.1

Reversible Protein Binding Interaction

Mechanisms of interactions at the level of protein binding might involve either competition for the binding site or induction of binding protein levels. The modeling of protein induction is discussed elsewhere in this chapter as well as in Chapter 7. Sugita et al. (1982) developed a PBPK model describing the competition between tolbutamide and sulfonamides (sulfaphenazol, sulfadimethoxin or sulfomethoxazol) for binding to plasma proteins. To estimate the free concentration of a chemical (Cf ) that binds to a protein, the following equation can be used: Cb =

n · β · Kd · C f (1 + K d · C f )

(4.1)

where C = Concentration (mg/liter), Kd = dissociation constant (mg/liter), and n β = binding capacity, and the subscripts b and f refer to bound and free forms. In the presence of a competitive inhibitor (I), Kd in the above equation increases by factor α: α =1+

4.2.3.2

[I ] Ki

(4.2)

Reversible Metabolic Inhibition

Among all the mixture PBPK models published to date, reversible metabolic inhibition is by far the most frequently encountered type of interaction (listed in Table 4.1). There are three simple cases of reversible enzyme inhibition: competitive, non-competitive, and uncompetitive (Table 4.2).

Warfarin Sodium tolbutamide

Dibromomethane Trichloroethylene Phenolsulfonphthalein

Luecke and Wosilait (1979) Sugita et al. (1982)

Clewell and Andersen (1985) Andersen et al. (1987) Russel, Wouterse, and van Ginneken (1987) Russel, Wouterse, and van Ginneken (1987) Russel, Wouterse, and Van Ginneken (1989) Purcell et al. (1990) Tardif et al. (1993) Filser et al. (1993) Bond et al. (1994) Bond et al. (1994) Barton et al. (1995) Tardif et al. (1995) Krishnan and Pelekis (1995) el-Masri et al. (1996a, 1996b) Probenecid Toluene m-Xylene Styrene Styrene Benzene Vinyl chloride Xylene Dichloromethane 1,1-Dichloroethylene

Benzene Toluene 1-3 butadiene 1,3-butadiene 1,3-butadiene 1,1-Dichloroethylene Toluene Toluene Trichloroethylene

Bromosulfophthalein Sulfaphenozol Sodium sulfadimethoxazole Sodium Sulfadimethoxine Isofluorane 1,1-Dichloroethylene Probenecid Saliuric acid Phenolsulfonphthalein

Chemical B

Iodopracet

Saliuric acid

Chemical A

Reference

Table 4.1 PBPK models developed to describe reversible inhibition in binary mixtures.

Non-competitive Competitive Competitive Competitive Competitive Competitive Competitive Competitive Competitive

Competitive

Competitive Non-competitive Non-competitive Non-competitive Competitive Competitive Competitive Competitive (2 sites) Non-competitive

Type of inhibition

m-xylene Trichloroethylene Xylenes Itraconazole Trichloroethylene

Toluene Toluene Methyl chloroform Toluene Ethylbenzene Simvastatin Chloroform

Yu et al. (1998) Ali and Tardif (1999)

Tardif and Charest-Tardif (1999) Thrall and Poet (2000) Jang, Droz, and Kim (2001) Ishigam et al. (2001) Isaacs, Evans, and Harris (2004)

Styrene Dichloromethane Cimetidine Probenecid n-Hexane n-Hexane

1-3 butadiene Toluene Ranitidine

Leavens and Bond (1996) Pelekis and Krishnan (1997) Boom et al. (1998)

Competitive Competitive Competitive Competitive

Competitive Competitive Competitive Competitive Non-competitive Uncompetitive or non-competitive Competitive

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Physiologically Based Modeling of Pharmacokinetic Interactions in Chemical Mixtures

Table 4.2 Descriptions of reversible metabolic inhibition on Vmax , and Km . (Based on Segel,1975).

E + S
ES → E + P + + I I

E + S
ES → E + P + I

Apparent Km Apparent V max a

Note: α = 1 +

EI αKm V max

EI + S
EIS Km V max /α




E + S
ES → E + P + I




Uncompetitive




Non-competitive




Equilibrium equation

Competitive

EIS Km /α V max /α

[I ] . Ki

Competitive inhibition occurs when chemicals compete for the enzyme’s active site, resulting in decreased apparent affinity (i.e., increased K m ) and, therefore, reduced rate of metabolism at lower substrate concentration. The competitive inhibitor may either be another substrate or strictly an inhibitor; the K i of a competing substrate is the same as its K m (Segel, 1975). Non-competitive inhibition occurs when a chemical binds to the enzyme (free or complexed with substrate) at a site that is away from the catalytic active site. This binding changes the conformation of the enzyme, resulting in a decreased catalytic activity (i.e., decreased V max ). The less frequently encountered uncompetitive inhibition occurs when a chemical binds to the enzyme-substrate complex. The catalytic function is affected without interfering with substrate binding. The inhibitor causes a structural distortion of the active site and inactivates it (Voet and Voet, 2004). This has the effect of reducing the available enzyme for the reaction (i.e., lowering V max ) and also driving the reaction (E+S→ES) to the right (i.e., decreasing K m ). It is noteworthy to point out that these types of reversible metabolic inhibition can also occur with active transport processes. In fact, Sugita et al. (1982) described non-competitive inhibition as the mechanism of binary interaction between sodium tolbutamide and three other drugs (sulfaphenozol, sodium sulfadimethoxazole, and sodium sulfadimethoxine). Metabolites may also interfere with the biotransfortmation of their parent compound. This phenomenon is called product inhibition and might invoke a competitive, non-competitive or uncompetitive mechanism. For example, n-hexane, which is metabolized to methyl n-butyl ketone (MnBK) and then to 2,5-hexanedione, has been reported to involve multiple interactions (competitive inhibition) occurring among n-hexane and its metabolites (Andersen and Clewell, 1983). 4.2.3.3

Irreversible Metabolic Inhibition

When an inhibitor binds irreversibly to the enzyme at the active site, it decreases the concentration of functional enzyme and thus the V max . This type of inhibition has been described

Pharmacokinetic Interactions and Mathematical Descriptions

89

by interaction-based PBPK models for mixtures of triazolam and erythromycin (Kanamitsu et al., 2000a), 5-fluorouracil and sorovidine (Kanamitsu et al., 2000b), trichloroethylene and its metabolite dichloracetate (Keys et al., 2004). Briefly, the modeling of this type of interaction consists of describing the change in V max of the substrate by taking into account the inactivation of enzyme in relation to the concentration of the inhibitor as follows. Accordingly, the concentration of active enzyme at steady state (i.e., in the absence of inactivator) equals the rate of enzyme synthesis (a zero order process) minus the rate of enzyme degradation (first order process that can be determined experimentally). This steady state is interrupted in the presence of an
enzyme inactivator and the levels of enzyme is decreased that is directly related to the concentration of the by a rate of enzyme inactivation dI nact dt inactivating chemicals in the liver (I h ), as follows:

dI nact = dt

kinact ∗ E a ∗ f b ∗ K i,app + f b ∗

Ih Kp

Ih Kp

(4.3)

where kinact represents the maximum inactivation rate constant, K p represents the liver-to blood partition coefficient, f b is the unbound fraction in blood, and I h is the inactivator’s concentration in the liver.

4.2.3.4

Induction

Enzyme induction increases the V max of its substrate, due to increased enzyme synthesis and/or decreased enzyme degradation. Induction of CYP2B1/2 by octamethylcyclotetrasiloxane (Sarangapani et al., 2002) and CYP1A1 and 1A2 by TCDD (2,3,7,8-tetrachlorodibenzo-p-dioxin) via interaction with the Ah-receptor (Andersen, 1995; Andersen et al., 1997) have been described quantitatively, as follows:   dSyn [R L]n = K syn basal + (K syn max − K syn basal ) × dt [R L]n + K d n

(4.4)

where Ksynbasal represents the basal rate of enzyme synthesis, Ksynmax represents the maximal rate of enzyme synthesis, [R L] is the concentration of the receptor-ligand complex and n is the hill coefficient. The decrease in enzyme degradation has been described by Chien, Thummel, and Slattery (1997) for modeling the induction of CYP2E1 by ethanol, acetone, and isoniazid via enzyme stabilization. Chien, Thummel, and Slattery (1997) described two pools of the enzyme. Accordingly, the first pool arising from synthesis is degraded rapidly in free form but slowly when bound to the stabilizing chemical; on the other hand, the second enzyme pool is described as being degraded slowly in either bound or unbound form (Chien, Thummel, and Slattery, 1997).

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Physiologically Based Modeling of Pharmacokinetic Interactions in Chemical Mixtures

4.3 PBPK Modeling of Mixtures A key feature of PBPK modeling is that it can be used to integrate information on pharmacokinetic interactions. Mixtures in which chemical components do not interact will not be dealt with in this chapter because constituents can be dealt with as single chemicals. Ideally, to develop mixture PBPK models, one should start with the PBPK models developed and validated for each of the mixture constituents. The interaction-based PBPK model can then be developed by linking together the single chemical models by known or hypothesized mathematical descriptions of their interaction mechanism (see above). For example, chemical A may inhibit the hepatic metabolism of chemical B and vice versa by competing for the enzyme (competitive inhibition) as depicted in Figure 4.1. The rate of metabolism (RAM) of chemicals A and B is then calculated by accounting for the inhibition constant and concentration of the other chemical (i.e., inhibitor) in the liver compartment. There are numerous examples of interaction-based PBPK models for binary mixtures (Krishnan et al., 1994; Reddy et al., 2005) and in all cases the interaction is primarily related to metabolic interference. Following initial work on the modeling of metabolic interactions in binary mixtures (toluene–benzene; toluene and m-xylene; toluene and ethylbenzene), Krishnan and co-workers (Tardif et al., 1993, 1995, 1997; Pelekis and Krishnan, 1997; Haddad et al., 1999, 2000a) extended this approach to more complex chemical mixtures. The hypothesis put forward and tested by this group was that the pharmacokinetics of interacting mixture components may be simulated if all binary level interactions in the mixtures are described in the model. Briefly, the approach consisted of constructing PBPK models for each mixture constituent and then connecting them at the binary level on the

Figure 4.1 Conceptual representation of a PBPK model for a binary mixture for chemicals A and B that compete with each other for metabolism.

PBPK Modeling of Mixtures

B

91

C

A D E Figure 4.2 A representation of a network of binary pharmacokinetic interactions between five chemicals (A, B, C, D, and E). All mixture constituents that interact are connected within this network.

basis of the interaction mechanism. By doing so, a network of binary pharmacokinetic interactions is created (Figure 4.2) and the kinetics of the mixture constituents becomes interdependent. Any change in the concentration of a mixture component will, therefore, necessarily have direct and/or indirect repercussions on the kinetics of other chemicals that are part of the interaction network (Haddad and Krishnan, 1998; Krishnan et al., 2002). Conceptually, this approach can be applied to mixtures of any complexity as long as information on all interacting pairs is taken into account by the model. Using this approach, Tardif et al. (1997) simulated interactions occurring in a ternary mixture of toluene, m-xylene, and ethylbenzene. Subsequently, Haddad et al. (1999, 2000a) demonstrated that additional mixture components could be modeled by simply incorporating mechanistic information on the new binary interactions. This led to the development, and validation of interaction-based PBPK models for mixtures of four chemicals (benzene, toluene, m-xylene, and ethylbenzene) and even of five chemicals (benzene, toluene, m-xylene, ethylbenzene, and dichloromethane) (Figure 4.3). Applying the same approach, the interactions occurring in a ternary mixture of trichloroethylene (TCE), tetrachloroethylene (PERC), and 1,1,1-trichloroethane (methyl chloroform, MC) in rats and humans have been modeled (Dobrev, Andersen, and Yang, 2001, 2002). Although all these studies dealt strictly with metabolic interactions, there is no reason to believe that the approach based on binary interaction network may not apply to other types of pharmacokinetic interactions. To use this mixture modeling approach, a priori studies on all binary interactions in the mixture must be characterized. This is a major limitation for the construction of mixture PBPK models, since the number of binary interactions (N) increases greatly with the number of mixture components (n) (i.e., N = n (n − 1)/2). Accordingly, for mixture of 5 and 10 chemicals, 10 and 45 binary interactions must be characterized. Considering the complexity of some of the mixtures to which humans and other species are exposed, the characterization of all binary interactions will be tedious or even impossible. In this regard, some alternative mixture modeling methods have been proposed. 4.3.1

Modeling Maximal Impact of Interactions

A pragmatic alternative approach, when there is insufficient information on mechanism of binary interactions or on the mixture composition, would be to focus on the modeling of maximal impact of interactions on the kinetics of the chemicals (Haddad, Charest-Tardif, and Krishnan, 200b). Although this approach does not allow the exact predictions of the

exhaled

Lungs

Lungs

Dichloromethane

Benzene

exhaled

Slowly perfused tissues

Slowly perfused tissues

inhaled

Richly perfused tissues

Richly perfused tissues

exhaled

Fat

Fat

inhaled

Liver

RAM B

RAM E

RAM D =

RAM B =

RAM E =

RAM X =

RAM T =

Liver

Slowly perfused tissues

Richly perfused tissues

Fat

Lungs

exhaled

Ethylbenzene inhaled

Liver

RAM D

RAM T

RAM X

Liver

Slowly perfused tissues

Richly perfused tissues

Fat

Lungs

exhaled

V max T ⋅ Cvl T

X ⋅

Cvl X

V max E ⋅ Cvl E

Cvl T Cvl E Cvl B Cvl D ⎞⎟⎟ + + + + Cvl X KiTX Ki EX Ki BX Ki DX ⎟⎠⎟

V max

Cvl X Cvl E Cvl B Cvl D ⎞⎟⎟ + + + + Cvl T Ki XT Ki ET Ki BT Ki DT ⎟⎟⎠

V max B ⋅ Cvl B

V max D ⋅ Cvl D Cvl T Cvl X Cvl E Cvl B ⎞⎟⎟ Km 1 + + + + + Cvl D KiTD Ki XD Ki ED Ki BD ⎟⎟⎠ ⎛ ⎜ ⎜ D⎜ ⎜ ⎝

Cvl T Cvl X Cvl E Cvl D ⎞⎟⎟ Km 1 + + + + + Cvl B KiTB Ki XB Ki EB Ki DB ⎟⎟⎠ ⎛ ⎜ ⎜ B⎜ ⎜ ⎝

Cvl T Cvl X Cvl B Cvl D ⎞⎟⎟ Km 1 + + + + + Cvl E KiTE Ki XE Ki BE Ki DE ⎟⎟⎠

⎛ ⎜ ⎜ E⎜ ⎜ ⎝

⎜ ⎝

⎛ ⎜

Km X ⎜⎜1 +

⎜ ⎝

⎛ ⎜

KmT ⎜⎜1 +

Figure 4.3 Representation of the PBPK model for a mixture of five VOCs (X: m-xylene, T: toluene, E: ethylbenzene, B: benzene, and D: dichloromethane) All binary interactions which occur at the level of the rate of metabolism (RAM) are taken into account. Modification of Km due to competitive inhibition among all mixture constituents is captured in the RAM equations. Figure adapted from Krishnan et al. (2002).

Liver

Slowly perfused tissues

Richly perfused tissues

Richly perfused tissues

Fat

Lungs

inhaled

Toluene

m-Xylene inhaled

PBPK Modeling of Mixtures

93

altered kinetics, it does permit the prediction of the upper or lower bound concentrations that could occur in the presence of interacting chemicals. The authors demonstrated the applicability of such an approach for mixtures of VOCs (m-xylene, ethylbenzene, benzene, toluene, dichloromethane, perchloroethylene, p-xylene, o-xylene, styrene, and trichloroethylene) of up to 10 constituents. For these chemicals, they assumed that interactions would occur only at the level of hepatic metabolism and described the rate of metabolism (RAM) as a function of the extraction ratio (E), as follows: R AM = Q l · E · Ca

(4.5)

where Ca is the arterial concentration and Ql is the blood flow to liver. Knowing that the values of E can only vary between 0 (i.e., maximal effect of inhibition) and 1 (maximal effect of induction), they simulated the concentration versus time profiles for defined exposure conditions of 10 chemicals in various mixtures. The modeling results showed that the limits were well predicted for nine chemicals out of ten (Figure 4.4). This approach produces a “prediction envelope” reflective of the maximal impact of interactions and is particularly useful in data-poor situations for inhaled volatile organics and has potential applications in screening-level risk assessments. 4.3.2

Lumping Chemicals

Another approach particularly applicable for very large or undefined mixtures is the “lumping” of chemicals. Dennison et al. (2003, 2004) modeled the pharmacokinetics of the constituents of two mixtures of gasoline (i.e., gasolines of summer blend and winter blend). In these studies, the mixture was treated as a composite of six chemicals, namely, benzene, toluene, ethylbenzene, o-xylene, n-hexane, and a pseudo-chemical which is an aggregate or lumping of all the other chemicals in the mixture (e.g., aromatics, isoparaffins, naphthalenes, olefins, paraffins, oxygenates, 4–10 carbon alkanes). The authors used the binary interaction-based approach to model the pharmacokinetics of all “six” components. Competitive inhibition was the principal mechanism of pharmacokinetic interactions among these “six” chemicals. Computer simulation results from the “six” chemical interaction model matched well with gas uptake pharmacokinetic experimental data from single chemicals, the five chemical mixture, and the two blends of gasoline. The kinetics of the pseudochemical was well predicted, partly due to the fact that interactions had very little impact on the mixed venous blood concentration. This lumping approach, likely to be more useful for modeling mixtures containing similar chemicals, would allow the reduction of the number of binary interaction studies for identifying interaction mechanisms and related parameters required for modeling. 4.3.3

Using Km as Ki for Competing Substrates

Price and Krishnan (2005) developed PBPK models for mixtures of chemical competing for metabolism, on the basis that K m values of substrates are sufficient for simulating competitive interactions within a multichemical mixture, in the absence of knowledge on binary inhibition constants. They validated this hypothesis with a mixture of VOCs (dichloromethane, toluene, ethylbenzene, m-xylene, o-xylene, p-xylene, trichloroethylene,

94

Physiologically Based Modeling of Pharmacokinetic Interactions in Chemical Mixtures TOLUENE

Venous concentration (mg/l)

10

1

0.1

0.01 0

1

2

3

4

5

6

7

Time (h) ETHYLBENZENE

Venous concentration (mg/l)

10

1

0.1

0.01 0

1

2

3

4

5

6

7

Time (h)

Figure 4.4 Simulations of venous blood concentrations of toluene and ethylbenzene during maximal impact of inhibition (E = 0; solid thick line) and maximal impact of induction (E = 1; dotted line) in rats exposed by inhalation for a duration of four hours to 100 ppm. Experimental data (symbols) are shown for toluene and ethylbenzene obtained in rats exposed alone and to mixtures of increasing complexity (2–10 volatile organic chemicals). The thin line represents the kinetic profile associated with the single chemical exposure scenario. Adapted from Haddad, Charest-Tardif, and Krishnan (2000b). Reprinted by permission of Taylor & Francis Group, http://www.informaworld.com.

Modeling and Simulations of Binary to Higher Order Interactions in Chemical Mixtures

95

and styrene) in rats. The V max and K m for these chemicals, in turn, were estimated by QSAR methods, which could prove useful for PBPK modeling of chemical mixtures in data-poor situations. The resulting simulations yielded predictions of pharmacokinetics within a factor of 1.5). Using such approaches in mixture PBPK modeling should greatly reduce the number of binary interaction studies for the development of multichemical PBPK models. The approach of Price and Krishnan (2005) is suitable in cases where chemicals compete for metabolism and do not interact in any other way. This approach could be used as a first step in identifying/validating the assumption of competitive inhibition as the mechanism of binary interaction in mixtures.

4.3.4

Fitting Parameter Values to Data Obtained During Exposures to Mixtures

When the kinetic data are available for all components of a mixture for relevant combined exposure scenarios, it becomes relatively straightforward to characterize the apparent rates and affinities of metabolism. In such cases, there is no need to individually characterize the behavior of each inhibitor, its concentration or its inhibition potency with regard to all other mixture components. Using this strategy, Emond, Charbonneau, and Krishnan (2005) modeled the pharmacokinetics of mixtures of PCB congeners (118, 138, 153, 170, 180, and 187) in rats. Because these compounds are highly lipophilic, the kinetics of these compounds were modeled by simply considering the lipid content of the tissue compartments and lipid flow via systemic circulation. Instead of characterizing every binary metabolic interaction in the mixture (i.e., 15 binary combinations), the authors used pharmacokinetic data for these compounds, determined following administration as mixtures, to optimize the metabolic rates on day 41 or 90 of repeated exposures by gavage. Using this approach, the values for metabolic rates generally increased in function of dose, which is consistent with CYP induction in rats following repeated exposures to PCBs. Although, this mixture modeling approach allows the simulation a posteriori of the kinetics of mixture constituents without the use of binary interaction data, it is only likely to be of value in conducting interpolations covering the range of doses and exposure scenarios for which the metabolic rates were optimized.

4.4 Modeling and Simulations of Binary to Higher Order Interactions in Chemical Mixtures Several commercially available simulation or programming software packages can be used for conducting PBPK model simulations (Krishnan and Andersen, 2007). Thy can also R R , QuattroPro
be accomplished using simple spreadsheet programs (e.g., Lotus 1-2-3

R and Microsoft Excel ) as demonstrated by Haddad, Pelekis, and Krishnan (1996), particularly when models are relatively simple. The “internal mechanics” of computer simulation in such cases can be visualized if the user can reconstruct the way in which the simulation software (i) solves each equation in the model, and (ii) takes the output of one equation and provides it as input to other equations of the model. Therefore, this approach is appropriate for individuals who do not have sufficient knowledge of numerical integration algorithms and simulation software. As an example, it is possible to view the

96

Physiologically Based Modeling of Pharmacokinetic Interactions in Chemical Mixtures

Figure 4.5 Computer screen display of the spreadsheet PBPK model of the binary mixture of toluene and m-xylene.

implementation of the PBPK model for the binary mixture of toluene (TOL) and m-xylene (XYL) (Tardif et al., 1995) on an Excel spreadsheet (see QMT Model Library folder HADDAD). In this example, all model parameters are introduced onto a table in a sheet called Parameters (Figure 4.5). The top portion of this sheet has a table containing the values of physiological parameters (tissues blood flows in column C and tissue volumes in column D), tissue:blood and blood:air partition coefficients (column E and G for TOL and XYL, respectively) and biochemical parameters (column F and H for TOL and XYL, respectively). Exposure conditions are located in the table located below to the left where inhaled concentrations (Cinh) and exposure duration (Length) are specified for each chemical. The length of the simulation and the integration time step are given in

Modeling and Simulations of Binary to Higher Order Interactions in Chemical Mixtures

97

the lower left table. Experimental values are also given on the lower right table (columns F–H; rows 23–30) for a six hour exposure to a mixture of TOL 100 ppm and XYL 200 ppm. In this example, a second sheet entitled Simulations (a part of the same EXCEL file) is used to integrate all mass balance differential equations (Figure 4.6). Each column is dedicated to calculate and display the results of a single equation at each integration interval. The progression through time is made by repeating the calculation in subsequent lines using the current values for the variables. To write this binary mixture model, a single chemical PBPK model is first written (Figure 4.6a), where column B corresponds to time progression during simulation, column C is the inhaled chemical concentration, column D is the arterial blood concentration (Ca), and column U is the venous blood concentration resulting from the venous blood leaving each tissue (Cvt). All equations referring to each tissue are grouped together (liver: columns E–H; Fat: columns I–L; richly perfused tissues: columns M–P; and slowly perfused tissues: columns Q–T). The first column corresponding to each tissue contains the mass balance differential equation (dAt/dt), the second calculates the amount of chemical in tissue at a given time (At), the third has the tissue concentration (Ct), and the fourth contains the Cvt. Once all columns required for simulating the kinetics of one chemical are created, these columns (C–U) are then copied and pasted onto columns V to AN (Figure 4.6b), and all references to TOL parameters found in equations are changed to those of XYL. The metabolic interaction between both chemicals is then introduced into the differential equation for liver (columns E and X), as follows: Cell E5 = (Ql∗ (D5 − H4)) − ((Vmax t∗ H4)/(Kmt∗ (1 + AA4/Kixt) + H4)) Cell X5 = (Ql∗ (W5 − AA4)) − ((Vmax x∗ AA4)/(Kmx∗ (1 + H4/Kitx) + AA4))

(4.6) (4.7)

where parameters Ql, V max , K m , and K i are the liver blood flow, the maximal rate of metabolism, the Michaelis affinity constant, and the inhibition constant, respectively, and the suffixes t and x refer to the chemicals, toluene (TOL) and xylene (XYL). The inhibition constant (K i ) xt signifies the inhibitory effect of XYL on TOL and tx the inhibitory effect of TOL on XYL. Variables D5 and W5 are the arterial blood concentrations for TOL and XYL, respectively. And, variables H4 and AA4 in the above equations refer to Cvl for TOL and XYL, respectively. When writing the model, only the first two lines (lines 4 and 5 of the sheet) need to be written, and then the second line can be copied onto the number of lines desired. The number of lines will depend on the integration step and the desired duration of simulation. In this example, line 5 is copied up to line 1303 to simulate kinetics during 6.5 hours (Figure 4.7). It does become tedious to conduct such simulations with increasingly complex mixtures. In this regard, the use of simulation software is needed to be efficient and pragmatic. This aspect is illustrated with the PBPK model for a quaternary mixture model, namely BTEX (benzene, toluene, ethylbenzene, and m-xylene) in rats (Haddad et al., 1999), written in a specialized simulation software ACSLXtreme (Aegis Technologies, Huntsville AL). This BTEX PBPK model (see folder HADDAD in the QMT Model Library) can be used to simulate exposures to any mixture combinations existing in BTEX (i.e., six binary mixtures, four ternary mixtures and one quaternary mixture) and it can, therefore, be used to reproduce simulations found in a number of previous publications (Tardif et al., 1993,

Figure 4.6 (a) Visual snapshot of the spreadsheet PBPK model of the binary mixture of toluene and xylene. The sheet presented in this screen is the one that has model equations and computational results for toluene (TOL). (b) Visual snapshot of the spreadsheet PBPK model of the binary mixture of toluene and xylene. The sheet presented in this screen is the one that has model equations and computational results for m-xylene (XYL).

Modeling and Simulations of Binary to Higher Order Interactions in Chemical Mixtures

99

Figure 4.7 Visual snapshot of the spreadsheet PBPK model of the binary mixture of toluene and m-xylene. The sheet presented in this screen captures the graphical output of the 6.5 hour simulation of venous blood concentrations in rats simultaneously exposed to 100 ppm toluene and 200 ppm m-xylene for four hours.

1997, Haddad et al., 1999). The use of this model for conducting simulations associated with mixed exposures is illustrated below with examples. The number of interacting chemicals in a mixture can have a great impact on the blood kinetics a given chemical. The BTEX PBPK model is used here to illustrate this point, as well as to show the impact of exposure concentrations on the magnitude of interactions. Figure 4.8 shows PBPK model simulations of blood toluene concentrations following exposure of a rat to toluene alone or with increasing number of chemicals (up to four). As the level of complexity of the mixture is increased, the mathematical description of the rate of metabolism of chemicals is complicated by the introduction of an additional binary interaction term (i.e., Cvlinhibitor /K i ) (Table 4.3). The addition of a third chemical, ethylbenzene (E), will affect the liver venous blood concentration of toluene (T) and mxylene (X). The addition E to the binary mixture affects the magnitude of the existing binary interaction of T–X by increasing the Cvl of T and that of X (Table 4.3). Similarly, the addition of E to the ternary mixture affects the kinetics of all three solvents. The magnitude of the modulation of interactions invoked upon the addition of another chemical to an existing “network” of binary interactions depends on its inhibition potency (reflected by its inhibition constant, K i ), and also on its Cvl. With increasing complexity of mixtures, the K i for binary

Physiologically Based Modeling of Pharmacokinetic Interactions in Chemical Mixtures Venous blood concentration (mg/l)

100

1.4 1.2 1 0.8

Cvt (T alone)

0.6

Cvt (TX)

0.4

Cvt (TEX) Cvt (BTEX)

0.2 0

0

1

2

3

4

5

6

7

Time (h)

Figure 4.8 Simulations of rat venous blood concentrations (Cvt) of toluene alone (T alone) or in mixtures of increasing complexity with m-xylene (TX), ethylbenzene (TEX) and benzene (BTEX). Inhaled concentrations of mixture constituents are 100 ppm each.

Venous blood concentrtaion (mg/l)

interactions is not modified; rather the Cvl is increased according to the potency and number of the inhibitors. The increasing effective concentration of chemicals in a mixture is due to cascade of inhibitory events at the binary level which are all interconnected within the PBPK model framework (Table 4.3). This is the reason why the tendency is to see a more marked inhibitory effect with increasing number of inhibitors on the metabolism of a substrate at a specific exposure concentration. The level of increase is also dependent on their exposure levels, as shown by the difference between Figures 4.8 and 4.9, where the number of constituents are similar but their exposure concentrations differ by 10-fold (10 ppm each vs 100 ppm each). To obtain

0.12 0.1 0.08 Cvt (T alone)

0.06

Cvt (TX) 0.04

Cvt (TEX) Cvt (BTEX)

0.02 0

0

1

2

3

4

5

6

7

Time (h)

Figure 4.9 Simulations of rat venous blood concentrations (Cvt) of toluene alone (T alone) or in mixtures of increasing complexity with m-xylene (TX), ethylbenzene (TEX) and benzene (BTEX). Inhaled concentrations of mixture constituents are 10 ppm each (B).

Modeling and Simulations of Binary to Higher Order Interactions in Chemical Mixtures

101

Table 4.3 Mathematical description of the (rate of metabolism) (RAM) of toluene (T) present alone or along with other chemicals (i.e., m-xylene (X), ethylbenzene (E), benzene (B)) that compete for the same but saturable enzyme catalytic sites.a Number of chemicals in mixture

Chemical

RAM equation

1

T

V maxT ·Cvl T K mT + Cvl T

2

T

V maxT ·Cvl T   X + Cvl T K mT 1 + KCvl iXT

X

V max X ·Cvl X   T + Cvl X K mX 1 + KCvl iT X

3

T

X

E

4

T

X

E

B



V maxT ·Cvl T

K mT 1 + 

Cvl E K iE T

Cvl T K iT X

+

Cvl E K iE X

V max E ·Cvl E

K mE 1 + 

K mT 1 + 

Cvl T K iT E

Cvl X K iX E





+ Cvl T

+ Cvl X

+ Cvl E

+

Cvl E K iE T

+

Cvl B K i BT

V max X ·Cvl X

K mX 1 +  K mE 1 +

Cvl T K iT E

K mB 1 +

+



V maxT ·Cvl T Cvl X K iXT

Cvl T K iT X



+

V max X ·Cvl X

K mX 1 + 

Cvl X K iXT

+

Cvl E K iE X

+

Cvl B K iBX

V max E ·Cvl E +

Cvl X K iX E

+

Cvl B K iBE

V max B ·Cvl B Cvl T K iT B

+

Cvl X K iX B

+

Cvl E K iE B









+ Cvl T

+ Cvl X

+ Cvl E

+ Cvl B

α KiXY = inhibition constant, for the effect of chemical X on chemical Y. Cvlx = concentration of chemical x in venous blood leaving liver.

these simulations, only the exposure concentrations of mixture constituents were changed during the modeling exercises. As the exposure concentrations of co-occurring chemicals decrease, the magnitude of interaction and change in toluene concentration in the venous blood also decrease (Figure 4.9 versus Figure 4.8). Due to the fact that the binary interaction terms are influenced by the Cvl of inhibitors and their inhibitory potency K i , it is obvious that as the chemical exposure levels decrease (yielding blood levels well below K i ), there is little impact on the overall rate of metabolism of toluene (Table 4.3).

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Physiologically Based Modeling of Pharmacokinetic Interactions in Chemical Mixtures

4.5

Conclusions

Pharmacokinetic interactions result when one chemical alters the determinants of absorption, distribution, metabolism or excretion of another chemical during co-exposures. The quantitative information on the interaction mechanism can be integrated within PBPK models to conduct simulations of kinetics of chemicals in mixtures. The binary interactionbased PBPK model can then be developed by linking together the single chemical models on the basis of known or hypothesized mathematical description of their interaction mechanism. These models have been shown to be able to simulate the kinetics of chemicals in increasingly complex mixtures. A number of alternative modeling approaches are also available and these do not require the knowledge of all binary level interactions in a given mixture. These approaches include: modeling maximal impact of interactions, lumping of mixture constituents, using K m as K i for competing substrates, as well as fitting parameter values to data obtained during exposures to mixtures.

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5 Physiological Parameters and Databases for PBPK Modeling* Douglas O. Johns1 , Elizabeth Oesterling Owens1 , Chad M. Thompson2 , Babasaheb Sonawane2 , Dale Hattis3 , and Kannan Krishnan4 1

National Center for Environmental Assessment, US Environmental Protection Agency, Research Triangle Park, NC, USA 2 National Center for Environmental Assessment, US Environmental Protection Agency, Washington, DC, USA 3 Marsh Institute, Center for Technology, Environment and Development, Clark University, USA 4 Groupe de Recherche Interdisciplinaire en Sant´e et D´epartement de Sant´e Environnementale et Sant´e au Travail, Universit´e de Montr´eal, Canada

5.1 Introduction One of the key issues in the development of physiologically based pharmacokinetic (PBPK) models involves the choice of values of various physiological parameters used to represent animal and human physiological processes. These parameters include, among others, body weight and body surface area, alveolar ventilation, blood flow to specific organs and tissues, organ and tissue volumes, and glomerular filtration rate. Physiological parameters must be well characterized both in terms of measures of central tendency as well as variability in order for a PBPK model to accurately simulate the absorption, distribution, metabolism, and excretion of environmental chemicals or drugs in a given population. The sensitivity of a model to changes in a given physiological parameter will vary depending in part on ∗ The views expressed in this chapter are those of the authors and do not necessarily reflect the views or policies of the US Environmental Protection Agency.

Quantitative Modeling in Toxicology  C 2010 John Wiley & Sons, Ltd

Edited by Kannan Krishnan and Melvin E. Andersen

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chemical specific physiochemical and biochemical parameters such as partition coefficients and hepatic clearance. As evaluations of PBPK models have gained support for use in human health risk assessments (Chiu et al., 2007), a greater emphasis has been placed on reducing uncertainty and better characterizing variability within and between models by eliminating inconsistencies in the information sources used to establish appropriate physiological parameter values for model development. Initial efforts were undertaken by Arms and Travis (1988) as well as Davies and Morris (1993) to create a compendium of reference values of physiological parameters for use in PBPK modeling. However, these publications presented only single reference values for physiological parameters in humans and various animal species, with no measures of variability provided. In a more recent and comprehensive review, Brown et al. (1997) provided summary values of physiological parameters that were derived by averaging mean values reported in individual studies. The variability of these parameter values was also presented as the standard deviations of the reported means. Although this work did provide very useful information related to the variability of physiological parameters, no individuallevel data were presented or used in deriving reference values. In addition, data on tissue volumes and blood flow rates were often grouped without stratification by age or gender. Age-related differences in physiological function can significantly affect the pharmacokinetics of environmental chemicals in various subpopulations of interest, namely young children and older adults (Ginsberg et al., 2002, 2005). Values of physiological parameters from these subpopulations have been assimilated from the scientific literature of both humans and experimental animals. Gentry et al. (2004) developed an extensive dataset of physiological parameter values relevant to PBPK modeling among neonate and young (<60 days old) mice and Sprague-Dawley rats. This database has recently been made available to the public (http://www.epa.gov/ncct/parameters.html). Thompson et al. (2009) have recently published a review of physiological parameters in older adult humans, as well as a description of a database containing parameter values from adults over the age of 65 years. This database (http://cfpub.epa.gov/ncea/cfm/recordisplay.cfm?deid=188288) is an extension of earlier work involving early human life stage physiological parameters, which was conducted by the International Life Sciences Institute (ILSI) under a cooperative agreement with the US Environmental Protection Agency (International Life Sciences Institute, 2008). In the databases described above, values of body weight, tissue volumes, tissue flows, and so on, have been stratified by species, strain, age, and gender, with individual data presented where available. The National Center for Environmental Assessment and the National Center for Computational Toxicology of the US Environmental Protection Agency’s Office of Research and Development are currently in the process of developing publicly available physiological parameters databases for both humans and experimental laboratory animals that will be continually updated as additional data become available. The initial steps in populating these databases have involved evaluating the data contained within the databases developed for the early life stages of humans and animals (Gentry et al., 2004; International Life Sciences Institute, 2008) as well as older humans (Thompson et al., 2009). A current project is underway to expand these databases to include available data on physiological parameters in adult humans and rodents, in what is essentially an update to the work of Brown et al. (1997). In this undertaking, all of the articles cited in Brown et al. (1997) have been

Introduction

109

collected and evaluated, and an additional literature search and review conducted to identify other physiological parameter data for humans aged 19–64 years, and rats and mice 60 days of age and older. Literature searches were conducted in both PubMed and Current Contents databases using search terms specific to species (human, rat, mouse), in combination with physiological parameter-specific terms related to body weight and body mass index, cardiac output, alveolar ventilation, tissue volumes, tissue blood flow rates, tissue composition, and clearance parameters including glomerular filtration rate. Clinical, toxicological, and in vivo pharmacokinetic studies with various drugs and environmental chemicals were excluded except in cases where the study reported measurements of physiological parameters in untreated humans or animals. Data presented in figures or without appropriate units were also excluded from consideration. Values were entered in the databases as either group or individual data and all entries were independently evaluated by two scientists. The structure of these databases is similar to that used by Thompson et al. (2009) with fields for age, gender, body weight, specific parameter evaluated, value of parameter, group or individual data, parameter variability, and number evaluated. The combined efforts to compile quantitative information on physiological parameters described in this chapter will ultimately be harmonized to produce two comprehensive databases representing parameters from across life stages, one for experimental animals and one for humans. In addition to physiological data taken from individual studies, the animal database will contain the suggested reference or summary values of tissue volumes and blood flow rates for rats and mice presented in Brown et al. (1997). Similarly, for comparison purposes, the human database will contain summary values for tissue volumes, tissue blood volumes, tissue density, tissue composition, and tissue blood flow rates which are presented in ICRP (2003), Leggett and Williams (1991), ICRP (1975), Woodard and White (1986), and Williams and Leggett (1989), respectively. These databases will serve as an evolving central repository of physiological parameter data, which will enable more consistent PBPK development within the scientific community. For the purpose of this chapter, the recently developed adult human physiological parameters database described above has been merged with the database described in Thompson et al. (2009), which contains parameters for older adults as well as developing infants and children (International Life Sciences Institute, 2008). This allows for a more comprehensive description of data availability and variability in physiological parameters across life stages. Database entries include both individual and grouped data, with grouped data typically representing physiological parameter values across a range of ages. In the analyses presented below, parameter values have been stratified by age, using the age of the individual, or, for grouped data, the average age or midpoint of the range of ages. The majority of the data have been collected from cross-sectional studies, with data collected at one time point from an individual or group of individuals. However, in some cases data were collected longitudinally, with parameters measured from the same individual(s) on multiple occasions over time. The availability and variability of data has not been stratified by gender or ethnicity, as the majority of available data comes from males and the ethnicity of individuals is frequently not reported. Although the database does include a limited number of parameter values from health-compromised individuals, only data from relatively healthy individuals are included in the analyses. Parameter units were not consistent across studies, with studies reporting both absolute and relative tissue weights and flows. To allow

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for the utilization of the maximum amount of data available, entries presenting relative tissue weights or flows were normalized to body or tissue weight.

5.2 Data Availability The data collected were sorted by tissue weights and volumes, flows, and intake values for healthy humans. Flow data included values such as tissue blood flows, creatinine clearance, glomerular filtration rates, bile flow, cardiac index, and cardiac output. Intake values were comprised of parameters such as energy intake, alveolar ventilation, tidal volume, minute ventilation, and vital capacity. The values were further stratified by age into the following categories: <1, 1–10, 11–20, 21–35, 36–50, 51–60, 61–70, 71–80, and >80 years of age. This age grouping classification was created as a matter of convenience in presenting the data and does not necessarily reflect breakpoints of ages where differences in physiological function have been demonstrated. Tables 5.1–5.3 present the data availability for healthy individuals in each age group. The information was analyzed based on the number of data points and time points (individual, midpoint, or average age) available for each age-stratified parameter and grouped into datarich (≥20 entries) to data-poor (1-2 entries) categories. Parameters that lacked sufficient individual level data were labeled as data gaps. Both individual and group level data were included in these analyses. The majority of physiological parameters available were tissue weights and volumes. Humans lacked a number of tissue weights in young individuals, including values for heart, kidney, lung, and spleen (Table 5.1). With increasing age, the number of tissues with available values increased, but the replication of these values decreased, such that few to no parameters were considered data rich. Tissue flow rates were data rich in some age groups, but in some cases were extremely limited, particularly in early life stages (Table 5.2). Human intake data were extremely limited in the older age populations (Table 5.3).

5.3 Data Variability Values of physiological parameters used in PBPK models are inherently variable and uncertain. The variability of these values represents, in part, the degree to which the parameters differ across a population. It is important to recognize and, to the extent possible, characterize this variability in order to better understand and characterize the variability in the overall model in which the parameters are used. The figures presented below illustrate this variability and range in the parameter measurements. The data include measured values from both males and females, and were not separated by ethnicity. This inclusive approach could account for some of the spread about the values, since both factors are known to influence physiological parameters. 5.3.1 Body Weight Body weight was provided for a majority of the studies compiled (Figure 5.1). The plotted graph only represents healthy individuals and excludes individuals classified as obese, which will likely result in an underestimation of the variability in this parameter. The large

Data Variability

111

Table 5.1 Individual healthy human data availability – Tissue Volume/Weight (data points–time points). Age (years)

Data rich

<1

Brain (23–11) Liver (25–13)

1–10

Brain (20–10)

11–20

21–35

36–50

Fat-free mass (27–10) Fat-mass (27–10) Total body water (24–9)

Data moderate

Data poor

Data gap

Fat volume (2–2) Protein volume (2–2) Water volume (2–2)

Adrenals Blood Fat mass Fat-free mass Heart Kidney Lung Spleen Adrenals Blood Fat mass Fat-free mass Heart Kidney Lung Spleen Adrenals Blood Fat mass Fat-free mass Heart Kidney Lung Spleen

Liver (19–10)

Fat volume (1–1) Protein volume (1–1) Water volume (1–1)

Brain (16–8) Liver (16–8)

Fat mass (1–1) Fat-free mass (1–1) Total body water (1–1)

Blood (10–4) Heart (10–3) Kidney (17–7) Liver (5–4) Lung (3–2) Plasma (10–4) Pulmonary blood volume (6–5) Spleen (4–4) Thyroid (6–4) Blood (21–10) Adrenals (4–3) Bone (25–3) Arm (3–3) Kidney Body fat (12–9) (56–17) Body water (5–5) Lung (27–8) Bone marrow (4–1) Thyroid Brain (9–8) (23–10) Colon (4–1) Eyes (4–3) Fat-free mass (13–10) Fat mass (6–4) Gall bladder (4–3) Heart (16–10) Lean body mass (3–3) Leg (3–3)

Adrenals (1–1) Body fat (1–1) Body water (2–2) Brain (2–2) Pancreas (1–1) Pituitary (1–1) Prostate (1–1)

Adipose tissue (2–1) Body fat mass index (2–1) Breasts (2–1) Cartilage (2–1) Epididymis (1–1) Fallopian tubes (1–1) Fat (2–1) Fat-free mass index (2–1) Larynx (2–1) Esophagus (2–1) Ovaries (1–1) Rectosigmoid (2–1) (Continued)

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Table 5.1 (Continued) Age (years)

Data rich

51–60

61–70

Fat-free mass (22–7) Fat mass (44–15)

Data moderate

Data poor

Liver (19–10) Muscle (6–4) Pancreas (14–7) Pituitary (4–3) Plasma (19–10) Prostate (3–3) Pulmonary blood volume (3–3) Spleen (16–9) Stomach (4–3) Thymus (3–2) Urinary bladder (4–3) Blood (6–4) Body fat (3–3) Kidney (12–5) Liver (5–4) Plasma (6–4)

Salivary glands (2–1) Skin (2–1) Small intestine (2–1) Teeth (2–1) Testes (2–1) Tongue (2–1) Total body water (1–1) Trachea (2–1) Ureters (2–1) Urethra (2–1) Uterus (2–1)

Adipose tissue (3–2) Blood (3–2) Body water (10–3) Brain (4–2) Extracellular water (3–2) Fat volume (6–4) Heart (4–2) Intracellular water (3–2) Kidney (16–6) Lean body mass (7–5) Liver (14–3) Muscle (7–3) Skin (3–2) Spleen (5–2) Thyroid (3–1)

Adipose tissue (1–1) Adrenals (1–1) Arm (1–1) Body water (2–2) Bone (1–1) Brain (1–1) Fat-free mass (2–2) Fat mass (1–1) Heart (1–1) Leg (1–1) Lung (2–1) Muscle (2–2) Pancreas (1–1) Pituitary (1–1) Prostate (1–1) Pulmonary blood volume (1–1) Skin (1–1) Spleen (2–2) Thyroids (5–3) Adrenal (1–1) Body fat (1–1) Bone (3–2) Gall bladder (1–1) Lean tissue mass (1–1) Lung (2–1) Pancreas (1–1) Pituitary (1–1) Plasma (1–1) Prostate (1–1) Testes (1–1)

Data gap

Data Variability

113

Table 5.1 (Continued) Age (years)

Data rich

Data moderate

Data poor

71–80

Fat-free mass (35–10) Fat mass (65–21)

Body fat (4–1) Body water (12–6) Bone free lean mass (3–2) Brain (4–3) Fat volume (7–3) Heart (4–3) Kidney (9–3) Lean body mass (7–6) Liver (5–3) Spleen (5–3)

Adrenals (1–1) Blood (2–2) Body fat index (2–1) Bone free mass (1–1) Extracellular water (1–1) Fat-free mass index (2–1) Intracellular water (1–1) Lung (2–1) Muscle (2–1) Pancreas (1–1) Pituitary (1–1) Prostate (1–1) Testes (1–1) Thyroid (1–1) Adrenals (1–1) Lean tissue mass (1–1) Prostate (1–1) Testes (1–1)

>80

Adipose (3–3) Body water (4–3) Bone (3–3) Brain (7–5) Extracellular water (4–3) Fat-free mass (12–5) Fat mass (11–6) Heart (6–4) Intracellular water (4–3) Kidney (17–8) Liver (13–10) Lung (4–2) Muscle (7–5) Skin (3–3) Spleen (9–6) Thyroid (3–3)

Data gap

Blood

Thomas, 1962; Shock et al., 1963; Young et al., 1963; Calloway, Foley, and Lagerbloom, 1965; Lesser and Deutsch, 1967; Malina, 1969; Forbes and Reina, 1970; Kjellberg and Reizenstein, 1970; Sato, Miwa, and Tauchi, 1970; Parizkova et al., 1971; Tauchi, Tsuboi, and Okutomi, 1971; Novak, 1972; Chien et al., 1975; Rasmussen et al., 1978; Swift et al., 1978; Bach et al., 1981; Hegedus et al., 1983; Clarys, Martin, and Drinkwater, 1984; Fulop et al., 1985; Pankow, Michalak, and McGee, 1985; Berghout et al., 1987; Inoue and Otsu, 1987; Deurenberg et al., 1989; Wynne et al., 1989; Hanzlick and Rydzewski, 1990; Schmitz, Nyengaard, and Bendtsen, 1990; Schwartz et al., 1990; Garby et al., 1993; Goldberg et al., 1993; Brudin et al., 1994; Kenney and Zappe, 1994; Khosla et al., 1996; Gallagher et al., 1997; Ogiu et al., 1997; Sprogoe-Jakobsen and Sprogoe-Jakobsen, 1997; Visser et al., 1997; Dinenno et al., 1999; Andersen et al., 2000; Gillette-Guyonnet et al., 2000; Hagberg et al., 2000; Bedogni et al., 2001; de la Grandmaison, Clairand, and Durigon, 2001; Dinenno et al., 2001; Frankenfield et al., 2001; Ito et al., 2001; Kyle et al., 2001a, b, c; Santana et al., 2001; Wang et al., 2001; Yee et al., 2001; Chumlea et al., 2002; Pedersen et al., 2002; Puggaard et al., 2002; Schutz, Kyle, and Pichard, 2002; Visser et al., 2002; International Commission of Radiological Protection, 2003; Alcorn and McNamara, 2003; Boito et al., 2003; Dey et al., 2003; Kyle et al., 2003; Movsesyan et al., 2003; Proctor et al., 2003; Zamboni et al., 2003; Chouker et al., 2004; Kanaya et al., 2004; Kwan, Woo, and Kwok, 2004; Kyle et al., 2004a, b; Nies, Chen, and Vander Wal, 2004; Strotmeyer et al., 2004; Goodpaster et al., 2005; Kyle et al., 2005; Chirachariyavej et al., 2006; Park et al., 2006.

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Table 5.2 Individual healthy human data availability – Human blood flow (data points–time points). Age (years)

Data rich

Data moderate

Data poor

Data gap

<1

Creatinine (18–7) Glomerular filtration rate (66–26)

Cutaneous (1–1) Diastolic blood pressure (2–1) Liver (1–1) Muscle (1–1) Subcutaneous (1–1) Systolic blood pressure (2–1) Umbilical artery pulsality index (1–1) Umbilical venous area (1–1) Umbilical venous flow (1–1) Umbilical venous velocity (1–1) Urinary albumin excretion (1–1)

Brain Cardiac index Cardiac output Kidney Lung

1–10

Glomerular filtration rate (26–9)

Cystatin C (9–4) Filtered beta-2-microglobin (6–6) Fraction urine flow rate (6–6) Fractional reabsorption of beta-2-microglobin (6–6) Fractional reabsorption of sodium (6–6) Hematocrit (6–6) Plasma beta-2-microglobulin concentration (6–6) Plasma flow (7–5) Plasma osmolality (6–6) Reabsorption of beta-2-microglobin (6–6) Serum Creatinine (9–4) Urine beta-2-microglobin (12–6) Urine flow rate (6–6) Creatinine (5–3) Cystatin C (5–3) Liver (7–2) Plasma flow (5–2) Serum Creatinine (5–5)

Urinary albumin excretion (1–1)

Cardiac index (3–3) Creatinine (2–2) Cystatin (2–2) Glomerular filtration rate (5–6) Liver (4–2)

Absolute distal re-absorption (1–1) Absolute proximal re-absorption (1–1) Distal Delivery (1–1) Renal plasma flow (1–1) Tubular creatinine secretion (1–1)

Brain Cardiac index Cardiac output Kidney Lung Brain Cardiac output Kidney Lung

11–20

Data Variability

115

Table 5.2 (Continued) Age (years)

Data rich

Data moderate

Data poor

21–35

Brain (35–9) Effective renal plasma flow (115–10) Glomerular filtration rate (133–14) Liver (28–13) Portal (28–13)

Adipose tissue (4–2) Bone marrow (10–2) Cardiac index (17–17) Cardiac output (17–10) Forearm (16–2) Leg (4–3) Large intestine (4–1) Muscle (3–2) Renal plasma flow (4–2)

36–50

Brain (22–8)

Calf (3–1) Cardiac index (16–16) Cardiac output (7–5) Effective renal plasma flow (10–2) Forearm (3–1) Glomerular filtration rate (16–5) Liver (7–3) Portal (6–5)

Adrenals (2–1) Bone (2–1) Creatinine excretion (1–1) GI tract (2–2) Heart (2–1) Hepatic artery (2–1) Iliac (2–1) Kidney (2–1) Lung (2–1) Lymph node (2–1) Pancreas (2–1) Skin (2–1) Small intestine (2–1) Spleen (2–1) Stomach and esophagus (2–1) Thyroid (2–1) Uterine (1–1) Adipose (1–1) Arm (2–1) Creatinine excretion (2–2) Muscle (1–1) Pancreas (1–1) Renal plasma flow (2–1) Skeleton (2–2) Skin (1–1) Thigh (1–1) Creatinine excretion (1–1) Forearm (2–2) Leg (1–1) Muscle (1–1) Skin (1–1) Splanchnic (2–1) Creatinine excretion (1–1) Femoral (1–1) Liver (1–1) Muscle (1–1)

51–60

61–70

Brain (23–8) Glomerular filtration rate (23–11)

Brain (17–5) Cardiac index (11–11) Cardiac output (4–4) Glomerular filtration rate (4–2) Liver (4–3) Portal (8–4) Adipose (4–3) Cardiac index (14–12) Cardiac output (10–5) Forearm (4–2) Portal flow (4–2) Renal (15–10) Splanchnic (8–6)

Data gap

Kidney Lung

Kidney Lung

Lung

(Continued)

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Table 5.2 (Continued) Age (years) 71–80

Data rich

Data moderate

Data poor

Data gap

Brain (26–6) Glomerular filtration rate (38–12)

Adipose tissue (3–2) Bone marrow (3–1) Cardiac index (12–11) Cardiac output (4–3) Renal (15–7)

Calf (1–1) Foot (1–1) Muscle (1–1) Portal (1–1) Skin (1–1) Splanchnic (1–1) Forearm (1–1) Portal (2–1)

Liver Lung

>80

Brain (9–5) Cardiac index (3–2) Cardiac output (3–2) Glomerular filtration rate (13–9) Liver (5–1) Renal (6–4)

Lung

Bradley et al., 1945; Bolomey et al., 1949; Davies and Shock, 1950; Olbrich et al., 1950; Sherlock et al., 1950; Fazekas, Alman, and Bessman, 1952; Fazekas, Kleh, and Witkin, 1953; Scheinberg et al., 1953; Schieve and Wilson, 1953; Brandfonbrener, Landowne, and Shock, 1955; Allwood, 1958; Hellon and Clarke, 1959; Fazekas et al., 1960; Granath and Strandell, 1964; Lassen, Lindbjerg, and Munck, 1964; Lindeman et al., 1966; Julius et al., 1967; Amery, Bossaert, and Verstraete, 1969; Roy, 1973; Rowe et al., 1976; Slack and Wilson, 1976; Bulow and Madsen, 1978; Katori et al., 1979; Frackowiak et al., 1980; Luisada, Bhat, and Knighten, 1980; Dunlop, 1981; Engle and Arant, 1983; Frostell, Pande, and Hedenstierna, 1983; Aperia et al., 1984; Stewart and Jose, 1985; Okazaki et al., 1986; Berghout et al., 1987; Perlmutter et al., 1987; Savard, Kiens, and Saltin, 1987; Schwartz, Brion, and Spitzer, 1987; Snell et al., 1987; Richter et al., 1988; Thomson et al., 1988; Williams and Leggett, 1989; Hartling et al., 1989; Robson et al., 1989; Zoli et al., 1989; Leenders et al., 1990; Robson et al. 1990; Leggett and Williams, 1991; Lemmer and Nold, 1991; Nicoll et al., 1991; Reiss et al., 1991; Palmer et al., 1992; Vanpee et al., 1992; Duvekot et al., 1993; Elia and Kurpad, 1993; Thomsen et al., 1993; Zoller, Wagner, and Zentner, 1993; Bauer et al., 1994; Houben et al., 1994; Kahn et al., 1994; Kiss et al., 1994; Pedrinelli et al., 1994; Rooke, Savage, and Brengelmann, 1994; Dwyer and Howe, 1995; Kenney and Ho, 1995; Rauramo et al., 1995; Wirta and Pasternack, 1995; van Oppen et al., 1996; Brown et al., 1997; Fliser et al., 1997; Ho et al., 1997; Dinenno et al., 1999; Marcus et al., 1999; Zoli et al., 1999; Finney et al., 2000; Johnson et al., 2000; Meltzer et al., 2000; Varga et al., 2000; Wang et al., 2001; Yee et al., 2001; Donckerwolcke and Coppes, 2001; Slosman et al., 2001; Alcorn and McNamara, 2002; International Commission of Radiological Protection, 2003; Dey et al., 2003; Kyle et al., 2003; Martini et al., 2003; Nolin et al., 2003; Zoetis and Hurtt, 2003; Hamon-Vilcot et al., 2004; Kamper et al., 2004; Liu et al., 2005; Berg, 2006.

number of individual values available caused the standard error of the mean (SEM) for each of the age groups to remain small, ranging from 0.4 kg in humans <1 year to 2.4 kg in humans 51–60 years of age. The dispersion of the data represented by the coefficient of variation (CV) is moderate, with values ranging from 12.5% (36–50 years) to 44.4% (<1 year). 5.3.2 5.3.2.1

Tissue Weights Liver

Liver weight has been shown to increase during growth and development and decrease with advanced age. This phenomenon is shown in Figure 5.2. The variability of the plotted measurements represented as standard deviation (SD) and SEM are inconsistent between the age groups. Measurements of the livers of humans <1 year varied by only 70.3 g, whereas individuals 61–70 years varied by 327.3 g and had a CV of 21.3%. Humans 11–20 years

Data Variability

117

Table 5.3 Individual healthy human data availability – Human intake (data points–time points). Age (years)

Data rich

Data moderate

Data poor

Data gap

<1

Energy Intake (9–5)

Alveolar ventilation rate (1–1) Inhalation rate (2–2) Minute ventilation (2–2)

Tidal volume Vital capacity

1–10

Energy Intake (23–11)

Calcium intake (5–4) Carbohydrate intake (5–4) Fat intake (5–4) Iron intake (5–4) Protein intake (9–5) Calcium intake (6–3) Carbohydrate intake (6–3) Fat intake (6–3) Inhalation rate (4–3) Iron intake (6–3) Protein intake (10–3) Total energy expenditure (13–8) Energy Intake (12–4) Inhalation rate (6–2) Tidal volume (7–2) Total energy expenditure (9–4) Vital capacity (7–2) Minute ventilation (7–3) Tidal volume (10–8)

Alveolar ventilation rate (2–2) Minute ventilation (2–2)

Tidal volume Vital capacity

Tidal volume (7–2) Vital capacity (5–2)

Alveolar ventilation rate (1–1) Dead space (1–1) Maximal voluntary ventilation (1–1) Tidal volume (1–1) Vital capacity (1–1) Volume of inspired air (1–1) Alveolar ventilation rate (2–2) Maximal voluntary ventilation (1–1) Minute ventilation (1–1) Ventilation rate (1–1) Vital Capacity (1–1)

11–20

21–35

36–50

51–60

61–70

Vital capacity (26–12)

Alveolar ventilation rate (1–1) Minute ventilation (1–1)

Alveolar ventilation rate Minute ventilation Alveolar ventilation rate Minute ventilation Tidal volume

(Continued)

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Physiological Parameters and Databases for PBPK Modeling

Table 5.3 (Continued) Age (years)

Data rich

71–80

>80

Data moderate

Data poor

Data gap

Alveolar ventilation rate (3–2)

Dead space (1–1) Minute ventilation (1–1) Total ventilation (1–1) Vital Capacity (1–1) Alveolar ventilation rate (2–1) Minute ventilation (1–1) Vital capacity (1–1)

Tidal volume

Tidal volume

Cugell et al., (1953); Norris, Mittman, and Shock, (1964); Falzone et al., 1956; Miller and Tenney, 1956; Bishop, Hirsch, and Thursby, 1978; Frackowiak et al., 1980; Morgan, 1980; Frostell, Pande, and Hedenstierna, 1983; Amis, Jones, and Hughes, 1984; Crawford et al., 1989; Lotgering et al., 1991; Carter, Nicotra, and Huber, 1994; Anderson, McKee, and Holford, 1997; United States Environmental Protection Agency, 1997; Johnson et al., 2000; Al-Hathlol et al., 2000; Livingstone and Robson, 2000; International Commission of Radiological Protection, 2003; Berg, 2006.

old had the lowest CV at 10.2%. The SEM also changed drastically between the groups ranging from 14.4 g (<1 year) to 95.9 g (71–80 years). 5.3.2.2

Brain

Brain weight was shown to reach its maximum early in life and gradually decrease throughout the remaining life stages (Figure 5.3). Few values were available for brain weight in

Figure 5.1 Human body weight. Graph illustrates mean (diamond), median (white line), interquartile range (gray box), maximum (top bar), and minimum (bottom bar) values.

Data Variability

119

Figure 5.2 Human liver weight. Graph illustrates mean (diamond), median (white line), interquartile range (gray box), maximum (top bar), and minimum (bottom bar) values.

middle and later age ranges (e.g., n = 1 in the 51–60 age group), making in difficult to assess variability in these subpopulations of individuals. The SEM was high at 39.9 g in both the <1 year and 36–50 year groups. The highest SD and CV were observed in the fastest growing age group, <1 year, with a variation of 191.5 g and 24.3%, respectively. The remaining groups maintained CV levels less than 8.8% (1–10 years) and as low as

Figure 5.3 Human brain weight. Graph illustrates mean (diamond), median (white line), interquartile range (gray box), maximum (top bar), and minimum (bottom bar) values.

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Figure 5.4 Human heart weight. Graph illustrates mean (diamond), median (white line), interquartile range (gray box), maximum (top bar), and minimum (bottom bar) values.

0.75% (21–35 years). The variability in the <1 year group underscores the need to further consider more refined age bins across age groups – particularly in the young (DeWoskin and Thompson, 2008). 5.3.2.3

Heart

The heart was shown to retain a reasonably constant weight throughout adulthood. Average adult heart weights varied only 103 g across the age groups; however, no data were available for individuals less than 21 years of age and only one value was available for the 51–60 years group (Figure 5.4). The variation between age groups was comparable to the interindividual variation within the groups. The SEM ranged from 11.9 g (>80 years) to 32.4 g (61– 70 years) and the SDs ranged from 29 g (>80 years) to 103.9 g (36–50 years). The CV ranged from 9.0% (>80 years) to 27.3% (36–50 years). 5.3.2.4

Kidney

Human kidney weight (data presented for single rather than paired kidneys) decreased in advanced age groups; however, there were no values of kidney weight reported for early life stages (Figure 5.5). The SD peaked at 60.6 g in individuals 51–60 years and dropped to 20.9 g in the 71–80 years age group, with corresponding CV of 32.7% and 16.1%. The SEM was similar, ranging from 17.5 g (51–60 years) to 4.9 g (>80 years). 5.3.2.5

Spleen

Spleen weight was observed to steadily decrease with increasing age (Figure 5.6). Similar to the kidney and heart, no data were available for individuals <21 years old. The limited

Data Variability

121

Figure 5.5 Human kidney weight. Graph illustrates mean (diamond), median (white line), interquartile range (gray box), maximum (top bar), and minimum (bottom bar) values.

availability of data values resulted in significant variability within the groups. The SD and SEM varied from 22.6 g (51–60 years) to 39.5 g (21–35 years) and 6.4 g (36–50 years) to 19.7 g (21–35 years), respectively. The CV indicated relatively high dispersion in most of the groups, ranging from 15.3% (51–60 years) to 39.1% (>80 years).

Figure 5.6 Human spleen weight. Graph illustrates mean (diamond), median (white line), interquartile range (gray box), maximum (top bar), and minimum (bottom bar) values.

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Figure 5.7 Human liver (hepatic) blood flow. Graph illustrates mean (diamond), median (white line), interquartile range (gray box), maximum (top bar), and minimum (bottom bar) values.

5.3.2.6

Other Tissue

The weights of a large number of other tissues are accessible in the database, including adrenal, adipose, lung, pancreas, pituitary, skin, and testes. 5.3.3 Tissue Blood Flows 5.3.3.1

Liver (Hepatic, Portal, and Splanchnic Blood Flow)

Liver blood flow can be expressed as hepatic arterial, portal venous, or splanchnic flow rates. Splanchnic blood flow describes the blood flow to the abdominal organs such as liver, spleen, stomach, pancreas, and intestine. Figure 5.7 illustrates age stratified total liver blood flow, which includes the combined flow through the hepatic artery and portal vein. A decrease in liver blood flow with age is noticeable; however, few or no values were available for hepatic blood flow for individuals less than 11 or older than 60. The data are moderately variable with SD between 153.3 ml/min (11–20 years) and 232.9 ml/min (51–60 years) and SEM from 66 ml/min (21–35 years) to 116.5 ml/min (51–60 years). The CV ranged from 11% (11–20 years) to 17.4% (21–35 years). 5.3.3.2

Cerebral

Many measurements for adult brain blood flow were collected; however, no values for humans less than 21 years were available. The values for blood flow of the gray and white matter were often reported separately. These values were combined in the volume ratio of 3:2 to calculate the mean cerebral blood flow and presented along with total cerebral blood flow in Figure 5.8. There was a moderate amount of variability in the values with SDs from

Data Variability

123

Figure 5.8 Human brain blood flow. Graph illustrates mean (diamond), median (white line), interquartile range (gray box), maximum (top bar), and minimum (bottom bar) values.

5.0 ml/100 g/min (>80 years) to 11.6 ml/100 g/min (71–80 years) and CV from 12.8% (51–60 years) to 31.1% (71–80 years). 5.3.3.3

Renal

Renal blood flow, referring to the volume of blood perfusing the kidney per unit time, decreases with increasing age. Few measurements of renal blood flow were available for humans of all ages. However, renal clearance measurements were available for all age groups analyzed. Renal clearance or glomerular filtration rates are highly variable (Figure 5.9). This variability could be the result of the multiple methods used to capture this value including inulin or creatinine clearance. The reliability of measurements using these methods varied substantially due to individual differences in endogenous production of creatinine. The values tended to decrease with increasing age, as has been reported, but were highly dispersed with CV as high as 65.1% (<1 year) and 28.6% (>80 years). 5.3.3.4

Other Organs

A large number of other tissue blood flows are accessible in the database, including adipose, muscle, and skin. 5.3.4 5.3.4.1

Cardiopulmonary Parameters Breathing Rate and Pulmonary Function Parameters

Measurements were available for various parameters related to pulmonary function, including alveolar ventilation rate, minute ventilation, tidal volume, and vital capacity. Vital

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Physiological Parameters and Databases for PBPK Modeling

Figure 5.9 Human glomerular filtration rate (GFR). Graph illustrates mean (diamond), median (white line), interquartile range (gray box), maximum (top bar), and minimum (bottom bar) values.

capacity is the maximum volume of air an individual can exhale after a maximum inhalation and tends to decrease with advancing age (Figure 5.10). There was only one value per age category representing individuals over 51 years and no values for children less than 11 years. The values for individuals between 11 and 50 were moderately variable with CV ranging from 12.6% (36–50 years) to 23.8% (11–20 years).

Figure 5.10 Human vital capacity. Graph illustrates mean (diamond), median (white line), interquartile range (gray box), maximum (top bar), and minimum (bottom bar) values.

Summary and Data Gaps

125

Figure 5.11 Human cardiac index. Graph illustrates mean (diamond), median (white line), interquartile range (gray box), maximum (top bar), and minimum (bottom bar) values.

5.3.4.2

Cardiac Output and Cardiac Index

Cardiac output is the volume of blood being pumped from each ventricle of the heart per unit time. Cardiac index relates cardiac output to body surface area, thus normalizing to the size of the individual. Values for cardiac index were available for humans over 11 years and were shown to steadily decline with increasing age (Figure 5.11). Cardiac index was the least variable of all of the parameters analyzed. The SD ranged from 0.03 to 0.37 l/min/m2 and the CV ranged from 0.6% (11–20 years) to 11.6% (61–70 years). The SEM values were equally low ranging from 0.01 to 0.1 l/min/m2 .

5.4

Summary and Data Gaps

The choice of values of key physiological parameters including tissue volumes and blood flow rates is an important step in PBPK model parameterization; it can significantly impact the ability of the model to accurately represent physiological processes. These parameters can be directly measured in humans and animal test species; however, differences in methodologies between laboratories can add to the variability in the reported values. Another important source of variability in physiological parameters is related to subjectspecific characteristics such as age, gender, ethnicity, and health status. While the former source of variability cannot be easily assessed, variability in physiological parameters stemming from differences in intrinsic subject characteristics can certainly be better characterized with additional data. There are currently several compilations of physiological parameter values available for use in developing PBPK models. However, at present there is no resource that includes physiological parameters of humans or animal test species across all life stages.

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A project is currently underway to create two publicly available physiological parameters databases, one for humans and one for animal test species. The analysis of data availability and variability of various human physiological parameters presented in this chapter provides insight into the breadth of data that will be used to populate these databases. There is a clear need for additional data from both children and older adults, as well as females of all ages and individuals representing a variety of ethnic backgrounds. In addition, very few data are available on physiological parameters in health-compromised individuals, who are often considered as a potentially susceptible population when conducting chemical health risk assessments. The structure of the databases under development will allow for continual updates as values of physiological parameters become available, particularly for these specific groups for whom data are lacking. As the quantity of relevant physiological parameter data increases, regression relationships between age, gender, ethnicity or body weight and various parameters of interest can be utilized to predict physiological parameter values for a given individual or population. In addition, a more accurate characterization of the variability of physiological parameters will be valuable in assessing the effect of various parameters on tissue dose using Monte Carlo simulation techniques. 5.4.1 Database Update In the time between the completion of this chapter and the publication date, an initial version of a harmonized physiological parameters database was completed, and is available for download at http://cfpub.epa.gov/ncea/cfm/recordisplay.cfm?deid=202847.

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Sprogoe-Jakobsen, S. and Sprogoe-Jakobsen, U. (1997) The weight of the normal spleen. Forensic Sci. Int., 88 (3), 215–223. Stewart, C.L. and Jose, P.A. (1985) Transitional nephrology. Urol. Clin. North Am., 12 (1), 143–149. Strotmeyer, E.S., Cauley, J.A., Schwartz, A.V., et al. (2004) Diabetes is associated independently of body composition with BMD and bone volume in older white and black men and women: The Health, Aging, and Body Composition Study. J. Bone Miner. Res., 19 (7), 1084–1091. Swift, C.G., Homeida, M., Halliwell, M., and Roberts, C.J. (1978) Antipyrine disposition and liver size in the elderly. Eur. J. Clin. Pharmacol., 14 (2), 149–152. Tauchi, H., Tsuboi, K., and Okutomi, J. (1971) Age changes in the human kidney of the different races. Gerontologia, 17 (2), 87–97. Thomas, L.W. (1962) The chemical composition of adipose tissue of man and mice. Q J Exp. Physiol. Cogn. Med. Sci., 47, 179–188. Thompson, C.M., Johns, D.O., Sonawane, B., et al. (2009) Database for physiologically based pharmacokinetic (PBPK) modeling: Physiological parameters for healthy and health-impaired elderly. J. Toxicol. Environ. Health A, 12, 1–24. Thomsen, J.K., Fogh-Andersen, N., Jaszczak, P., and Giese, J. (1993) Atrial natriuretic peptide (ANP) decrease during normal pregnancy as related to hemodynamic changes and volume regulation. Acta Obstet. Gynecol. Scand., 72 (2), 103–110. Thomson, A., Fletcher, P.J., Harris, P.J., et al. (1988) Regional distribution of cardiac output at rest and during exercise in patients with exertional angina pectoris before and after nifedipine therapy. J. Am. Coll. Cardiol., 11 (4), 837–842. United States Environmental Protection Agency (1997) Exposure Factors Handbook: Volume 1General Factors (EPA/600/P-95/002Fa), Washington, DC, Office of Research and Development, National Center for Environmental Assessment. van Oppen, A.C., Van Der Tweel, I., Alsbach, G.P., et al. (1996) A longitudinal study of maternal hemodynamics during normal pregnancy. Obstet. Gynecol., 88 (1), 40–46. Vanpee, M., Blennow, M., Linne, T., et al. (1992) Renal function in very low birth weight infants: normal maturity reached during early childhood. J. Pediatr., 121 (5 Pt 1), 784–788. Varga, I., Rigo, J., Jr., Somos, P., et al. (2000) Analysis of maternal circulation and renal function in physiologic pregnancies; parallel examinations of the changes in the cardiac output and the glomerular filtration rate. J. Matern. Fetal Med., 9 (2), 97–104. Visser, M., Gallagher, D., Deurenberg, P., et al. (1997) Density of fat-free body mass: relationship with race, age, and level of body fatness. Am. J. Physiol., 272 (5 Pt 1), E781–E787. Visser, M., Kritchevsky, S.B., Goodpaster, B.H., et al. (2002) Leg muscle mass and composition in relation to lower extremity performance in men and women aged 70 to 79: the health, aging and body composition study. J. Am. Geriatr. Soc., 50 (5), 897–904. Wang, Z., Heo, M., Lee, R.C., et al. (2001) Muscularity in adult humans: proportion of adipose tissue-free body mass as skeletal muscle. Am. J. Hum. Biol., 13 (5), 612–619. Williams, L.R. and Leggett, R.W. (1989) Reference values for resting blood flow to organs of man. Clin. Phys. Physiol. Meas., 10 (3), 187–217. Wirta, O.R. and Pasternack, A.I. (1995) Glomerular filtration rate and kidney size in type 2 (noninsulin-dependent) diabetes mellitus. Clin. Nephrol., 44 (1), 1–7. Woodard, H.Q. and White, D.R. (1986) The composition of body tissues. Br. J. Radiol., 59 (708), 1209–1218. Wynne, H.A., Cope, L.H., Mutch, E., et al. (1989) The effect of age upon liver volume and apparent liver blood flow in healthy man. Hepatology, 9 (2), 297–301. Yee, A.J., Fuerst, T., Salamone, L., et al. (2001) Calibration and validation of an air-displacement plethysmography method for estimating percentage body fat in an elderly population: a comparison among compartmental models. Am. J. Clin. Nutr., 74 (5), 637–642. Young, C.M., Blondin, J., Tensuan, R., and Fryer, J.H. (1963) Body composition of “Older” women. J. Am. Diet. Assoc., 43, 344–348. Zamboni, M., Zoico, E., Scartezzini, T., et al. (2003) Body composition changes in stable-weight elderly subjects: the effect of sex. Aging Clin. Exp. Res., 15 (4), 321–327. Zoetis, T. and Hurtt, M.E. (2003) Species comparison of anatomical and functional renal development. Birth Defects Res. B Dev. Reprod. Toxicol., 68 (2), 111–120.

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Zoli, M., Iervese, T., Abbati, S., et al. (1989) Portal blood velocity and flow in aging man. Gerontology, 35 (2–3), 61–65. Zoli, M., Magalotti, D., Bianchi, G., et al. (1999) Total and functional hepatic blood flow decrease in parallel with ageing. Age Ageing, 28 (1), 29–33. Zoller, W.G., Wagner, D.R., and Zentner, J. (1993) Effect of propranolol on portal vein hemodynamics: assessment by duplex sonography and indocyanine green clearance in healthy volunteers. Clin. Investig., 71 (8), 654–658.

Section 3 Modeling toxicant-target interactions

6 Modeling Cholinesterase Inhibition Charles Timchalk, Paul M. Hinderliter, and Torka S. Poet Center for Biological Monitoring and Modeling, Pacific Northwest National Laboratory, USA

6.1

Background

This chapter is focused on the development and application of pharmacokinetic (PK) and pharmacodynamic (PD) models to better understand the toxicology of organophosphosphorus (OP) and carbamate insecticides and chemical warfare agents (CWA) in animals and humans. Although both PK and PD elements of the model will be described, the primary focus will be on highlighting the PD components within the model structure. In this regard, the approach will not entail a comprehensive review of the extensive literature, but rather a focused presentation highlighting important principles using more recently published models for organophosphorus insecticides as specific examples. Organophosphorus and carbamate insecticides and chemical warfare agents have high affinity for binding to and inhibiting the enzyme acetylcholinesterase (AChE), an enzyme specifically responsible for the destruction of the neurotransmitter acetylcholine (ACh) within nerve tissue (Wilson, 2001; Ecobichon, 2001). Since the cholinergic system is widely distributed within both the central and peripheral nervous systems, chemicals that inhibit AChE are known to produce a broad range of well characterized symptoms (for a review see Savolainen, 2001). A comparison of the AChE inhibition dynamics for the interaction of ACh, carbaryl (carbamate), chlorpyrifos-oxon (organophosphate), and Sarin with AChE is illustrated in Figure 6.1. All four substrates have relatively high affinities for AChE and will readily complex with the enzyme. However, the rates of hydrolysis and reactivation of AChE following carbamylation or phosphorylation of the active site will be drastically slower than for the hydrolysis of the acetylated enzyme (Ecobichon, 2001). Specifically, the turnover time for the neurotransmitter ACh is on the order of ∼150 µsec; Quantitative Modeling in Toxicology  C 2010 John Wiley & Sons, Ltd

Edited by Kannan Krishnan and Melvin E. Andersen

138

Modeling Cholinesterase Inhibition

I. Acetylcholine

II. Carbamates

Acetylcholine CH3

+

++

CH3 N

CH2

Carbaryl

AChE Active Site

HO

O

CH2 O

CH3

C O

O

Rapid

H

CH3

H

CH3 CH 3 + CH2 CH3 N AChE Active Site

o

C

CH3 CH 3

H CH 22

CH 33

CH 22 OH

HO

(H2O) Acetate

CH

CH3 C O

C

AChE Active Site

HO

&

O

3N H

AChE Active Site

HO

&

&

Slow (H2O)

+

CH33 N

Rapid

HO H O

AChE Active Site

O

CH 3N

Choline

&

OH

O

Acetylated Enzyme

O

α-naphthol

Carbamylated Enzyme

-OO

AChE Active Site

AChE Active Site

HO

Rapid

CH3 C

O

+

CH 2 O CH

CH33

CH3 C CH 3

CH3

N

IV. Sarin

III. Organophosphates

Sarin Chlorpyrifos-oxon Cl O

+

P O

N

HO

AChE Active Site

P

Cl

CH3

O

Phosphorylated Enzyme O

AChE Active Site

o

P

Cll C

O

Cl

CH3

Hydrogen Fluoride

O

C H33 CH O

P

o

AChE Active Site

+

HF

P

O H P P OH

O

AChE Active Site

Aging

O OH

O

CH C H33

O

HO

N

CH3

O

&

AChE Active Site

Cl

Aging

Diethylphosophate O

HO

Phosphorylated Enzyme OH

H3 C CH

C H33 CH

+

Rapid

+

O

Very Slow (H2O)

F

Trichlorpyridinol

O

CH C H3

O CH3

Rapid

H3 C CH

O

CH 3

Cl

O

CH C H33

H3 C CH

AChE Active Site

P OH

O

AChE Active Site

CH3

Figure 6.1 Schematic illustrating the interaction of the endogenous substrate, acetylcholine (I), the pesticide, carbamate carbaryl (II) the organophosphate pesticide, chlorpyrifos-oxon (III), and the chemical warfare agent Sarin (IV) with the active site of acetylcholinesterase (AChE). The general rate of bound AChE hydrolysis is: ACh  carbaryl > chlorpyrifos-oxon  Sarin.

Background

139

whereas, the carbamylated enzyme t1/2 for hydrolysis is substantially slower (∼15–30 min). The phosphorylated enzyme is highly stable (t1/2 ∼ days) and further dealkylation of the phosphorylation group produces an “aged” AChE enzyme which is irreversibly inhibited (Taylor, 1980; Murphy, 1986; Ecobichon, 2001; Sogorb and Vilanova, 2002). 6.1.1

Organophosphate Biotransformation

A more detailed overview of the metabolism of organophosphorus insecticides can be found in Calabrese (1991), Jakanovic (2001), Sogorb and Vilanova (2002), and Knaak et al. (2004). Phosphorothionate insecticides, such as chlorpyrifos, are weak inhibitors of AChE but once they undergo metabolic activation (desulfation) to their corresponding oxygen analogs (oxon) they become extremely potent inhibitors. This enhanced toxicity is due to the oxon having a higher affinity and potency for phosphorylating the serine hydroxyl group within the active site of AChE (Mileson et al., 1998; Sultatos, 1994). The toxic potency is dependent upon the balance between a delivered dose to the target site and the rates of bioactivation and/or detoxification (Calabrese, 1991). In Figure 6.2, the

Cl

AChE Inhibition Toxicity

O

P O

CYP450

Cl

50 P4

CH 3

Cl

O

Chlorpyrifos-oxon

Cl

Chlorpyrifos

CY

O

N

O

s

CH 3

Cl

S

CH3

P O

Diethylthiophosphate S

CH 3 O

N

ter B-e ase ( ste PO ras N-1 ) e

O

CH 3

P OH

ACl es

O

3,5,6-trichloro-2-pyridinol (TCP) Cl

CH 3

Cl

O

CH 3 O

P OH

Diethylphosphate

OH

N

Cl

O

CH3

Cl

Conjugates- O

Cl

N

Cl

Sulfate or glucuronides of TCP

Figure 6.2 Metabolic scheme for the metabolism of chlorpyrifos and the major metabolites chlorpyrifos-oxon, trichloropyridinol (and conjugates), diethylphosphate and diethythiophosphate. Adapted with permission from Timchalk et al. (2002a).

140

Modeling Cholinesterase Inhibition

thionophosphate pesticide chlorpyrifos (O,O-diethyl-O [3,5,6-trichloro-2-pyridyl]- phosphorothioate) is used for illustration of a common mode of action readily extended to other structurally related OP insecticides. As previously mentioned, phosphorothionates do not directly inhibit AChE but must first be metabolized to the corresponding oxygen analog (i.e., chlorpyrifos-oxon) (M¨ucke, Alt, and Esser, 1970; Iverson, Grant, and Lacroix, 1975; Murphy, 1986; Sultatos, 1994). Activation to the oxon-metabolite is mediated by cytochrome P450 mixed function oxidases (CYP450) primarily within the liver, although extra-hepatic metabolism has been reported in other tissues including the brain (Guengerich, 1977; Chambers and Chambers, 1989). In the case of chlorpyrifos (CPF), oxidative dearylation produces both 3,5,6- trichloro-2-pyridinol (TCP), and diethylthiophosphate (DETP), and represents a competing detoxification pathway that is also mediated by hepatic CYP450 (Ma and Chambers, 1994). These initial activation/detoxification reactions are believed to share a common phosphooxythiran intermediate and represent critical biotransformation steps required for toxicity (Neal, 1980). Differences in the ratio of activation to detoxification are associated with chemical-, species-, gender-, and age-dependent sensitivity to organophosphates (Ma and Chambers, 1994). Hepatic and extra-hepatic (i.e., blood and tissue) esterases, such as PON-1, effectively metabolize chlorpyrifos-oxon (CPF-oxon) forming TCP and diethylphosphate (DEP). Likewise B-esterases, such as carboxylesterase (CaE) and butyrylcholinesterase (BChE), are also well distributed across tissues and can metabolize the oxon; however, B-esterases become irreversibly bound (1:1 ratio) to the oxon and inactivated (Chanda et al., 1997; Clement, 1984). Studies in both humans and rodents indicate that the primary metabolite, TCP, can likewise undergo additional glucuronide or sulfate conjugation (Bakke, Feil, and Price, 1976; Nolan et al., 1984). Although binding to AChE is associated with acute neurotoxicity, binding to BChE and CaE is suggested to be without adverse physiological effect and, as such, represents detoxification pathways (Pond, Chambers, and Chambers, 1995; Clement, 1984; Fonnum et al., 1985).

6.1.2 Physiologically Based Pharmacokinetic Models for Organophosphorus Agents Physiologically based pharmacokinetic (PBPK) models have emerged as important tools that have broad applications in toxicology and, more specifically, in human health risk assessment (Andersen, 2003; Krishnan and Andersen, 2001; Clewell and Andersen, 1996; Andersen, 1995; Leung and Paustenbach, 1995). As suggested by Andersen (2003), PBPK models can be extended to incorporate pharmacodynamics if we have a fundamental understanding of the biological mode of action. In this regard, the coupling of ChE inhibition dynamics to target tissue dosimetry within the framework of a PBPK model structure is appropriate and achievable. To illustrate the application of this modeling approach, PBPK models that also incorporate a pharmacodynamic component to describe ChE inhibition following exposure to the phosphorothionate insecticides (for example chlorpyrifos and diazinon) in rodents and humans will be described (Poet et al., 2004; Timchalk et al., 2002b). These models are based on the conceptual structure developed by Gearhart et al. (1990) to describe AChE inhibition following an acute exposure to diisopropylfluorophosphate (DFP).

Background

141

Parent Compound Qc

Kp Qsk

SA

Oxon

Cvsk Skin

Qf

Ca

Cv f

Cao

Cv

Fat

Qfo

Cvfo

Cvo

Fat

Qs

Cvs

Qso

Cvr

Qro

Slowly Perfused

Cv s o

Cvd Diaphragm

Qb

Cv b

Venous Blood

Rapidly Perfused Qd

Arterial Blood

Slowly Perfused

Qr

Arterial Blood

Qc

Blood

Cvro

Rapidly Perfused Qdo

Cvdo Diaphragm Qbo

Venous Blood

Dermal Exposure

Cvbo

Brain

Brain

Ql

Cvl

Qlo

Cvlo Liver

Liver Km , Vmax

KaI

A-EST Km , Vmax

Oxon

Intestine

Compartment Model KaS

Hydrolysis Km , Vmax

KsI

B-EST (AChE, BuChE, CaE) Liver and blood only’ Ke

Stomach Kzero

Metabolite(s)

Fa

Fa

Gavage Exposure Dietary Exposure

B-Esterase (B-EST) Inhibition (shaded compartments)

Synthesis of New Esterase µmole

“Free” Oxon

+

h-1

Inhibition uM -1 h -1

Free Esterase

h-1 Degradation of Esterase

h-1 Oxon-Esterase

Aged Complex

h-1 Regeneration

Leaving Group

Figure 6.3 Physiologically based pharmacokinetic and pharmacodynamic model used to describe the disposition for a parent phosphorothionate insecticide, its oxon metabolite, associated leaving groups, and B-esterase inhibition in rats and humans following oral (gavage, dietary) and dermal exposures. The shaded tissues compartments indicate organs in which Besterase (AChE, BChE, and CaE) enzyme activity is described. Figure adapted with permission from Timchalk et al. (2002b). Model parameter definitions: QC cardiac output (l/h); Qi , blood flow to “i” tissue (l/h), Ca, arterial blood concentration (µmol/l); Cao, arterial blood concentration of oxon (µmol/l); Cv, pooled venous blood concentration (µmol/l); Cvi , venous blood concentration draining “i” tissue (µmol/l); Cvi o, venous blood concentration of oxon draining “i” tissue (µmol/l); SA surface area of skin exposed (cm2 ); KP, skin permeability coefficient (cm/h); Kzero , zero (µmol/h) rate of absorption from diet; Fa fractional absorption (%); KaS and KaI, first-order rate constants for absorption from compartments 1 and 2 (per hour); KsI first-order rate constant for transfer from compartment 1 and 2 (per hour); Ke, first-order rate constant for elimination of metabolite from compartment 3; Km(1-4) , Michaelis constant for saturable processes (µmol/l); V max (1-4) , maximum velocity for saturable process (µmol/h).

A diagram of the PBPK and PD model structure for thionophosphorus organophosphate insecticides is illustrated in Figure 6.3. The conceptual representation of the PBPK/PD model for these insecticides is based on the anatomical and physiological characteristics of the rat and human. The major determinants of insecticide disposition include: absorption rates, tissue partitioning, plasma protein binding, CYP450 metabolism, PON-1 metabolism, and esterase binding and hydrolysis (Poet et al., 2004; Timchalk et al., 2002b).

142

Modeling Cholinesterase Inhibition

The PBPK/PD model allows for the simulation of differing exposure scenarios including acute oral “gavage,” chronic dietary, and dermal. In these models, physiological and metabolic parameters were scaled as a function of body weight, according to the methods of Ramsey and Andersen (1984). The CYP450 mediated activation and detoxification was limited to the liver, and was linked to the oxon models that incorporated equations to describe PON-1 metabolism in both liver and blood. The CYP450 activation/detoxification and PON-1 detoxification were all described as saturable enzymatic processes modeled with the Michaelis–Menten equation. In this model the major metabolites were formed by CYP450 metabolism of the parent compounds, or PON-1 and B-esterase hydrolysis of oxons. The pharmacokinetics of the non-oxon degradation metabolites were described using a simple one-compartment model, which was based on the model structure developed by Nolan et al. (1984) to describe the pharmacokinetics of trichloropyridinol (TCP) in blood and urine. Oxon metabolites bind with and inhibit AChE, BChE, and CaE. Interactions of the oxon with B-esterase were modeled as second-order processes (a stoichiometric function of both the oxon and esterase concentrations) occurring in the liver, blood (plasma and RBC), diaphragm, and brain. The B-esterase enzyme levels (µmol) were calculated based on the enzyme turnover rates and enzyme activities (Maxwell et al., 1987). The balance between the bimolecular inhibition and ChE regeneration and aging determined the amount of free ChE. The PBPK/PD models developed for OP insecticides are fairly complex and data intensive, so to adequately develop and validate these models generally requires extensive experimentation to support model parameterization and validation. The following sections provide a more detailed description of the PBPK/PD model structure including: the PBPK/PD modeling assumptions and parameters; and the PK and PD model structures. In addition, a brief description of cross-species extrapolation, age-dependent PK/PD responses and binary mixture exposures will be presented. Finally, the CPF PBPK/PD model ACSL “core” code is included in the QMT Model Library (Folder TIMCHALK).

6.2

PBPK/PD Modeling Assumptions and Parameters

6.2.1 Pharmacokinetics The physiological and biochemical parameters used to develop the PBPK/PD model for the organophosphate insecticide chlorpyrifos (CPF) are presented in Tables 6.1 and 6.2. In general, many of these parameters have been previously measured in both animals and humans (Brown et al., 1997; Arms and Travis, 1988). However, it is important to recognize, particularly as one attempts to address questions concerning age-dependent or disease-state specific pharmacokinetics, that appropriate physiological parameters may not be available. An initial first approximation should use available parameters, recognizing the potential uncertainty, but it should also be understood that the experimental determination of new physiological parameters may need to be considered. As previously suggested, the metabolism of phosphorothionate insecticides is complex, involving CYP450s, esterase hydrolysis, and conjugation reactions (Figure 6.2). A number of in vivo and in vitro approaches have been used to determine metabolic parameters (for a review see Krishnan and Andersen, 2001). However, for these non-volatile insecticides in vitro cellular and subcellular metabolizing systems are the most appropriate for obtaining

PBPK/PD Modeling Assumptions and Parameters

143

Table 6.1 General physiological parameters used in the PBPK/PD model for CPF. Body weight (kg) Cardiac output (l/kg/h) Tissue Blood Brain Diaphragm Liver Rapidly perfused Slowly perfused Fat

0.274–0.303 ∼70 15 Tissue Volume (% of body weight) 6.0 1.2 0.03 4.0 4.0 78 7.0

Rat Human Percentage of cardiac output 25 3.0 0.6 44 14 9.0

metabolic rate constants. For a more detailed review on the metabolism of organophosphorus insecticides and the integration of these data into PBPK models see Knaak et al. (2004). Model development, validation, and refinement is an ongoing process which is accomplished by exploiting the results from in vivo PK and PD studies conducted in both animal models and, where appropriate, in humans (Timchalk et al., 2002b, 2005; Timchalk, Kousba, and Poet, 2006). For example, representative results and model simulations demonstrating the ability of the model to adequately simulate blood CPF and CPF-oxon dosimetry in the adult rat are presented in Figure 6.4 (Timchalk, Kousba, and Poet, 2007). In general, the model reasonably simulated the available CPF blood concentrations at doses ranging from 1–50 mg/kg (Figure 6.4a). In addition, although CPF-oxon was only detectable in a very limited number of blood samples (i.e., peak blood levels at 10 and 50 mg/kg), the peak concentration simulations are appropriate. Recent model improvements, associated with ongoing efforts to experimentally update and improve model parameter estimates (Timchalk, Kousba, and Poet, 2007), show slightly improved fits to the experimental data relative to the previously published model (Timchalk et al., 2002b).

6.2.2

Pharmacodynamics

To develop a pharmacodynamic model for ChE inhibiting compounds, the steady-state levels (µmol) of B-esterase enzyme(s) (AChE, BChE, and CaE) were determined for the various tissues. Based on the rates of enzyme synthesis (zero order) and degradation (first order), ChE turnover rates, enzyme activity, and degradation rates were calculated (Table 6.3). Initial estimates of the amounts (µmol) of AChE, BChE, and CaE in tissues from naive rats (Maxwell et al., 1987) were used for both the rat and human models (Timchalk et al., 2002b). It is important to note that since the model is highly dependent upon the estimates of these enzyme levels, additional experimental measurements may be warranted, particularly in humans (Knaak et al., 2004). The enzyme degradation rates for AChE, BChE, and CaE were initially based on the first-order loss of rat brain AChE (Wenthold, Mahler, and Moore, 1974) as described by Gearhart et al. (1990). As a first approximation the synthesis and loss rates for BChE were set the same as for AChE; however, for CaE the rates were optimized

144

Modeling Cholinesterase Inhibition

Table 6.2 Chlorpyrifos (CPF) specific parameters used in the PBPK model. Parameter

CPF

CPF-oxon

Estimation Method

Partition Coefficients Brain/Blood Diaphragm/Blood Fat/Blood Liver/Blood Rapidly perfused/Blood Slowly perfused/Blood

28.8 3.6 228 11.7 6.8 3.6

10.1 2.3 119 6.5 6.5 2.3

Lowe et al., 2006

0.93 14.3

– –

Poet et al., 2003

16.4 60.9

– –

Poet et al., 2003

60 0.003

– –

Optimized Chambers and Chambers, 1989

– –

450 38002

Optimized Mortensen et al., 1996

– –

450 40377

Optimized Mortensen et al., 1996

Oral absorption parameters KaS (stomach; h−1 ) KaI (intestine; h−1 ) KsI (transfer stomach–intestine; h−1 ) Fa (fractional Abs; %) Protein Binding (%)

0.01a 0.5a 0.5a 80 95a,b

– – – – 95a,b

TCP model parameters Vd (L) Ke (h−1 )

0.30 0.41

Metabolic Constants Liver CYP450 (CPF → CPF-oxon) Km (µmole/l) VmaxC (µmole/(h kg)) Liver CYP450 (CPF → TCP) Km (µmole/l) VmaxC (µmole/(h kg)) Brain CYP450 (CPF → CPF-oxon) Km (µmole/l) VmaxC (µmole/(h kg)) Blood PON-1 (CPF-oxon → TCP) Km (µmole/l) VmaxC (µmole/(h kg)) Liver PON-1 (CPF-oxon → TCP) Km (µmole/l) VmaxC (µmole/(h kg))

a b

Timchalk et al., 2002b Timchalk, Kousba, and Poet, 2007

Optimized

The model parameters were estimated independently and held fixed, calculated or fitted as previously described (Timchalk et al., 2002b).

with the PD model to fit CaE inhibition data from Chanda et al. (1997), as described (Timchalk et al., 2002b). In developing PD models for ChE inhibiting insecticides an important consideration is to adequately characterize the type of B-esterases (i.e., AChE vs BChE) present in a given tissue, since across species there are marked quantitative differences in the amount and types of tissue esterases present (Timchalk et al., 2002b). For example, rat plasma ChE is the sum of both plasma AChE and BChE activity (Maxwell et al., 1987), whereas in humans,

PBPK/PD Modeling Assumptions and Parameters

(a)

(b) CPF-oxon umol/l

Chlorpyrifos

CPF umol/l

1.E+01 50 mg/kg

1.E+00

10 mg/kg

1.E-01 1.E-02

1 mg/kg

1.E-03 1.E-04 0

10

20

145

Chlorpyrifos-oxon 50 mg/kg

1.E-02

10 mg/kg

1.E-03 1.E-04 1.E-05

1 mg/kg

1.E-06 1.E-07

30

0

10

20

30

Time (h)

Time (h)

Figure 6.4 Blood time-course of (a) chlorpyrifos (CPF) and (b) chlorpyrifos oxon (CPF-oxon) in rats following oral administration of 1 (black diamond), 10 (open triangle) or 50 (ray square) mg CPF/kg of body weight, respectively. The lines represent the model simulation of the experimental data. Adapted with permission from Timchalk, Kousba, and Poet (2007). Table 6.3 Parameters used in the Pharmacodynamic Model for CPF-Oxon Inhibition of AChE, BuChE and CaE. AChE

BuChE

CaE −1 a

Enzyme Hydrolysis (h ) 1.17 × 107 3.66 × 106 1.09 × 105 Tissue Brain Diaphragm Liver Plasma

Enzyme Activity (µmole/(kg h))a 4.4 × 105 4.68 × 104 6.0 × 104 4 4 7.74 × 10 2.64 × 10 3.18 × 105 4 4 1.02 × 10 3.00 × 10 1.94 × 106 1.32 × 105 1.56 × 104 4.56 × 105 Esterase Parametersb Enzyme Degradation Rate (h−1 )

Enzyme Reactivation Rate (h−1 )

Enzyme Aging Rate (h−1 )

AChE Brain, Diaphragm, Liverc , Plasmac RBC

0.01 0.01

0.014 0.014c

0.0113 0.0113

BuChE Brain, Diaphragm, Liverc , Plasmac

0.01

0.014

0.0113

2000

7.54 × 10−4 0.001 0.0033

0.014 0.014 0.014

0.0113 0.0113 0.0113

20 20 20

CaE Brain Diaphragm, Liver Plasma

Bimolecular Inhibition Ki (µM h)−1 243 243c

The model parameters were estimated independently and held fixed, calculated or fitted as previously described (Timchalk et al., 2002b). a Maxwell et al. (1987) b Timchalk et al. (2002b); c Parameter estimates have been updated from published value in Timchalk et al. (2002b).

146

Modeling Cholinesterase Inhibition

(a)

ChE activity using BTC substrate

Activity (mOD/min)

0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000

Control

Activity (mOD/min)

(b)

iso-OMPA

BW284C51

ChE activity using ATC substrate

Brain plasma

0.040 0.035 0.030 0.025 0.020 0.015 0.010 0.005 0.000

Saliva

Control

iso-OMPA

BW284C51

Figure 6.5 In vitro determination of total ChE activity described as (a) butyrylthiocholine (BTC) and (b) acetylthiocholine (ATC) hydrolysis rates in tissues following iso-OMPA (BuChE inhibitor) or BW284C51 (AChE inhibitor) incubation (15 min) with brain, plasma, and saliva samples obtained from na¨ıve adult male rats. The data represents the mean ± S.D. for three determinations. Figure adapted with permission from Kousba, Poet, and Timchalk (2003).

plasma ChE is exclusively BChE (ORNL, 2000). To characterize tissue ChE activity the specific inhibitors of AChE (BW284C51) and BChE (iso-OMPA) activity can be used in combination with differing substrates such as acetylthiochoine (ATC) or butyrylthiocholine (BTC). Although AChE and BChE can both hydrolyze ATC, only BChE can hydrolyze BTC (Lassiter, Barone, and Padilla, 1998; Chuiko, 2000). Therefore, a combination of specific enzyme inhibitors and substrates makes it possible to quantitatively determine the specific types of ChE activity present within a given tissue. This is clearly illustrated in Figure 6.5, where Kousba, Poet, and Timchalk (2003) compared the in vitro ChE activity in rat brain (∼100% AChE), plasma (∼50 : 50% AChE : BChE), and saliva using both ATC and BTC as substrates with and without specific ChE inhibitors. Based on these results, it was determined that rat saliva ChE is primarily BChE. This type of experimental approach can be used to determine tissue specific ChE activity for PD model development in a broad range of tissues.

PBPK/PD Modeling Assumptions and Parameters

147

(a) 100

% BuChE activity

0.25 nM 0.55 nM

10

1 nM

5 nM

1 0

0.1

0.2

0.3

0.4

0.5

Incubation time (h)

1/CPF-oxon (nM)

(b)

-1

Ki = 8.83nM h 2 R = 0.9753

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0

0.1

0.2

0.3

-1

0.4

0.5

1/Slope

Figure 6.6 (a) In vitro rat BuChE activity (% BuChE activity) described as the rate of acetylthiocholine (ATC) substrate hydrolysis as a function of oxon concentration for different incubation periods (mean ± S.D. of triplicate samples); (b) Final Ki determination plot. Each symbol represents a specific slope obtained from a given oxon concentration (0.25 nM•:, 0.5 nM:
, 1 nM:, 5 nM:). For both data sets the line(s) represent the best fit from linear regression analysis. Figure adapted from Kousba, Poet, and Timchalk (2003) with permission.

The bimolecular inhibition rate constant (Ki) describes both the affinity of the oxon for B-esterase enzyme and the rate of ChE phosphorylation, and is an indicator of inhibitory potency (Kousba et al., 2004; Kardos and Sultatos, 2000; Amitai et al., 1998; Carr and Chambers, 1996). A typical Ki determination is illustrated in Figure 6.6 for the in vitro inhibition of rat BChE with chlorpyrifos-oxon (CPF-oxon). In this particular example the Ki was determined by incubating saliva BChE with varying concentrations of CPF-oxon (0.25–5 nM); the maximum inhibition ranged from 10 to 90% over a 7–30 min incubation period (Kousba, Poet, and Timchalk, 2003). The slopes obtained from this analysis were then analyzed by linear regression to calculate a Ki (Figure 6.6b). Similar in vitro approaches have been used to calculate the spontaneous first-order reactivation rate constant (Kr) as is illustrated in Figure 6.7. In this example, the reactivation rate following in vitro incubation

Modeling Cholinesterase Inhibition %AChE inhibition

148

100

Kr = 0.078 h

-1

10

1 0

5

10

15

20

Incubation time (hours) Figure 6.7 In vitro determination of rat brain AChE spontaneous reactivation (Kr) following incubation with paraoxon. The line represents the best fit for the terminal portion of the curve where Kr equals the slope of the line. Figure adapted from Kousba et al. (2004) with permission.

of brain AChE with paraoxon was obtained from a linear regression of the terminal slope of the percentage of AChE inhibition (Kousba et al., 2004; Levine and Murphy, 1977). A summary of the bimolecular inhibition rate constants, reactivation, and aging rates for AChE, BChE, and CaE inhibition with CPF-oxon that were used in the PD models are presented in Table 6.3. The extent and rate of B-esterase inhibition and recovery are dependent upon the amount of available enzyme, the Ki, and the amount of time the B-esterase is exposed to the oxon (Vale, 1998). The amount of available B-esterase binding sites (µmol) follows the order: CaE  BuChE ≈ AChE (Maxwell et al., 1987), whereas the Ki rates for CPF-oxon follow the order: BuChE  AChE > CaE. Also, since experimental data was only available for AChE, for modeling purposes, it was assumed that BChE and CaE would have similar rates of reactivation and aging (Poet et al., 2004; Timchalk et al., 2002b). The time-course of plasma and brain ChE inhibition dynamics in adult and juvenile rats have been determined over a broad range of CPF doses (Timchalk et al., 2002b; Timchalk, Kousba, and Poet, 2006). In this regard, the time-course of ChE inhibition (plasma and brain) in adult rats following single oral gavage administration of CPF at doses of 1 or 10 mg/kg along with the PD model predictions are presented in Figure 6.8. The PD model response is consistent with the observed experimental results, with the plasma having substantially greater ChE inhibition that the brain at 1 and 10 mg/kg. As discussed above (pharmacokinetic modeling), recent model simulations (Timchalk, Kousba, and Poet, 2007) show a slightly improved fit to the experimental data relative to the previously published model (Timchalk et al., 2002b).

6.3 Detailed Pharmacokinetic (PK) and Pharmacodynamic (PD) Model Structure In the following section, a more detailed description of key aspects of the model code is provided. The primary focus will be on the PD model structure. However, a limited description of the PK structure within the liver compartment is also described. For a full

Detailed Pharmacokinetic (PK) and Pharmacodynamic (PD) Model Structure

(a)

Plasma ChE

% of Control

120

149

MaxI (% Control) 1 mg/kg: 60.2 ± 8.70 10 mg/kg: 22.8 ± 9.90

100 80 60 40 20 0 0

5

10

15

20

25

30

Time (h)

(b)

Brain ChE

MaxI (% Control) 1 mg/kg: 103 ± 3.60 10 mg/kg: 84.9 ± 3.20

% of Control

120 100 80 60 40 20 0 0

5

10

15

20

25

30

Time (h)

Figure 6.8 (a) Plasma time-course of ChE; and (b) brain AChE inhibition in adult rats following oral administration of 1 (open diamond) or 10 (black triangle) mg CPF /kg of body weight, respectively. The lines represent the model simulation of the experimental data. Figure adapted with permission from Timchalk and Poet (2008).

description of the PBPK/PD model for CPF the reader is referred to the complete model R ) which has been code written in Advanced Continuous Simulation Language (acslXtreme included in the QMT Model Library, or to the original manuscripts that describe the model structure in greater detail (Timchalk et al., 2002b; Timchalk, Kousba, and Poet, 2007; Timchalk and Poet, 2008). 6.3.1

Pharmacokinetics

Figure 6.9 illustrates the key model compartment (i.e., liver), and its defining equations for the metabolism of CPF and CPF-oxon, and the elimination of the major metabolite TCP. In this model structure, CYP450 mediated desulfation or dearylation of CPF occurs in the liver (designated H) compartment (Figure 6.9b Equations 1–5). The rate of change of CPF in the liver (dAH/ dt, µmol/h) is described by the rate of CPF entering from the GI tract (gavage or dietary, dOral/ dt, µmol/h), the systemic circulation balance of free CPF, and metabolism to either CPF-oxon or TCP (Equation 1). Circulatory delivery and removal of free CPF are determined by blood flow to the liver (QH, l/h), and the concentrations (µmol/l) of free CPF in arterial blood entering the liver (CAHf ), and venous blood draining the liver

150

Modeling Cholinesterase Inhibition

(b)

(a)

CPF-oxon

CPF QH

Liver

CVH

AH

QHo

CVHo

AHo

CYP450 Km , Vmax

Oxon

PON-1 Km , Vmax

Gavage or Dietary Exposure

Ke

dAH dOral dAML1 dAML 2 = QH ∗ (CAHf − CVHf ) + − − dt dt dt dt dAML1 V max 1 ∗ CH (2) = dt Km1 + CH

t

B-esterase

AH = ∫ dAHdt (4) 0

TCPexc CH =

AH (5) VH

(c)

(d)

CPF-oxon:

TCP Elimination:

dAHo dAML1 dAML3 ⎛ dAML 4 dAML5 dAML 6 ⎞ = QH ∗ (CAHof − CVHof ) + − −⎜ + + ⎟ (6) dt dt dt dt dt ⎠ ⎝ dt

dATCP ⎛ dATCP (i) ⎞ = ⎜∑ ⎟ − ( ATCP ∗ Ke ) (11) dt dt ⎠ ⎝

dAML3 V max 3 ∗ CHo (7) = dt Km3 + CHo

ATCP = ∫ dTCPexcdt (12)

dAML (4 − 6) = AHce * Ki * CHO (8) dt

dTCPexc = ATCP ∗ Ke (13) dt

t

0

t

AHo = ∫ dAHdt (9) 0

(1)

dAML 2 V max 2 ∗ CH (3) = dt Km 2 + CH

ATCP CYP450 Km , Vmax

CPF:

t

TCPexc = ∫ dTCPexcdt (14) 0

CHo =

AHo (10) VH

cbTCP =

ATCP (15) Vd

Figure 6.9 (a) PBPK liver and trichloropyridinol (TCP) compartment model structures and differential equations for (b) chlorpyrifos (CPF), (c) CPF-oxon, and (d) TCP elimination.

(CVHf ). The rates of CYP450 metabolism (µmol/h) of CPF to CPF-oxon (dAML1/ dt) and TCP (dAML2/ dt), with the associated maximum velocities (V max1 , V max2 , µmol/h) and Michaelis constants (K m1 , K m2 , µmol/l) are described in Equations 2 and 3. Integration of the rate of change yields the amount (AH, µmol) and concentration (CH, µmol/l) of CPF in the liver (Equations 4 and 5). As illustrated in Figures 6.3 and 6.9a, the liver compartment represents the linkage between the CPF and CPF-oxon PK models. The disposition and metabolism equations of CPF-oxon in the liver are presented in Figure 6.9c (Equations 6–10) and are largely parallel to the CPF equations presented above. The rate of change of CPF-oxon in the liver (dAHo/ dt, µmol/h) is defined as the rate of input from the metabolism of CPF to CPF-oxon (dAML1/ dt; Equation 2), and the circulatory balance of arterial (CAHof , µmol/l) and venous blood (CVHof , µmol/l) free CPF-oxon concentrations (Equation 6). Additional loss of CPF-oxon (to TCP) is described by PON-1 metabolism (dAML3/ dt) modeled as a saturable Michaelis–Menton type process (Equation 7), and B-esterase metabolism (dAML(4-6)/dt (i.e., AChE, BChE, and CaE)) modeled as second order processes (Equation 8). B-esterase metabolism is calculated as the product of the amount of available enzyme (AHce, µmol), bimolecular inhibition rate constant (Ki, µM−1 h−1 ), and the liver concentration of CPF-oxon (CHo, µmol/l). Integration of Equation 6 yields the amount (AHo, µmol) and concentration of CPF-oxon in the liver (Equations 9 and 10).

Detailed Pharmacokinetic (PK) and Pharmacodynamic (PD) Model Structure

151

As illustrated in Figure 6.9a and described by equations in Figure 6.9d the kinetics of TCP resulting from the CYP450 and B-esterase metabolism of CPF and CPF-oxon was modeled using a simple one-compartment analysis to describe blood and urinary elimination (Equations 11–15). The rate of change for TCP (dATCP/ dt, µmol/h) is the summed rate of TCP formation from all sources (dATCP(i) dt, i.e., CYP450, PON-1, and B-esterase, Equations 3, 7 and 8) minus a first order urinary elimination. Integration of Equation (11) yields the amount (µmol) of TCP remaining (ATCP). For matching biomonitoring type data, the rate of urinary elimination of TCP is explicitly defined (Equation 13) using the first order elimination rate constant (Ke, h−1 ). Total TCP excreted in urine (TCPexc) is also calculated (Equation 14). The blood concentration of TCP is estimated as cbTCP (µmol/l), where Vd is the volume of distribution (l) (Equation 15). To further illustrate the performance of the pharmacokinetic model, simulations of the kinetics of CPF and its metabolites in the rat following a single oral gavage dose of CPF at 50 mg/kg of body weight are presented in Figures 6.10 and 6.11. Model simulations of liver CPF and CPF-oxon concentrations (Figure 6.10a) indicate that peak levels of the

(a)

Liver concentration of CPF and CPF-oxon Liver Concentration (µmol/l)

1.4 1.2 1.0 0.8

Chlorpyrifos

0.6 0.4 Chlorpyrifos-oxon 0.2 0.0 0

4

8

12

16

20

24

Time (h)

(b)

4.5

4.5

Production Rate (µmol/h)

Chlorpyrifos-oxon

4.0

Production Rate (µmol/h)

PON-1 metabolism CPF-oxon →TCP

(c)

CYP-450 metabolism CPF→CPF-oxon & TCP

3.5 3.0 2.5 2.0

Trichloropyridinol

1.5 1.0

4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5

0.5 0.0

0.0

0

4

8

12

Time (h)

16

20

24

0

4

8

12

16

20

24

Time (h)

Figure 6.10 PBPK model simulations following a single oral dose administration of 50 mg CPF/kg of body weight in the rat. (a) Time-course of CPF and CPF-oxon concentration (µmol/l) in the liver; (b) rate (µmol/h) of CYP450 liver metabolism of CPF to CPF-oxon and TCP; and (c) rate of liver PON-1 metabolism of CPF-oxon to TCP.

152

Modeling Cholinesterase Inhibition

(b)

TCP in urine

TCP in blood

35

40

30

35

Urine TCP Amount (µmol)

Blood TCP Concentration (µmol/L)

(a)

25 20 15 10 5 0

30 25 20 15 10 5 0

0

4

8

12 Time (h)

16

20

24

0

4

8

12

16

20

24

Time (h)

Figure 6.11 PBPK model simulations following a single oral dose administration of 50 mg CPF/kg of body weight in the rat. Time-course of TCP concentration (µmol/l) in blood (a) and amount of TCP in urine (b).

parent and the oxon metabolite are achieved by ∼3 h post dosing with the levels of oxon ∼10× lower than CPF. The rates of liver CYP450 metabolism (Figure 6.10b) suggest that liver oxon formation is ∼2× greater than the rate of metabolism to TCP, which would result in very large oxon concentrations in the liver compartment. However, the PON-1 liver metabolic capacity (along with B-esterase), as illustrated in Figure 6.10c, effectively metabolizes a substantial amount of CPF-oxon to the TCP metabolite is nearly equivalent to oxon production; thereby, the liver CPF-oxon concentrations are lower than CPF. The response of the one-compartment model for total TCP in both blood and urine is illustrated in Figure 6.11. The inclusion of TCP in the model is particularly useful since metabolism to TCP accounts for ∼99% of administered dose, and the determination of urinary TCP is currently a key biomarker for quantifying exposure to CPF. In this regard, the coupling of the TCP compartment model with the PD model can be used to establish a dosimetric relationship between a measured biomarker of dose and response (i.e., blood ChE). 6.3.2 Pharmacodynamics Figures 6.12–6.15 illustrate the PD model structure and code that is used to describe the extent of B-esterase inhibition (i.e., AChE, BChE, and CaE) in brain; similar code was also used to describe liver, diaphragm, and blood (plasma and RBC) B-esterase inhibition. This PD model was based on the Gearhart et al. (1990) model for diisopropylfluorophospate as adapted and modified in the current CPF and diazinon PBPK/PD models (Timchalk et al., 2002b; Timchalk, Kousba, and Poet, 2007, 2008; Poet et al., 2004). Chlorpyrifos specific parameters for bimolecular inhibition (Ki), reactivation (Kr), and aging (Ka) were incorporated into the code (Amitai et al., 1998; Carr and Chambers, 1996). The CaE enzyme degradation rate (Kd) and Ki constant were estimated for each tissue by fitting the model to data obtained by Chanda et al. (1997). The PD model for CPF that was initially developed (Timchalk et al., 2002b) has continued to be refined as new parameter estimates have become available.

Detailed Pharmacokinetic (PK) and Pharmacodynamic (PD) Model Structure

Synthesis

(a)

153

(b)

KsChE(i) µmol h -1

Calculation of Available B-Esterase: KsChE(i ) =

Total Enzyme(i)

(ChE( ) ∗ V( ) ) i

TotalEnzym e(i ) =

KdChE(i) h-1

i

TRce(i )

∗ KdChE(i ) (16)

ChE (i ) ∗ V(i ) TRce(i )

(17)

Degradation (c)

Brain B-Esterase Synthesis (AChE, BChE, CaE)

Brain Free Esterase (AChE, BChE, CaE) 2.00E-04 1.75E-04

1.20E-06

Brain Free Esterase (µmol)

Brain Esterase Synthesis (µmol/h)

1.50E-06

9.00E-07

6.00E-07

3.00E-07

1.50E-04 1.25E-04 1.00E-04 7.50E-05 5.00E-05 2.50E-05

0.00E+00 AChE

BChE

CaE

0.00E+00 AChE

BChE

CaE

Figure 6.12 (a) Model structure describing the synthesis and degradation of B-esterase (Total Enzyme(i) ); (b) differential equations for calculating the amount (µmol) of available B-esterase; and (c) predicted brain synthesis rates (KsChE; µmol/l) and total amount (µmol) of AChE, BChE, and CaE in the brain compartment for rats.

As previously noted, the amount of B-esterase enzyme binding sites (µmol), zero-order synthesis rate (µmol/h), and first order degradation rate (h−1 ) of AChE, BChE, and CaE for each compartment was calculated as previously described (Gearhart et al., 1990; Maxwell et al., 1987). The model structure and equations describing the brain initial enzyme levels, and the associated synthesis and degradation rates are presented in Figure 6.12. The Total Enzyme (i.e., number of esterase binding sites) for each esterase was calculated as the product of the enzyme activities (ChE(i) ; µmol/min/mg protein) and the tissue weight divided by the enzyme turnover rate (TRce(i) ; substrated/hydrolyzed/min/active site) as described by Maxwell et al. (1987) (Equation 17). The zero-order enzyme synthesis rate (KSChE(i) , µmol/h) was calculated as the product of the Total Enzyme and the first-order degradation

CAo(i)

+

Synthesis

Degradation

KdChE(i) h-1

AmChE(i)

KsChE(i) µmol h -1

Kr(i) h-1

Ki(i) µM -1 h -1

Brain [INactive] (AChE, BChE, CaE)

0

0.0E+00

4.0E-05

8.0E-05

1.2E-04

1.6E-04

0

4

AChE

8

12

BChE

Time (h)

CaE

Ka (i) h-1

16

20

Aged

24

Figure 6.13 (a) Model structure describing the inactivation (INactive(i) ) of B-esterase synthesis and degradation of B-esterase (Total Enzyme(i) ); (b) differential equations for calculating the amount (µmol) of inactive enzyme; and (c) model simulations of total amount (µmol) of INactive AChE, BChE, and CaE in the brain compartment for rats.

(c)

t

= AmChE (i ) ∗ Ki(i ) ∗ CAo(i ) − INactive (i ) ∗ (Ka(i ) + Kr(i ) ) (18)

Inactive (i ) = ∫ dINactive (i ) dt (19)

dt

dINactive (i )

INactive(i)

AM(i) (TCP metabolites)

(b) Inactivation and Aging of Inhibited B-Esterase:

(a)

Total Inactive Esterase (µmol)

Detailed Pharmacokinetic (PK) and Pharmacodynamic (PD) Model Structure (a)

155

Synthesis KsChE(i) µmol h-1

CAo(i)

+

Ki(i) µM -1 h-1

AmChE(i)

Ka(i) h-1

INactive(i)

Aged

Kr(i) h-1

KdChE(i) h-1

AM(i) (TCP metabolites)

Degradation

(b) Inhibition and Reactivation of B-Esterase: dAmChE (i ) dt

= KsChE (i ) − AmChE (i ) ∗ (KdChE (i ) + Ki(i ) ∗ CAo(i ) ) + INactive(i ) ∗ Kr(i ) (20) t

AmChE(i ) = ∫ dAmChE(i ) dt (21) 0

Rate of Metabolite (TCP) Formation from B-Esterase: dAM (i ) ( 4 − 6) dt

(c)

= AmChE(i ) ∗ Ki(i ) ∗ Cao(i ) (22)

Rate TCP Formation (AChE, BChE, CaE)

Brain [AmChE] (AChE, BChE, CaE)

1.5E-04 CaE 1.0E-04

5.0E-05 AChE BChE 0.0E+00 0

4

8

12

Time (h)

16

20

24

Rate Trichloropyridinol Formation from Brain Esterases (µmol/h/kg)

Total Amount of Esterase (µmol)

6E-05 2.0E-04

5E-05 4E-05

AChE

3E-05

BChE

2E-05 CaE 1E-05 0E+00 0

4

8

12

16

20

24

Time (h)

Figure 6.14 (a) Model structure describing the amount of available B-esterase (AmChE(i) ); (b) differential equations for calculating the amount (µmol) of available enzyme; and (c) model simulations of total amount (µmol) of AmChE AChE, BChE, and CaE in the brain compartment for rats.

rate (KdChE(i) , h−1 , Equation 16). Figure 6.12c illustrates the calculated enzyme synthesis rates for brain AChE, BChE, and CaE and initial brain “free” esterase concentrations which are constant and are the basis for determining baseline B-esterase activity in each tissue. For the brain compartment the zero-order synthesis rates were 4.6 × 10−7 , 1.4 × 10−6 , and 1.5 × 10−7 µmol/h for BChE, AChE, and CaE, respectively, which equated to brain esterase concentrations of 4.6 × 10−5 , 1.4 × 10−4 and 2.0 × 10−4 µmol of BChE, AChE, and CaE, respectively. The model presented in Figure 6.12 describes the B-esterase enzyme balance in the absence of any inhibition or aging processes. Expanding the PD model to include enzyme inhibition results in the model structure, equations, and simulations illustrated in Figure 6.13. In this example, the amount of B-esterase inactivated due to phosphorylation

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

0

[

4

8

12

Time (h)

AChE

CaE

16

Brain [AmChE ] (AChE, BChE,

Degradation

h-1

KdChE(i)

Total Enzyme(i)

KsChE(i) µmol h-1

Synthesis

20

24

BChE

..

Steady-State Enzyme Level

Brain Free Esterase (µmol) 0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

0

+ Degradation

KdChE(i) h-1

AmChE(i)

KsChE(i) µmol h-1

Synthesis

Kr(i) h-1

Ki(i) µM -1 h-1

4

CaE

8

AChE

Brain Total Enzyme

Time (h)

12

BChE

16

]

InhibitedChE (i ) = 100 ∗

AmChE (i )

20

24

=

TotalEnzyme(i )

0

10

20

30

40

50

60

70

80

90

100

0

(23)

Ka(i) h-1 Aged

4

8

Time (h)

12

AChE

CaE

16

Brain InhibitedChE (%) (AChE, BChE, CaE)

AM(i) (TCP metabolites)

INactive(i)

Inhibited Enzyme Level

Cholinesterase (ChE) Inhibition:

CAo(i)

(b)

20

24

BChE

Figure 6.15 (a) Model structure describing steady-state (Total Enzyme) enzyme levels and; (b) inhibited enzyme (AmChE(i) ) along with equation for calculation of ChE inhibition (% of control); (c) model simulation of AmChE, Total Enzyme and % inhibited brain B-esterase following a single oral gavage dose of 50 mg CPF/kg in rats (Compare middle panel to Figure 6.12c).

Total Amount of Esterase (µmol)

(c)

(a)

Total Inhibited B-esterase (percent of control)

Example ChE Model Simulations

157

(INactive(i) , µmol) is described as a balance of inhibition, aging, and reactivation (Equation 19). The rate of change (dINactive(i) /dt, µmol/h) for inactivated brain B-esterase is calculated from the second-order inhibition, the product of the amount of available enzyme (AmChE(i) , µmol), the bimolecular rate of inhibition (Ki(i) , µM−1 h−1 ) and the oxon concentration (CAo(i) , µmol/l), along with the first-order rates for enzyme aging and reactivation (Ka(i) and Kr(i) , h−1 ). Model simulations for the amount of inactive enzyme for AChE, BChE, and CaE are illustrated in Figure 6.13c. Peak inactivation of brain AChE and CaE occurred at ∼7–11 h post dosing, whereas for BChE the peak was attained by ∼ 2–3 h post dosing. For each of the B-esterases the amount of inactivated enzyme was substantially different, for example the maximum inhibited AChE, CaE, and BChE were 1.3 × 10−4 , 7.7 × 10−5 , and 4.6 × 10−5 µmol, respectively. These observed differences are primarily a function of the differing inhibition rates and amounts of available B-esterases in the brain. To complete the PD description of the enzyme activity, calculation of the active enzyme levels are needed (Figure 6.14). The amount of enzyme (AmChE(i) ) is a function of rates of enzyme synthesis and degradation (KsChE(i) and KdChE(i) ), as well as the rate of loss (Ki(i) ) and reactivation (Kr(i) ) of the inactive enzyme (INactive(i) ) (Equations 20 and 21). The rate of TCP (dAM (i) (4–6)/dt) release is a function of the stoichiometric interactions between AmChE(i) , CPF-oxon (CAo(i) ), and the bimolecular inhibition rate constant (Ki(i) ) (Equation 22). The time-courses for the amounts of non-inhibited B-esterase enzyme (AmChE(i) ) following an acute oral 50 mg/kg dose of CPF are illustrated in Figure 6.14c. The amount of available brain BChE showed the most dramatic drop with the maximal inactivation of the enzyme occurring within ∼ 2 h postdosing with nearly all of the enzyme (∼99%) being inactivated. For brain AChE and CaE the time to maximum inactivation was slightly delayed to 10–12 h post dosing. The formation of TCP due to the phosphorylation of brain B-esterases is likewise illustrated in Figure 6.14c. The rates of TCP formation (dAM (i) (4–6)/dt) are consistent with the observed rates for the inactivation of each of the B-esterases in the brain. For the BChE inhibition the maximum rate of TCP formation was observed at ∼1.5 h post dosing; whereas, for AChE and CaE peak rates of TCP formation were achieved at 3 and 4 hr post dosing, respectively. Since each of the B-esterases has differing baseline levels, a more relevant dose metric is percentage of enzyme inhibited, as illustrated in Figure 6.15 (Equation 23). As is illustrated in Figure 6.15c the calculation of the percentage of inhibited enzyme at any point in time before or following exposure to CPF is based on the ratio of available enzyme (AmChE(i) ) to the Total Enzyme(i) . Therefore, in the presented model simulation the extent of inhibition followed the order of BChE  AChE  CaE in the brain following a single oral dose of 50 mg/kg. Specifically peak inhibitions for BChE, AChE, and CaE were achieved at ∼ 3, 6, and 12 h post dosing and the relative % of control (baseline) B-esterase activities were ∼0, 5, and 60%, respectively.

6.4 Example ChE Model Simulations As has been discussed and suggested by Andersen (2003), if there is a fundamental understanding of how target tissue dosimetry modulates a pharmacological or toxicological response, then it is feasible to extend these models to incorporate pharmacodynamics. To

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% of Control

100

Rat Plasma AChE

80 60 40 20 0 0.001

Rat Plasma ChE (AChE + BuChE)

Rat Plasma BuChE Human Plasma BuChE

0.01

0.1

1

10

100

Dose (mg/kg) Figure 6.16 Simulation of peak plasma total ChE (AChE, BuChE), AChE and BuChE inhibition dose response in rat and humans BuChE following an acute exposure to a broad range of chlorpyrifos doses. Figure adapted with permission from Timchalk et al. (2002b).

briefly illustrate the utility of these PD models for ChE inhibition, the following section will discuss their use for cross-species extrapolation, evaluation of age-dependent response, and for understanding mixture interactions.

6.4.1 Rodent to Human Extrapolation In evaluating the overall response of the PBPK/PD model for CPF over a broad dose range (0.001–100 mg/kg body weight), model simulations (rat vs human) suggested that, for humans, increasing the dose above 1 mg/kg resulted in a non-linear “crossover” response, so that at high doses the simulated human AUC0–α for CPF-oxon exceeded that of the rat (∼1.1 to sixfold) (Timchalk et al., 2002b). In evaluating this response, it was suggested that species difference in dose-dependent depletion of non-target B-esterase may be a key component contributing to the observed effect. It was suggested that by comparing the dosedependent depletion of plasma ChE in rats and humans, it may be possible to illustrate the potential protective role of non-target B-esterase. A simulation of the maximum plasma ChE inhibition in rats and humans, following acute oral exposure to a broad range of CPF doses (0.001–100 mg/kg), is presented in Figure 6.16. In this model simulation both rat and human plasma BChE have a similar dose response and are essentially depleted at doses between 1 and 10 mg/kg. However, in the rat the available plasma AChE enzyme (not present in human plasma) is not depleted until the dosage is ≥ 10 mg/kg. These results are consistent with the dose-dependent AUC0–α response for CPF and CPF-oxon (Timchalk et al., 2002b) and suggest a plausible relationship between CPF activation, the depletion of non-target B-esterase, and the nonlinear increase in human CPF-oxon blood and brain concentration at dose ≥1 mg/kg.

6.4.2 Neonatal Rat Pharmacodynamic Model A number of studies conducted in preweanling rats provide important perspective on age- and dose-dependent sensitivity to organophosphate insecticides. Collectively they suggest that the age-dependent sensitivity in preweanling animals is associated with a

Example ChE Model Simulations

159

lower CYP450 dearylation (detoxification) capacity, and an age-dependent lower PON-1 and CaE-mediated oxon hydrolysis (also detoxification) capacity in preweanling relative to adult animals (Atterberry, Burnett, and Chambers, 1997; Li et al., 1997; Mortensen et al., 1996). Since oxon metabolism represents a much smaller fraction of total CPF metabolism, the decreases in bioactivation for neonatal animals are not as important as the deficit in detoxification. These findings in animals are in agreement with observations in which newborn and young humans have lower metabolic capacity for CYP450 and PON-1 activity compared to adults (Johnson, 2003; Augustinsson and Barr, 1963; Mueller et al., 1983). The application of PBPK/PD modeling offers a unique opportunity to integrate agedependent changes in metabolic activation and detoxification pathways into a comprehensive model that is capable of quantifying dosimetry and response across all ages (for review see Corley et al., 2003). In this context, the PBPK/PD model for CPF was modified by incorporating age-dependent scaling to adjust physiology, organ volumes, blood flows, metabolism rates, B-esterase tissue levels, and bimolecular inhibition rates for CPF-oxon and ChE as a function of age (Timchalk, Kousba, and Poet, 2007). The model was then used to predict tissue dosimetry, and PD response in preweanling and adult rats exposed to CPF. For a more detailed description of the age-dependent rat model see Timchalk, Kousba, and Poet (2007). The time-course of RBC and brain AChE inhibition data (Timchalk, Kousba, and Poet, 2006) and model simulations are presented in Figure 6.17. For both RBC and brain the time-course of PD response following an acute oral exposure to CPF demonstrated an ageand dose-dependency in preweanling rats with the extent of inhibition following the pattern post-natal day (PND)-5  PND-12  PND-17  adult (brain only). In particular, the PD response in brain was striking when comparing the response in adult animals (Figure 6.17; Brain AChE D) versus the response in the preweanling rats. These findings along with other model simulations (Timchalk, Kousba, and Poet, 2007) suggest this age-dependent PBPK/PD model behaves consistently with the general understanding of CPF toxicity, pharmacokinetics, and tissue ChE inhibition in neonatal and adult rats. However, although these simulations illustrate the ability to scale age-dependent changes within a species, the different timescales between development in neonatal animals and human infants creates uncertainty in extrapolation across species (Ginsberg, Hattis, and Sonawane, 2004). 6.4.3

Binary OP Mixture Pharmacodynamic Interactions

Organophosphorus insecticides have routinely been used to control pests in virtually all crop and commercial applications. Therefore, it is entirely feasible to anticipate exposure to insecticide mixtures. Based upon a shared common mechanism of toxicity (i.e., inhibition of AChE) (Mileson et al., 1998), the US Environmental Protection Agency (EPA) under the Food Quality Protection Act is required to consider the cumulative risk associated with OP pesticide mixture exposures. To help address this concern, a binary PBPK/PD model has been developed to evaluate dosimetry and PD interactions between the organothiophosphorus insecticides chlorpyrifos (CPF) and diazinon (DZN) in the rat. The binary model code describes both metabolic (i.e., CYP450; competitive vs noncompetitive inhibition) and PD (B-esterase; dose-additive) interactions based upon in vitro and in vivo studies in the rat (Timchalk et al., 2005; 2008). The modification to the model code that was needed to accommodate an additive inhibition of B-esterase, and the model

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RBC AChE

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MaxI (% Control) 1 mg/kg: 55.0 ± 18.6 10 mg/kg: 16.5 ± 2.23

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MaxI (% Control) 1 mg/kg: 78.0 73.0 ± 8.59 10 mg/kg: 19.1 ± 4.86

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MaxI (% Control) 1 mg/kg: 94.8 ± 17.5 10 mg/kg: 19.6 ± 5.37

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MaxI (% Control) 1 mg/kg: 103 ± 3.60 10 mg/kg: 84.9 ± 3.20

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Figure 6.17 Observed data and model prediction (line) for the RBC and brain AChE inhibition in (a) post-natal day 5 (PND-5), (b) PND-12, (c) PND-17, and (d) adult rats (brain only) following a single acute oral gavage dose of 1 (open diamond) or 10 (closed triangle) mg CPF/kg of body weight. The observed data are presented as mean ± SD of 4–5 animals per time point. The MaxI is expressed as % of control activity for each of the dose levels. Figure adapted with permission from Timchalk, Kousba, and Poet (2007).

simulations of brain, plasma and RBC ChE following a binary exposure to CPF and DZN, in the rat are presented in Figures 6.18 and 6.19, respectively. Equations 24 and 26 illustrate the minor modification to the model code, which involved the addition of a second equation for the DZN-oxon interaction between its bimolecular inhibition rate constants (Ki2(i) ) and the DZN-oxon concentrations (CAo2(i) ). Since both CPF-oxon and DZN-oxon produce the same phosphorylation product (diethylphosphate) all other model parameters (Ka(i) , Kr(i) ) were assumed to be the same. In addition, it was also assumed that there were no changes in the synthesis (KsChE(i) ) or degradation rates (KdChE(i) ) of the B-esterases based on a binary mixture interaction.

Example ChE Model Simulations

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B-Esterase Additive Inhibition (AChE, BChE, and CaE): dAmChE(i ) dt

= KsChE(i ) − AmChE(i ) ∗ [KdChE(i ) + (Ki1(i ) ∗ CAo1(i ) ) + (Ki 2 (2 ) ∗ CAo2 (i ) ) ] + INactive(i ) ∗ Kr(i ) (24) t

AmChE(i ) = ∫ dAmChE(i )dt (25) 0

dINactive(i ) dt

= AmChE(i ) ∗ (Ki1(i ) ∗ CAo1(i ) + Ki2 (i ) ∗ CAo2 (i ) ) − INactive(i ) ∗ (Ka(i ) + Kr(i ) ) (26) t

Inactive(i ) = ∫ dINactive(i ) dt (27) 0

Figure 6.18 Differential equations used to describe additive inhibition of chlopyrifos-oxon (CAo1(i) ) and diazinon-oxon (Cao2(i) ) on brain B-esterase (AChE, BChE, and CaE) in the rat.

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Figure 6.19 Brain (AChE), RBC (AChE), and plasma (ChE) activity in rats following 15 mg/kg oral gavage dose of chlorpyrifos (CPF) (solid black diamond), diazinon (open black diamond), and their binary mixtures (solid or open gray circle). The data are expressed as a percentage of total ChE activity as a function of time (hours) and represents the mean ± SD for four animals per time-point. The lines represent the PBPK/PD model simulations. Figure adapted with permission from Timchalk et al. (2008).

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As is illustrated in Figure 6.19, the degree of experimentally determined ChE inhibition followed the order plasma  RBC > brain and the relative potency was CPF + DZN ≥ CPF  DZN (Timchalk et al., 2005; 2008). The PD model response suggest that the overall potency for ChE inhibition was greater for CPF than DZN and the binary mixture response appeared to be strongly influenced by CPF. The greater in vivo potency for CPF relative to DZN was consistent with in vitro findings, which suggested that the metabolism of CPF to its oxon was ∼5× faster than for DZN (Timchalk et al., 2008; Poet et al., 2003).

6.5

Summary and Conclusions

This chapter has provided a detailed description of the computational model code developed for PBPK/PD modeling of organophosphorus insecticides with a specific emphasis on the PD modeling of B-esterase (ChE) inhibition, which is the most relevant toxicological response for this class of insecticides. Since OP insecticides share a common mode of action through their capability to inhibit AChE activity, it is feasible to develop pharmacokinetic strategies that link quantitative dosimetry with biologically based PD response modeling. Pharmacokinetic and pharmacodynamic studies that have been conducted in multiple species, at various dose levels, and across different routes of exposure have provided important insight into the in vivo behavior of these insecticides. The development and application of PBPK/PD modeling for these insecticides represents a unique opportunity to quantitatively assess human health risk and to understand the toxicological implications of known or suspected exposures.

Acknowledgements The research contained within this chapter was partially supported by grants RO1 OH003629 and RO1 OH 008 173 from the US Centers for Disease Control and Prevention (CDC)/National Institute of Occupational Safety and Health (NIOSH). Its contents are solely the responsibility of the authors and have not been subject to any review by CDC/NIOSH and therefore do not necessarily represent the official view of CDC/NIOSH, and no official endorsement should be inferred.

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Sogorb, M.A. and Vilanova, E. (2002) Enzymes involved in the detoxification of organophosphorus, carbamate and pyrethroid insecticides through hydrolysis. Toxicol. Lett., 128, 215–228. Sultatos, L.G. (1994) Mammalian toxicology of organophosphorus pesticides. J. Toxicol. Environ. Health, 43, 271–289. Taylor, P. (1980) Anticholinesterase agents, in Goodman and Gilman’s The Pharmacology of Therapeutics, 6th edn (eds A. Goodman Gilman, L.S. Goodman, and A. Gilman), MacMillan Publishers Inc., New York. Timchalk, C., Kousba, A.A., and Poet, T.S. (2002a) Monte Carlo analysis of the human chlorpyrifosoxonase (PON1) polymorphism using a physiologically based pharmacokinetic and pharmacodynamic (PBPK/PD) model.Toxicol. Lett., 135, 51–59. Timchalk, C., Kousba, A.A., and Poet, T.S. (2006) Age-dependent pharmacokinetic and pharmacodynamic response in neonatal rats following oral exposure to the organophosphorus insecticide chlorpyrifos.Toxicol., 220, 13–25. Timchalk, C., Kousba, A.A., and Poet, T.S. (2007) An age-dependent physiologically based pharmacokinetic model for the organophosphorus insecticide chlorpyrifos in the preweanling rat. Toxicol. Sci., 98 (2), 348–365. Timchalk, C., Nolan, R.J., Mendrala, A.L., et al. (2002b) A physiologically based pharmacokinetic and pharmacodynamic (PBPK/PD) model for the organophosphate insecticide chlorpyrifos in rats and humans. Toxicol. Sci., 66, 34–53. Timchalk, C., Poet, T.S., Hinman, M.N., et al. (2005) Pharmacokinetic & pharmacodynamic interaction for a binary mixture of chlorpyrifos and diazinon in the rat. Toxicol. Appl. Pharmacol., 205 (1), 21–32. Timchalk, C. and Poet, T.S. (2008) Development of a physiologically based pharmacokinetic and pharmacodynamic model to determine dosimetry and cholinesterase inhibition for a binary mixture of chlorpyrifos and diazinon in the rat. NeuroTox., 29, 428–443. Vale, J.A. (1998) Toxicokinetic and toxicodynamic aspects of organophospate (OP) insecticide poisoning. Toxicol. Lett., 102–103, 649–652. Wenthold, R.J., Mahler, H.R., and Moore, W.J. (1974) The half-life of acetylcholinesterase in mature rat brain. J. Neuroochem., 22, 941–943. Wilson, B.W. (2001) Cholinesterases, in Handbook of Pesticide Toxicology, vol 2 (ed. R.I. Krieger), Academic Press, San Diego.

7 Modeling of Protein Induction and Dose-Dependent Hepatic Sequestration* Andy Nong1, 2 and Melvin E. Andersen1 1

7.1

The Hamner Institutes for Health Sciences, USA 2 Current address: Health Canada, Canada

Introduction

Time-course studies of blood, tissue, and excreta concentrations of 2,3,7,8tetrachlorodibenzo-p-dioxin (TCDD) have provided opportunities to examine many interesting kinetic behaviors that are consequences of TCDD interacting with a specific cellular protein – the aryl hydrocarbon receptor (AhR). The history of PBPK model development for TCDD has been reviewed in brief (Andersen, 1995) and more exhaustively in the United States Environmental Protection Agency’s (EPA) risk assessment for TCDD and related compounds (USEPA, 2004). TCDD preferentially distributes to liver and adipose tissues. Uncharacteristic of lipophilic chemicals, TCDD was found at higher concentrations in the liver compared to fat under many dosing situations (Abraham, Krowke, and Neubert, 1988). This sequestration in the liver indicated induction of a TCDD-binding protein with

∗ This chapter discusses a series of modeling papers on TCDD developed over a period of more than 20 years. The nomenclature for binding affinity constants and the definition of binding constants vary from paper to paper. In most cases, two binding processes are included – TCDD with the AhR and TCDD with CYP1A2. In addition, an empirical model used a half-saturation binding constant, not directly related to any specific biochemical process, also has a Kd value. We have not attempted to unify all these models with the differing binding constant nomenclature. The reader should be cautious in reading through the model descriptions and recognize that similar terminology may be used for different interactions.

Quantitative Modeling in Toxicology Edited by Kannan Krishnan and Melvin E. Andersen  C 2010 John Wiley & Sons, Ltd

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Modeling of Protein Induction and Dose-Dependent Hepatic Sequestration

increasing dose. The inducible binding protein was subsequently identified as CYP1A2. Because the induction increased the hepatic uptake, PBPK models for TCDD had to account for changes in the binding protein over time in relation to the liver concentrations of TCDD. In this fashion, pharmacokinetic modeling of TCDD invariably has had to consider the pharmacodynamics of protein induction. In this chapter, we describe different PBPK/PD models developed for dioxin over the past two decades. These models include protein induction and evaluate dose-dependent, hepatic distribution of TCDD and allow more direct evaluation of the various factors that contribute to differential tissue sequestration of dioxin, that is, liver binding proteins, diffusion-limited fat uptake, dose-dependent induction of CYP 1A1/2 in liver, and regional differences in response within the liver acinus. The emphasis is on the application of diverse modeling strategies to assess the pharmacodynamic responses associated with receptor binding and the consequences of binding in relation to induction of CYP1A2. Receptor-mediated responses are also discussed in other chapters (Chapters 8, 9 and 10).

7.2 PBPK Modeling Strategies with TCDD Leung and colleagues (1988) developed the first model of dose dependent distribution of TCDD in mice. In this initial effort, the tissue partitioning of liver was set to be equal to that observed in kidney. Sequestration in liver in excess of that in kidney was assumed to be associated with protein binding. A PBPK model in mice evaluated the binding parameters that would be required to achieve the dose-dependent sequestration of TCDD in the liver. This first section develops the equations used by Leung et al. (1990) to analyze the dosedependent distribution of TCDD (Figure 7.1) that was reported by Abraham, Krowke, and Neubert (1988). TCDD in the liver was described with a free concentration consistent with a venous equilibration description of the organ. A protein in the liver, known today as the aryl hydrocarbon receptor, that is, AhR, binds TCDD with high affinity. The AhR–TCDD complex then acts as a transcriptional regulator to increase concentrations of various proteins in the liver. Leung et al. (1990) described induction of the binding protein in relation to the occupancy of the AhR by free TCDD in the liver. The equations required for these calculations were (1) the mass balance differential equation for TCDD in liver and (2) the conservation equation for total liver TCDD, describing the amounts of TCDD that were free, bound to the AhR, or bound to the inducible CYP1A2. The level of induction of CYP 1A2 was related to the instantaneous occupancy of the AhR by TCDD. Equation 7.1 describes the conservation of mass in these three pools (i.e., free TCDD in the liver, TCDD bound to AhR, and TCDD bound to CYP1A2): AL = VL ∗ C VL ∗ PL +

BM1 ∗ C VL BM2T ∗ C VL + K B1 + C VL K B2 + C VL

(7.1)

Here, AL is the amount in the liver, PL is liver:blood partition coefficient and CV L is the free concentration of TCDD in liver. BM1 is the binding maximum for the AhR in liver and K B1 is the affinity of the AhR for TCDD. BM2T is the liver binding capacity of CYP1A2 at any time, t, and K B2 is the binding affinity for TCDD with CYP1A2. In the PBPK model as implemented by Leung et al. (1990), CV L was calculated by rearranging this equation

PBPK Modeling Strategies with TCDD

169

6.0

% Dose/g tissue

4.5 Liver

3.0

1.5 Fat

0 10–3

10–1 Dose TCDD - mg/kg bw

10

Figure 7.1 Dose dependence of dioxin tissue disposition in female Wistar rats seven days following a single subcutaneous dose of TCDD from Abraham, Krowke, and Neubert (1988). The data are percentage dose per gram tissue versus the initial dose of TCDD. The smooth curves are simulations from a PBPK model (Andersen et al., 1993). Reprinted with permission from Wiley-Blackwell.

to provide an assignment statement where CV L is a function of AL and CV L . C VL =

VL ∗ PL +

AL BM1 K B1 +C VL

+

BM2T K B2 +C VL

(7.2)

The venous hepatic concentration was calculated implicitly using a root solver in the model codes. Then, the amount of binding protein at any time (BM2T ) depends on the occupancy of the Ah receptor by TCDD. BM2T = BM20 +

BM2I ∗ C VL K B1 + C VL

(7.3)

Here, BM20 is the amount of CYP1A2 in the na¨ıve animal before treatment with TCDD and BM2I is the maximum extent of induction achievable at high doses of TCDD. The model used in this chapter was written in Berkeley MadonnaTM (see QMT model library folder: Nong 2) and simulates inducible binding to datasets on dose- and time-dependent liver sequestration from Abraham, Krowke, and Neubert (1988). Using time-course results for liver and fat after a single dose of TCDD, parameters for distribution and liver sequestration can be optimized in relation to factors controlling tissue uptake.

170

Modeling of Protein Induction and Dose-Dependent Hepatic Sequestration

7.3

Diffusion-Limited Tissue Uptake

A second PBPK model for TCDD (Andersen et al., 1993) included diffusion-limited uptake in fat. The fat compartment had two subcompartments – discrete volumes of blood and tissue. Each of the two compartments has a state equation, described by a mass balance differential equation that is integrated to track total mass in the compartment. In this case, the fat blood has a volume of 0.05 (5%) times the fat compartment. Compound diffuses from the fat blood compartment into the fat tissues by diffusional clearance with units similar to blood flow, that is, l/h. Thus, we have the following two equations for the rate of change of amount in fat blood (AFB) and amount in fat tissue (AF), respectively.
 CF dAFB − CVF = Q F ∗ (CA − CVB ) + PAF ∗ (7.4) dt PF and


 CF dAF = PAF ∗ CVF − dt PF

(7.5)

The diffusional term is called PAF, the permeation area (PA) cross product for the capillary bed in the fat (F). In our formulation of the tissue compartment, diffusional clearance is calculated as a multiple of fat blood flow (QF ). Here, the diffusional transport clearance, PAF, is calculated as PAFC times QF . This implementation of diffusional transfer from blood to tissue is a convenience. There is no direct relationship expected between flow and diffusion. However, when PAFC is expressed in relation to QF , it is readily apparent whether tissue uptake is flow-limited or diffusion-limited. If PAFC is much greater than QFC , tissue uptake is flow-limited and the reverse is also true. For the early uptake phases in fat and liver, PAFC values of near 0.1 provided a better fit to the peak tissue concentrations of TCDD (Figure 7.2), indicating that a PAFC of 0.1 provided a better fit than an assumption of flow-limited uptake into fat. Using this model, it is possible for the reader to evaluate changes in various parameters for liver metabolism (KFC) and the extent of induction with full AhR occupancy. These curves were generated with stoptime = 2500 h.

7.4 Dose-Dependent Hepatic Sequestration In order to evaluate the dose-dependent liver distribution of TCDD (smooth curves in Figure 7.1), the PBPK model is run for multiple doses and the tstop value must be equivalent to the time of sacrifice for the rats in the study, that is, seven days or 168 hours. After each run, the simulation output for percentage dose per gram tissue in liver and fat could be tabulated versus administered dose. In Berkeley MadonnaTM , plots of this kind are generated with the parameter plot option from the parameter pull down tab in the B–M command window. The resulting simulation of the dose dependence of hepatic sequestration, consistent with Abraham, Krowke, and Neubert (1988), shows that the percentage dose per gram liver at 72 hours increases with increasing dose until a maximum is reached at 10–100 µg/kg. Surprisingly, the curve then falls steeply at higher doses (Figure 7.3). The model can be used to determine the dependence of this curve on various parameters, that is, to assess sensitivity

Dose-Dependent Hepatic Sequestration

171

5 Liver

4.5 4

% Dose/g tissue

3.5 3 2.5 2 1.5 1 0.5

Fat

0 0

250

500

750

1000

1250 Hours

1500

1750

2000

2250

2500

Figure 7.2 Time-course of dioxin tissue disposition in female Wistar rats seven days following a single subcutaneous dose of TCDD, from Abraham, Krowke, and Neubert (1988). The data are percentage dose per gram tissue versus the initial dose of TCDD. The smooth curves are simulations from the PBPK model in the codes in Berkeley Madonna.

5 4.5

‘LIV’

4

% Dose/g tissue

3.5 3 2.5 2 1.5 ‘FAT’

1 0.5 0 0.001

0.01

0.1

1 10 Dose TCDD - mg/kg bw

100

1000

1e+4

Figure 7.3 Dose dependence of dioxin tissue disposition simulated with the PBPK model (see codes in Berkeley Madonna) over a broader dose range than in the original study by Abraham, Krowke, and Neubert (1988). The ‘LIV (liver)’ curve dropped off unexpectedly after 10 µg/kg.

172

Modeling of Protein Induction and Dose-Dependent Hepatic Sequestration

of the curve shape to specific model parameters. By changing parameters with the model in Berleley Madonna, an interested reader can show that the inflection and placement of the curve along the dose axis depends primarily on the value of K B1 , the affinity of the AhR complex for AhR response elements on DNA, and less so to K B2 , the binding affinity of TCDD for CYP1A2. In contrast, the peak value for percentage dose per gram liver depends on factors such as fat partition coefficient and BM2I . When the PBPK/PD modeling of liver induction was initially performed, the simulations were conducted for the experimental dosing region (up to 10 µg/kg). The curve (Figure 7.1) showed a small decrease at the highest dose. Instead of asking about the parameters that control the peak value, another physiological question is to examine the processes of induction and binding and understand how they interact to give a peak in the percentage dose per gram plot. Another model-based exercise evaluates factors controlling the plateau in liver concentration as dose increases to greater than10 µg/kg. The model allows simulation of the percentage occupancy of the AhR (BOUND) and percentage occupancy of CYP1A2 (BOUND1). The curve for percentage dose per gram liver reaches a peak when there is maximum induction of binding protein (BOUND ∼1.0) and minimal occupancy of the induced protein (BOUND1 ∼0.0). Occupancy of the binding protein only becomes significant when the curve for percentage dose per gram liver begins to fall (Figure 7.4). 5

1

4.5

0.9

4

0.8 LIV 0.7

3

0.6

BOUND

2.5

0.5

2

0.4

1.5

0.3

1

0.2

0.5 0 0.001

BOUND 1

0.01

0.1

1 10 Dose TCDD - mg/kg bw

100

1000

Fraction Bound

% Dose/g tissue

3.5

0.1 0 1e+4

Figure 7.4 Dose dependence of dioxin tissue disposition simulated with the PBPK model (see codes in Berkeley Madonna) over a broader dose range than in the original study by Abraham, Krowke, and Neubert (1988). The LIV curve drops off after about 10 µg/kg. BOUND and BOUND1 were also calculated from the PBPK model. BOUND is the proportionate occupancy of the AhR protein and BOUND1 is the proportionate occupancy of the CYP 1A2 binding protein. ‘LIV (liver)’ (maximum) occurs at a point with maximal AhR induction and minimal CYP1A2 occupancy.

Hill Coefficients and Nonlinearities

173

Andersen (1991) noted that the effective partitioning to liver could be described by taking Equation 7.1 and dividing both sides by V L ∗ PL . This term, neglecting the contribution from the low capacity AhR binding, has a maximum value when the denominator term (K B2 + CV L ) is as small as possible, that is, with small values of liver TCDD, small occupancy of the binding protein, and maximal induction to give the largest values of BM2T .

7.5

Alternative Modeling Approaches for Assessing Dose Dependencies

Carrier, Brunet, and Brodeur (1995a, b) described the dose-dependent induction of liver sequestration of TCDD and related compounds in rats and humans with an empirical model for disposition. This model had a basal fraction in liver (f 0 ) at very small body burdens of TCDD and a maximal fraction in liver (f max ) at high body burdens of TCDD. The shift between the basal level and the maximally induced level was described with a Michaelis–Menten rectangular hyperbola with a half-saturation body burden, Kd. The development of the mathematical description simply assumed that TCDD in the body was instantaneously distributed to fat and liver based on fat partitioning and a combination of partitioning and saturable binding in liver. For a given body burden in micrograms, a conservation equation was solved to apportion the dose to these two tissues, allowing estimation of the two model parameters f0 and f max . Using the more mechanistic model for TCDD distribution (see codes in Berkeley Madonna), we can unravel the physiological and biochemical factors that contribute to these macroscopic variables as reported by Evans and Andersen (2000). In this case the model structure can be extended to permit simulation of the fraction in liver, fliver. The half-maximal binding can be examined with respect to other model parameters. In addition, another variable can also be assessed, the ratio of liver to fat concentrations, LTOF. The analysis of these parameters with the mechanistic model of induction of liver sequestration by dioxin showed the complex dependencies of the fliver and Kd on model parameters (see also Evans and Andersen, 2000). The fraction in liver (Figure 7.5) has the same shape as noted for the LIV variable with f max dependencies and “Kd” dependencies as discussed previously. In this case, a mechanistic model provided specific insights into the processes involved in distribution that are lacking in application of the empirical PK structure. Higher chlorinated analogs, that is, pentachloro- or hexachlorodibenzo-p-dioxins, have higher liver to fat ratios than TCDD, presumably a reflection of higher affinity of these compounds for CYP1A2 binding (Abraham, Krowke, and Neubert, 1988; Evans and Andersen, 2000). The expected change in shapes of the Fliver and LTOF curves can be used to predict tissue sequestration expected for these higher chlorinated compounds with higher affinity binding to CYP1A2 (K B2 = 1). As the affinity increases (Figure 7.6), liver to fat ratios become more informative than does Fliver.

7.6

Hill Coefficients and Nonlinearities

Metabolism, AhR binding, and induced transcription all are going on after TCDD treatment. The initial PBPK models used fractional occupancy of a transcriptionally active receptor to

174

Modeling of Protein Induction and Dose-Dependent Hepatic Sequestration 1 Kb2 = 1.5 0.8

Fraction in liver

Kb2 = 3.25 0.6

Kb2 = 6.5

0.4

0.2

0 0.001

0.01

0.1 Dose TCDD - mg/kg bw

1

10

Figure 7.5 Dependence of fmax on CYP 1A2 Affinity. The PBPK model for dioxin (see codes in Berkeley Madonna) was used to calculate fraction of dioxin body burden in the liver for varying values of the affinity constant for the inducing compound binding to CYP1A2. The maximum value of fmax asymptotically approaches 1.0. As affinity increases (lower Kb2 values) the curves become compressed into a small region on the x-axis.

provide an instantaneous adjustment of the protein levels depending on occupancy of the DNA-response elements for AhR in the CYP 1A1/2 genes. This approach lumped together complex steps associated with translation and transcription and ignored protein synthesis and degradation rates. Some second generation PBPK/PBPD models provided explicit rates for production and degradation of CYP1A1/2 mRNA and protein (Kohn et al., 1993). The induction of mRNA was modeled with a Hill relationship that allowed for cooperative promoter binding. In other models (Andersen et al., 1993), the protein synthesis process was accounted for with a Hill-type equation, but the mRNA to protein step was still not included explicitly. The decision to include these steps depends on the philosophy during model development. In keeping the model structure simple, the decision is usually to leave out steps until they are determined to be necessary. For inclusion of time dependent increases in CYP 1A1/2 protein levels, more detail was added to the model description (Equation 7.6).

 [Ah − TCDD]n1 d(CYP1A1t ) = K 0 1 + K 0 max − k1 ∗ CYP1A1t (7.6) dt [Ah − TCDD]n1 + K d1n1 Here, [Ah-TCDD] is the concentration of the complex in liver and Kd1 is the affinity of binding for the depends on various parameters, including the basal synthesis rate (K 0 ),

Regional Hepatic Induction

175

25

Kb2 = 1.5

Liver to Fat Ratio

20

15

Kb2 = 3.25 10

5 Kb2 = 6.5

0 0.001

0.01

0.1 Dose TCDD – mg/kg bw

1

10

Figure 7.6 Liver to fat (LTOF) dependence on CYP 1A2 Affinity. The PBPK model for dioxin (see codes in Berkeley Madonna) was used to calculate LTOF concentration ratios for varying values of the affinity constant for the inducing compound binding to CYP1A2. The maximum value of LTOF is theoretically unbounded and provides a better means of estimating the Kb2 value for any specific compound. These curves do not become compressed as fliver in Figure 7.5.

maximum increase in synthesis rate (K 0max ), Ah receptor-TCDD complex concentration, complex-DNA dissociation constant (Kd1 ), appropriate Hill term (n1), and CYP1A1 degradation rate constant (k1 ). This equation still lumps transcription and translation. Andersen et al. (1993, 1997b) also included delay terms to account for expected lags between activation of transcription and appearance of new protein. Kohn and colleagues (1993) had separate equations for CYP 1A1/2 mRNA and protein. In general, when accounting for total induction of protein in the liver as a function of dose of TCDD, the dose dependencies could be adequately accounted for with Hill coefficients of 1.0, indicating linear processes with no cooperativity in gene activation. However, other studies had evaluated regional induction in the liver by immunohistochemistry (Tritscher et al., 1992). These studies were inconsistent with uniform changes throughout the liver with increasing doses of TCDD.

7.7

Regional Hepatic Induction

In recent years, the PBPK/PD modeling with TCDD has wrestled with the observation that protein induction occurs non-uniformly in the intact liver. At low inducing doses, induction occurs in the centrilobular areas of the liver acini and progresses to the periportal

176

Modeling of Protein Induction and Dose-Dependent Hepatic Sequestration

Figure 7.7 Simulations of the geometric distribution of induced CYP protein in the fivesubcompartment model following a single dose of the inducer (0.3 mg/kg). The geometric model in Panel A has n = 4, Kbi = 1.0, Kd3 = 0.05, and varying the Kdi by a factor of four between adjoining compartments. Panel B shows a 120 h simulation point. Darker shades of color correspond to higher levels of induced protein. Note that in this work “Kd” refers to binding to the AhR and Kb, binding to CYP1A2.

areas as dose increases. Responses of individual cells are dichotomous. Cells appear to be either in a basal non-induced phenotype or to be completely induced, as if a switch occurs leading to a transition from a normal to an induced phenotype. Geometric models have been developed to describe regional induction of CYP1A1/2 in liver by TCDD (Andersen et al., 1997a, b). In this structure, differential sensitivity to induction in each zone occurs due to different binding affinity of the DNA-sites for the Ah-TCDD complex; Hill coefficients for induction are high to insure steepness in the induction in each separate region. Andersen et al. (1997b) implemented this structure with five zones within the liver: a concentric peritportal zone, a fenestrated periportal region that interconnected multiple functional units, and three concentric centrilobular areas (Figure 7.7; Panel B). Estimates of regional induction were calculated by a PBPK/PD model and then converted into color intensities to compare model output with immunohistochemical data (Figure 7.7; Panel A). High n values and threefold differences in AhR-TCDD binding constants for the gene responsive elements of CYP1A1 and CYP1A2 between adjacent compartments produced a consistent description of the tissue TCDD concentrations and for the protein and mRNA induction throughout the liver (Andersen et al, 1997a, b). This five-subcompartment liver model has sharp boundaries between induced and non-induced regions as seen with the immunochemistry of the liver. Descriptions treating the liver as a homogeneous compartment cannot account for these regional differences. The geometric liver model with the induction of gene mediated response of TCDD provided further insight on the induction of these proteins at low exposure concentrations,

Regional Hepatic Induction

177

CYP 1A1 m-RNA - relative units

100000

10000

1-compartment Kd1 = 2 nM

1000

Kd1 = 4 nM 5-compartment Kd13 = 0.6 nM ∆Ki = 3

100

10

0.01

.1

1.0

100 10 dose - ng/kg

1000

10000

Figure 7.8 Dose dependence of mRNA production in female Sprague–Dawley rats dosed with single oral doses of TCDD (from Andersen et al., 1997b; reprinted with permission from Elsevier, Copyright 1997). The induction parameters for the five-compartment model were Kd13 = 2.0/3 with “Kd” increasing by a factor of three between each adjacent compartment. With the one-compartment model, Kd values were constant across the liver. The modeled mRNA data were obtained from Vanden Heuvel et al. (1994).

indicating the presence of a threshold for activation, even in the centrilobular region, the zone most sensitive to induction. The most convincing evidence for nonlinearities in tissue response was noted with induction of CYP1A1 mRNA. This enzyme is not constitutively expressed in rat liver and increases nearly 10 000 fold with maximal induction (Vanden Heuvel et al., 1994). The model for regional induction (Andersen et al., 1997a) was also used to estimate expected increases in CYP1A1 mRNA by including code similar to Equation 7.6 for mRNA time courses in liver (Figure 7.8). Its behavior was also consistent with highly nonlinear behavior and the presence of a switch in activation of transcription. The next round of model refinement for induction of proteins by TCDD will focus on biological details of promoter formation and the cellular circuitry that regulates nonlinear activation cascades. The addition of more biological detail in these models for protein induction and receptor activation, however, requires targeted experiments to further unravel the cellular response to TCDD treatment that leads to non-uniform induction and the appearance of this all-or-none behavior of individual cells. Combination of in vitro and in vivo studies will be required to decipher the molecular mechanisms of receptor activation and cellular responses to activation. As these processes are uncovered, they can be incorporated into a new round of PBPK/PD models to more confidently evaluate dose-response relationships in the intact animal and consider the expected risks posed at low doses of dioxin in human populations. Further quantitative modeling work with TCDD, as a prototype protein inducer, could be valuable in providing new approaches for risk assessments with receptor-mediated toxicants.

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Modeling of Protein Induction and Dose-Dependent Hepatic Sequestration

7.8 Conclusions Multiple modeling strategies used with TCDD have provided a variety of quantitative tools for understanding the biological determinants of the disposition and kinetic behaviors of compounds that act via receptor based interactions in target tissues. Persistence is largely related to poor clearance mechanisms from the body, while lipophilicity leads to bioaccumulation. Some time-dependent changes in compartments required for persistent compounds are simply an acknowledgment of the dynamics of compounds that have long half-lives (Figure 7.2). Development of PBPD models for transcript and protein induction still present many challenges, since the cellular processes involved in induction of single genes and battery of genes are under active investigation with the new methods of cellular and molecular biology (Chapter 10). An important step in regard to evaluating the adverse responses to chemicals (both toxicants and drugs) is the need to understand and create quantitative PD models of the innate biology. With TCDD, the process of tissue binding and liver sequestration is intimately associated with signaling mediated via receptor activation and transcriptional enhancement. It was impossible to develop a PK model alone for TCDD disposition; it had to be combined with PK and PD elements. Current work on involvement of protein kinase cascades and histone modification in transcriptional activation of gene expression may underlie aspects of the transcriptional switch. Increasing detail regarding these molecular processes will permit development of a new suite of PD models that should be of use for toxicological and pharmacological applications.

References Abraham, K., Krowke, R., and Neubert, D. (1988) Pharmacokinetics and biological activity of 2,3,7,8-tetrachlorodibenzo-p-dioxin. 1. Dose-dependent tissue distribution and induction of hepatic ethoxyresorufin O-deethylase in rats following a single injection. Arch. Toxicol., 62, 359–368. Andersen, M.E. (1991) Physiological modeling of organic compounds. Ann. Occup. Hyg., 35, 309–321. Andersen, M.E., Mills, J.J., Gargas, M.L., et al. (1993) Modeling receptor-mediated processes with dioxin: implications for pharmacokinetics and risk assessment. Risk Anal., 13, 25–36. Andersen, M.E. (1995) Development of physiologically based pharmacokinetic and physiologically based pharmacodynamic models for applications in toxicology and risk assessment. Toxicol. Lett. 79, 35–44. Andersen, M.E., Birnbaum, L.S., Barton, H.A., and Eklund, C.R. (1997a) Regional hepatic CYP1A1 and CYP1A2 induction with 2,3,7,8-tetrachlorodibenzo-p-dioxin evaluated with a multicompartment geometric model of hepatic zonation. Toxicol. Appl. Pharmacol., 144, 145–155. Andersen, M.E., Eklund, C.R., Mills, J.J., et al. (1997b) A multicompartment geometric model of the liver in relation to regional induction of cytochrome P450s. Toxicol. Appl. Pharmacol., 144, 135–144. Carrier, G., Brunet, R.C., and Brodeur, J. (1995a) Modeling of the toxicokinetics of polychlorinated dibenzo-p-dioxins and dibenzofurans in mammalians, including humans. II. Kinetics of absorption and disposition of PCDDs/PCDFs. Toxicol. Appl. Pharmacol., 131, 267–276. Carrier, G., Brunet, R.C., and Brodeur, J. (1995b) Modeling of the toxicokinetics of polychlorinated dibenzo-p-dioxins and dibenzofurans in mammalians, including humans. I. Nonlinear distribution of PCDD/PCDF body burden between liver and adipose tissues. Toxicol. Appl. Pharmacol., 131, 253–266.

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Evans, M.V., and Andersen, M.E. (2000) Sensitivity analysis of a physiological model for 2,3,7, 8-tetrachlorodibenzo-p-dioxin (TCDD): assessing the impact or specific model parameters on sequestration in liver and fat in the rat. Toxicol. Sci., 54, 71–80. Kohn, M.C., Lucier, G.W., Clark, G.C., et al. (1993) A mechanistic model of effects of dioxin on gene expression in the rat liver. Toxicol. Appl. Pharmacol., 120, 138–154. Leung, H.W., Ku, R.H., Paustenbach, D.J., and Andersen, M.E. (1988) A physiologically based pharmacokinetic model for 2,3,7,8-tetrachlorodibenzo-p-dioxin in C57BL/6J and DBA/2J mice. Toxicol. Lett., 42, 15–28. Leung, H.W., Paustenbach, D.J., Murray, F.J., and Andersen, M.E. (1990) A physiological pharmacokinetic description of the tissue distribution and enzyme-inducing properties of 2,3,7,8tetrachlorodibenzo-p-dioxin in the rat. Toxicol. Appl. Pharmacol., 103, 399–410. Tritscher, A.M., Goldstein, J.A., Portier, C.J., et al. (1992) Dose-response relationships for chronic exposure to 2,3,7,8-tetrachlorodibenzo-p-dioxin in a rat tumor promotion model: quantification and immunolocalization of CYP1A1 and CYP1A2 in the liver. Cancer Res., 52, 3436–3442. USEPA (2004) Dioxin Reassessment. NAS Review Draft 2004, US Environmental Protection Agency, Washington, D.C., EPA/600/P-00/001Cb. Vanden Heuvel, J.P., Clark, G.C., Kohn, M.C., et al. (1994) Dioxin-responsive genes: examination of dose-response relationships using quantitative reverse transcriptase-polymerase chain reaction. Cancer Res. 54, 62–68.

8 Bistable Signaling Motifs and Cell Fate Decisions Sudin Bhattacharya, Qiang Zhang, and Melvin E. Andersen Division of Computational Biology, The Hamner Institutes for Health Sciences, USA

8.1 Biological Switches and Signaling Motifs To coordinately activate suites of genes, cells in all living organisms have evolved molecular modules to allow transitions, or switching, between distinct functional states over a small range of signal (dose of hormone or other ligand concentration), as well as mechanisms to stabilize the new state. In many cases, such coordinated control of sets of gene products leads to an extensive change in the properties of the cell – for instance irreversible differentiation, or a reversible phenotypic alteration that persists until the activation signal falls back to very low concentration. Switching in this context does not refer simply to a process with an “off” state and an “on” state but, more broadly, to a dynamic process where small changes in the concentration of the active ligand lead to relatively large changes in cellular response. A typical example is the all-or-none regional induction of metabolizing enzymes in the liver by xenobiotics (Andersen et al., 1997a, b). The presence of switches for concerted transcriptional regulation of gene batteries and their nonlinear input/output (I/O) properties have important consequences for the shape of dose-response curves. Molecular control processes for switching are inherently nonlinear and often use autoregulatory feedback loops. Some of the biological processes that contribute to switching phenomena are receptor autoinduction, induction of enzymes for ligand synthesis, mRNA stabilization/activation, and receptor polymerization (Bhalla and Iyengar, 1999; Lisman and Fallon, 1999). Specifically, switching phenomena require a positive feedback loop architecture in the underlying signaling cascade. The positive feedback loop can be

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implemented in a double-positive form with two mutually activating components. This network architecture is useful in situations where a cell needs to execute an “on–off” switch. Positive feedback can also be implemented in the form of a double-negative loop with two mutually inhibiting components, which acts as a “toggle switch” helping a cell choose between two alternative states (Becskei, Seraphin, and Serrano, 2001; Ferrell, 2002; Gardner, Cantor, and Collins, 2000). The positive feedback loop is one of a common set of signaling motifs. Over the past decade, investigation of the transcriptional regulatory networks in the bacterium Escherichia coli (Shen-Orr et al., 2002) and the budding yeast Saccharomyces cerevisiae (Lee et al., 2002) has revealed a core set of recurring regulatory motifs, each with a characteristic structure and the capacity to perform specific information-processing functions (Alon, 2007; Bhalla and Iyengar, 1999; Tyson, Chen, and Novak, 2003). Similar motifs have also been identified in the cells of higher organisms – for example in the circuits that control gene expression in the pancreas and liver (Odom et al., 2004), as well as in the regulatory circuits of human embryonic stem cells (Boyer et al., 2005) and hematopoietic stem cells (Rothenberg, 2007; Swiers, Patient, and Loose, 2006).

8.2

Discreteness in Cellular Fates and the Underlying Genetic Program

“Cellular fates” represent developmental states or processes that are (a) discrete, (b) stable, and (c) mutually exclusive. A quiescent cell at a particular point in development, might, for example, have to decide among three alternative fates: proliferation, apoptosis, and differentiation (Figure 8.1a). All three of these non-overlapping states must be robust to small perturbations and must not allow cells to get “stuck” in intermediate states. A more complex example of cell fate determination is the hierarchical decision making process in any cellular lineage – for instance, the hematopoietic stem cell lineage, which gives rise to blood cells as well as cells of the innate and adaptive immune systems (Orkin and Zon, 2008). Each stage in the lineage is marked by a binary decision point where a precursor cell differentiates to one of two alternative fates (Figure 8.1b). The idea of the discreteness of developmental decisions is captured vividly in the visual metaphor of an “epigenetic landscape,” invoked by the embryologist C.H. Waddington (Waddington, 1957) (Figure 8.2a). Since cell fates must correspond to particular states of the underlying gene expression program, the discreteness of cellular fates implies a corresponding discreteness in the gene expression program or the transcriptome. For example, the erythroid, lymphoid (B, T, and NK cell) and myeloid cell fates in the hematopoietic stem cell lineage are marked by discrete levels of expression of the key regulatory transcription factors Notch, PU.1 and E2A/HEB (Warren and Rothenberg, 2003) (Figure 8.2b). But how does the genome generate the discrete, stable gene expression profiles that characterize different cell fates? The key to this question lies in the fact that individual genes and proteins are not expressed independently of each other. Rather, groups of genes and proteins regulate each other through a small set of recurring network motifs. It is the complex web of gene–protein and protein–protein interactions arising from combinations of these motifs that generates stable attractor states for the dynamic system represented by the genetic program of a cell. These attractor states correspond to the distinct, stable and mutually exclusive cell fates (see Huang, 2005 for a detailed discussion of these ideas).

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Figure 8.1 (a) Cell fate determination involves choosing among developmental states or processes that are discrete, stable and mutually exclusive; for instance, a cell may have to choose between proliferation, apoptosis, and differentiation (adapted from Huang, 2005). (b) Hierarchical decision making in the hematopoietic stem cell lineage: successive developmental stages along with the critical transcription factors for each stage (Orkin and Zon, 2008; reprinted with permission from Elsevier, Copyright 2008).

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Figure 8.2 (a) The image of a marble rolling down a landscape of branching ravines is used to illustrate the concept of the developmental potential of a multipotent progenitor cell becoming more restricted with each successive differentiation. The visual metaphor of an “epigenetic landscape,” proposed by the embryologist C.H. Waddington (Reprinted with permission from (Waddington, 1957)). (b) The erythroid, lymphoid (B, T, and NK cell) and myeloid cell fates in the hematopoietic stem cell lineage are marked by discrete levels of expression of the transcription factors Notch, PU.1 and E2A/HEB (Warren and Rothenberg, 2003; reprinted with permission from Elsevier, Copyright 2003).

Switching and Bistability

8.3

185

Switching and Bistability

A bistable system can reside in one of two discrete, stable steady states (Box 8.1). This phenomenon can be visually represented by a “bifurcation diagram” (Figure 8.3a), which shows the steady states of the system plotted against a particular parameter. If the input (stimulus) to the system is chosen as the parameter, the bifurcation diagram would represent the dose-response curve of the bistable system. The solid lines in Figure 8.3a correspond to stable steady states, and the dashed line corresponds to unstable steady states that are theoretically predicted but can never be attained in practice. As the stimulus is increased from zero, the system switches from the low response (“off”) to the high response (“on”) state at a “threshold” value of the stimulus (indicated by the vertical arrow in Figure 8.3a). A bistable system also exhibits hysteresis; that is, different dose-response curves are obtained depending on whether the dose is increasing or decreasing, as indicated by the left- and right-pointing arrows, respectively, in Figure 8.3a. Stated otherwise, over a certain dose range, a bistable system exhibiting hysteresis will reside in one of two alternative steady states for a given dose, depending on the history of the system. As we will show with the example of the gene autoregulation motif, bistable switching behavior arises from the nonlinearity and positive feedback inherent in the system (Angeli, Ferrell, and Sontag, 2004; Ferrell, 2002; Ferrell and Xiong, 2001; Tyson, Chen, and Novak, 2003). Bistability has been demonstrated in a number of natural biological systems (Bagowski and Ferrell, 2001; Chang et al., 2006; Xiong and Ferrell, 2003) as well as in synthetic biological circuits (Becskei, Seraphin, and Serrano, 2001; Gardner, Cantor, and Collins, 2000; Ozbudak et al., 2004). It is likely to be an important mechanism in the control of cellular differentiation processes (Chang et al., 2006; Chickarmane et al., 2006), where a cell needs to reside in one of two mutually exclusive phenotypic states. The other notable feature of the switch portrayed in the bifurcation diagram (Figure 8.3a) is that it is irreversible – that is, the system stays in the “on” state as the triggering stimulus is gradually lowered to zero, as indicated by the left-pointing arrows in this figure. Irreversibility arises from the strength of the feedback loops involved in the regulatory circuit (Bagowski and Ferrell, 2001; Ferrell, 2002). Bistable switches need not be

Box 8.1: Evolution of the Idea of Bistability Huang (2005) has listed the key events in the development of the idea of bistability as follows: r Delbr¨uck (1949) proposes bistability as a general principle to explain discontinuous transitions in biochemical reactions. r Novick and Weiner (1957) demonstrate all-or-none transitions between cell states in E. Coli lactose metabolism. r Monod and Jacob (1961) propose bistable gene regulatory circuits to explain cell differentiation. r Thomas (1978) shows that a positive feedback loop is a necessary element of a regulatory network for bistability and switching behavior.

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Figure 8.3 (a) A bifurcation diagram illustrating the stimulus-response behavior of a bistable system acting as an “irreversible” switch. The solid and dashed lines represent stable and unstable steady states respectively. Solid arrows indicate switching from a low-response state to a high-response state. Dashed arrows indicate the “hysteresis” exhibited by the system (see text). (b) A bifurcation diagram describing the stimulus response of a “reversible” switch.

irreversible – weaker feedback in the system would allow the system to return to the “off” state as the stimulus is decreased. This scenario of a “reversible” switch that still exhibits hysteresis is illustrated in Figure 8.3b. Biological switches abound in nature – some examples are discussed below: (1) Xenopus laevis oocytes undergo a switch from a state of G2 arrest to metaphase arrest in response to the maturation-inducing hormone progesterone. The biochemical basis

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187

of this all-or-none response at the level of individual oocytes is signaling through a mitogen-activated protein kinase (MAPK) cascade (Ferrell, 1999a; Ferrell, 1999b; Ferrell and Machleder, 1998). A combination of ultrasensitivity in MAPK signaling, which filters out small stimuli, and positive feedback in the cascade, which prevents the oocyte from getting stuck in intermediate states, is responsible for converting a continuously variable stimulus (progesterone) to a highly switch-like, quantal response, with effective Hill coefficients ∼ = 42 for individual oocytes (Ferrell and Machleder, 1998). (2) The induction of cytochrome P450 (CYP450) enzymes in the liver by the environmental contaminant 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) involves binding of TCDD to the aryl hydrocarbon receptor (AhR), followed by migration of the AhR-TCDD complex to the nucleus, where it forms a heterodimer with the aryl hydrocarbon receptor nuclear translocator (ARNT) protein. The heterodimer binds to specific DNA sites to initiate transcription of several genes, including members of the CYP450 family of xenobiotic-metabolizing enzymes. Induction of one member of the family, CYP450 1A1, in liver cells by TCDD in vitro is switch-like, with some cells fully induced and others not induced at all (Bars et al., 1989). Patterns of induction in vivo also appear to be switch-like (Bars and Elcombe, 1991; Tritscher et al., 1992). Pharmacokinetic models of CYP1A1 induction in the liver showed that ultrasensitivity, in the form of a Hill coefficient higher than 4.0, was required to explain this all-or-none response (Andersen et al., 1997a), implying the existence of a dose threshold. The use of the Hill term in these models to generate ultrasensitivity is a mere convenience, accounting for other intrinsically ultrasensitive biochemical processes that likely include MAPK cascades and multiple transcription factor activation. Receptor-mediated feedback mechanisms are also likely to be involved in this induction process, as Ah receptor levels in the liver increase following treatment by TCDD (Sloop and Lucier, 1987). (3) A biological switch appears to underlie temperature-dependent sex determination (TSD) in many species of egg laying reptiles, where the incubation temperature of the egg determines the sex of the offspring. Here the continuously varying external signal of temperature must be transduced into an all-or-none genetic response that determines gonadal sex (Crews et al., 1994; Crews, Bergeron, and Mclachlan, 1995; Pieau, 1996). Temperature acts on genes encoding hormone receptors and steroid-synthesizing enzymes, activating either the ovary-determining cascade or the testis-determining cascade. In one hypothesis, estradiol- or dihydrotestosterone-forming enzymes compete for testosterone, a precursor common to both sex steroids (Crews et al., 1994). Either estradiol or dihydrotestosterone can take part in a positive feedback loop, increasing the amount of the enzyme (aromatase or reductase, respectively) responsible for its own synthesis. Depending on the temperature, one or the other feedback loop is activated first. Once a loop is initiated, because of the common precursor (testosterone), the formation of the other sex steroid is inhibited, locking the direction of gonadal development towards either an ovary or a testis. Environmental estrogens or anti-androgens could influence this switch and change the gender distribution within a population. (4) A computational model of the transcriptional circuitry that regulates the fate of embryonic stem cells showed that a network of three transcription factors, OCT4, SOX2, and NANOG, connected by multiple positive feedback loops can generate a bistable switch, alternating between two phenotypic states of the system: self-renewal and

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differentiation (Chickarmane et al., 2006). Curiously, these positive feedback loops, like many others in developmental processes, appear to comprise double-negative feedback processes to provide the required positive feedback. (5) Similar theoretical models (Huang et al., 2007; Roeder and Glauche, 2006) have been used to show that mutual inhibition of the two transcription factors GATA-1 and PU.1 coupled with positive auto-catalytic regulation can help explain lineage choice (myeloid vs erythroid differentiation) in hematopoietic stem cells. This system switches from a “primed” state representing the stem cell fate with low-level co-expression of the two transcription factors, to a differentiated state where one factor dominates at the expense of the other.

8.4 The Gene Autoregulation Motif As discussed above, response motifs are relatively simple building blocks that frequently appear in complex molecular networks and possess a specific input/output (I/O) signaling property. Different network motifs serve specific biological functions. In the rest of this chapter, we discuss one such motif used by organisms to enable ligand-mediated switching between different cellular states: gene autoregulation. In the gene autoregulation response motif (Figure 8.4, Box 8.2) a protein activates its own gene, either directly as a transcription factor, or indirectly through a signaling cascade – thereby implementing a positive feedback loop. An example of this motif is the operon structure common in bacterial systems, where a set of genes is simultaneously controlled to regulate a particular physiological process. In the lac operon of the bacterium E. coli, the transcription of the set of genes that produce proteins responsible for lactose metabolism is controlled by the lac repressor, which binds to the promoter in the absence of a ligand and blocks transcription of the genes in the operon. One of the gene products of the operon, the enzyme β-galactosidase, converts lactose to allolactose, which binds the repressor, causing it to dissociate from the promoter and allow transcription of the genes in the operon. In this case, the positive feedback is indirectly implemented by inhibition of a repressor. Another example can be found in the regulation of

S

k2 , kd2

k1, kd1

mRNA

k4

protein

k0 k5

k3

gene

Φ

Φ

Figure 8.4 The gene autoregulation module. The symbols S and φ denote activating input signal and mRNA/protein degradation, respectively. Other symbols are explained in Box 8.2.

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189

Box 8.2: Mathematical Model of Gene Autoregulation In this chapter, we use a simplified mathematical representation of a transcriptional regulatory circuit with both constitutive activation and autoregulatory induction of a gene (Figure 8.4a). The equations that describe the model dynamics are: k1 · S k2 · P n dM − k3 · M (8.1) = k0 + + n dt kd1 + S kd2 + P n dP (8.2) = k4 · M − k5 · P dt In these equations, M and P are the variables representing amounts of the mRNA and protein, respectively, while S represents a saturable input signal (hormone/ligand) that activates the gene. The parameter k0 is the basal (constitutive) transcription rate; k1 and kd1 are the transcription rate constant and the effective affinity constant, respectively, for the input signal S acting on the gene, while k2 and kd2 represent the transcription rate constant and the effective affinity constant, respectively, for the protein P acting as a transcription factor to induce activation of the gene. The parameter n is the Hill coefficient that describes an ultrasensitive activation of gene transcription by P. P and S are assumed to act on two independent promoters, leading to an additive effect on the transcription rate. The parameter k4 denotes the basal translation rate constant, and k3 and k5 represent the first-order degradation rate constants for mRNA and protein respectively. For this simplified model we use dimensionless parameters with the following values: k0 = 1, k1 = 1, kd1 = 5, k2 = 10, kd2 = 5, k3 = 1, k4 = 1, k5 = 1, n = 4. These values were selected to ensure bistable switching behavior in the model. The value of S is varied to explore the dynamic behavior of the model. Initial values of the variables M and P (i.e., initial amounts of mRNA and protein) need to be specified for each “run” (simulation) of the model. The action of the protein P to activate its own gene forms a positive feedback loop that gives the module its switching properties (see text). All R program. simulations were run with the Berkeley Madonna
the comK gene in the soil bacterium Bacillus subtilis. The comK gene is the master regulator for the transition from a “vegetative” state to a “competent” state where the bacterium can take up DNA from the environment. The ComK protein itself acts as a transcription factor for the comK gene, thus forming a direct autoregulatory positive feedback loop (Hamoen et al., 1998; Vansinderen et al., 1995; Vansinderen and Venema, 1994). 8.4.1

Bistability in the Gene Autoregulation Motif

The dynamic behavior of our generalized gene autoregulation model (Box 8.2; Berkeley R code for model in Box 8.3; QMT model library folder BHATTACHARYA) is Madonna
first explored by running simulations with a range of initial conditions for protein amount P, with input signal S set to 0, and then plotting the time-course of P (Figure 8.5a). The curves show that the system settles into one of two different stable steady states depending on the initial condition, thus exhibiting “bistable” behavior even in the absence of the signal S. One of the steady states corresponds to low protein expression (the “off” state) and the other to

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R Box 8.3: Berkeley–Madonna
Code for the Gene Autoregulation Model

;Equation for pulse input ;S = pulseStrength∗ squarepulse(t start, t dur) ;Differential equations to solve d/dt(M) = k0 + k1∗ S/(kd1+S) + k2∗ Pˆn/(kd2ˆn+Pˆn) - k3∗ M d/dt(P) = k4∗ M-k5∗ P ;Initial conditions init M=1 init P=1 ;Parameter values k0=1 ; basal transcription rate constant k1=1 ; S-activated transcription rate constant k2=10 ; P-activated transcription rate constant kd1=5 ; effective affinity constant for signal S activating gene kd2=5 ; effective affinity constant for protein P activating gene n=4 ; Hill-coefficient for gene activation by protein P k3=1 ; degradation rate constant for mRNA k4=1 ; basal translation rate constant k5=1 ; degradation rate constant for protein S=0 ; input signal ;Parameter values for pulse input ; start time of pulse input ;t start = 0 ; duration of pulse input ;t dur = 20 ;pulseStrength = 1 ; strength of pulse input

high protein expression (the “on” state). This bistable dynamics can also be demonstrated by keeping the initial amount of protein fixed at a low level and varying the strength of the input signal S (Figure 8.5b). Again, the system settles into a low-expression or highexpression state depending on the signal strength; there is a threshold value of S below which it settles into the “off” state and above which it settles into the “on” state – showing that the system acts as a threshold-dependent switch. The switch is also “irreversible” in that it can stay “on” once the stimulus is removed, provided the strength and duration of the dose are both sufficiently high (Figure 8.6). To see how the switching property of the gene autoregulation motif arises, one would need to derive the dose-response behavior of the model from the rate equations for mRNA and protein amounts described in Box 8.2. The protein synthesis rate is given by the first term in Equation 8.2, k4 · M, and the protein degradation rate by the second term, k5 · P. These two rate terms can be plotted as functions of the protein level P (Figure 8.7a, schematic), where the points of intersection of the two curves give the steady states of the

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(a)

(b)

Figure 8.5 Simulations of the gene autoregulation model with protein amount P plotted against time, demonstrating bistable behavior as: (a) initial value of P is varied from 0 to 20, with initial value of M = 1, and input signal S = 0; (b) S is varied from 0 to 100, with the initial values of P and M fixed at 1. (Screenshots from model implemented in the Berkeley R program) Madonna


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Bistable Signaling Motifs and Cell Fate Decisions

Figure 8.6 Irreversibility of the gene autoregulation switch: protein level P remains high (i.e., the switch stays “on”) even after the stimulus S is removed. (Duration of pulse for input stimulus S = 60; strength of pulse = 80.)

system (i.e., where the protein synthesis rate equals the degradation rate). The three steady states thus obtained, however, are not all stable. As indicated by the arrows in Figure 8.7a, small perturbations in protein level from steady state 2 lead the system away from that state towards either steady state 1 or steady state 3. Small perturbations from states 1 or 3, on the other hand, would restore the system back to the original state. Thus states 1 and 3 are stable steady states, whereas state 2 is an unstable steady state. Variation in the dose of stimulus S would change the mRNA, and hence protein, synthesis rates (Equations 8.1 and 8.2, Box 8.2), thus altering the locations of the steady states (Figure 8.7b, schematic). Plotting the steady-state protein levels as a function of S gives the bifurcation curve for the model, representing its dose-response behavior. The dashed portion of the bifurcation curve represents unstable steady states or states that are physically unattainable (negative S). The schematic bifurcation curve (Figure 8.7b) shows that the system switches from State 1 (“off” state, low protein level) to State 2 (“on” state, high protein level) in a discrete fashion at a threshold dose of the stimulus S. It also illustrates the hysteresis in the system, where for a range of doses of the stimulus, the system could reside in either State 1 or State 2; as well as the irreversibility of the switch, that is, the ability of the system to remain in the high protein-expression state once the input signal S (hormone or other ligand) is removed: an outcome consistent with cellular differentiation. The multiple steady states of the system arise from the shapes of the protein synthesis and degradation rate plots and their resulting points of intersection. In particular, the sigmoidal shape of the protein synthesis rate curve in our model causes it to intersect

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193

(a) Degradation rate, k5. P

3

Rate

Synthesis rate, k4. M 2

1

P

Rate

S3 S2 S1

(b)

Bifurcation curve P

State 2

S

P

S3 S2 S1

State 1 P

s

Figure 8.7 Schematic derivation of bistable switching properties from rate equations in the gene autoregulation model. (a) Points of intersection of the protein synthesis (sigmoidal) and degradation (linear) rate plots give the three steady states of the system. States 1 and 3 are stable steady states, whereas state 2 is an unstable steady state, as indicated by the arrows and dashed lines (also see text). (b) Derivation of the bifurcation curve representing dose-response behavior of the model. Varying the synthesis rate by changing the value of the dose S leads to variation in the steady-state value of the protein level P as a function of S. Plotting the steady-state proteins levels as a function of S gives the bifurcation curve for the model. S3 > S2 > S1 represent three values of the stimulus S. Dashed portion of bifurcation curve represents unstable steady states or states that are physically unattainable (negative S). States 1 and 2 represent “off” (low protein level) and “on” (high protein level) states of this bistable switch.

the degradation rate curve at three separate points, leading to three steady states (Figure 8.7a). The sigmoidal shape of the protein synthesis rate curve, in turn, arises from the ultrasensitivity in the positive feedback loop, represented by the Hill coefficient n describing the activation of gene transcription by the protein in our model (Box 8.2; n > 1 is required for ultrasensitivity). The gene autoregulation module is representative of a broader range

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of positive feedback control processes found both in bacteria and eukaryotes. Although the Hill coefficient n in our model formulation ostensibly describes cooperative binding of a transcription factor to its own promoter, it can also implicitly represent more common forms of nonlinear positive feedback, including receptor-mediated effects (Andersen and Barton, 1999) or signaling through ultrasensitive protein kinase cascades (Ferrell, 1996). The combination of ultrasensitivity and positive feedback in signal transduction is responsible for all-or-none switch-like cellular responses (Ferrell and Machleder, 1998). Such cellular switches are likely to be the basis of dose thresholds observed in biological responses both to environmental agents and to pharmaceuticals. 8.4.2 The Phase Plane: Nullclines and Basins of Attraction The bistability of the gene autoregulation motif can also be portrayed by its behavior on the M-P phase plane, where one can track the evolution of the system by following the trajectories of one system variable (M, mRNA) against another (P, protein). These trajectories converge towards the stable steady states and away from the unstable steady state (Figure 8.8a; for simple, two-variable systems, trajectories on the phase plane can be R ). There are thus two generated from the “initial condition” feature of Berkeley Madonna
basins of attraction in the phase plane of this model, each corresponding to the range of initial conditions (M-P pairs) that lead the system to converge on one stable steady state or the other (Figure 8.8b). It is instructive to plot the nullclines for the system, obtained by setting the time derivatives of the system variables in the rate equations to zero. In our model, setting ddtM = 0 and ddtP = 0 in Equations 8.1 and 8.2 (Box 8.2) yields the M-nullcline and P-nullcline, respectively: r M-nullcline:


 k1 · S k2 · P n 1 · k0 + + n M= k3 kd1 + S kd2 + P n

(8.3)

r P-nullcline: M=

k5 ·P k4

(8.4)

The M-nullcline represents the steady-state response of variable M to variable P, and the P-nullcline the steady-state response of variable P to variable M. The points of intersection of the two nullclines thus give the steady states for the system (Figure 8.9, generated using R ). As with the rate plots, ultrasensitivity in the nullcline feature in Berkeley Madonna
the feedback loop and the consequent sigmoidal shape of the M-nullcline ensure multiple steady states for the system. (For details on the concepts of phase planes and nullclines, see Strogatz, 2001).

8.5

Conclusions

To summarize: r Cells need to choose between different “fates”: differentiation, apoptosis, cell division, coordinated induction of groups of gene products, and so on.

Conclusions

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(a)

(b)

Figure 8.8 (a) Trajectories followed by the gene autoregulation model on the M-P phase plane. Arrows and lines indicate convergence of trajectories towards the stable steady states (1 and 2) and away from the unstable steady state (3). (b) Thick dashed line passing through the unstable steady state represents the “separatrix” dividing the phase plane into the “basins of attraction” of the two stable steady states.

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M-nullcline

P-nullcline

Figure 8.9 Points of intersection of the M- and P-nullclines (thick lines) give the steady states of the system.

r These discrete fates correspond to discrete “attractor states” in the underlying genetic program. r Bistability is a mechanism that allows cells to choose between discrete, stable, and mutually exclusive states. r Positive feedback loops with ultrasensitivity are a means of achieving bistability. r Bistability produces hysteresis, a “cellular memory” mechanism, and allows stabilization of alternative cell fates. r Bistable switches may be either irreversible (an outcome consistent with cellular differentiation) or reversible. r For simple two-variable systems with ultrasensitive positive feedback, the generation of bistable behavior can be graphically illustrated by rate plots and nullclines on the phase plane.

References Alon, U. (2007) Network motifs: theory and experimental approaches. Nat. Rev. Genet., 8, 450–461. Andersen, M.E. and Barton, H.A. (1999) Biological regulation of receptor-hormone complex concentrations in relation to dose-response assessments for endocrine-active compounds. Toxicol. Sci., 48, 38–50.

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9 Ultrasensitive Response Motifs in Biochemical Networks Qiang Zhang, Sudin Bhattacharya, Courtney G. Woods, and Melvin E. Andersen Division of Computational Biology, The Hamner Institutes for Health Sciences, USA

9.1 Introduction Cells in vivo constantly receive inputs from the residential microenvironment in which they live and execute specific functions. Some of these inputs are endogenous, physiological signals from neighboring cells or from remote tissues/organs, instructing cells to function in a systemically coordinated fashion. In response, cells may proliferate, differentiate, activate certain metabolic pathways, or secrete hormones, and so on. In contrast, some changes in the residential microenvironment are stressful to the cells. These include unfavorable alterations in the concentrations of nutrients, oxygen, ions, and other molecules that are vital to the survival of residential cells and their uncompromised execution of cellular functions. In some cases, xenobiotic molecules appear in the microenvironment through exposure of the animal or human body to chemicals in the environment at large. Entrance of xenobiotic molecules into the cell may affect general cellular health and interrupt specific cellular processes. Regardless of the type of perturbations, cells must be able to adapt to the stressful changes at first and manage to maintain a relatively stable intracellular milieu for survival and functionality. Certainly, if the stress level exceeds the cellular homeostatic capacity, decisions may also have to be made for a graceful exit such as apoptosis. Whether the inputs are physiological signals or deleterious environmental perturbations, their presence is usually sensed through specific receptor molecules in the cell. The outright impacts on the cell rarely stop at these initial targets, however. The consequences of the inputs are often felt throughout a nebula of interconnected biomolecules in the cell,

Quantitative Modeling in Toxicology
C 2010 John Wiley & Sons, Ltd

Edited by Kannan Krishnan and Melvin E. Andersen

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perturbing specific signaling pathways and gene networks, and consequently causing changes in cellular behaviors. As signals move along the molecular paths and circuits within the cell, it is sometimes desirable to preserve a high fidelity to the upstream input, so that the downstream output may respond proportionately to the environmental cues. Nevertheless, it seems more frequent though that signals are usually altered from station to station along the transduction pathways with respect to their magnitude and duration, that is, propagating in a highly nonlinear manner (Kholodenko, 2006; Alon, 2007). One type of nonlinear response that is observed very frequently in the cell and that is the subject of intensive study by theoretical biologists is ultrasensitivity – a small percentage change in the input signal is amplified leading to a larger percentage change in the downstream output molecule (Goldbeter and Koshland, 1984; Huang and Ferrell, 1996; Legewie, Bluthgen, and Herzel, 2005). The stimulus-response curve associated with an ultrasensitive response is often sigmoid in shape on a linear plot. Those small building blocks in the molecular network that can transfer signal in an ultrasensitive manner are termed as ultrasensitive motifs. The importance of transducing signals in an ultrasensitive manner is multi-faceted. Without ultrasensitivity it is not even easy to maintain a proportionate response throughout a signaling cascade. This situation occurs because biochemical reactions mediating signal propagation invariably involve molecular binding events which are linear only at low concentrations of participating molecules. At higher concentrations the underlying process is near maximal binding, leading to a saturated response. The consequent loss of sensitivity through a long signaling cascade can be so severe that the terminal response loses the original contrast of the input signal. In these cases, periodic local ultrasensitive response may be needed along the signaling cascade to compensate the sensitivity loss in order to retain a nearly linear response at the distal end of the cascade. A highly ultrasensitive response, often characterized by a steep sigmoid stimulusresponse curve, can function as an all-or-none switch. This type of switch can be used to convert graded input into binary response characteristic of many cellular behaviors, such as discrete fate decision making (Bagowski et al., 2003). With a threshold, the switch-like response may also function as a noise filter, preventing cells from responding to small irrelevant fluctuations in the environment. In addition to the role as a straightforward signal amplifier, the importance of ultrasensitive motifs is best appreciated in the context of protein and gene feedback networks that exhibit bistability, homeostasis, and oscillation depending on system parameters. These network properties are fundamental to the execution of various cellular functions. Bistability is believed to be responsible for discrete irreversible cellular behaviors such as differentiation, proliferation, and apoptosis (Ferrell and Machleder, 1998; Ozbudak et al., 2004). Homeostasis is important for robust adaptation of cells to survive and carry out prescribed tasks in a fluctuating environment riddled with stressors (Zhang and Andersen, 2007). A gene network that can oscillate with an approximate 24-hour period is the underlying biological clock for circadian rhythm (Roenneberg and Merrow, 2003). Ultrasensitivity is critical for these emergent behaviors to arise in a properly structured network. Chapter 8 illustrates the essential role of ultrasensitive response in generating bistable behavior. This chapter begins with an introduction to the concepts of ultrasensitivity and its relationship to the Hill function. It is followed by a list of well-studied ultrasensitive motifs and the elucidation of their respective ultrasensitive mechanisms. The MAPK cascade is

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201

then used as an example to demonstrate that combinations of ultrasensitive motifs can achieve highly sigmoid responses (QMT model library folder ZHANG). It needs to be noted that although most of the concepts discussed here are mainly in the context of biochemical networks within the cell, they are equally applicable to biological networks at higher organization levels.

9.2 Ultrasensitivity and Hill Function Strictly speaking, ultrasensitivity is defined as a nonlinear steady-state response that a small percentage change in the input results in a larger percentage change in the output. More often, ultrasensitivity is loosely described by a full-range steady-state stimulusresponse that is sigmoid in shape, or significantly steeper than the rectangular, hyperbolic curve represented by the Michaelis–Menten equation. In practice a sigmoid ultrasensitive stimulus-response curve is conveniently approximated or represented by the Hill function (Weiss, 1997): Y = Ymax

Kn

Xn , + Xn

(9.1)

where Y max is the maximum response or activity of Y, K the concentration of X that gives rise to half of the maximum response, and n the Hill coefficient. While K determines the horizontal position of the Y vs X stimulus-response curve, n determines the steepness of the curve, or the degree of ultrasensitivity (Figure 9.1). Notice that when n is equal to one, Equation 9.1 reduces to the Michaelis–Menten form.

1.0

Hill coefficient

0.9

n=

0.8 0.6

Y Y=

0.4

X 0.9 /X 0.1

Xn Kn + X n

0.2 0.1

0

0

X0.1

1

X0.9 2

3

4

5

ln 81 X ln 0.9 X 0.1 n

81

1

9

2

4.33

3

3

4

6

X Figure 9.1 The Hill function is often used to represent an ultrasensitive response, which usually has a globally sigmoid shape. The steepness of the response curve represented by the Hill function is defined by the Hill coefficient, n, which quantitatively describes the relative fold change in the concentration of X that produces from 10 to 90% of the maximum response, with the Michaelis–Menten response as a reference. The black curve has a Hill coefficient of one, and the gray curve has a Hill coefficient of four.

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Functionally, the Hill coefficient (n) of an ultrasensitive response curve can be estimated empirically as follows: n=

ln 81 ln

X 0.9 X 0.1

,

(9.2)

where X 0.9 and X 0.1 are the concentrations of X producing 90% and 10% of the maximum response, respectively. For a Michaelis–Menten type of response where n is one, the fold change in the concentration of X producing from 10 to 90% of the maximum response is 81. Therefore, according to Equation 9.2, the Hill coefficient represents the relative steepness of an ultrasensitive curve with the Michaelis–Menten response as a reference. The higher the value of n, the smaller the fold change in the concentration of X required to go from 10 to 90% of the maximum response, and the steeper the sigmoid curve (Figure 9.1).

9.3 Ultrasensitive Motifs Although the Hill function, initially derived from the study of the cooperative O2 binding of hemoglobin molecules (Hill, 1913), is a convenient way to represent an ultrasensitive response, this empirical form usually falls short in precisely describing ultrasensitive stimulus-response relationships observed in biochemical networks. Many biochemical interactions and processes can form response motifs that transfer signal in an ultrasensitive manner but are not well represented by the Hill function throughout the full range of response. So far a number of ultrasensitive motifs with distinct underlying mechanisms have been identified, including positive cooperative binding, homo-multimerization, multistep signaling, zero-order ultrasensitivity, substrate competition, and positive feedback loop. In the following sections, a detailed description of each of the ultrasensitive motifs is provided. 9.3.1 Positive Cooperative Binding A recurring event in molecular interactions is that a ligand molecule (X) physically binds to a receptor molecule (Y). In some cases, the receptor molecule may have more than one binding site for the ligand molecule. If the initial binding of molecule X facilitates its subsequent binding to the remaining sites on Y, positive cooperative binding occurs. Formally, cooperative binding is defined when the dissociation constant for the initial binding events is larger than that for the subsequent binding events. A familiar example is the cooperative binding between O2 and the hemoglobin molecule (Hill, 1913). A hemoglobin molecule has four subunits, ααββ, each containing one heme site for an O2 molecule to bind. After an O2 molecule occupies one of the subunits, the oxygen-bound subunit can enhance, through allosteric interaction, the affinity of the remaining unoccupied subunits for other O2 molecules. A second oxygen-bound subunit will further increase the affinity of subsequent O2 bindings to the remaining two unoccupied subunits, and so on. This sequentially increased binding affinity between O2 and hemoglobin subunits renders a steep ultrasensitive dose-response curve for the percentage of O2 occupancy of hemoglobin molecules, which can be approximated by the Hill function with an apparent Hill coefficient of 2.8 for human hemoglobin.

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Another context in which cooperative binding may occur is the binding of transcription factors to gene promoters. For many genes, their promoter regions may contain multiple copies of response elements for a particular transcription factor, and these response elements may be spaced in proximity to each other. This spatial arrangement provides a possibility for cooperative binding of transcription factors to these DNA sequences, such that occupancy of one of the response elements may enhance the binding of the transcription factors to the remaining unoccupied response elements. This cooperativity may be mediated by allosteric interactions between adjacent response elements. The promoter of the gene encoding heat shock proteins contains two or more heat shock response elements, and it has been demonstrated both in vitro and in vivo that heat-activated heat shock factor (HSF) can bind to these response elements in a very cooperative fashion to enhance induction of heat shock proteins to recover mis-folded proteins resulting from heat shock (Amin et al., 1994; Erkine et al., 1999). Box 9.1 describes a simple model of positive cooperative binding of promoter by a transcription factor. The overall response is ultrasensitive, depending on the degree of cooperativity.

Box 9.1: Ultrasensitive Motif: Positive Cooperative Binding In this example, a transcription factor (T) binds to a gene promoter (P) containing three identical response elements for T. The gene transcription rate is assumed to be proportional to the percentage occupancy of the promoter binding sites. The following ordinary differential equations (ODEs) and parameters describe the binding process, and the stimulus-response relationship examined here is percentage promoter occupancy vs T. 1

TP

k2 k3 T + TP

k4 T + T 2P

T 2P

k5 k6

%occupancy

k1 T+P

0.8 0.6 0.4 0.2 0

T 3P

0

0.06

0.12

0.18

0.24

0.3

T

d[TP]/dt = k1 ∗ [T] ∗ (Ptot − [TP] − [T2 P] − [T3 P]) − k2 ∗ [TP] − k3 ∗ [T] ∗ [TP] + k4 ∗ [T2 P] d[T2 P]/dt = k3 ∗ [T] ∗ [TP] − k4 ∗ [T2 P] − k5 ∗ [T] ∗ [T2 P] + k6 ∗ [T3 P] d[T3 P]/dt = k5 ∗ [T] ∗ [T2 P] − k6 ∗ [T3 P] %occupancy = ([TP] + 2 ∗ [T2 P] + 3 ∗ [T3 P])/(3 ∗ Ptot ) Ptot = 1, k1 = 1, k2 = 1, k3 = 1, k4 = 0.1, k5 = 1, k6 = 0.01. TP, T2 P, and T3 P are the promoters that are occupied by one, two, and three molecules of T, respectively. Ptot is the total amount of P including free and occupied forms. k1 , k3 , and k5 are second-order association rate constants and k2 , k4 , and k6 are first-order dissociation rate constants. Cooperative binding is indicated by the parameter values

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Ultrasensitive Response Motifs in Biochemical Networks

given above, which indicate that the binding affinity increases by 10-fold for each sequential binding event (i.e., k1 /k2 = 1, k3 /k4 = 10, and k5 /k6 = 100). The steady-state percentage occupancy vs T response curve is sigmoid with an approximate Hill coefficient of 2.5, indicating ultrasensitivity.

9.3.2 Homo-Multimerization Another frequently encountered ultrasensitive motif in biochemical networks is homo-multimerization, including homo-dimerization, homo-trimerization, and homotetramerization, and so on. Homo-multimerization is often seen with the activation of transcription factors and de novo formation of enzymes in gene induction and stress response. For steroid hormone receptors, such as androgen, estrogen, and glucocorticoid receptors, after being bound by their respective hormonal ligands, two receptor monomer will come together to form a homodimer in order to gain access with high affinity to the hormone response elements located in target genes (Wrange, Eriksson, and Perlmann, 1989; Wang et al., 1995; Kuntz and Shapiro, 1997). In the case of heat shock response, the heat shock factor forms a homotrimer as a result of heat stress to induce gene expression of heat shock proteins (Liu and Thiele, 1999). OxyR is a transcription factor mediating the antioxidant response in bacteria and it is believed that OxyR functions as either a tetramer or dimer of dimers (Knapp, Tsai, and Hu, 2009). The active forms of many enzymes responsible for defending against cellular stresses are homo-multimers. A number of antioxidants enzymes involved in oxidative stress response, which function to eliminate and/or scavenge reactive oxygen species, are homodimers or homotetramers in their active form. For instance, glutathione reductase, which recycles GSSG back to reduced glutathione GSH, and cytosolic superoxide dismutase, which converts superoxide anion to hydrogen peroxide, are homodimers (Carlberg and Mannervik, 1975; Lindberg et al., 2004). Glutathione peroxidase and catalase, the two major enzymes responsible for eliminating hydrogen peroxide are homotetramers (Kirkman and Gaetani, 1984; Asayama et al., 1994). Formation of these enzymes through multimerization of protein monomers is believed to play an important ultrasensitive role in the homeostatic gene network that copes with oxidative/electrophilic stress (Zhang and Andersen, 2007). The mathematical rationale for ultrasensitivity generated via homo-multimerization stems from the kinetics that the monomer has to appear twice or more, depending on the order of the multimer, in a multiplicative manner in the equation describing the formation of the multimers (Box 9.2). Ideally homo-dimerization can give rise to a Hill coefficient of 2, homo-trimerization can give rise to a Hill coefficient of 3, and so on.

Box 9.2: Ultrasensitive Motif: Homo-Dimerization In this example, a ligand (L) binds to its cognate receptor (R) and then the liganded receptor monomers (LR) associate with each other to form receptor dimers (LRRL), which are the active transcription factors for inducing the transcription of target genes. The following ODEs and parameters describe the binding processes, and the stimulusresponse relationship examined here is LRRL vs L.

Ultrasensitive Motifs

205

0.25 0.2

k1 k2

LR

LRRL

L+ R

k3 LR + LR

0.15 0.1 0.05

LRRL

k4

0 0

1

2

3

4

5

L

d[LR]/dt = k1 ∗ [L] ∗ (Rtot − [LR] − 2 ∗ [LRRL]) − k2 ∗ [LR] − 2 ∗ k3 ∗ [LR][LR] + 2 ∗ k4 ∗ [LRRL] d[LRRL]/dt = k3 ∗ [LR][LR] − k4 ∗ [LRRL] Rtot = 1, k1 = 1, k2 = 1, k3 = 1, k4 = 1. Rtot is the total amount of receptor including the free, monomeric and dimeric forms. k1 and k3 are second-order association rate constants and k2 and k4 are first-order dissociation rate constants. The above parameter values give rise to a sigmoid steadystate LRRL vs L response with a Hill coefficient of 1.27.

9.3.3

Multistep Signaling

A third ultrasensitive motif that often appears in signal transduction and gene regulatory networks is multistep signaling. The scenario involves a signaling molecule participating in more than one process or step that contribute to the activation of a target molecule, and these processes/steps operate multiplicatively in determining the final steady-state level of the target molecule. A typical example is the non-processive dual phosphorylation of mitogen-activated protein kinase (MAPK). A MAPK molecule contains two phosphorylation sites and both sites have to be phosphorylated by MAPK kinase (MKK) for MAPK to gain full kinase activity. MKK phosphorylates the two sites in two separate collision events instead of one (Ferrell and Bhatt, 1997). The first collision between MKK and MAPK makes one of the two sites phosphorylated, then the single-phosphorylated MAPK dissociates from MKK. A second collision between MKK and the single-phosphorylated MAPK, likely in a different orientation from the first collision, provides the opportunity for the other site to be phosphorylated. Therefore, MKK, viewed as the input signal here, participates (1) in the reaction to provide the substrate (single-phosphorylated MAPK) for second phosphorylation of MAPK and (2) in the subsequent reaction to catalyze the second phosphorylation. Thus, MKK appears twice in a multiplicative manner in the mathematical term describing the production of dual phosphorylated MAPK (Box 9.3), contributing to the ultrasensitive response mediated by the MAPK cascade (Huang and Ferrell, 1996).

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Ultrasensitive Response Motifs in Biochemical Networks

Box 9.3: Ultrasensitive Motif: Multistep Signaling In this example, the MAPK kinase (MKK) participates twice, via two separate collisions with its substrate, in the sequential dual phosphorylation of MAPK. The first results in single-phosphorylated MAPK (MAPKp ) and the second dual-phosphorylated MAPK (MAPKpp ). The following ODEs and parameters describe the phosphorylation and the counterbalancing dephosphorylation processes. And the stimulus-response relationship examined here is MAPKpp versus MKK. For simplicity, only linear kinetics is used, assuming that the total amount of MAPK is far below the Michaelis–Menten constants for MKK. 1

k1 MAPK

k2

k3 MAPK p

k4

MAPKpp

MAPKpp

0.8

MKK

0.6 0.4 0.2 0 0

0.4

0.8

1.2

1.6

2

MKK

d[MAPKp]/dt = k1 ∗ [MKK] ∗ (MAPKtot − [MAPKp ] − [MAPKpp ]) − k2 ∗ [MAPKp ] − k3 ∗ [MKK] ∗ [MAPKp ] + k4 ∗ [MAPKpp ] d[MAPKpp ]/dt = k3 ∗ [MKK] ∗ [MAPKp ] − k4 ∗ [MAPKpp ] MAPKtot = 1, k1 = 1, k2 = 1, k3 = 10, k4 = 1. MAPKtot is the total amount of MAPK including the unphosphorylated, singlephosphorylated, and dual-phosphorylated forms. k1 and k3 are second-order rate constants for phosphorylation, and k2 and k4 are first-order rate constants for dephosphorylation. The above parameter values give rise to a sigmoid steady-state MAPKpp vs MKK response with a Hill coefficient of 1.58.

In response to low O2 concentrations, the hypoxic response gene network is responsible for increasing O2 supply and limiting O2 consumption. Hypoxia inducible factor 1 (HIF-1) is a transcription factor that activates the stress response. Both the abundance and activity of HIF-1 are regulated by O2 (Semenza, 2004). O2 is used as a co-substrate for hydroxylation of certain proline residues of the HIF-1 molecule by prolyl hydroxylase (PHD) (Bruick and McKnight, 2001; Epstein et al., 2001). Hydroxylation of proline residues makes HIF-1 a target of the ubiquitin-protesome system for degradation (Huang et al., 1998; Kallio et al., 1999). Under normoxia, HIF-1 is kept at a low level due to high turnover rate. O2 is also used as a co-substrate for hydroxylation of an asparagine residue on the activational domain of HIF-1. Hydroxylation of asparagine prevents the activational domain from interacting with co-activators such as p300/CBP, thus keeping the transcriptional activity of HIF-1 low (Lando et al., 2002a, b). Under hypoxia, the O2 level drops, leading to a decrease in the degree of hydroxylation of the proline and asparagine residues. This alteration in oxidized product results in (1) stabilization of HIF-1, leading to an increase in the abundance of HIF-1, and (2) an increase in the p300/CBP-recruiting activity of the HIF-1 as a

Ultrasensitive Motifs

207

transcriptional factor. In this way, by acting upon two separate steps (HIF-1 degradation and activity), a drop in O2 is expected to result in an ultrasensitive activation of HIF-1 and potentially its target hypoxic genes (Jiang et al., 1996). 9.3.4

Zero-Order Ultrasensitivity

In addition to being controlled through gene transcription on a relatively slow time scale, proteins are also regulated in their activity through fast post-translational modification. These modifications, often covalent in nature, include phosphorylation, methylation, and sumoylation, and so on. The modifications are reversible processes such that a protein molecule may exist either in the modified or unmodified form. Both the modification and demodification reactions are catalyzed by specific enzymes, which themselves are often regulated by other factors. By controlling the fraction of the protein in the modified form, these enzymes can control the activity of the target protein. The most important and ubiquitous covalent modification cycle is protein phosphorylation and dephosphorylation, which are catalyzed by protein kinase and phosphatase, respectively. Early theoretical work by Goldbeter and Koshland pointed out that if the kinase and/or phosphatase work in a condition where their protein substrates nearly saturates the enzymes, an ultrasensitive response is expected to arise for the fraction of phosphorylated (or unphosphorylated) protein vs the kinase (or phosphatase) (Goldbeter and Koshland, 1981, 1984). Subsequent experimental evidence has confirmed that zeroorder ultrasensitivity occurs with the regulation of many signaling proteins and enzymes, such as regulation of glucose-metabolizing enzymes phosphorylase and isocitrate dehydrogenase (LaPorte and Koshland, 1983; Meinke, Bishop, and Edstrom, 1986), activation of AMP-activated protein kinase in β-cells (Hardie et al., 1999), and activation of MAPK in Xenopus oocytes and other cell types (Huang and Ferrell, 1996; Bagowski et al., 2003). The rationale for zero-order ultrasensitivity is illustrated in Box 9.4 with a generic example of the protein phosphorylation/dephosphorylation cycle. Box 9.4: Ultrasensitive Motif: Zero-Order Ultrasensitivity In this example, protein R is phosphorylated by kinase to become Rp, which is then dephosphorylated by phosphatase. The following ODE and parameters describe the reversible covalent modification cycle, and the stimulus-response relationship examined here is Rp vs kinase. 1

Kinase

0.8

k1, Km1

k2, Km2 Phosphatase

Rp

Rp

R

0.6 0.4 0.2 0 0

0.1

0.2

Kinase

0.3

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Ultrasensitive Response Motifs in Biochemical Networks

d[Rp ]/dt = k1 ∗ [Kinase] ∗ (Rtot − [Rp ])/(Km1 + (Rtot − [Rp ])) −k2 ∗ [Phosphatase] ∗ [Rp ]/(Km2 + [Rp ])) Rtot = 1, k1 = 1, k2 = 1, Km1 = 0.1, Km2 = 0.1, [Phosphatase] = 0.1 Rtot is the total amount of protein R, including the unphosphorylated (R) and phosphorylated (Rp ) forms. k1 and k2 are catalytic rate constants for phosphorylation and dephosphorylation, respectively. Km1 and Km2 are Michaelis–Menten constants for phosphorylation and dephosphorylation, respectively. The amount of phosphatase is fixed, and the amount of kinase is varied here to regulate the rate of phosphorylation. The above parameter values give rise to a very steeply sigmoid steady-state Rp vs kinase response with a Hill coefficient of 3.6 (middle black line). The ultrasensitive response can be understood as follows. If the system is initially at [Kinase] = [Phosphatase] = 0.1, the phosphorylation and dephosphorylation reactions are balanced such that [R] = [Rp ] = 0.5, that is, the system is at the middle point. At these concentrations and given that Km1 = Km2 = 0.1, the kinase and phosphatase are operating very close to saturation (5/6 saturated). Now if [Kinase] is increased by a small percentage, the phosphorylation rate becomes, for the moment, greater than the dephosphorylation rate. As a result, more R is converted to Rp . However, because the phosphatase is already operating near saturation, an increase in Rp will not increase the dephosphorylation rate as much (i.e., the reaction rate is insensitive to changes in the substrate, thus a nearly zero-order reaction) to rebalance the cycled reactions. Likewise, because the kinase is also operating near saturation, a decrease in R of similar magnitude to the percentage increase in [Kinase] will not decrease the phosphorylation rate as much to rebalance the cycled reactions, either. To reach a new steady state, the concentration of R has to drop by a larger percentage (consequently Rp increases by a larger percentage) for the phosphorylation rate finally to match with the dephosphorylation rate. A similar situation but in the opposite direction occurs when [Kinase] is decreased by a small percentage from the middle point. The dramatic changes in [R] and [Rp ] in response to small changes in [Kinase] around the middle point give rise to an ultrasensitive response. How close the two enzymes operate to saturation at the middle point determines how steep the sigmoid ultrasensitive response can be. When Km1 and Km2 are reduced to 0.05, the two enzymes are working closer to saturation, thus the ultrasensitive response becomes steeper (Hill coefficient = 5.3). When Km1 and Km2 are increased to 0.2, the two enzymes are further away from saturation, thus the ultrasensitive response becomes less steep (Hill coefficient = 2.44). If Km1 and Km2 are very large compared to Rtot , ultrasensitivity can disappear altogether and only Michaelis–Menten type of response occurs.

9.3.5 Substrate Competition In cell signaling networks, many signal transduction steps are enzyme mediated. For example, proteins can be phosphorylated by kinases and dephosphorylated by phosphatases to change their activity. An enzyme may have more than one type of substrate or, in certain cases, competitive inhibitors. Competitive inhibitors, when present in substantial amounts, would soak up the free enzyme molecules, making the enzyme unavailable for

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targeted substrate molecules. The presence of a competitive inhibitor would increase the total amount of the enzyme required to achieve the same level of response, thus shifting the stimulus-response curve to the right. In certain cases where the inhibitor has a higher binding affinity for the enzyme than the signaling substrate and the inhibitor exists in an excessive amount, the response could exhibit ultrasensitivity. In Xenopus oocyte, Cdk1 and Wee1 are two protein components that are part of a larger bistable circuit responsible for cell cycle transition from the interphase to mitosis. Cdk1 and Wee1 constitute a double negative feedback loop through reciprocally phosphorylating each other and thus inhibiting each other’s activity (Pomerening, Sontag, and Ferrell, 2003; Sha et al., 2003). Phosphorylation and thus inhibition of Wee1 by Cdk1 is demonstrated to be ultrasensitive in vitro, which is responsible, at least in part, for the bistable behavior of the molecular circuit (Kim and Ferrell, 2007). The ultrasensitive inhibition is shown to arise partially from intermolecular competition, by which some unknown substrates that compete against Wee1 for Cdk1. This competitive inhibition, in combination with some other ultrasensitive mechanisms, produces a sigmoid response with a Hill coefficient of 3.5 in reconstituted Xenopus egg extract (Kim and Ferrell, 2007). The rationale for ultrasensitivity is illustrated in Box 9.5 with a generic example of substrate inhibition.

Box 9.5: Ultrasensitive Motif: Substrate Competition In this example, the substrate protein (S) first associates with the enzyme (E) to form a complex (SE). Within the complex S is converted to product P by E and, finally, P dissociates from E. P is then converted back to S by another enzyme not explicitly counted here. The competitive inhibitor (I) can also bind to E forming a non-productive complex IE, thus making less E available for S. The following ODEs and parameters describe the competitive process, and the stimulus-response relationship examined here is P vs total amount of E in the system. k1 k2

+ I

k5

SE

0.4

E+ P

k4

0.3

P

S+ E

0.5

k3

0.2

k6

S

0.1 0

IE

0

6

12

18

24

30

Etot

d[SE]/dt = k1 ∗ (Etot − [SE] − [IE]) ∗ (Stot − [SE] − [P]) − k2 ∗ [SE] − k3 ∗ [SE] d[P]/dt = k3 ∗ [SE] − k4 ∗ [P] d[IE]/dt = k5 ∗ (Itot − [IE]) ∗ (Etot − [SE] − [IE]) − k6 ∗ [IE] Stot = 1, Itot = 10, k1 = 1, k2 = 1, k3 = 1, k4 = 1, k5 = 10, k6 = 1. Stot is the total amount of the substrate including free S, those in the SE complex, and the product P. Etot is the total amount of the enzyme including free E, those in the SE

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Ultrasensitive Response Motifs in Biochemical Networks

complex, and those in the IE complex. Itot is the total amount of the competitive inhibitor including free I and that in the IE complex. k1 and k5 are second-order association rate constants and k2 and k6 are first-order dissociation rate constants. k3 is first-order catalytic rate constant. The above parameter values give rise to a sigmoid steady-state P vs Etot response with a Hill coefficient of 3.39. The ultrasensitive response can be understood as follows. Since the binding affinity between the inhibitor I and enzyme E (k5 /k6 = 10) is far greater than that between the substrate S and E (k1 /k2 = 1), most molecules of E are soaked up by I when Etot is much less than Itot (10 in this example). Therefore, there is only a very small amount of E available for the reaction that converts S to P and the concentration of P is low, which only increases linearly with Etot . As Etot in the system increases to approach Itot , most molecules of I will be gradually used up by E. With few free I molecules around, the additionally increased E molecules will be more used for converting S to P than being titrated away by I. This would result in an ultrasensitive increase in free E and a similar ultrasensitive increase in the concentration of P when Etot is in the vicinity of Itot . This ultrasensitive mechanism indicates that the higher the affinity between I and E and/or the larger the total amount of I (i.e., Itot ), the more ultrasensitive the response would be, and Itot also determines the concentration range of Etot in which ultrasensitivity occurs.

Ultrasensitivity by a similar mechanism also occurs when a signaling molecule A has to partner with another molecule B to form an active complex AB and, in the mean time, A can also form, with a third molecule C, an inactive complex AC. This scenario, called molecular titration (Salazar and Hofer, 2006; Buchler and Louis, 2008), produces ultrasensitivity under similar conditions to substrate competition. Ultrasensitive response occurs for the complex AB vs total amount of A in the system. In the cell, molecular titration occurs when a transcription factor has to form a dimer with a nuclear factor to become transcriptionally active, while the transcription factor may also form a transcriptionally inactive dimer with another repressive nuclear factor.

9.3.6 Positive Feedback An important signaling/network motif in biological systems is positive feedback. With a positive feedback, a signaling molecular species can enhance its own abundance or activity either directly or indirectly through intermediate molecular species along the feedback loop. A positive feedback could be either in the form of double positive feedback, where two molecular species reciprocally activate each other, or in the form of double negative feedback, where two molecular species reciprocally inhibit each other. While positive feedback loops have the potential to exhibit bistable behaviors, when the feedback strength is mild (i.e., no ultrasensitivity within either of the two arms of the feedback loop), the feedback loop as a whole could function as an ultrasensitive motif. In Box 9.6, an example of receptor autoregulation is given to illustrate the origin of ultrasensitivity.

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211

Box 9.6: Ultrasensitive Motif: Positive Feedback In this example, ligand L binds to receptor R to form a transcriptionally active complex LR. LR can increase the transcription of R itself, forming a positive auto-regulatory loop. The following ODEs and parameters describe the positive feedback loop, and the stimulus-response relationship examined here is LR vs L. 40

L+ R

k1

LR

k3

30

LR

k2 k4, Kd R

k5

20 10 0 0

5

10

15

20

L

d[LR]/dt = k1 ∗ [L] ∗ [R] − k2 ∗ [LR] − k3 ∗ [LR] d[R]/dt = −k1 ∗ [L] ∗ [R] + k2 ∗ [LR] + k0 + k4 ∗ [LR]/(Kd + [LR]) − k5 ∗ [R] k0 = 0.5, k1 = 1, k2 = 1, k3 = 1, k4 = 60, k5 = 1, K d = 20. k0 is the basal production rate of R. k1 is the second-order association rate constant and k2 the first-order dissociation rate constant for the L and R interaction. k3 and k5 are the first-order degradation rate constants for LR and R, respectively. k4 is the LR-induced production rate constant for R and Kd is the dissociation constant for LR binding to the gene promoter. The above parameter values give rise to a sigmoid steady-state LR vs L response with a Hill coefficient of 1.43. Positive feedback loops seem to be a recurring ultrasensitive motif in signaling transduction and gene regulatory networks. An example is positive gene autoregulation where the protein product of a gene is a transcription factor that can upregulate its own transcription. This type of motif appears quite common in developmental and differentiation gene networks. For instance, the three key genes OCT4, SOX2, and NANOG responsible for maintaining embryonic stem cell identity can all upregulate their own transcription through auto-regulatory loops (Chickarmane et al., 2006). Transcription factor autoregulation is also a common theme in stress response pathways where anti-stress genes are induced by stress-activated transcription factors. In oxidative stress response, Nrf2 is the primary transcription factor that induces antioxidant genes. To do this Nrf2 has to partner with small Maf proteins to form a heterodimer to become transcriptionally active. Both Nrf2 and MafG contain antioxidant response elements in their promoters that can be occupied by the Nrf2-MafG dimer and these two genes are upregulated under oxidative stress (Kwak et al., 2002; Pi et al., 2003; Katsuoka et al., 2005). Ultrasensitivity arising from such autoregulations is likely to contribute to enhanced antioxidant gene expression and robust redox homeostasis (Zhang and Andersen, 2007).

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Ultrasensitive Response Motifs in Biochemical Networks

9.4 Combination of Motifs The above section describes six ultrasensitive motifs that are frequently observed in signal transduction and gene networks. Each of the motifs is capable of outputting a sigmoid response with respect to the input signal by a distinct mechanism. Although a single ultrasensitive motif has the potential to generate steeply sigmoid curves, such high degree ultrasensitivity requires parameter conditions that may be constrained by the biochemistry of the molecules comprising the motif. For instance, to achieve a sigmoid curve with a high Hill coefficient through cooperative binding, it requires not only multiple binding sites on the receptor molecules but also highly allosteric interactions between these sites. For substrate competition-mediated ultrasensitivity, the inhibitor has to be in large abundance and have a high affinity for the enzyme to achieve high degree ultrasensitivity. These requirements would pose structural and chemical challenges to the underlying molecules, which may not be readily met in cells. Also, relying on a single motif for high degree ultrasensitivity is vulnerable to gene mutations, which may change the structure and abundance of the protein molecules comprising the motif, leading to loss of ultrasensitive function. Therefore, it is quite unusual that high degree ultrasensitivity is achieved through a single ultrasensitive motif. More often, multiple ultrasensitive motifs are combined to generate highly ultrasensitive responses. A classical example of multiplicity of ultrasensitive motifs occurs with the MAPK signaling cascade. MAPK and its upstream kinases constitute a highly conserved signaling cascade across eukaryotic species. The cascade is activated in response to a variety of extracellular signals and stressors and mediates a host of cellular responses including proliferation, differentiation, apoptosis, survival, mating behavior, stress response, and so on (Yang, Sharrocks, and Whitmarsh, 2003). In its generic form, the MAPK cascade is composed of three layers of kinases that sequentially phosphorylate and therefore activate downstream counterparts – MAPK kinase kinase (MKKK) phosphorylates MAPK kinase (MKK) and MKK phosphorylates MAPK. The seminal work by Ferrell Jr. and his colleagues demonstrated that the MAPK cascade is a network module that transfers signal in an ultrasensitive manner and their work also shed light on the molecular mechanisms underpinning the ultrasensitivity (Huang and Ferrell, 1996). Ultrasensitivity in the MAPK cascade originates from three independent sources: (1) multistep signaling, (2) zero-order ultrasensitivity, and (3) layered arrangement of the participant proteins. MKK at the second layer and MAPK at the third layer of the cascade each contain two of either serine, threonine, or tyrosine sites for phosphorylation by their upstream kinases. And, only when both of the two sites are phosphorylated do the kinases gain full enzymatic activity. Phosphorylation of the two sites occurs in a nonprocessive way involving two separate collisions between the upstream enzymes and their downstream substrates. As indicated in an earlier section of this chapter (Section 9.3.3), this dual phosphorylation mechanism for MKK and MAPK activation provides a basis for multistep signaling and, thus, some degree of ultrasensitivity. Secondly, kinases in the cascade are phosphorylated by their upstream kinases and dephosphorylated by specific phosphatases, constituting a covalent modification cycle. As suggested by Ferrell Jr. et al., some kinases in the cascade may work under conditions that are close to saturation, providing the possibility for zero-order ultrasensitivity. Thus, multistep signaling and covalent modification cycle together afford certain degrees of ultrasensitivity to the second and third

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213

layers of the MAPK cascade. The third source of ultrasensitivity lies in the fact that the MAPK cascade is a layered signaling structure, such that the output of one layer is fed as an input into the next layer. Provided that the output of one layer is appropriately aligned with the input range of the next layer, the overall response of the MAPK cascade as a whole would be highly sigmoidal, as the signal is propagated through individual ultrasensitive layers. This multiplicative effect is equivalent to having several amplifiers connected in tandem and the overall gain is the product of the gain of each individual amplifier. Experimental measurement with Xenopus oocyte extract and other cell types has shown that the ultrasensitive response mediated by the MAPK cascade can have a Hill coefficient as high as 10 (Bagowski et al., 2003). Box 9.7 illustrates a MAPK cascade model.

Box 9.7: MAPK Cascade At the top layer of the cascade, an input signal S activates the MAPK kinase kinase (MKKK) to become MKKKa . MKKKa then phosphorylates the MAPK kinase (MKK) at the second layer into single-phosphorylated MKKp and dual-phosphorylated MKKpp . MKKpp is an active kinase that can phosphorylate the MAPK at the third layer into single-phosphorylated MAPKp and dual-phosphorylated MAPKpp . The following ODEs and parameters describe the reactions in the cascade.

MKKKa

S MKKK

S

MKKKa MKKpp

MKK

MKKp

MKKpp S

MAPK

MAPKp

MAPKpp

MAPKpp S

d[MKKKa ]/dt = k1 ∗ S ∗ (MKKKtot − [MKKKa ])/(Km1 + (MKKKtot − [MKKKa ])) − k2 ∗ [MKKKa ]/(Km2 + [MKKKa ]) d[MKKp ]/dt = k3 ∗ [MKKKa ] ∗ (MKKtot − [MKKp ] − [MKKpp ])/ (Km3 + (MKKtot − [MKKp ] − [MKKpp ])) + k6 ∗ [MKKpp ]/(Km6 + [MKKpp ]) − k4 ∗ [MKKKa ] ∗ [MKKp ]/ (Km4 + [MKKp ]) − k5 ∗ [MKKp ]/(Km5 + [MKKp ]) d[MKKpp ]/dt = k4 ∗ [MKKKa ] ∗ [MKKp ]/(Km4 + [MKKp ]) − k6 ∗ [MKKpp ]/ (Km6 + [MKKpp ])

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Ultrasensitive Response Motifs in Biochemical Networks

d[MAPKp ]/dt = k7 ∗ [MKKpp ] ∗ (MAPKtot − [MAPKp ] − [MAPKpp ])/(Km7 + (MAPKtot − [MAPKp ] − [MAPKpp ])) + k10 ∗ [MAPKpp ]/(Km10 + [MAPKpp ]) − k8 ∗ [MKKpp ] ∗ [MAPKp ]/(Km8 + [MAPKp ]) −k9 ∗ [MAPKp ]/(Km9 + [MAPKp ]) d[MAPKpp ]/dt = k8 ∗ [MKKpp ] ∗ [MAPKp ]/(Km8 + [MAPKp ]) − k10 ∗ [MAPKpp ]/(Km10 + [MAPKpp ]) MKKKtot = 500, MKKtot = 1200, MAPKtot = 300, k1 = 0.06, k2 = 5, k3 = 0.064, k4 = 0.064, k5 = 5, k6 = 5, k7 = 0.06, k8 = 0.06, k9 = 5, k10 = 5, Km1 = 1000, Km2 = 1000, Km3 = 1200, Km4 = 1200, Km5 = 1200, Km6 = 1200, Km7 = 300, Km8 = 300, Km9 = 300, Km10 = 300. MKKKtot is the total amount of MKKK including the inactive (MKKK) and active (MKKKa ) form. MKKtot is the total amount of MKK including unphosphorylated (MKK), single-phosphorylated (MKKp ), and dual-phosphorylated (MKKpp ) form. MAPKtot is the total amount of MAPK including unphosphorylated (MAPK), singlephosphorylated (MAPKp ), and dual-phosphorylated (MAPKpp ) form. k1 , k3 , k4 , k7 , and k8 are activation or phosphorylation rate constants. k2 , k5 , k6 , k9 , and k10 are deactivation or dephosphorylation rate constants. Km1 , Km3 , Km4 , Km7 , and Km8 are Michaelis–Menten constants for activation or phosphorylation. Km2 , Km5 , Km6 , Km9 , and Km10 are Michaelis–Menten constants for deactivation or dephosphorylation. The above parameter values give rise to increasingly sigmoid steady-state responses down through each layer of the cascade. The MKKKa vs S response at the first layer has a Hill coefficient of 1.17, the MKKpp vs S response at the second layer has a Hill coefficient of 1.82, and the MAPKpp vs S response at the third layer has a Hill coefficient of 3.29. The conserved structure of the MAPK cascade across species suggests that a conserved function of the cascade is to act as an ultrasensitive motif in the cellular signaling network. The ultrasensitive role has been demonstrated in Xenopus oocyte in which the MAPK cascade is situated in a positive feedback loop that is responsible for the bistable switching to oocyte maturation in response to progesterone (Ferrell and Machleder, 1998; Xiong and Ferrell, 2003). In fibroblasts the MAPK cascade is responsible for an ultrasensitive and sustained response to platelet-derived growth factor (Bhalla, Ram, and Iyengar, 2002).

9.5

Conclusion

In the current post-genomic era, research focus in biology is steadily shifting from characterizing the structure and function of one gene and one protein to understanding the systems-level behavior of biochemical networks comprising those genes and proteins. This transition requires a bottom-up engineering approach by which small response motifs and subnetworks have to be first identified and their functions understood before they are assembled to form larger protein and gene networks that are responsible for

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more advanced cellular functions. Ultrasensitive response motifs, which typically have a sigmoid input/output relationship, appear frequently in biochemical networks. The list of ultrasensitive motifs, as enumerated throughout this chapter, is likely to expand in the future. Ultrasensitive response arises through a variety of kinetic mechanisms, and a highly ultrasensitive response is usually achieved through combination of single ultrasensitive motifs. The crucial importance of ultrasensitivity is demonstrated by its essentiality to network behaviors such as bistability, homeostasis, and oscillation. Understanding ultrasensitive response and these network properties are instrumental for predicting dose response patterns exhibited by toxic chemicals. As the intracellular biochemical networks are being quickly mapped out using high-throughput and high-content technologies, it is imperative to educate biologists regarding the quantitative aspect of cell signaling, which certainly provides a new perspective to the investigation of existing research questions. Such education would equip biologists with a more discerning eye to “lift up” ultrasensitive and other signaling motifs from their familiar biochemical pathways and networks, and ultimately expedite their understanding of the functions of the networks and associated cellular behaviors.

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10 Gene and Protein Expression – Modeling Nested Motifs in Cellular and Tissue Response Networks Melvin E. Andersen, Qiang Zhang and Sudin Bhattacharya The Hamner Institutes for Health Sciences, USA

10.1 Introduction 10.1.1

Transcriptional Responses of Cells and Tissues to Chemical Exposures

In the early 1990s, there were significant discussions about whether there should be different default procedures for risk assessment for carcinogens that were directly reactive with DNA and protein, such as vinyl chloride, and those such as dioxin, which first bind to a receptor to initiate changes in expression of various gene transcripts and proteins. One of the key areas of discussion, then and extending through to the present day, was the nature of the incidence-dose curve in regions of low incidence for receptor-mediated processes (Andersen et al., 2005). Is the dose response curve at low doses expected to be linear or nonlinear? With dioxin, several groups developed quantitative models for its pharmacokinetics and for the induction of genes and proteins (Chapter 7). These models focused on induction of individual genes. If models of induction of multiple genes had been pursued, they would have required competition among various promoters for the dioxin-AhR (aryl hydrocarbon receptor) complex, since promoter sites on individual genes are distributed through the mammalian genome. With dioxin, however, there is a coordinated program of expression of a broad suite of genes in the liver after dosing. How can we model coordinated,

Quantitative Modeling in Toxicology
C 2010 John Wiley & Sons, Ltd

Edited by Kannan Krishnan and Melvin E. Andersen

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dose- and time-dependent induction of groups of genes and proteins, and for which endpoints should we be developing these models? Over the past decade, the line between receptor-mediated and non-receptor-mediated toxicity has blurred considerably. While initial interactions of reactive compounds may not be primarily through receptors, increasing levels of various types of cellular damage activate homeostatic mechanisms, such as anti-oxidant response, endoplasmic reticulum stress responses and DNA-damage response. All of these negative feedback networks are driven by receptor-mediated processes coordinating patterns of gene expression through transcriptional networks (TNs). As dose increases, the system may undergo a further transition from the adaptive stress response to inflammation and apoptosis (Nel et al., 2006). Zhang and Andersen (Zhang and Andersen, 2007) have examined design characteristics of stress response networks and noted that their function requires significant ultrasensitivity within the negative feedback loops (Chapter 9). It may well be that many of the so-called receptor-mediated processes involved in induction of metabolic enzymes in the liver, as with dioxin and the AhR, are components of multi-organ, negative feedback loops that are designed to regulate the levels of biologically active endogenous ligands throughout the body (Nebert, 1994). Global gene induction studies following treatment with ligands that activate key nuclear receptors produce complex patterns of gene expression (N’Jai et al., 2008). Over time, groups of regulated genes show a variety of correlated patterns of behavior (see Figure 10.1 for example). Landers and Spelsberg (1992) suggested that the tissue changes after estrogen administration could be conceptualized as a cascade with primary, secondary and tertiary levels of gene expression. This cascade model for steroid hormone action has been discussed and elaborated over the past two decades; little progress, however, has been made in providing quantitative modeling tools to evaluate the dose-response characteristics of these TNs or in providing experimental strategies to examine the time course of key transcription factors (TFs) during the progress of information through these networks. Steady improvements in modeling cell signaling pathways (Alon, 2006; Alon, 2007) and in high throughput biology (Bromberg et al., 2008) now provide a timely opportunity to develop strategies to map and model receptor-mediated responses. These new approaches also make it possible to interrogate the biological basis of dose response for receptormediated processes controlling gene expression and protein synthesis. In this chapter the focus is on modeling feedback and feedforward processes that determine the structure and function of networks activated by key transcriptional factors.

10.1.2

Transcriptional Networks (TNs)

Electronic circuits consist of various components – resistors, transistors, capacitors, diodes, rheostat, and so on. These parts become organized into a wide array of circuits with broad functions. Similarly, TNs describe interactions between TFs, such as the AhR and estrogen receptor, and the gene transcripts and the proteins that they regulate. Many TFs bind to either endogenous or exogenous small molecules to change the rate of mRNA production for specific genes, allowing cells to make new proteins and achieve new functions. These TNs have a small set of recurring components, called motifs. These occur much more often

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Figure 10.1 Representative gene expression patterns after treating immature mice with a sufficient dose of estrogen to elicit an uterotrophic response. A large number of genes were altered in a variety of directions by a process that starts with interactions of estrogen with the estrogen receptor targeting estrogen responsive promoters on specific genes. Numbers of genes with similar time courses are shown in parentheses. Data redrawn from from Kwekel et al. (2005). Compared to the large number of genes altered, only a small percentage has estrogen response elements in their promoter regions. Networks pass information from primary genes (those directly affected by the signal) through secondary and tertiary portions of this cascade controlling this coordinated response of the tissue. This chapter discusses how to describe and model networks of this kind both for reversible tissue responses, such as this estrogenic response of the uterus, and for unidirectional responses, such as cell differentiation.

than would be expected in random networks. Common motifs and components of biological signaling networks, for example feedback and feedforward loops, are found in all living organisms. These motifs, whether in electronic or biological networks, can also be described by quantitative models. Our goal here is to describe a network in which a small molecule binds a key TF, such as estrogen binding to the estrogen receptor (ER), leading to activation of a TN with a cascade of downstream gene expression. Firstly, the function of a positive feedback motif that can serve as a switch is described; then the dynamics of the motif for various starting conditions are examined. While the example traces the dependence f of the motif on the two interacting proteins, X and Y, it could include activation by

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exogenous compounds that cause the system to switch from one transcriptional state to another. 10.1.3

All-or-None Responses

All-or-none patterns of response, with genes in cells either fully induced or remaining in a basal condition are not at all uncommon (Louis and Becskei, 2002). These dichotomous patterns of cellular response are generated by a combination of ultrasensitivity and positive feedback (Chapters 8 and 9), implemented by either double-positive or double-negative feedback motifs in the TN architecture. This combination can be achieved through a variety of cell signaling mechanisms, including receptor auto-induction (Andersen and Barton, 1999) and mitogen-activated protein kinase (MAPK) cascades (Ferrell, 1996; Ferrell, 1997). All-or-none in the context of dose response means that the shift from a basal level of induction to a fully-induced state in individual cells occurs over a narrow range of input. Sharp transitions from one transcriptional state to another can also be recapitulated using Hill-type equations with large values of n, the Hill coefficient, for the dependence of gene expression rate on dose (or concentration). For example, the models used to describe regional induction of cytochrome P450 1A1 (Andersen et al., 1997) had n = 5 within separate anatomical regions of the acinus to describe the immunohistochemical distribution of induced proteins within the liver. In this case, the high n value was more a convenience than a depiction of specific biological processes.

10.2 10.2.1

Modeling Motifs and Transcriptional Networks Making a Transcriptional Switch with Positive Feedback through Two Transcriptional Factors

In the examples that follow, the model equations do not include separate steps for transcription (synthesis of mRNA from DNA) and translation (synthesis of protein from the cognate mRNA). They are simplified representations where transcriptional factors interact to enhance production of protein. The enhanced synthesis terms lump together transcriptional processes and protein synthesis. A common motif, especially in differentiation of cells from one to another phenotype is double-negative feedback. Two equations depict this motif: d/dt(X ) = B x + fold yx ∗ (K d yxˆn/(K d yxˆn + Y ˆn)) − deg x ∗ X d/dt(Y ) = B y + fold x y ∗ (K d x yˆn/(K d x yn + X ˆn)) − deg y ∗ Y

(10.1) (10.2)

Here, X and Y represent TFs. Each has a basal rate of production (B x and B y) and firstorder degradation (deg x and deg y). The rate of synthesis in each case is diminished in the presence of increasing concentrations of the other TFs. For both X and Y, the interaction is described with a Hill coefficient (n), capturing ultrasensitivity in the response (Chapter 9). Interaction occurs through inhibitory binding of X with the promoter for the opposite gene, that is, Y, with an inhibitory constant Kd xy, and vice versa. The terms expressing the effect of X on Y, or Y on X, in these equations is inhibitory since (Yˆn) or (Xˆn)

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Figure 10.2 Nullclines (thick solid lines) for (a) double-negative and (b) double-positive feedback loop motifs. In each of these cases, both the nullclines are sigmoidal with three intersection points, that is, three steady states, of which two are stable and one is unstable (Chapter 8). A separatrix (thick dashed line) would run through the unstable steady state in both.

appears in the denominator. These terms take values from one to zero as the concentration of the gene product increases. A double-positive feedback loop can be generated from the same equations by replacing the terms (Kd yxˆn) and (Kd xyˆn) in the numerator with the respective concentration terms, Yˆn and Xˆn. For the double-negative feedback simulations (Figure 10.2a), n = 4; fold xy and fold yx = 2; deg x and deg y = 1.0; B x and B y = 0.2; the inhibitory constants differed for the two hypothetical compounds, Kd xy = 0.5 and

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Figure 10.3 Nullclines in a system with only a single steady state. These two nullclines intersect at a single point. While both X and Y are controlled by mutual inhibition (doublenegative feedback) the concentration at which the curves show half-maximal inhibition are very different – Kd xy = 2.0; Kd yx = 0.7. Despite the fact that there is positive feedback through a double-negative feedback motif, the system is not bistable.

Kd yx = 0.7. The nullclines (Chapter 8) for the two cases are easily interpreted: for doublenegative feedback, the graphs have high levels of one factor and low levels of the other at the two stable steady states. For double-positive feedback, the steady states have either high or low levels for each of the interacting factors (Figure 10.2b). The inhibitory or activating binding constants and, importantly, the Hill coefficients, determine whether the two nullclines have multiple intersecting points, indicating bistability. To a large extent, the inhibitory affinity constants in this example allow tuning of the interactions in order to bring the nullclines into position for bistability. The two inhibitory constants need to be relatively similar to generate bistability. When the reciprocal inhibitory constants differ (Figure 10.3) the positive feedback is still intact; the system demonstrates ultrasensitivity, but there is only a single steady state (at the intersection of the nullclines) and no bistable behavior. Positive feedback is thus necessary but not sufficient for bistability to occur. The bistability in the double-negative feedback loop motif can be visually represented by a “bifurcation diagram” (Figure 10.4), which shows the steady states of the system plotted against a parameter, for example Kd xy (Chapter 8). Also, Strogatz (2000) in his highly regarded textbook, “Nonlinear Dynamics and Chaos with Applications to Physics,

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Figure 10.4 Bifurcation diagram showing bistability of the double-negative feedback loop motif. The solid lines correspond to stable steady states, and the dashed line corresponds to unstable steady states that are theoretically predicted but can never be attained in practice. The arrows indicate the behavior of the system as the value of the parameter Kd xy is changed (Chapter 8).

Biology, Chemistry, and Engineering,” has provided a useful graphical depiction of bistable behavior with respect to two system parameters. The three-dimensional representation of the so-called cusp catastrophe surface depicts the bifurcation curve across a range of values of the two parameters, for instance the inhibitory binding constant and the basal rate of production B x (Figure 10.5). This figure plots steady states of X versus Kd xy increasing from left to right and B x increasing from front to back. At an appropriate set of parameter values, the system becomes bistable, generating the fold in the surface. The arrow in Figure 10.5a shows the discontinuity as the inhibitory binding constant Kd xy is increased and the x-variable falls abruptly. As the basal rate of production B x is also increased; moving further backward (away from the reader) in this schematic, the single sigmoidal (ultrasensitive) behavior would reappear with loss of the surface fold (i.e., bistability). Similar surfaces can be generated with respect to other parameter pairs. When modeling TNs requires close matching of feedback processes, the mutual inhibitory or activating constants, regardless of the biological underpinnings of the interactions, will have to be tuned to provide similar strengths of interaction (i.e., similar effective affinity constants). After activation of the primary TF, information must now course through the TN in a series of coordinated waves of transcription. While this example shows the bistability with double negative feedback, there was no provision for input of exogenous compound. If the basal state were as shown in Figure 10.2a – high-Y, low-X – and an activator of X were added, it could generate a switch between the two steady-state conditions. Equation 10.3 depicts a situation where treatment with a

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Figure 10.5 Two views of the Cusp Catastrophe Surface for the double-negative feedback loop motif: a representation of a potentially bistable system with steady states plotted against two system parameters, Kd xy and B x. (a) The arrow indicates the discontinuity in the system as Kd xy is increased at constant B x. (b) The area within the wedge on the projected plane indicates the set of values of Kd xy and B x for which the system is bistable.

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Figure 10.6 Feed Forward Loops: Two general types of FFLs can be generated from combinations of two interacting factors, X and Y, controlling Z. For the coherent FFLs, the two arms of the loop have similar effect on expression of Z – either both positive or both negative. Remember that negative x negative relationships are equivalent to a positive in the FFL. In incoherent FFLs, the two arms of the loop have different signs. In the four coherent examples, the arms are, respectively, +/+, −/−, −/−, and +/+. For the four incoherent loops, the arms are, respectively, +/−, −/+, −/+, and +/−. Nomenclature based on Alon (2007).

regulatory xenobiotic, Xeno, could serve to incorporate switch-like behavior. d/dt(X ) = B x + fold yx ∗ ((K d yxˆn/(K d yxˆn + Y ˆn) + (Xenoˆn/(Xenoˆn + K d xenoxˆn)) − deg x ∗ X

(10.3)

The switch behavior could also be driven by coordinate activation of X and repression of Y. 10.2.2

(Feed Forward Loop) (FFL) Motifs

Alon (2007) has delineated representative FFLs, a motif that appears widely in transcriptional networks in various organisms. These motifs consist of three gene components: a regulator, X, which controls expression of gene Y, and Z, whose expression is regulated by both X and Y. Because each of these regulatory interactions in FFLs can be either activation or repression, there are eight possible FFLs (Figure 10.6). Coherent FFLs have similar signs of both arms of the processes affecting transcription; incoherent loops have different signs

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for the two arms. FFL motifs provide specific functional capabilities. The coherent FFLs filter out transient, signals since the output requires contributions from both signaling arms and the longer arm introduces a delay to the input signal, making action of both arms by the transient signal at the same time unlikely. Incoherent FFLs (type I) accelerate approach of the output product to a maximum concentration and generate pulses of gene expression. 10.2.3

Organizing Motifs into a Transcriptional Network (TN)

In organism development transcriptional information is often passed on, after activation by key TFs, through consecutive waves of gene expression, both within individual cells, and is also passed between cells to create the diverse phenotypes of differentiated cells in the fully formed organism. While these networks are common during development, signaling in mature cells can also be associated with activation of TNs, including waves of gene and protein expression, leading to altered cell and tissue phenotype. Many of the responses in these TNs are reversible with removal of the initiating stimulus – for example, estrogen in the uterus or dioxin and phenobaribital in the liver. While TNs are sometimes referred to as development networks, the broader terminology, “transcriptional networks,” covers both irreversible movement of information through the TN and reversible activation and relaxation of the TN with varying levels of stimulus. The second example for the chapter has multiple motifs organized to create a three-tiered TN (Figure 10.7) that has seven equations providing time course information for seven TFs. d/dt(Y 1) = B y1 + beta y1∗ (X ˆn/(K x y1ˆn + X ˆn)) − alpha y1∗ Y 1 d/dt(Y 2) = B y2 + beta y2∗ (X ˆn/(K x y2ˆn + X ˆn))∗ (Y 1ˆn/(K y1y2ˆn + Y 1ˆn)) −alpha y2∗ Y 2 d/dt(Y 3) = B y3 + beta y3∗ (Y 2ˆn/(K y2y3ˆn + Y 2ˆn)) − alpha y3∗ Y 3 d/dt(Y 4) = B y4 + beta y4∗ (Y 3ˆn/(K y3y4ˆn + Y 3ˆn)) − alpha y4∗ Y 4 d/dt(Z 1) = B z1 + beta z1∗ (X ˆn/(K x z1ˆn + X ˆn))∗ (1/(1 + (Y 1/K y1z1)ˆn)) −alpha z1∗ Z 1 d/dt(Z 2) = B z2 + beta z2∗ (Y 2ˆn/(K y2z2ˆn + Y 2ˆn))∗ (1/(1 + (Y 3/K y3z2)ˆn)) −alpha z2∗ Z 2 d/dt(Z 3) = B z3 + beta z3∗ (Y 3ˆn/(K y3z3ˆn + Y 3ˆn))∗ (1/(1 + (Y 4/K y4z3)ˆn)) −alpha z3∗ Z 3 Once again the Y and Z terms represent TFs and the equations lump transcription and translation. The Z-factors are all controlled by incoherent FFLs, creating transient TF pulses. Y2 is controlled by a coherent FFL. Each TF has a basal rate of production (B i) and first-order rate constant for degradation (alpha i). The third term in each (beta i) is the maximal induction rate. For the transcription factors Y1, Y3 and Y4 these terms simply have a Hill form controlled by the concentration of the immediate upstream TF. With Y2, the coherent FFL, the inducible synthesis term is controlled by two TFs with Hill forms that have values from zero to one as the concentrations of X and Y1 increase. With Z1, Z2 and Z3, the incoherent FFLs, the inducible synthesis terms are controlled by two TFs, each of them displaying ultrasensitivity in binding. One term varies from zero to one as concentration of the TF increases (e.g., the activating effect of X on transcription of Z1).

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Figure 10.7 A Schematic of a TN consisting of several parallel and serial feed forward loops. Boxes marked iFFL are incoherent FFLs in which the product of the multiple inputs first increases and then decreases as the inhibitory input becomes significant in controlling the transcripts and regulated proteins. Y2 is the product of a coherent FFL (marked as cFFL). Y1, Y3 and Y4 are simply regulated by the upstream transcriptional factor. The input noted, at the top of the figure, is representative of small molecule transcriptional regulators interacting with TFs, such as estrogen with the estrogen receptor, clofibrate with PPAR-a, or dioxin with AhR, and so on.

The other varies from one to zero with increasing TF activation (e.g., the repressive effect of Y1 on Z1). The overall behavior of this TN (Figure 10.8) is shown for a simulation where the stimulus is added at one hour and maintained throughout the simulation (t dur >tstop). With fully activating levels of the stimulus (above 2.0), four TFs (the Y factors) increase to a plateau and three (the Z factors) are transiently increased during the waves of gene and protein expression. In a cascade, these individual TFs could themselves regulate large numbers of gene products and give rise to coordinated changes in large numbers of genes, even though only a small number have promoter binding elements for the initiating TF (ER, AhR, etc.). Even in this simplified network, simulations illustrate dose-response challenges with receptor-mediated TF networks. A maximally inducing stimulus (∼ 2.0) creates the steady state levels of Y1 through Y4 and pulses of all the Z-TFs. At lower stimuli, there is partial activation of the pathway, but it is not a proportionate level of signaling throughout the TN as input is reduced. At input = 0.2, there is a pulse of Y1 that increases to an intermediate

Figure 10.8 Time and dose dependence of induction of “transcription factors” in the TN (Figure 10.7) during an exposure to a constant level of stimulus, X (t dur > tstop). From top to bottom the inputs are 2.0, 0.8, 0.6, 0.4, and 0.2. The behavior shows complex dose- and time-dependent patterns of gene/protein expression expected with the TN from Figure 10.7. Top panel left shows Y1, Y2, Y3, and Y4, respectively from left to right. The right panel shows pulses of Z1, Z2 and Z3, respectively from left to right in the figure.

Discussion

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level; Y2 does not increase substantially and the Z1 pulse is at a reduced level. Other TFs are not induced appreciably. At input = 0.4, the primary TF product Y1 is nearly maximally induced, the TF controlled by the coherent FFL Y2 is only partially induced and Z2 is partially induced as well, but its synthesis never shuts off, that is, the incoherent FFL input does not reach sufficient intensity to reduce expression of Z2 to near zero and create the pulse behavior. A variety of response patterns are observed as the stimulus increases. With TNs the dose-response behaviors are expected to show complex time- and dosedependencies of the groups of TFs and TF-controlled genes. Even this relatively simple TN model provides an opportunity to alter exposure patterns and assess expected differences in TN activation for a variety of exposures.

10.2.4

Exercises for the TN Model

This hypothetical TN is reversible upon withdrawal of the input signal X. When the input is removed, all the expressed gene products decay with half-lives given by the alpha i rate constants. The interested reader can visualize this using the Berkeley Madonna software with t-stop longer than t-dur (QMT model library folder ANDERSEN). During relaxation to the original un-induced state, there is no transient production of the Z factors. Other characteristics can be easily added to this example, such as bistability at key steps that could render the activation irreversible or including feedback of downstream TFs on earlier steps in the cascade. The simulations had persistence of the activating stimulus, X. The behavior of components in the network could also be evaluated for different input levels and durations through the variable t dur. Finally, all the simulations had increases in TFs. The reader should consider how the model would be altered to account for decreased gene expression (e.g., for some of the response patterns in Figure 10.1).

10.3

Discussion

This volume covers many modeling approaches for problems in toxicology and risk assessment. Most of these methodologies are well worked out and have advanced to the stage of almost routine applications. PBPK modeling and the associated tools for assessing internal dose and accounting for aspects of metabolism, macromolecular reactivity, and initial interactions of compounds and metabolites with biological structures are quite advanced. In contrast, the computational systems biology modeling of cell signaling motifs and TNs is in its formative stages. Nonetheless, the field is exploding through contributions from the biomedical engineering community and the elucidation of a wide array of signaling networks by the biomedical research community. The models provided here are greatly simplified, for example, in the inclusion of ultrasensitivity through Hill equations. Many of these nonlinear steps in mammalian systems are expected to be associated with MAPK cascades. One valuable contribution for TN modeling would be providing a direct steady state solution for MAPK cascades (Huang and Ferrell, 1996) to show the manner in which empirical n values used for these cascades relate to specific rate constants and concentrations of components in the multikinase pathways.

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In the TF networks, studies to date have generally focused on time course gene induction. It will also be necessary to account for time courses of nuclear transcription factors (Bromberg et al., 2008) to allow a better mapping of the TF involved at the nodes in the primary, secondary, and tertiary levels of gene expression. Receptor-mediated risk assessment will be advanced by a detailed characterization of one or more prototype TN. The studies optimally would assess the behavior of the TN over both dose and time, perhaps including experimental studies in vivo and in vitro. The field of modeling of TNs is now poised, as was PBPK modeling in the late 1970s, to play a large role in bringing important new technologies and approaches to chemical risk assessment. For the first time, practicing toxicologists have at their disposal the biological and modeling tools to more fully interrogate the shape of the dose response curves in regions of low incidence for a wide range of cellular and tissue level responses. These evaluations will help decide whether these receptor-mediated responses are expected to be low-dose linear or to have real, biological thresholds. Even the early work on the TNs is more consistent with expectations of dose-dependent transitions – firstly, regions where no effects are expected, progressing to doses that cause signal recognition and adaptation, and finally on to high doses with activation of multiple cellular signaling pathways and overt adverse responses. Lastly, these tools for modeling gene and protein induction in TNs are essential components of the toxicity testing paradigm espoused by the NAS report, “Toxicity Testing in the 21st Century: A Vision and A Strategy” (NAS/NRC, 2007). This vision included a future in which virtually all toxicity testing for environmental agents will be done by assessing toxicity pathway perturbations in vitro using human cell systems. Data generated from these assays will be interpreted through physiologically based pharmacokinetic models to assist in vitro to in vivo dosimetry extrapolations and through computational systems biology models of the perturbations in motifs and TNs that constitute the pathways to assess dose-response extrapolations. The refinement and fleshing out of the TN models will be an essential component of new directions for toxicity testing of environmental agents and drugs (Andersen and Krewski, 2009).

References Alon, U. (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman & Hall/CRC, Boca Raton, FL. Alon, U. (2007) Network motifs: theory and experimental approaches. Nat. Rev. Genet., 8, 450–461. Andersen, M.E. and Barton, H.A. (1999) Biological regulation of receptor-hormone complex concentrations in relation to dose-response assessments for endocrine-active compounds. Toxicol. Sci., 48, 38–50. Andersen, M.E., Birnbaum, L.S., Barton, H.A., and Eklund, C.R. (1997) Regional hepatic CYP1A1 and CYP1A2 induction with 2,3,7,8-tetrachlorodibenzo-p-dioxin evaluated with a multicompartment geometric model of hepatic zonation. Toxicol. Appl. Pharmacol., 144, 145–155. Andersen, M.E., Dennison, J.E., Thomas, R.S., and Conolly, R.B. (2005) New directions in incidencedose modeling. Trends Biotechnol., 23, 122–127. Andersen, M.E. and Krewski, D. (2009) Toxicity Testing in the 21st Century: Bringing the Vision to Life. Toxicol. Sci., 107, 324–330. Bromberg, K.D., Ma’ayan, A., Neves, S.R., and Iyengar, R. (2008) Design logic of a cannabinoid receptor signaling network that triggers neurite outgrowth. Science, 320, 903–909.

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Ferrell, J.E. (1996) Tripping the switch fantastic: How a protein kinase cascade can convert graded inputs into switch-like outputs. Trends Biochem. Sci., 21, 460–466. Ferrell, J.E. (1997) How responses get more switch like as you move down a protein kinase cascade. Trends Biochem. Sci., 22, 288–289. Huang, C.Y.F. and Ferrell, J.E. (1996) Ultrasensitivity in the mitogen-activated protein kinase cascade. Proc. Natl. Acad. Sci. USA, 93, 10078–10083. Kwekel, J.C., Burgoon, L.D., Burt, J.W., et al. (2005) A cross-species analysis of the rodent uterotrophic program: elucidation of conserved responses and targets of estrogen signaling. Physiol. Genomics, 23, 327–342. Landers, J.P. and Spelsberg, T.C. (1992) New concepts in steroid hormone action: transcription factors, proto-oncogenes, and the cascade model for steroid regulation of gene expression. Crit. Rev. Eukaryot. Gene Expr., 2, 19–63. Louis, M. and Becskei, A. (2002) Binary and graded responses in gene networks. Sci. STKE, PE33. NAS/NRC (2007) Toxicity Testing in the 21st Century: A Vision and a Strategy, NAS Press, Washington, DC. Nebert, D.W. (1994) Drug-metabolizing-enzymes in ligand-modulated transcription. Biochem. Pharmacol., 47, 25–37. Nel, A., Xia, T., Madler, L., and Li, N. (2006) Toxic potential of materials at the nanolevel. Science, 311, 622–627. N’Jai, A., Boverhof, D.R., Dere, E., et al. (2008) Comparative temporal toxicogenomic analysis of TCDD- and TCDF-mediated hepatic effects in immature female C57BL/6 mice. Toxicol. Sci., 103, 285–297. Strogatz, S. (2000) Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Perseus Books Group, Cambridge, MA. Zhang, Q. and Andersen, M.E. (2007) Dose response relationship in anti-stress gene regulatory networks. PLoS Comput. Biol., 3, 345–363.

11 Modeling Liver and Kidney Cytotoxicity Kai H. Liao1 , Yu M. Tan2 , Harvey J. Clewell, III 2 , and Melvin E. Andersen2 1

2

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Drug Safety and Metabolism, Wyeth Research USA Center for Human Health Assessment, The Hamner Institutes for Health Sciences, USA

Introduction

The development of quantitative models for cytotoxicity based on mechanisms of action would enhance the scientific basis for conducting human health risk assessment for some environmental chemicals. The modeling can also assist with designing future laboratory studies to quantitatively characterize key steps in the mechanism of cytotoxicity. A number of efforts have been made to develop models for cytotoxicity that is related to xenobiotic metabolism (Liao et al., 2007; Tan et al., 2003; El-Masri et al., 1996; Reitz et al., 1990) using physiologically based pharmacokinetic/pharmacodynamic (PBPK/PD) modeling approaches. Reitz and colleagues (1990) modeled the cytotoxicity of chloroform (CHCl3 ) by describing liver cell damage as a combined function of the rate of chloroform metabolism, the fraction of chloroform metabolites covalently bound to macromolecules, and a normally distributed susceptibility of the cells to damage. The cells in the damaged fraction were assumed to die at a first-order rate and the cumulative fraction of liver cells killed by chloroform exposure was simulated (Reitz et al., 1990). In a separate effort, the cytotoxicity of carbon tetrachloride (CCl4 ) was modeled by El-Masri and colleagues (El-Masri et al., 1996); the cytotoxicity was described by two mechanisms related to the amount of reactive CCl4 metabolite produced (Figure 11.1). In the primary mechanism of cytotoxity, the reactive CCl4 metabolite was assumed to cause cellular injury through lipid accumulation and the injured cell can either be repaired Quantitative Modeling in Toxicology
C 2010 John Wiley & Sons, Ltd

Edited by Kannan Krishnan and Melvin E. Andersen

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Figure 11.1 A schematic of the cytotoxicity model of carbon tetrachloride (CCl4 ) from ElMasri et al. (1996). The dashed lines depict the processes that are affected by the presence of Kepone. (a) The final pharmacodynamic model used in this work. When cells are exposed to the reactive metabolites of CCl4 , their inherent death rate is influenced by two mechanisms. A major mechanism of cellular injury leading to death is through lipid accumulation, which is illustrated here as the formation of injured cells and dead cells via two rate constants KINJ and KDIE1. For simplicity, all other causes of cell death including natural cell death and other CCl4 related toxicities are lumped together into a hybrid constant KDIEI as a second mechanism. The injured cells can either be restored to viable cells or continue to die. All dead cells, whether induced to die or injured to death, are removed from the liver by phagocytosis. Additionally, the PBPD model considers the effects of CCl4 , alone or in combination with Kepone, on cellular mitotic and birth rates. A box around the normal (G0 ) cells and mitotic cell was drawn to reflect the susceptibility of both cell types to injury by CCl4 . (b) Initial pharmacodynamic model where two distinct cellular injury processes were considered. This model was modified to the one in (a) (El-Masri et al., 1996) because of the lack of quantitative data to support the extra injury compartment (Adapted with kind permission from Springer Science + Business Media, Copyright 1996).

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or die. In the secondary mechanism, all other causes of cell death including natural cell death and other CCl4 -related toxicities were lumped together with a death rate described as a function of the amount of reactive CCl4 metabolite produced (El-Masri et al., 1996). Furthermore, using 50% hepatic cell death as an indicator of animal death, the CCl4 cytotoxicity model was applied to simulate the mortality in rats following CCl4 exposure (El-Masri et al., 1996). More recently, Tan and colleagues (Tan et al., 2003) developed a cytotoxicity model for chloroform based on a pharmacodynamic endpoint of regenerative cellular proliferation, which can be measured quantitatively with higher sensitivity than traditional histopathological evaluations (Butterworth and Bogdanffy, 1999). In this model (Tan et al., 2003), the relationship between chloroform metabolism, repairable cell damage, and regenerative cellular proliferation was quantitatively described. This cyotoxicity model for chloroform was then refined (Figure 11.2) and applied to support a mode-of-action based cancer risk assessment for chloroform (Liao et al., 2007). The latter two models (Liao et al., 2007; Tan et al., 2003) are discussed in greater detail in this article. Chloroform became a good candidate for developing a cytotoxicity model because of the tremendous past efforts on studying the mode of toxicity, including studies over the past decade (Constan et al., 1999, 2002; Templin et al., 1996, 1998). Chloroform has been shown to cause increases in the incidence of liver and kidney tumors in rodents by several exposure routes (USEPA, 2001). The weight of evidence indicates that the carcinogenicity observed in animals is a secondary effect of regenerative hyperplasia that occurs in response to cytotoxicity (USEPA, 2001; ILSI, 1997). In addition, the cytotoxicity of chloroform occurs when its toxic metabolites are generated at a rate that exceeds the

PBPK model (modified from Corley et al., 1990) • Rate of chloroform metabolism per tissue volume

Cellular damage k2 Th Cell death rate as a function of damage

kmax k1 Saturable repair

Cell death

Total cell numbers

Cell division rate as a function of the discrepancy in cell numbers due to cytotoxicity

LI simulation

Cell division

Figure 11.2 A schematic of the cytotoxicity model of chloroform (Reported in Liao et al., 2007) LI: Labeling Index.

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capacity of cellular protective and repair mechanisms (ILSI, 1997). Based on such a mode of action for chloroform carcinogenicity, Tan and colleagues (Tan et al., 2003) first developed a PBPK/PD model to link the processes of chloroform metabolism, repairable cell damage, and regenerative cellular proliferation. Recently, a refined model was reported and applied to support a mode-of-action based cancer risk assessment for chloroform (Liao et al., 2007). In this PBPK/PD model, regenerative cellular proliferation, inferred by labeling index (LI) data that provide an estimate of the percentage of cells in S-phase during the period of exposure to bromodeoxyuridine (BrdU), was used as the pharmacodynamic endpoint. Cytotoxicity was not directly used as the pharmacodynamic endpoint in this model (Liao et al., 2007; Tan et al., 2003) because cellular proliferation measurements (i.e., LI data) are more sensitive and quantitative than traditional histopathological evaluations: Following the occurrence of cytotoxicity, the increase in LI can be determined before overt histological changes can be observed (Butterworth and Bogdanffy, 1999). Simulink/MATLAB software (The Mathworks Inc., Natick, MA) was used for the initial development of the model (Tan et al., 2003) because the robust optimization algorithm from MATLAB Optimization Toolbox was ideal for the estimation of PD parameters, with limited prior knowledge on the values, using maximum likelihood approach. On the other hand, MCSim software (Bois and Maszle, 2005) was used in the refined model by Liao et al. (2007) because the Markov Chain Monte Carlo (MCMC) technique implemented in MCSim was ideal for supporting risk assessment application, for which model evaluation often requires quantitative uncertainty analysis that covers both model uncertainty and parameter uncertainty (USEPA, 2005). In the earlier cytotoxicity model of chloroform by Reitz et al. (1990), liver cell damage was assumed to occur when chloroform metabolites bind to macromolecules, based on a correlation between the covalent binding of chloroform metabolites to macromolecules and areas of hepatic and renal necrosis induced by chloroform (Ilett et al., 1973). In contrast, Tan and colleagues (Liao et al., 2007; Tan et al., 2003) described the cell damage as a function of the rate of chloroform metabolism, without considering the metabolite binding to macromolecules as in Reitz et al. (1990), in order to more broadly include the possible cytotoxicity caused by the hydrochloric acid produced by chloroform metabolism. In addition, compared to the Reitz et al. (1990) model where the cumulative fraction of liver cells killed by chloroform exposure was simulated, Tan and colleagues (Liao et al., 2007; Tan et al., 2003) further modeled the regenerative proliferation, a pharmacodynamic endpoint that is more sensitive and more relevant to the objective of supporting cancer risk assessment for chloroform. In this chapter, the PBPK/PD model for chloroform cytotoxicity developed by Tan and colleagues (Liao et al., 2007; Tan et al., 2003) is presented, in relation to model structure, parameter estimation, uncertainty analysis, and the application to human risk assessment.

11.2 11.2.1

Model Structure PBPK Model Structure

The PBPK portion of the chloroform cytotoxicity model was adopted from a chloroform model developed by Corley et al. (1990), with modification to the description of chloroform

Model Structure

239

pharmacokinetics in kidneys. The pharmacokinetics of chloroform in kidneys was modified from a one-compartment (Corley et al., 1990) to a two-compartment description because the data used as the pharmacodynamic endpoint (labeling index) in kidneys were measured, separately, in the cortical and medullary regions (Templin et al., 1996, 1998). The twocompartment description for kidneys was based on the PBPK model reported in Health Canada’s Priority Substances List Assessment Report for Chloroform (Health Canada, 1999). Liver was described as a single compartment (Corley et al., 1990) because the collection of hepatic labeling index data were not region specific (Constan et al., 2002; Templin et al., 1996, 1998). The parameterization of the PBPK model will be discussed in a separate section of this chapter. 11.2.2

PBPD Model Structure

The PBPD model developed by Tan and colleagues (Liao et al., 2007; Tan et al., 2003) provided the description of the linked processes of chloroform metabolism, repairable cell damage, cell death, and regenerative cellular proliferation in liver and kidneys (Figure 11.2). 11.2.2.1

From Chloroform Metabolism to Repairable Cell Damage

Although the cyotoxicity of chloroform in liver and kidneys is clearly related to chloroform metabolism (USEPA, 2001), the molecular mechanism of such cytotoxicity has not been well characterized. Therefore, a virtual entity not specifically characterized at the biochemical level was used to represent the repairable cell damage (Liao et al., 2007; Tan et al.,
dAdamage was proportional to the rate of chloroform metabolism 2003). The rate of damage dt per tissue volume and the repair of the damage was described as a saturable process: kmax Adamage dAdamage = kdamage Rmet − dt k1 + Adamage

(11.1)

where Adamage is the amount of damage (damage units), Rmet is the rate of chloroform metabolism per tissue volume (mg/h/l), kdamage is a proportionality constant (damage unitsl/mg), kmax is the maximum repair capacity (damage units/h), and k1 is the half-maximal amount of damage (damage units). 11.2.2.2

From Cell Damage to Cell Death

Tan et al. (2003) described the cell death rate as a function of the amount of damage by two alternative functions, that is, threshold (Equation 11.2) and low-dose linear (Equation 11.3). On the other hand, the refined model reported by Liao et al. (2007) only included the threshold function:   βctrl + k2 ( Adamage − T h) when Adamage > Th (11.2) βtotal = when Adamage ≤ Th βctrl where β total is the cell death rate (h−1 ) in the liver or kidney of chloroform-exposed animals, β crtl is the cell death rate (h−1 ) in the liver or kidney of control (unexposed) animals and is

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set to the control division rate (α crtl ), k2 ([damage units-h]−1 ) is the sensitivity parameter of cell death rate to amount of damage, and Th (damage units) is the threshold level of damage below which chloroform exposure and metabolism induces no alteration in cell death rate. In addition, Tan et al. (2003) evaluated a low-dose linear relationship for linking the amount of damage to the death rate: βtotal = βctrl + k3 Adamage

(11.3)

−1

where k3 ([damage units-h] ) is the linear term.

11.2.2.3

From Cell Death to Regenerative Cellular Proliferation

The chloroform-induced cytotoxicity (described by an increased β total ) results in a decrease in the cell number, which in turn leads to compensatory increase in cell division. The rate of change of viable liver or kidney cells (N total for chloroform-exposed animals; N ctrl for control animals) was described as a function of their respective cell division (α total , α ctrl ) and death (β total , β ctrl ) rates (h−1 ): dN = N (α − β) (11.4) dt Prior to chloroform exposure, the number of viable cells (N total ) was constant, that is, α total equals β total and is the same as the control division rate (α crtl ). Following chloroform exposure, N total might decrease if β total increases (Equation 11.2) while α total remains unchanged. Subsequently, the decrease in N total results in compensatory regenerative proliferation, which was described as an increased α total using two different approaches by Tan et al. (2003) and by Liao et al. (2007). Specifically, in the refined model reported by Liao et al. (2007), the difference between the unexposed (N ctrl ) and exposed (N total ) cell number was described as the driving force for the compensatory regenerative proliferation (increasing α total ):     Ntotal Ntotal + αmax 1 − (11.5) αtotal = αctrl Nctrl Nctrl where α max is the maximum possible division rate (h−1 ). On the other hand, Tan et al. (2003) described the regenerative proliferation based on a signaling mechanism that each cell was assumed to secrete a signal into the blood at a constant rate and this signal is cleared at a first-order rate. When cell numbers decrease due to chloroform-induced cytotoxicity, the rate of signal production falls and the deficit in the signal level in blood drives an increase in cellular division rate. Tan et al. (2003) tracked the blood level of the signal for control (Sctrl ) and chloroform-exposed (Stotal ) animals by the equation: dS (11.6) = k p N − kcp S dt where kp (signal units/cell-h) is the zero-order rate constant for signal secretion from each cell into the blood, kcp (h−1 ) is the first-order rate constant for the clearance of signal from the blood, and N denotes either N ctrl or N total . Next, the difference in signal levels between the control and chloroform-exposed animals (Sctrl − Stotal ) was described in Tan et al.

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(2003) as the driving force for the increase in division rate (i.e., compensatory regenerative proliferation):   1 −1 (11.7) αtotal = αctrl − αmax,S e(Sctrl −Stotal ) where α max,S is the maximum possible division rate (h−1 ) based on the signal mechanism approach (comparing to α max based on cell numbers used in Equation 11.5). Based on Equation 11.7, the maximum value of division rate is α ctrl + α max,S . Although the regenerative proliferation was described using slightly different approaches in Tan et al. (2003) and in Liao et al. (2007), in both the deficit in cell number due to chloroform-induced cytotoxicity caused a compensatory increase in the division rate of the surviving cells, with this process diminishing as the cell number returned to the control level. The refined model by Liao et al. (2007) used a simpler model structure (Equation 11.5) to reduce the number of empirical parameters. 11.2.2.4

Simulation of Regenerative Cellular Proliferation

The pharmacodynamic endpoint used in the PBPK/PD model by Tan et al. (2003) and Liao et al. (2007) was LI data. LI was measured in rodents exposed to chloroform for various periods and osmotic pumps were surgically implanted in these animals 3.5 days before scheduled necropsies to continually administer BrdU to detect proliferating cells in liver and kidney tissues (Constan et al., 2002; Templin et al., 1998; Templin et al., 1996); the LI was determined as the percentage of nuclei that stained positive for BrdU incorporation during the S-phase of the cell cycle. In Liao et al. (2007), the simulated LI expressed in percentage was calculated from the number of cells stained positive for BrdU (N labeled ) and total number of cells (N total ): dNlabeled = αtotal (2Ntotal − Nlabeled ) − βtotal Nlabeled dt Nlabeled LI = 100 Ntotal

(11.8) (11.9)

In the original model developed by Tan et al. (2003), the simulated LI was calculated using the following equation:   NDiv (T ) − NDiv (T − 3.5 day) (11.10) LI = 200 Ntotal (T ) where the numerator represents the number of cell divisions that have occurred during the 3.5 days of exposure to BrdU; N div (t) represents the number of division between the start of simulation (t = 0) and time t, while t = T at the end of the study. N total (T) is the number of cells at the end of the study. The factor of 200 was used because each cell division generates two labeled cells during exposure to BrdU and LI was expressed as percentage. N div can be obtained by the following equation: dNdiv = αtotal Ntotal dt

(11.11)

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Tan et al. (2003), that is, Equations 11.10 and 11.11, did not account for the possibility of multiple divisions originating from a single cell within the 3.5-day labeling period. Although the division of previously labeled cell was not accounted for in its overall impact on the simulated LI, results might be minimal as multiple divisions within 3.5-day is a relatively rare event unless severe cytotoxicity occurs. The hepatic LI data reported by Constan et al. (2002) was only up to 20%, suggesting that the labeled cells were most likely derived from unlabeled cells. The cell divisions from both labeled and unlabeled cells are accounted for using Equations 11.8 and 11.9.

11.3

Parameter Estimation

The PBPK/PD model for chloroform cytotoxicity was first developed in rodents to evaluate the relationship between chloroform pharmacokinetics, cytotoxicity, and regenerative cellular proliferation; the model was subsequently extended to support a mode-of-actionbased cancer risk assessment for chloroform in humans. Although the majority of the PBPK model parameters can be obtained from the literature for both humans and rodents, the PD model parameters had to be estimated based on experimental measures in the rodents and extrapolated to humans.

11.3.1

Estimation of the Rodent Model Parameters

The PD model parameters for rodents were estimated from experimental measurements of regenerative cellular proliferation (i.e., LI data), which are more sensitive and quantitative than traditional histopathological evaluations (Butterworth and Bogdanffy, 1999). The metabolism parameters (V max and K m ) were estimated using experimental measurements (closed-chamber gas uptake data). During the development of the PBPK/PD model for chloroform cytotoxicity, the rate of cell damage formation (Equation 11.1) was assumed to be proportional to the rate of chloroform metabolism per tissue volume and the rate of chloroform metabolism was species- and gender-specific. However, these parameters were not available for both genders of mice and rats where LI data were available. The other PBPK model parameters were adopted from the published data on physiological parameters (Arms and Travis, 1988; Brown et al., 1997; OSHA, 1997) and partition coefficients for chloroform (Corley et al., 1990). Because the formation of chloroform metabolite is defined as a prerequisite for chloroform cytotoxicity, the metabolism parameters (V max and K m ) were estimated (using the closed chamber gas uptake data) prior to the estimation of the PD parameters (using the LI data). The first generation of the model (2003) was parameterized using a maximum likelihood approach, while a Bayesian approach was used in the second generation of the model (Liao et al., 2007). Different parameterization approaches (maximum likelihood versus Bayesian) were selected based on practical consideration during the time that each generation of the model was developed. The parameterization using a maximum likelihood approach is generally acceptable for the initial development of a PBPK/PD model such as that reported by Tan et al (2003). On the other hand, the second-generation model (Liao et al., 2007) was developed to support a mode-of-action based cancer risk assessment, for which model evaluation often requires quantitative uncertainty analysis

Parameter Estimation

243

that covers both model uncertainty and parameter uncertainty (USEPA, 2005). In order to address such uncertainty as well as inter-individual variability, a hierarchical statistical tool within a Bayesian framework developed by Bois and colleagues (Bois, 1999; Gelman, Bois, and Jiang, 1996) was used for the parameterization in Liao et al. (2007). The approach and datasets used to parameterize each generation of the model are discussed separately. 11.3.1.1

Maximum Likelihood Approach for Parameter Estimation

In Tan et al. (2003), the PBPK/PD model parameters were estimated using a maximum likelihood approach. The data used for the parameterization of the PD model were hepatic LI data in female B6C3F1 mice following inhalation exposure to chloroform (Constan et al., 2002) with seven combinations of chloroform concentration (10, 30, or 90 ppm) and exposure duration (2, 6, 12, or 18 h/day for seven consecutive days). This dataset with various chloroform concentration and exposure duration was ideal for the initial development of a PBPK/PD model of chloroform cytotoxicity (Tan et al., 2003), as the objective for developing the first generation of the model was to obtain quantitative knowledge of the relationship between chloroform pharmacokinetics, cytotoxicity, and regenerative cellular proliferation. Prior to the estimation of PD model parameters, the metabolism parameters for female B6C3F1 mice (not available previously) were estimated using closed-chamber gas uptake experiments with nominal initial chloroform concentrations of 350, 1050, 1700, 2350, or 3200 ppm (Tan et al., 2003). The software used was Simulink/MATLAB with the fmincon algorithm from the MATLAB Optimization Toolbox used for the optimization. Grid search was also used in the optimization to identify the starting values that lead to global optima. 11.3.1.2

Bayesian Approach for Parameter Estimation

The PBPK/PD model for chloroform cytotoxicity was refined to support a mode-of-action based cancer risk assessment (Liao et al., 2007), for which model evaluation often requires quantitative uncertainty analysis that covers both model uncertainty and parameter uncertainty (Liao et al., 2007). These two types of uncertainty are difficult to separate because most experimental data reflect a combination of uncertainty together with inter-individual variability (heterogeneity) in pharmacokinetics and pharmacodynamics. To disentangle different elements of uncertainty and variability, a hierarchical statistical tool was developed by Bois and colleagues (Constan et al., 1999; USEPA, 2001) within a Bayesian framework that incorporates two forms of information: (1) prior distributions of the parameters; and (2) experimental data. Using these two inputs, the numerical algorithm of Markov Chain Monte Carlo (MCMC) technique obtains posterior distributions of model parameters (Constan et al., 1999; USEPA, 2001). The resulting posteriors can become inputs for formal quantitative uncertainty analysis of the model in risk assessment. The MCMC technique was implemented in the software of MCSim (Bois and Maszle, 2005), which was used in Liao et al. (2007) to parameterize the PBPK/PD model for chloroform cytotoxicity. Instead of obtaining a point estimate for each parameter, as in a maximum likelihood approach, the hierarchical MCMC approach (Bois, 1999; Bernillon and Bois, 2000) characterizes each model parameter with a population distribution (with a population mean [M] and a population variance [S2 ]). Through iterative sampling processes (Monte Carlo

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integration), MCSim software constructs Markov Chains that converge toward the dataadjusted posterior distributions, which were then used to characterize the model parameters with information on variability and uncertainty. The metabolic parameters were estimated separately for male mice, female mice, male rats, and female rats using the closed-chamber gas uptake data from the respective groups, as the rate of chloroform metabolism was species- and gender-specific (USEPA, 2001). To better characterize uncertainty and variability in the model parameters using MCMC analysis, Liao et al. (2007) had included a large set of gas uptake data in parameterization. For each of the four groups of rodents, the experiment data covered a wide range of chloroform concentrations (7–10 concentrations ranging from 100 to 5000 ppm), in order to provide estimates for both the capacity (V max ) and affinity (K m ) parameters. The other piece of input required for MCMC analysis are the prior knowledge on the distributions of V max and K m , which were defined based on estimates from Corley et al. (1990), that is, the priors for population mean were assumed to be log-normally distributed. Although the V max and K m values had only been estimated for male mice and rats (Corley et al., 1990), the gender- and species-specific gas uptake data were used in MCMC analysis to update these parameters and form posterior distributions for the corresponding gender and species (Liao et al., 2007). In turn, these posterior distributions were used to characterize the V max and K m values with inter-individual variability during the MCMC analysis for PD parameters. The PD parameters in liver were estimated against the hepatic LI data from male and female BDF1 mice because both the hepatic LI (Templin et al., 1998) and liver tumor incidence (Yamamoto et al., 2002) increased with increasing chloroform exposure (inhalation) in BDF1 mice. On the other hand, rat hepatic LI data were not included in the analysis, since no significant increases in hepatic LI (Templin et al., 1996) or liver tumors (Yamamoto et al., 2002) were observed in F344 rats for chloroform exposure up to 90 ppm. This observation was consistent with the lower V max values in rats compared to those in mice (Liao et al., 2007). The use of only the mouse data is consistent with the common risk assessment practice of using the most sensitive species. Templin and colleagues (1998) conducted LI studies in male and female BDF1 mice, using various concentrations of chloroform (0, 1, 5, 30, or 90 ppm) 6 h/day, 5 days/week, for 3, 7, or 13 weeks. Only data from the 13-week exposures were used in the MCMC analysis because such duration, among the data available, was most relevant for characterizing the long-term effects associated with chloroform exposures and for supporting cancer risk assessment. The exposure scenario, 6 h/day, 5 days/week, was consistent with that used in the inhalation bioassay (Yamamoto et al., 2002). PD parameters in kidney were estimated against the renal LI data from male BDF1 mice and both genders of F344 rats (Templin et al., 1998; Templin et al., 1996). Renal LI data from female BDF1 mice were not included in the analysis because chloroform exposure did not result in any increases in renal LI (Templin et al., 1998) or renal tumor incidence (Yamamoto et al., 2002) in these animals. The gender-specific cytotoxicity in BDF1 mice is consistent with sexual dimorphism in the expression of mouse renal cytochrome P450 2E1 (CYP2E1) (Henderson et al., 1990; Henderson and Wolf, 1991), the major enzyme responsible for the metabolism of chloroform to generate toxic metabolites (Guengerich, Kim, and Iwasaki, 1991). The renal LI data (in kidney cortex and outer stripe of the outer

Parameter Estimation

245

medulla) for male BDF1 mice were from the animals examined for hepatic LI in Templin et al. (1998). For male and female F344 rats, the renal LI data in kidney cortex were obtained following exposure to chloroform vapor at 30, 90, or 300 ppm for 6 h/day, 5 days/week for 13 weeks (Templin et al., 1996). Prior distributions of pharmacodynamic parameters were from the first generation PBPK/PD model for chloroform cytotoxicity (Tan et al., 2003). Although these initial priors were estimated only based on hepatic LI in female mice, they represented our best prior knowledge on the parameter values. Thus, the same priors were used for both liver and kidneys in mice and rats, on the basic assumption that cells in both organs in both species would require similar amounts of metabolized CHCl3 to cause toxicity. These prior distributions were later updated using the hepatic and renal LI data from the corresponding gender and species (Templin et al., 1998; Templin et al., 1996) and converged toward posterior distributions specific for the respective groups (Liao et al., 2007).

11.3.2

Estimation of the Human Model Parameters

A human PBPK/PD model for chloroform cytotoxicity was then developed (Liao et al., 2007) using the rodent PBPD parameters from the MCMC analysis together with the human physiological, partitioning and metabolism parameters from the literature (Corley et al., 1990; Lipscomb et al., 2004; Sarangapani et al., 2003; Ogiu et al., 1997; Rubin, Bruck, and Rapoport, 1949). As part of the risk assessment application, the human model was exercised across genders and a range of age groups (1-month-, 3-month-, 6-month-, 1-year-, 5-year-, and 25-year-old females and males). The PBPK model parameters were further specified, when appropriate, in an age- and gender-dependent manner. Specifically, the physiological parameters were considered age- and gender-dependent in humans (up to the age of 25) as a result of maturation and, thus, these age- and gender-specific parameters were adopted from published studies (Sarangapani et al., 2003; Ogiu et al., 1997; Rubin, Bruck, and Rapoport, 1949). The partition coefficients were obtained from Corley et al. (1990) and used unchanged between genders within the age range of interest. The metabolism parameters for chloroform in adult humans were from Lipscomb et al. (2004), where the V max and K m values were extrapolated from in vitro measurements using human liver microsomes. The metabolic capacity parameter (V max ) was further adjusted for age based on the activity of CYP2E1, the major enzyme responsible for chloroform metabolism (Guengerich, Kim, and Iwasaki, 1991), following Sarangapani et al. (2003). The PD model parameters estimated for rodents (liver and kidney) were scaled to humans with the assumption that the pharmacodynamics of chloroform is similar in human and rodent tissues, and similar between children and adults. In general, the MCMC analyses resulted in similar PD parameter estimates regardless of gender and species in rodents. Therefore, the majority of the human PD model parameters were based on the mean of the rodent values (the mean of those from male and female mice for the liver compartment; the mean of those from male mice and male and female rats for the kidney compartment). There was one exception that the sensitivity of cell death to damage (k2 ) was set to the values from the most sensitive group (female mouse value for liver and female rat value for kidney).

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11.4 Model Results and Risk Assessment The PBPK/PD model for chloroform cytotoxicity (Liao et al., 2007; Tan et al., 2003) described the quantitative relationship between the processes of chloroform metabolism, cell damage, cell death, and regenerative cellular proliferation in liver and kidneys. The key model parameters are the metabolic parameters (V max and K m ), since chloroform metabolism is required for cytotoxicity, and the PD parameters, including those that characterize the cell repair process (k1 and kmax ), sensitivity of cell death to damage (k2 ), threshold for damage to affect cell death (Th), and cell division rates (α ctrl and α max ). The model was first validated using a comprehensive (seven combinations of chloroform concentration and exposure duration) dataset of pharmacodynamic endpoint (LI data) in single target organ (liver) from a single group of rodents (female mice) using maximal likelihood approach (Tan et al., 2003). The first generation of the model provided initial estimates for PD parameters that were subsequently used to set the prior distributions for the MCMC analysis to parameterize the cytotoxicity model in the livers of male and female mice as well as in the kidneys of male mice and both gender of rats (Liao et al., 2007). The posterior distributions following MCMC analysis were used to characterize the genderand species-specific parameter values. For the liver PD model in female mice, the original parameters (Tan et al., 2003) were generally similar to updated ones (Liao et al., 2007), particularly the sensitivity of cell death to damage (k2 ), despite the datasets used in the two reports being considerably different in the exposure duration (seven day exposure at various duration per day (Constan et al., 2002) versus 13 week exposure at 6 h/day (Templin et al., 1998)). The consistency of PD parameters estimated across different datasets using different parameterization approaches (maximal likelihood versus MCMC analysis) further support the robustness of the PBPK/PD model for chloroform cytotoxicity. When comparing the chloroform cytotoxicity across tissues (liver versus kidneys) in male mice (the only group with increasing LI in both tissues), a higher LI was observed in kidney (Templin et al., 1998) even though the intrinsic rate of metabolism is lower in kidneys compared to that in liver. Such an observation can be rationalized using the PBPK/PD model from both PK and PD aspects. From the PK aspect, the simulated in vivo rate of metabolism per tissue volume are similar between liver and kidneys: The higher intrinsic metabolic rate in liver results in a lower chloroform concentration in liver, which limits the amount of chloroform available for metabolism and thus compensates the in vivo rate of chloroform metabolism (see Section 11.5; QMT model library folder LIAO). From the PD aspect, the estimated threshold parameter (Th) was lower in kidneys compared to liver, suggesting that the cell death rate in kidneys might manifest at a lower level of cell damage (Equation 11.2). All PD parameters in kidneys are generally similar across different groups (male mice, both genders of rats) with a maximum of a 3.2-fold difference (in the sensitivity parameter [k2 ] between male mice and female rats). The PD parameters in liver are also similar between male and female mice with a maximum of a 3.3-fold difference in k2 values. The MCMC analysis showed that the control division rate (α crtl ) is the PD parameter with the lowest uncertainty. This conclusion is expected because only the LI data in control animals are informative for this parameter and the parameter is unlikely to covariate with other PD parameters in the model. In contrast, other PD model parameters are more conceptual and associated with “virtual” processes (e.g., kmax , k1 , k2 ). Quantitative

Model Results and Risk Assessment

247

knowledge on the biological underpinning of these parameters may be obtained by examining dose-dependent changes in gene expression from tissue of the rats and mice following chloroform exposure. Such data would enhance our understanding of the biological processes at work controlling the nonlinear mode of action for chloroform cytotoxicity. The metabolic parameters were estimated using MCMC analysis with gas uptake data for both genders of mice and rats. The posteriors from MCMC analysis resulted in similar V max values compared to published data in male mice and rats (Corley et al., 1990) and female mice (Tan et al., 2003). However, the K m values from MCMC analysis were ∼1.7to 2.8-fold lower than the published data. As the V max parameter is only sensitive to the gas uptake data at the high chloroform concentrations where metabolism is saturated, similar V max estimates were expected because most available gas uptake data included sufficiently high chloroform concentrations. In contrast, the K m parameter is more sensitive to the gas uptake data at the lower concentration region, where the blood flow to liver also affects the metabolism. During the MCMC analysis for estimating V max and K m (Liao et al., 2007), the uncertainty and variability of liver blood flow were taken into account. Therefore, the resulting V max and K m from the MCMC analysis are likely to represent improved estimates. A cancer risk assessment for chloroform was conducted based on the human PBPK/PD model for chloroform cytotoxicity (Liao et al., 2007) using the rodent PBPD parameters from the MCMC analysis together with the human physiological, partitioning, and metabolism parameters from the literature (Corley et al., 1990; Lipscomb et al., 2004; Ogiu et al., 1997; Rubin, Bruck, and Rapoport, 1949; Sarangapani et al., 2003). For various age groups, the human model was exercised to steady state over a range of inhalation and water concentrations to identify the point of departure, that is, the exposure concentrations that result in an Adamage value equal to Th (Equation 11.2). Below this threshold, no chloroform-mediated cytotoxicity or tumor would be expected to occur. The simulation results indicate that a child would have less risk than an adult in all but one cases examined (inhalation and ingestion exposure for liver and kidney effects). The only exception was the liver effects from inhalation where a child would be a factor of two more sensitive, which is well within the standard uncertainty factor of 10 for human variability. An oral Reference Dose (RfD) and an inhalation Reference Concentration (RfC) for chloroform exposure were derived based on the estimates of threshold exposure for male adults (which was consistently lower than those for female adults), together with an uncertainty factor of 10 to account for the inter-individual variability in humans. The estimated RfCs were 0.9 and 0.09 ppm for the liver and kidney effects, respectively. The RfDs were 0.4 and 3 mg/kg/day for the liver and kidney effects, respectively.

11.5 Exercise: Modeling Cytotoxicity Using the Chloroform PBPK/PD Model The objective of this exercise is to learn the effect of several PD parameters on model output (Labeling Index; LI for liver and LIK for kidneys). The model codes, written in acslX version 2.4.2.1 (The Aegis Technologies Group, Inc., Huntsville, AL), are based on the PBPK/PD model for chloroform cytotoxicity from Liao et al. (2007). The main program file is CHCl3.csl (with parameters set to those for male mice), while several

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Modeling Liver and Kidney Cytotoxicity

Figure 11.3 An example of the dose-response simulations for renal labeling index (LI) using the model codes listed in Exercise 11.1 (CHCl3.csl and M Mice long.m). The simulations (solid line) were based on the model parameters for male mice reported in Liao et al. (2007) and a 13-week continuous exposure scenario with time-weighted average of the exposure concentration for intermittent (6 h/day, 5 days/week) exposure as used in Templin et al. (1998). The experimental data (squares) on the 13-week exposure were based on Templin et al. (1998).

m-files with pre-set experimental conditions and plot function can be used to execute the program. Continuous inhalation exposure conditions are used to reduce the time required for simulations for practical purpose of this exercise: r M Mice long.m: A m-file to simulate renal LI for 13 week (2112 h) exposure, compared with the renal LI data from Templin et al. (1998). The exposure condition described in the m-file is continuous exposure with time-weighted average of the exposure concentration for intermittent (6 h/day, 5 days/week) exposure as used in Templin et al. (1998), for example, 30 ppm intermittent × (6/24) × (5/7) = 5.36 ppm continuous. The readers with acslX software should be able to reproduce the results shown in Figure 11.3 (simulations of renal LI versus experimental measures). This dose-response curve will take several minutes to run. r M Mice.m: Similar to the previous file, but the execution should be faster (∼30 s) as TSTOP is set to 144 h. The m-file will allow the user to change PD parameter values and observe the impact on the simulations of LI in liver and kidney. The nomenclature of PD parameters in the acslX model: – Sensitivity of cell death to damage: K2 (liver) and K2K (kidney), – Threshold for damage to affect cell death: TH (liver) and THK (kidney), – Cell repair process: K1 and KMAX for liver; K1K and KMAXK for kidneys, For example, to set K2 to a value of 1 × 10−6 , type K2 = 1e-6 in the command window, press enter, then Run the M Mice.m file to start simulation. To set all parameters to their original values, click “Reload” icon on the toolbar.

References

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r For advanced users who would like to simulate intermittent exposure (6 h/day, 5 days/week) as in the bioassay conducted by Yamamoto et al. (2002) or LI study by Templin et al. (1998), two parameters will need to be modified: TCHNG = 6 (6 h/day) and DAYS = 5 (5 days/week).

References Arms, A.D. and Travis, C.C. (1988) Reference Physiological Parameters in Pharmacokinetic Modeling. EPA/600/6-88/004, US Environmental Protection Agency, Washington, DC. Bernillon, P. and Bois, F.Y. (2000) Statistical issues in toxicokinetic modeling: A Bayesian perspective. Environmental Health Perspectives, 108, 883–893. Bois, F.Y. and Maszle, D.R. (2005) MCSim: A Monte Carlo Simulation Program, Available at: http://toxi.ineris.fr/activites/toxicologie quantitative/mcsim/mcsim.php (accessed 4 November 2009). Bois, F.Y. (1999) Analysis of PBPK models for risk characterization. Ann. NY Acad. Sci., 895, 317–337 Brown, R.P., Delp, M.D., Lindstedt, S.L., et al. (1997) Physiological parameter values for physiologically based pharmacokinetic models. Toxicol. Ind. Health, 13, 407–484. Butterworth, B.E. and Bogdanffy, M.S. (1999) A comprehensive approach for integration of toxicity and cancer risk assessments. Regulatory Toxicology and Pharmacology, 29, 23–36. Constan, A.A., Wong, B.A., Everitt, J.I., and Butterworth, B.E. (2002) Chloroform inhalation exposure conditions necessary to initiate liver toxicity in female B6C3F1 mice. Toxicological Sciences, 66, 201–208. Constan, A.A., Sprankle, C.S., Peters, J.M, et al. (1999) Metabolism of chloroform by cytochrome P450 2E1 is required for induction of toxicity in the liver, kidney, and nose of male mice. Toxicology and Applied Pharmacology, 160, 120–126. Corley, R.A., Mendrala, A.L., Smith, F.A., et al. (1990) Development of a physiologically based pharmacokinetic model for chloroform. Toxicol. Appl. Pharmacol., 103, 512–527. El-Masri, H.A., Thomas, R.S., Sabados, G.R., et al. (1996) Physiologically based pharmacokinetic/pharmacodynamic modeling of the toxicologic interaction between carbon tetrachloride and Kepone. Archives of Toxicology, 70, 704–713. Gelman, A., Bois, F., and Jiang, J.M. (1996) Physiological pharmacokinetic analysis using population modeling and informative prior distributions. Journal of the American Statistical Association, 91, 1400–1412. Guengerich, F.P., Kim, D.H., and Iwasaki, M. (1991) Role of human cytochrome P-450 IIE1 in the oxidation of many low-molecular-weight cancer suspects. Chemical Research in Toxicology, 4, 168–179. Health Canada (Canadian Environmental Protection Act, 1999) (1999) Priority Substances List Assessment Report: Chloroform, Health Canada, Ottawa, Ontario. Henderson, C.J. and Wolf, C.R. (1991) Evidence that the androgen receptor mediates sexual differentiation of mouse renal cytochrome P450 expression. Biochemical Journal, 278, 499–503. Henderson, C.J., Scott, A.R., Yang, C.S., and Wolf, C.R. (1990) Testosterone-mediated regulation of mouse renal cytochrome P-450 isoenzymes. Biochemical Journal, 266, 675–681. Ilett, K.F., Reid, W.D., Sipes, I.G., and Krishna, G. (1973) Chloroform toxicity in mice: correlation of renal and hepatic necrosis with covalent binding of metabolites to tissue macromolecules. Experimental and Molecular Pathology, 19, 215–229. ILSI (1997) An Evaluation of EPA’s Proposed Guidelines for Carcinogen Risk Assessment Using Chloroform and Dichloroacetate as Case Studies: Report of an Expert Panel, International Life Sciences Institute, Washington, DC. Liao, K.H., Tan, Y.M., Conolly, R.B., et al. (2007) Bayesian estimation of pharmacokinetic and pharmacodynamic parameters in a mode-of-action-based cancer risk assessment for chloroform. Risk Analysis, 27, 1535–1551.

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Lipscomb, J.C., Barton, H.A., Tornero-Velez, R., et al. (2004). The metabolic rate constants and specific activity of human and rat hepatic cytochrome P-450 2E1 toward toluene and chloroform. J. Toxicol. Environ. Health A, 67, 537–553. Ogiu, N., Nakamura, Y., Ijiri, I., et al. (1997) A statistical analysis of the internal organ weights of normal Japanese people. Health Physics, 72, 368–383. OSHA (1997) Occupational Exposure to Methylene Chloride – 68:1494–1619, Occupational Safety and Health Administration. Reitz, R.H., Mendrala, A.L., Corley, R.A., et al. (1990) Estimating the risk of liver cancer associated with human exposures to chloroform using physiologically based pharmacokinetic modeling. Toxicology and Applied Pharmacology, 105, 443–459. Rubin, M.I., Bruck, E., and Rapoport, M. (1949) Maturation of renal function in childhood – Clearance studies. Journal of Clinical Investigation, 28, 1144–1162. Sarangapani, R., Gentry, P.R., Covington, T.R., et al. (2003) Evaluation of the potential impact of age- and gender-specific lung morphology and ventilation rate on the dosimetry of vapors. Inhal. Toxicol., 15, 987–1016. Tan, Y.M., Butterworth, B.E., Gargas, M.L., and Conolly, R.B. (2003) Biologically motivated computational modeling of chloroform cytolethality and regenerative cellular proliferation. Toxicological Sciences, 75, 192–200. Templin, M.V., Constan, A.A., Wolf, D.C., et al. (1998) Patterns of chloroform-induced regenerative cell proliferation in BDF1 mice correlate with organ specificity and dose-response of tumor formation. Carcinogenesis, 19, 187–193. Templin, M.V., Larson, J.L., Butterworth, B.E., et al. (1996) A 90-day chloroform inhalation study in F-344 rats: Profile of toxicity and relevance to cancer studies. Fundamental and Applied Toxicology, 32, 109–125. USEPA (2005) Guidelines for Carcinogen Risk Assessment, Risk Assessment Forum, US Environmental Protection Agency, Washington, DC. USEPA (2001) Toxicological Review for Chloroform: In Support of Summary Information on the Integrated Risk Information System (IRIS), US Environmental Protection Agency, Washington, DC. Yamamoto, S., Kasai, T., Matsumoto, M., et al. (2002) Carcinogenicity and chronic toxicity in rats and mice exposed to chloroform by inhalation. Journal of Occupational Health, 44, 283–293.

Section 4 Modeling tissue and organism responses

12 Computational Model for Iodide Economy and the HPT Axis in the Adult Rat Jeffrey W. Fisher and Eva D. McLanahan1 1

College of Public Health, University of Georgia, USA Current address: National Center for Environmental Assessment, US Environmental Protection Agency, USA

12.1 Introduction Pharmacokinetic analyses or compartmental models of the hypothalamic-pituitary-thyroid (HPT) axis have played an important historic role in trying to understand complex relationships between biological action of thyroid hormones and their production, transport, distribution, interaction with receptors and proteins, and their metabolism (Oppenheimer, 1983; DiStefano and Landaw 1984). This chapter gives a brief review of previously published modeling approaches for the HPT axis and provides information about the conception, development, and utility of a biologically based dose-response (BBDR) model developed for the adult rat HPT axis (McLanahan, Andersen, and Fisher, 2008). Several challenges encountered during model development and the lessons learned from this exercise are also presented. The BBDR-HPT axis model that will be discussed in detail describes dietary iodide and overall iodide economy, as it corresponds to changes in thyroidal iodide stores, thyroid hormones, and thyroid stimulating hormone. An adequate supply (neither too low nor too high) of dietary iodide is critical for maintaining normal functioning of the HPT axis. Insufficient iodide intake during the early stages of life is responsible for impaired Quantitative Modeling in Toxicology
C 2010 John Wiley & Sons, Ltd

Edited by Kannan Krishnan and Melvin E. Andersen

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TSH

Iodide Dietary intake

T4 and T3 Hormone metabolism (recycle iodide)

elim

prod

Volume of Distribution

Volume of Distribution

feces

Liver Tissue urine

Liver Blood

T4

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Thyroid Tissue Free Bound

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Figure 12.1 Model structure of the BBDR-HPT axis model in the adult rat. Dark gray arrows represent stimulation of thyroidal iodide processes, stimulation of thyroid hormone production, and T4 /TSH negative feedback loop. Bound iodide in the form of thyroid hormone precursors is used in the production of thyroid hormones from the thyroid (dash-dotted line). Iodide is recycled from the deiodination/metabolism of thyroid hormones in the liver and Vd (shown by the dotted line). Adapted from McLanahan, Andersen, and Fisher (2008).

neurodevelopment and is highly preventable (Delange, 2001). The long-range goal is to use these modeling tools to better understand, quantitatively, the maturation and functioning of the HPT axis during development and chemical induced developmental neurotoxicity caused by HPT axis perturbations. The adult rat BBDR-HPT axis submodels were constructed using simple model structures that allowed a focus on an empirical “system based evaluation” of key biochemical features of the HPT axis (Figure 12.1). For example, the production of thyroid hormones is controlled, in part, by the model predicted serum thyroid stimulating hormone (TSH) concentration, while the rate of sequestration of iodide into the thyroid from blood is also controlled by serum TSH concentration. Other investigators have used these empirical approaches for in vivo descriptions of signaling molecules to control feedback loops such as the hypothalamic-pituitary-gonadal (HPG) axis (Barton and Andersen, 1998) and the HPG axis/menstrual cycle (Schlosser and Selgrade, 2000; Rasgon et al., 2003). The current BBDR-HPT axis model includes submodels for dietary iodide, TSH, T4 , and T3 that are linked together via key biological processes (Figure 12.1). Key biological processes described in the current version of the BBDR-HPT axis model are: (1) the primary HPT axis negative feedback loop (influence of T4 on TSH production; (2) TSH stimulation of thyroidal T4 and T3 production; (3) TSH upregulation of the thyroid sodium/iodide symporter (NIS) and formation of thyroid hormone precursors; (4) recycling of iodide liberated from extrathyroidal metabolism of thyroid hormones; and (5) changes in ratio of T4 :T3 production under iodide deficient conditions.

Rationale for the Current BBDR Model for the HPT Axis

12.2

255

Previous Modeling Approaches for the HPT Axis

Landmark classical pharmacokinetic multicompartmental models for the thyroid hormones (thyroxine, T4; 3,5,3 -triiodothyronine, T3 ) and their derivatives (3,3 ,5 triiodothyronine, rT3 ; 3,3 -diiodothyronine, 3,3 -T2 ; 3 ,5 -diiodothyronine, 3 ,5 -T2 ; and 3 -monoiodothyronine, T1 ) have been developed for the rodent by DiStefano and colleagues (DiStefano et al., 1982; DiStefano and Feng, 1988). In general, these models were based upon radiolabeled injections of the inactive and active thyroid hormones and consisted of three or more compartments (e.g., plasma, fast, and slow pools). These models, employing polynomial equations and multicompartmental models, were used to estimate thyroid hormone production rates, transport rates, and metabolic rates. The models were capable of reproducing kinetics of intravenous (iv) doses of radiolabeled T3 and T4 . These models provided important quantitative insights into the functioning of the HPT axis. Kohn et al. (1996) developed a PBPK model for the distribution of 2,3,7,8tetrachlorodibenzo-p-dioxin (TCDD) in the rodent that also included a description of the HPT axis as a submodel. The submodel for thyroid hormone regulation comprised five compartments (liver, thyroid, pituitary, rapidly perfused tissues, and blood), including TSH control of T4 and T3 production in the thyroid and the regulation TSH production by hypothalamic peptides (somatostatin and TRH). The authors did not describe the primary negative feedback loop of the HPT axis nor dietary intake of iodide. The TCDD HPT axis model successfully predicted decreases in serum T4 , via a TCDD-dependent increase in phase II conjugation of T4 . This modeling approach represented a sound computational tactic for integrating biological, physiological, and biochemical information into a model structure to describe perturbations in the HPT axis. Chait and colleagues (Degon et al., 2008) developed a complex biochemical network model for the regulation and synthesis of thyroid hormones in the thyroid gland solely based on thyroidal uptake of iodide. The authors were interested in understanding the mechanisms associated with perturbations in thyroid hormone production caused by excess iodide in humans. This model offers detailed biochemical feedback interactions that may occur as thyroid hormones are produced.

12.3

Rationale for the Current BBDR Model for the HPT Axis

A challenge is, “Where to begin to develop a HPT axis model after reading the first 1000 thyroid papers?” Armed with many facts and conflicting information from the literature, the basis for the HPT axis model was developed using data collected by leading scientists in thyroid research that showed important HPT axis relationships. For example, Figure 12.2a shows that thyroidal iodide stores in rats reach a maximum, despite a continued increase in dietary intake and absorption of iodide, indicated by a corresponding increase in serum iodide levels. Figure 12.2b portrays the nonlinear relationship between serum concentrations of T4 and TSH. This relationship is fundamental in understanding the negative feedback loop. Data from human population studies suggested that thyroidal iodide stores were key in understanding the functional relationships of the HPT axis, and thus thyroidal iodide content was determined to be a critical measurement to include in the

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Serum TSH (ng rTSH RP-3/ml)

8

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(b)

Figure 12.2 a. Relationship between dietary iodide intake and plasma and thyroidal iodide content. Thyroidal iodide concentrations begin to level off and plasma iodide continues to increase at dietary iodide intakes between 100 and 405 µg/day. Data adapted from Pedraza et al. (2006) and Nagataki, Shizume, and Nakao (1966). b. Example of the nonlinear inverse relationship between serum T4 and serum TSH. Data adapted from Pedraza et al. (2006).

How Can We Create Equations to Describe the HPT Axis?

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BBDR-HPT axis rodent model. Delange and Dunn (2005) reported on the relationships between urinary iodide excretion in humans (a biomarker for dietary intake of iodide), thyroidal organic iodide content, and prevalence of goiter. When urinary iodide increases (as a consequence of increased dietary intake of iodide) from 100 to 500 µg iodide/day, the organic thyroidal iodide content randomly ranges from 12 to20 mg, showing no relationship between increased dietary intake of iodide and thyroidal iodide content. Under these iodide intake conditions the incidence of goiter is low. However, if urinary iodide decreases below 50–60 µg/day, to perhaps 5–10 µg/day, thyroidal organic iodide content drops dramatically to an extreme low of near 2 mg and the incidence of goiter is increased. These relationships were used in the development of a preliminary HPT axis model for the human (Fisher, Campbell, and Guth, 2005). The goal of our first-generation adult rat HPT axis model was simply to describe thyroidal iodide stores and serum TSH, T4 , and T3 in the iodide sufficient (normal, euthyroid) and iodide deficient (perturbed, hypothyroid) rodent. In humans, thyroidal iodide stores represent mostly thyroid hormones (Delange and Dunn 2005), thus the human thyroid was viewed as a reservoir of thyroid hormones and if depleted sufficiently would result is increased TSH secretion in response to a decline in serum thyroid hormones. For the rat, the thyroidal iodide stores are much less (12–18 µg, McLanahan et al. (2007)), thus the prevailing thinking is that the thyroidal iodide stores are more quickly depleted, compared to humans. As a consequence, rats are thought to be more sensitive to the effects of thyroid active chemicals than humans. Dietary intake of iodide in the United States is about 240– 300 µg/day for men and 190–210 µg/day for women, with a Recommended Dietary Allowance (RDA) of 150 µg/day (NAS, 2000). In adult rats, using normal lab rodent chow, the iodide intake is near 20 µg/day, of which about 1–2 µg/day of iodide is needed to maintain normal thyroid hormone synthesis (Pedraza et al., 2006). The euthyroid human stores 10–20 mg of thyroidal iodide and in the rat 12–18 µg (McLanahan et al., 2007).

12.4

How Can We Create Equations to Describe the HPT Axis?

Firstly, each individual sub-model (iodide, T4 , T3 , and TSH) was constructed independently using published radiotracer studies in the euthyroid rat (McLanahan, Andersen, and Fisher, 2008). This pharmacokinetic modeling approach provided information on selection of model structures or compartments and pharmacokinetic properties (potential model parameter values) that were used in the BBDR-HPT axis model. The eventual linking of the submodels in the euthyroid rat for endogenously produced T4 , T3 , TSH and for intake of dietary iodide required making decisions about how to describe the linkages mathematically. One issue was how to describe control or influence of the signaling molecule, TSH, on the regulation of the sodium/iodide symporter (NIS) protein in the thyroid gland. NIS is responsible for actively sequestering iodide into the thyroid against a concentration gradient. TSH controls NIS synthesis via a receptor-mediated process at the basal lateral side of the thyroid gland, which modulates the rate of uptake of iodide from the blood supply into the thyroid gland. Additionally, TSH, via a second messanger, cAMP cascade, influences the rate of organification (binding) of iodide in the thyroid gland. This increased/decreased organification (binding) of iodide in the thyroid results in more/less precursor thyroid

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Computational Model for Iodide Economy and the HPT Axis in the Adult Rat

hormones. TSH also influences the rate of secretion of thyroid hormones into the blood supply. Another related issue was describing the relationship between serum TSH and T4 concentrations (negative feedback loop, Figure 12.2b). The process of obtaining model parameter values was an iterative process, requiring multiple simulations, visual fitting and, finally, formal optimization. A series of equations were used to describe iodide handling by the thyroid and the influence of TSH on these processes (described above). A Michaelis–Menten (M–M) equation was implemented to describe uptake of iodide into the thyroid gland by the NIS protein (rTNISi , nmol/h) based on the model predicted concentration of iodide in the thyroid venous blood (Cvti , nmol/l). The maximal rate of uptake (VmaxTi TSH , nmol/h), which varied based on serum TSH concentrations (CaTSH , nmol/l), was fitted initially to radiolabeled iodide studies (for a measured, euthyroid TSH concentration) and then with studies that measured stable or dietary iodide over a range of TSH concentrations. The equations used to describe the process of NIS active transport of iodide into the thyroid were as follows: r TNISi =

V max TiTSH × Cvti K m i + Cvti

V max TiTSH =

V max Ti × CaTSH TSH K NIS + CaTSH

(12.1)

(12.2)

The affinity of iodide (Kmi ) for the NIS protein was previously determined experimentally (Gluzman and Niepomniszcze, 1983) and used unaltered in the model. Once iodide was in the thyroid gland, the process of iodide binding to thyroglobulin (Tg) and forming precursor thyroid hormones was simply described with a M–M equation (rIB, nmol/h) using the model predicted concentration of free iodide in the thyroid gland (CTFi , nmol/l), and the maximal rate (VmaxBi TSH , nmol/h) varied based on serum TSH concentrations (CaTSH , nmol/l). Published reports of thyroidal iodide stores for rats were used as a guide to fit both the apparent binding constant (Kbi , nmol/l) and the rate of formation of precursor hormones (VmaxBi , nmol/h). The VmaxBi TSH (nmol/h) value for the rate of binding was controlled by serum TSH concentrations using a nested M–M approach, similar to the rate of iodide uptake by the NIS protein. Thus, the description for the rate of iodide organification or binding to Tg to form precursors to thyroid hormones was as follows: r IB =

V max BiTSH × CTF i K bi + CTF i

V max BiTSH =

V max Bi × CaTSH K bTSH + CaTSH

(12.3)

(12.4)

Therefore, when serum TSH concentration increased, the rate of iodide uptake (rTNISi , nmol/h) would increase along with the rate organification or binding (rIB, nmol/h) to form precursor thyroid hormones. The secretion rate of T3 and T4 from the thyroid gland was described somewhat differently (rTHprod , nmol/h), as a linear process, which was also dependent on the serum concentration of TSH (CaTSH , nmol/l) and the model predicted concentration of thyroidal bound iodide (CTBi , nmol/l) available for secretion into systemic

How Can We Create Equations to Describe the HPT Axis?

259

circulation as thyroid hormones. The linear rate term (kTSH IB , l2 /nmol/h) was fit to provide euthyroid serum T4 and T3 concentrations using literature derived data for thyroidal iodide stores and serum TSH concentrations. Overall secretion of thyroid hormones was described by: IB × CaTSH × CTBi r THprod = kTSH

(12.5)

The individual secretion rates of each hormone (T4 and T3 ) were then described as a fraction of the overall production rate of thyroid hormones (rTHprod , nmol/h). The fraction of overall thyroid hormone production that occurred as T3 (FT3 , unitless) under normal dietary iodide intakes was derived from literature and this fraction changed in relationship to the availability of iodide in the thyroid. A shift in the thyroid from primarily T4 to T3 secretion has been observed in conditions of low dietary iodide intake (Greer, Grimm, and Studer, 1968; Pedraza et al., 2006). Our model simulates this physiological shift in proportion of T4 and T3 thyroid hormone production as shown in Figure 12.3. The negative feedback loop of T4 on TSH production is important in describing HPT axis compensation and perturbations from environmental chemicals. The secretion of TSH from the pituitary gland was described with a modified version of the M–M equation that accounted for the inverse relationship between serum T4 and TSH concentrations. That is, as serum T4 concentration (CaT4 , nmol/l) drops, the production of TSH (rTSHprod ,

0.35

Fraction of Thyroid Hormone Production that is T3 (FT3)

0.30

0.25

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2

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Total Thyroidal Iodide ( g)

Figure 12.3 Model predicted shift in thyroid hormone production as total thyroidal iodide stores decrease while feeding an iodide deficient diet (0.33 µg I/day) for 12 weeks. This model simulation corresponds to the HPT axis perturbations shown in Figure 12.5. Data points in this plot adapted from Pedraza et al. (2006).

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nmol/h) increases (negative feedback loop). The modified M–M equation for the rate of TSH production from the pituitary includes the basal rate of TSH production in the absence of T4 (k0 TSH , nmol/h) that was derived from literature data on thyroidectomized animals (Connors, DeVito, and Hedge, 1984) and the concentration of serum T4 that results in half-maximal rate of TSH production (K T4 inh , nmol/l): rTSH prod =

inh k0TSH × K T4 inh K T4 + CaT4

(12.6)

These and additional equations are described in further detail in McLanahan, Andersen, and Fisher (2008).

12.5 What did We Learn from the Development of the BBDR-HPT Axis Modeling? 12.5.1

Model Development and Simulations

The rat has been used as an animal model for several decades to study many aspects of the HPT axis from a mechanistic and nutrition point of view. Using many published works and selected studies from our laboratory, a BBDR-HPT axis model for the adult rat for quasi-steady state conditions was successfully developed. That is, we predicted the effects of dietary changes in iodide intake on the HPT axis over days and months, not hours. The philosophy was to develop one set of model parameters that would describe the datasets reasonably well. Thus, agreement between model prediction and observation varied across datasets. In some cases, the experimental datasets for serum TSH and thyroid hormones were in modest disagreement. Datasets used for the BBDR-HPT axis model came from many laboratories over a period spanning three to four decades. The model was calibrated using several datasets collected in the euthyroid rat given approximately 20 µg iodide/day in rat chow. Model steady state predictions were based on iterative fittings of several parameter values (with biological constraints) and fixing the values of some model parameter values. Ultimately, the steady state model predictions were in good agreement with the range of experimentally reported total thyroidal iodide stores, free serum iodide concentration, serum and liver T4 and T3 concentrations, and serum TSH concentrations (McLanahan, Andersen, and Fisher, 2008). The next phase was to simulate ingestion of various low iodide deficient intakes of dietary iodide used in rodent studies that reported HPT axis perturbations for several endpoints of interest for modeling. Figure 12.4 shows model predicted and measured responses of the HPT axis to a low iodide diet of about 0.35 µg iodide per day for 26 days. In this case, the model slightly over predicted the rate of increase in serum TSH concentration (as fold increase from control levels) between days 10 and 15 of treatment and the maximal fold increase in TSH by day 26 of treatment. The model did adequately predict the iodide deficiency-induced gradual decline in serum T4 concentrations, reaching a nearly 10-fold drop in serum T4 concentration by day 26 of treatment. These data suggest that serum T4 concentrations were unaffected by iodide deficient diet for 3–4 days of treatment. Also, a slight decline in serum T3 concentration was predicted and was consistent with

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Figure 12.4 Short-term BBDR-HPT axis model predictions (lines) compared to data (points) following administration of a low iodide diet of 0.35 µg I/day for 26 days. Data for serum T4 , T3 , TSH, and total thyroidal iodide in adult male Holtzman Sprague–Dawley rats were adapted from Riesco et al. (1977).

the experimental data. Over the treatment period, the measured thyroidal iodide stores dropped in a quasi-linear fashion by almost two orders of magnitude, demonstrating that the thyroidal iodide reserves were severely depleted by the end of the treatment period. The model slightly overestimated the beginning amount of thyroidal iodide and the amount remaining at the end of the treatment period. The model predictions for a longer treatment period (84 days, 12 weeks) of iodide deficiency are shown in Figure 12.5. Using the same model parameter values as in Figure 12.4 and an iodide intake rate of 0.33 µg/day, the model adequately predicted the increase in serum TSH and slightly under predicted the maximal induction of TSH. Agreement was obtained between the model predicted and observed maximal decline in serum T4 concentrations by day 56 of treatment. On the other hand, by the end of treatment, model predictions of serum T3 concentrations were slightly under predicted. Thyroidal iodide stores dropped in a linear fashion until about day 25 and then loss in thyroidal iodide stores appeared to be minimal for the remainder of the study. This inflection point for thyroidal iodide stores represents a transition from the use of thyroidal iodide stores available when the study was initiated to the utilization of dietary iodide only (0.33 µg/day). The model predictions captured the depletion of thyroidal iodide stores caused by the iodide deficient diet and the transition to the new steady state using existing dietary iodide.

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Figure 12.5 Long-term BBDR-HPT axis model predictions (lines) for serum T4 , T3 , TSH, and total thyroidal iodide compared to data (points) following administration of a low iodide diet of approximately 0.33 µg I/day for 12 weeks to Simonsen Albino rats. Data were adapted from Okamura, Taurog, and Krulich (1981a).

12.5.2

Challenges Using Data from Published Literature

While developing the BBDR-HPT axis model and using it to simulate a variety of datasets (iodide sufficient and iodide deficient) from literature, it became apparent that there were many obstacles and challenges to integrating endocrine data into a toxicological kinetic analysis framework. Firstly, a number of published HPT axis datasets vary dramatically, even for control, euthyroid adult rats. For example, we elected to plot model predictions of TSH as fold change in many instances, because the database for TSH concentrations varied significantly from one laboratory to the next. For instance, the reported serum TSH concentrations for “control, euthyroid” adult male Sprague–Dawley rats ranged from 4.6 ± 0.49 ng/ml to 8.73 ± 0.81 ng/ml (McLanahan et al., 2007), approximately 15– 20 ng/ml (Siglin et al., 2000), 327 ± 174 ng/ml (Okamura, Taurog, and Krulich, 1981a), and to a highest concentration of 440 ± 220 ng/ml (Lemarchand-Beraud and Berthier, 1981). Reported serum T4 also varied across studies, though to a lesser extent. There are many factors that could contribute to this variability and should be considered in future experiments examining HPT axis effects, including time of sampling, the weight and age of the animal, and analytical methods. Analytical methods need to be standardized and improved for increased sensitivity and precision. Figures 12.2a, 12.3, and 12.4 in this chapter show how iodide intake can also severely affect the HPT axis, thus it is important that iodide intake be monitored and reported in studies of thyroid active compounds.

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Additionally, the majority of the studies of the thyroid axis include data for one dose rate and determination of effects at one or two time points; these were not ideal datasets for use in the development of the BBDR-HPT axis model. Instead, to quantify and develop effects of iodide intake on the HPT axis, we searched for and found only a handful of datasets that presented a profile of HPT axis changes over time (Okamura, Taurog, and Krulich, 1981a, b; and Riesco, Taurog, and Larsen, 1976; Riesco et al., 1977) following administration of iodine deficient diets. Toxicology studies to evaluate HPT axis effects of thyroid active compounds should also consider obtaining some time-course data on perturbations, rather than single “snapshots.”

12.6 Utility of the BBDR-HPT Axis Model The current BBDR-HPT axis model for the adult rat is a first-generation model that is being used as a starting point for the development of mathematical models of the maturation of the HPT axis. The maturing HPT axis model will be used to further the quantitative understanding of the maturation and functionality of the HPT axis during development (early life stages). In addition to serving as a starting point for the development of the maturing HPT axis models, one of the most important uses for the current BBDR-HPT axis is to link it with environmentally relevant thyroid active compounds to predict the HPT induced perturbations. Many environmental contaminants have been shown to alter HPT axis homeostasis in laboratory animals (Brucker-Davis, 1998; Zoeller, 2007), while direct evidence for HPT axis alterations in humans are suggestive or equivocal (Boas et al, 2006).

12.7

Mathematical Modeling Computer Code

One of the first steps in linking a physiologically based pharmacokinetic (PBPK) model for a thyroid active compound with the BBDR-HPT axis model is to determine the mode of action that will be used to link the models together. For example, perchlorate, an ubiquitous environmental contaminant (Motzer, 2001), has a well defined mode of action that includes the competitive inhibition of NIS-mediated uptake of iodide into the thyroid gland. We have included model code (Berkeley Madonna, Version, 8.3.18, University of California, Berkeley, California) that illustrates an approach for integration of a PBPK model of perchlorate with the BBDR-HPT axis model described previously (see QMT model library folder FISHER). The included mode code describes a theoretical in silico study examining the inhibitory effects of perchlorate on NIS-mediated thyroidal uptake of iodide under conditions where serum TSH and thyroid hormones are held constant. Serum iodide and perchlorate are also constant, steady state values in this model code; nonetheless, this demonstrates how perchlorate and iodide codes can be joined to analyze effects based upon mode of action. In rats and humans, this approach for perchlorate and iodide interaction has been used to describe the inhibitory effects on thyroidal uptake of radiolabeled iodide (Clewell et al., 2003a, b, 2007; Merrill et al., 2003, 2005). Integrating a complete PBPK model for perchlorate with the BBDR-HPT axis model will provide for quantitative evaluation of perchlorate’s mode of action linked with down-stream effects.

264

Computational Model for Iodide Economy and the HPT Axis in the Adult Rat Thyroid gland (follicle & lumen) RT4

PAT_i *CTL_i PAT_i *CTB_i

RNIS QT*CA_i

QT*CTB_i Thyroid blood

Figure 12.6 Schematic of the two-compartment model for the human thyroid gland with a blood compartment and combined follicule/lumen compartment.

Additionally, the combined models can be used to determine if the decrease in available iodide in the thyroid is solely responsible for decreases in serum T4 , which is not easily evaluated in the laboratory. The model code describes an in situ two-compartment model for the human thyroid gland (only) with a blood compartment and combined follicle/lumen compartment (Figure 12.6). Body weight of humans is 70 kg for calculating model parameters originally expressed using body weight. This model will simulate the thyroidal uptake of iodide by active transport by the sodium/iodide symporter (NIS) protein and by simple diffusion. The model is configured to track only iodide in the thyroid gland, not perchlorate. Loss of iodide from the thyroid occurs by secretion of T4 (thyroxine contains four iodide atoms) and by simple diffusion into the blood supply perfusing the thyroid. The blood supply of iodide perfusing the thyroid is assumed to be constant. The concentration of iodide in the blood (CA i) and perchlorate (CA p) can be varied, but are assumed to be at steady state concentrations. The differential equation (RNIS; see chapter and model code) describes the active uptake of iodide into the thyroid gland (tissue; follicle, and lumen lumped) from thyroid blood, as well as the competitive inhibition by perchlorate. The rate equation to describe thyroidal uptake of iodide and competitive inhibition by perchlorate is a nonlinear Michaelis–Menten equation. The Vmax i represents a maximum rate of iodide uptake by the NIS, while the Km i is the affinity constant for thyroidal NIS protein and iodide. Competitive inhibition of thyroidal uptake of iodide by perchlorate is described by (1 + (CA p/Km p)) in the denominator and multiplied by Km i. If the perchlorate blood concentration (CA p) is zero, there will be no competition between perchlorate and iodide for thyroidal uptake of iodide. When perchlorate is present in the blood (CA p = 0) then the value of Km i will be multiplied by (1 + (CA p/Km p)) resulting in competitive inhibition of thyroidal uptake of iodide by NIS. Sample Activities with model code: 1. Set the level of exposure to perchlorate equal to zero (CA p = 0.) and examine the effect of iodide intake on the amount of iodide transported into the thyroid by the NIS

References

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(ANIS). Vary the concentration of iodide in the blood (CA i = 0.01 − 100 µg/l) and record results after a 24 hour simulation (stoptime = 24). Plot results with blood iodide concentration (CA i) on the x-axis and amount of iodide transported by the NIS (ANIS) on the y-axis. 2. To demonstrate the in situ and in silico impact of varying exposures of perchlorate in a euthyroid population, set the iodide concentration in the blood (CA i = 10 µg/l) and vary the perchlorate concentration in the blood (CA p = 0 − 1000 µg/l). Note: The assumption is that the thyroid iodide content of the population is constant (20 mg) and is not depleted. Record results after a 24 hour simulation (stoptime = 24). Develop a spreadsheet to calculate the percent inhibition in uptake of iodide by perchlorate at 24 hours compared to controls for three iodide concentrations and five perchlorate concentrations. Plot results with perchlorate concentration (CA p) on the x-axis and percent inhibition (calculated in a spreadsheet) on the y-axis. 3. Because human thyroids can store large amounts of iodide in the form of thyroid hormones, the blocking effect of perchlorate (percentage inhibition of iodide uptake) results in a slow loss of stored iodide in the thyroid, depending upon the degree of inhibition of iodide uptake. Can a CA i concentration of 10 µg/l sustain the thyroid if the blood perchlorate concentration (CA p) is 50 or 150 µg/l? Run the simulations for 20 000 hours and evaluate the total mass of iodide in the thyroid (Tmass thy). a. Assume that a thyroid iodide concentration less than 10 mg will cause a decline in serum T4 concentrations and subsequent increase in serum TSH to compensate (negative feedback loop – not included in this model code). Use the model to determine the lowest concentration of perchlorate in the blood (CA p) that would cause the decline in serum T4 and increase in serum TSH. Run the model for 20 000 hours. b. You may also wish to vary the concentration of iodide in the blood (CA i) and initial stores of iodide in the thyroid (iATB i and iATL i) to simulate different scenarios. For example, how does a decrease in iodide intake by 20% that is proportional to the blood concentration (from CA i = 10 to CA i = 8) shift the perchlorate dose response curve (e.g., the dose of perchlorate that would cause a change in serum T4 and TSH concentrations)? These are just several examples of theoretical simulations that can be performed with this model to examine the effect of perchlorate on NIS active uptake of thyroidal iodide.

References Barton, H.A. and Andersen, M.E. (1998) A model for pharmacokinetics and physiological feedback among hormones of the testicular-pituitary axis in adult male rats: A framework for evaluating effects of endocrine active compounds. Toxicol. Sci., 45, 174–187. Boas, M., Feldt-Rasmussen, U., Skakkebaek, N.E., and Main, K.M. (2006) Environmental chemicals and thyroid fuction. European J. Endocrin., 154, 599–611. Brucker-Davis, F. (1998) Effects of environmental synthetic chemicals on thyroid function. Thyroid., 8, 827–856. Clewell, R.A., Merrill, E.A, Yu, K.O., et al. (2003a) Predicting neonatal perchlorate dose and inhibition of iodide uptake in the rat during lactation using physiologically-based pharmacokinetic modeling. Toxicol. Sci., 74, 416–436.

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Clewell, R.A., Merrill, E.A., Yu, K.O., et al. (2003b) Predicting fetal perchlorate dose and inhibition of iodide kinetics during gestation: A physiologically-based pharmacokinetic analysis of perchlorate and iodide kinetics in the rat. Toxicol. Sci., 73, 235–255. Clewell, R.A., Merrill, E.A., Gearhart, J.M., et al. (2007) Perchlorate and radioiodide kinetics across life stages in the human: using PBPK models to predict dosimetry and thyroid inhibition and sensitive subpopulations based on developmental stage. J. Toxicol. Environ. Health Part A, 70, 408–428. Connors, J.M., DeVito, W.J., and Hedge, G.A. (1984) The effects of the duration of severe hypothyroidism and aging on the metabolic clearance rate of thyrotropin (TSH) and the pituitary TSH response to TSH-releasing hormone. Endocrinol., 114, 1930–1937. Degon, M., Chipkin, S.R., Hollot, C.V., et al. (2008) A computational model of the human thyroid. Math. Biosci., 212, 22–53. Delange, F. (2001) Iodine deficiency as a cause of brain damage. Postgrad. Med. J., 77, 217–220. Delange, F.M. and Dunn, J.T. (2005) Iodine Deficiency, in Werner & Ingbar’s The Thyroid A Fundamental and Clinical Text, 9th edn (ed. L.E. Bravermann, and R.D. Utiger), Lippincott Williams and Wilkins. DiStefano, J.J. III, Jang, M., Malone, T.K., and Broutman, M. (1982) Comprehensive kinetics of triiodothyronine production, distribution, and metabolism in blood and tissue pools of the rat using optimized blood-sampling protocols. Endocrinol., 110, 198–213. DiStefano, J.J. III and Feng, D. (1988) Comparative aspects of the distribution, metabolism, and excretion of six iodothyronines in the rat. Endocrinol., 123, 2514–2525. DiStefano, J.J. III and Landaw, E.M. (1984) Multiexponential, multicompartmental, and noncompartmental modeling. I. Methodological limitations and physiological interpretations. Am. J. Physiol., 246, R651–R654. Fisher, J.W., Campbell, J.L., and Guth, D. (2005) A human dietary iodide PBPK model to evaluate the effects of perchlorate on thyroidal iodide content. Toxicol. Sci., 84 (suppl. 1), 869 (abstr.). Gluzman, B.E. and Niepomniszcze, H. (1983) Kinetics of iodide trapping mechanism in normal and pathological human thyroid slices. Acta Endocrinol., 103, 34–39. Greer, M.A., Grimm, Y., and Studer, H. (1968) Qualitative changes in the secretion of thyroid hormones induced by iodide deficiency. Endocrinol., 83, 1193–1198. Kohn, M.C., Sewall, C.H., Lucier, G.W., and Portier, C.J. (1996) A mechanistic model of effects of dioxin on thyroid hormones in the rat. Toxicol. Appl. Pharmacol., 165, 29–48. Lemarchand-Beraud, T. and Berthier, C. (1981) Effects of graded doses of triiodothyronine on TSH synthesis and secretion rates in hypothyroid rats. Acta Endocrinol., 97, 74–84. McLanahan, E.D., Campbell, J.L. Jr., Ferguson, D.C., et al. (2007) Low-dose effects of ammonium perchlorate on the hypothalamic-pituitary-thyroid (HPT) axis of adult male rats pretreated with PCB126. Toxicol. Sci., 97, 308–317. McLanahan, E.D., Andersen, M.E., and Fisher, J.W. (2008) A biologically based dose-response model for dietary iodide and the hypothalamic-pituitary-thyroid axis in the adult rat: Evaluation of iodide deficiency. Toxicol. Sci., 102, 241–253. Merrill, E.A., Clewell, R.A., Gearhart, J.M., et al. (2003) PBPK predictions of perchlorate distribution and its effect on thyroid uptake of radioiodide in the male rat. Toxicol. Sci., 73, 256–269. Merrill, E.A., Clewell, R.A., Sterner, T.R., and Fisher, J.W. (2005) PBPK model for radioactive iodide and perchlorate kinetics and perchlorate-induced inhibition of iodide uptake in humans. Toxicol. Sci., 83, 25–43. Motzer, W.E. (2001) Perchlorate: Problems, detection, and solutions. Environ. Foren., 2, 301–311. Nagataki, S., Shizume, K., and Nakao, K. (1966) Effect of chronic graded doses of iodide on thyroid hormone synthesis. Endocrinol., 79, 667–674. NAS (National Academy of Sciences) (2000) Dietary Reference Intakes for Vitamin A, Vitamin K, Arsenic, Boron, Chromium, Copper, Iodine, Iron, Manganese, Molybdenum, Nickel, Silicon, Vanadium, and Zinc. A report of the panel on micronutrients, subcommittees on upper reference levels of nutrients and of interpretation and use of dietary reference intakes, and the standing committee on the scientific evaluation of dietary reference intakes, Food and Nutrition Board and Institute of Medicine, National Academy Press, Washington, DC. URL: 4 November 2009). http://www.nap.edu/books/0309072794/html/ (accessed 4 November 2009).

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Okamura, K., Taurog, A., and Krulich, L. (1981a) Strain differences among rats in response to Remington iodine-deficient diets. Endocrinol., 109, 458–463. Okamura, K., Taurog, A., and Krulich, L. (1981b) Elevation of serum 3, 5, 3 -triiodothyronine and thyroxine levels in rats fed Remington diets: opposing effects of nutritional deficiency and iodine deficiency. Endocrinol., 108, 1247–1256. Oppenheimer, J.H. (1983) The nuclear receptor-triiodothyronine complex: Relationship to thyroid hormone distribution, metabolism, and biological action, in Molecular Basis of Thyroid Hormone Action (eds. J.H. Oppenheimer and H.H. Samuels), Academic Press, New York, pp. 1–34. Pedraza, P.E., Obregon, M., Escobar-Morreale, H.F., et al. (2006) Mechanisms of adaptation to iodine deficiency in rats: Thyroid status is tissue specific. Its relevance for man. Endocrinol., 147, 2098–2108. Rasgon, N.L., Pumphrey, L., Prolo, P., et al. (2003) Emergent oscillations in mathematical model of the human menstrual cycle. CNS Spectr., 8, 805–814. Riesco, G., Taurog, A., and Larsen, P.R. (1976) Variations in the response of the thyroid gland of the rat to different low-iodine diets: Correlation with iodine content of diet. Endocrinol., 99, 270–280. Riesco, G., Taurog, A., Larsen, P.R., and Krulich, L. (1977) Acute and chronic response to iodine deficiency in rats. Endocrinol., 100, 303–313. Schlosser, P.M. and Selgrade, J.F. (2000) A model of gonadotropin regulation during the menstrual cycle in women: Qualitative features. Environ. Health Perspect., 108, 873–881. Siglin, J.C., Mattie, D.R., Dodd, D.E., et al. (2000) A 90-day drinking water toxicity study in rats of the environmental contaminant ammonium perchlorate. Toxicol. Sci., 57, 61–74. Zoeller, R.T. (2007) Environmental chemicals impacting the thyroid: Targets and consequences. Thyroid., 17, 811–817.

13 Two-Stage Clonal Growth Modeling of Cancer* Rory B. Conolly1 and Melvin E. Andersen2 1

National Center for Computational Toxicology, US Environmental Protection Agency, USA 2 The Hamner Institutes for Health Sciences, USA

13.1 Introduction Chemical toxicity and especially carcinogenicity testing became high visibility scientific and political concerns of the 1970s. Laboratory methods were developed and institutionalized for evaluating whether chemicals could cause cancer in rodent species exposed to high concentrations of chemicals for up to two years (almost their entire lifespan). A variety of compounds produced tumors in organs in these mice and rats and methods were required to evaluate the risk to humans of lower exposures based on these rodent studies. The dose-response approach used a multistage model of cancer causation by exposure to a compound. In this model the probability of tumors after a specific period of dosing was: p(t) = 1 − exp(a0 + a1 ∗ d + a2 ∗ d 2 + a3 ∗ d 3 + . . . an ∗ d n )

(13.1)

This equation portrays a situation in which tumor induction at anytime is related to progress through a number of specific stages. In the 1970s, this model structure was regarded as a good representation of the biology of cancer (Crump et al., 1976). In the ∗ This manuscript has been reviewed by the National Center for Computational Toxicology, US Environmental Protection Agency and approved for publication. Approval dose not signify that the contents necessarily reflect the views and policies of the agency nor does the mention of trade names or commercial products constitute endorsement or recommendation for use.

Quantitative Modeling in Toxicology Edited by Kannan Krishnan and Melvin E. Andersen  C 2010 John Wiley & Sons, Ltd

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human epidemiology literature incidence models for various human cancers were described with equations that were polynomial in time to tumor. This time relationship is consistent with the sharp increases of many tumor types with age. The mathematics of Equation 13.1 is such that, at low doses, the linear term predominates and the expected probability of tumors becomes: p(t) ∼ a0 + a1 ∗ d

(13.2)

For risk assessment purposes, the results from a tumor study, in relation to dose groups, group sizes, control, and so on, was used to derive a 95% upper bound value on the linear coefficient, a1 , and this upper bound value used in estimating expected cancer risks at low levels of exposure. In the same decade, the molecular basis of cancer was also being more extensively investigated and this new knowledge was being introduced into models of carcinogenesis. Observations with human retinoblastoma for both sporadic and inherited forms of the disease (Knudson, 1971) led to a two-hit model of certain human cancers focusing on silencing of both alleles of tumor suppressor genes. Moolgavkar and co-workers (Moolgavkar and Venzon, 1979; Moolgavkar and Knudson, 1981) described a two-stage model for cancer. This two-stage clonal growth model has undergone extensive development and application for studying various human cancers and for applications in tumor-promotion studies. It has seen only limited use for cancer risk assessment (e.g., Moolgavkaret al., 1999; Kodell and Turturro, 2004), although a particularly thorough application has been provided for nasal cancer associated with formaldehyde (Conolly et al., 2003, 2004).

13.2 Equations for the Two-Stage Clonal Growth Model The two-stage clonal growth model (TSCGM) of cancer (Figure 13.1) contains three cell types – normal, intermediate, and malignant cells. The mathematics of these models allows evaluation of the role of mutation, cell replication, promotion, and apoptosis in the development of cancer over time. The factors that determine the time evolution of the probability of tumors in an individual include normal and intermediate cell birth and death rates, mutation frequencies for conversion of N to I cells and from I to M cells. Cancer would appear with some delay after formation of the M cell in the individual (see Portier, Sherman, and Kopp-Schneider, 2000; Little and Wright, 2003 for an entree into the literature describing the mathematical development of the model). The incidence and prevalence of tumors are calculated from the rate of formation of malignant cells (M) from the expectation of the number of intermediate cells (I) in previously tumor free animals, that is, E[I(t)M(t) = 0]. The exact formulation of the change in the conditional probability, that is, in the expectation of I cells in individuals with no M cells, is: dE[I(t)|M(t) = 0/dt = (alpha I − beta I)∗ E[I(t)|M(t) = 0] + alpha N(t)∗ µ N(t)∗ E[I(t)|M(t) = 0] − alpha I(t)∗ µ I(t)∗ V [I(t)|M(t) = 0]

(13.3)

Equations for the Two-Stage Clonal Growth Model

271

cell division alpha_N

alpha_I µ_N

N

µ_I

I mutation

beta_N

beta_I

M mutation

beta_I

tumor

cell death

Figure 13.1 Depiction of the two-stage clonal growth model for carcinogenesis. The terms are defined in the text. For the transition from one state to another, for example, from N to I cells, the rate for formation is the birth rate for N cells (alpha N) times a mutation probability, µ N.

where

alpha I = 1.0∗ alpha N, birth rate constant for N cells, beta I = beta N, death rate constant for I cells, alpha N = birth rate constant for N cells, µ N = probability of N cell mutation per division, µ I = u N, probability of N cell mutation per division, and V = variance of I(t).

The hazard at any time: d (hazard (t))/dt = alpha I(t)∗ u I(t)∗ E[I(t)|M(t) = 0]

(13.4)

The probability of tumor at any time p(tum) is determined by the integrated hazard rate up to time, t: p(tum) = 1 − exp(hazard)

(13.5)

The conditional probability leads to mathematical complexity, making the application of the model less attractive. To avoid the difficulties of the conditional probability, a simplification has been used, called the approximate solution. With this representation, tumors are considered only to arise in previously tumor-free animals. The equation for I cells developed with this assumption (Equation 13.6) overestimates incidence at high prevalence in the population, since it does not account for the variance of the expectation of I cells as in Equation 13.3. dE[I(t)/dt = (alpha I − beta I)∗ E[I(t)] + alpha N(t)∗ µ N(t)∗ E[I(t)]

(13.6)

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Two-Stage Clonal Growth Modeling of Cancer

Clewell et al. (1995) argued that the variance term in Equation 13.3 could be thought of as a correction on the approximate solution in Equation 13.6 to adjust the unconditional expectation of intermediate cells based on the time history of formation of intermediate cells by mutation of normal cells (called recruitment) and by cell division of the intermediate cell population (called expansion). This correction, added to the approximate solution with unconditional probability produced much better correspondence with the exact solutions of the conditional probability equations. Subsequently, Hoogenveen et al. (1999) extended the more intuitive approach of Clewell and derived what they called an alternative exact solution of the TSCGM for time-invariant parameters. In this form of the clonal growth model, the variance term becomes: V [I(t)|M(t) = 0] = E(I(t)|M(t) = 0] + alpha I/(µ N∗ alpha N ∗ N)∗ {E(I(t)|M(t) = 0]}2

(13.7)

Using this correction, as in the exercises in this chapter, it is possible to write straightforward sets of differential equations to predict the hazard function and the probability of tumor in a control or treated population. With these equations, it is possible to simulate a variety of conditions that mimic specific mechanisms of chemical carcinogenicity and view the predicted probability of tumor from equations that show the conditional expectation of I cells for cases where the model parameters are time invariant. The population of I cells described in the TSCGM is also of interest in studies of preneoplastic lesions, as a commonly observed in hepatocarcinogenesis (e.g., Dragan et al., 1995). The number and size of the clones of these, presumed to be clones of I cells in the context of the TSCGM, are of interest and specific analytical techniques have been developed for their study (Dewanjii, Venzon, and Moolgavkar, 1989). The equations presented herein for the TSCGM, however, track only the population of I cells as a whole and provide no information on the size and number of I cell clones. This kind of detailed analysis is beyond the scope of this chapter.

13.3 Modeling Multiple Modes of Action for Carcinogens The TSCGM equations, written for Berkeley Madonna in Box 13.1 (QMT model library folder CONOLLY), permit simulation of p(tum) of expected probability in a liver for various conditions. Cancer is a disease of disregulated cell growth and the target populations for mutation are normal and intermediate cells. To estimate the number of hepatocytes (N cells), the volume of liver is divided by volume of a single hepatocyte. With a particular set of parameters, even in the absence of chemical input, p(tum) will actually increase due to basal mutation rates per cell division and growth characteristics coded for the I cells. For the rat simulation, p(tum) at the end of 18 000 hours (750 days) can be adjusted by setting the parameters to provide a background tumor at 750 days of about 0.25 (Figure 13.2). In this approach scaling to humans would simply require increasing the volume of liver. However, if liver size is increased with all other parameters unchanged, p(tum) increases to near 1.00 in about 150 days. To simulate p(tum) in humans the simulation needs to be carried out over a human lifetime (700 800 hours for an 80-year lifespan). In order to

Modeling Multiple Modes of Action for Carcinogens

273

have p(tum) values over the human lifetime similar to those for the rat, it is necessary to alter other model parameters. Equivalent lifetime tumor probabilities would be expected if mutation probabilities in the human were lower than in the rat (2 × 10−10 rather than 1 × 10−7 ). This species difference likely represents improved DNA-repair and DNA-integrity surveillance processes in humans versus laboratory rodents.

Box 13.1: Model for Cytotoxicity and Influence on Tumor Probability Using the Hoogenveen Correction Hepatocyte volume = 5.608E-12 ;(L)

{The Hepatocyte volume is assumed to be the same for rats and humans. It’s probably not identical, but close.} LWBW = 0.04

;Liver weight as fraction of BW

BW = 0.25 STOPTIME = 18000

; Rat BW (kg) ;(hr),750 days, rat lifetime

init N = BW*LWBW/Hepatocyte volume init I = 0. init hazard = 0. u N = 1.e-7

;probability of N-cell mutation per division uI = uN ;probability of N-cell mutation per division alpha N = 0.01 ;birth rate constant N-cells(1/hr) beta N = alpha N ;death rate constant N-cells(1/hr) alpha I = 1.0*alpha N ;birth rat constant N-cells(1/hr) beta I = beta N ;death rate constant I-cells(1/hr) {Hoogenveen approximation. Hoogenveen, R.T., Clewell, H.J., Andersen, M.E., and Slob, W. (1999). An alternative exact solution of the two-stage clonal growth model of cancer. Risk Analysis 19, 9-14.} var I = I*(1 + I*alpha I/(N*alpha N*u N)) N’ = N*(alpha N - beta N) I’ = I*(alpha I - beta I) + N*alpha N*u N alpha I*u I*var I hazard’ = I*alpha I*u I ;hazard rate ptum = 1 - exp(-hazard) ;probability of tumor

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Two-Stage Clonal Growth Modeling of Cancer 1

1

(a)

0.8

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

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0.1

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0

(b)

0.9

ptum

ptum

0.9

0 0

2000

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6000

8000 1e+4 1.2e+4 1.4e+4 1.6e+4 TIME

0

1e+5

2e+5

3e+5

4e+5

5e+5

6e+5

7e+5

8e+5

TIME

Figure 13.2 Background tumor probability in rats and humans. The TSCGM was parameterized for the 750-day lifespan of the rat to provide a background probability of tumor of 25% (a proportion of 0.25 of the population), as seen on the lower line in Panel (a). This simulation had u N = 10−7 and alpha N = 0.01. When extrapolating the TSCGM to humans, the first consideration is the increasing size of the liver and the resulting increase in numbers of hepatocytes, that is, number of target cells. The upper curve in Panel (a) is the model run with all the same parameters except the larger number of cells. In Panel (b), the simulations had the appropriate number of cells for the human and the human lifetime, but the mutation probabilities for the transitions were lower, from 10−8 , 10−9 , 2 × 10−10 , and 10−10 .

13.3.1

Compensatory Cell Replication in Relation to Tumor Promotion

In the MVK model formally and in this TSCGM implementation, there are two broad modes of actions of carcinogens. One is alteration in the growth characteristics of N and I cells to change tumor probability. A second is alteration of DNA, for instance by adduction, to change the probability of mutation per division. Some reactive compounds might have both modes of action. This TSCGM model formulation allows evaluation of expected responses for compounds with these differing modes of carcinogenicity. With cytotoxic compounds such as chloroform in liver and kidney or formaldehyde in the nasal cavity of rats, exposure leads to cytotoxicity, cell death (through necrosis or apotosis), and, finally, compensatory cell replication to preserve cell number in the organ. This process of cytotoxicity and likely tumor promotion can be simulated with this first version of the TSCGM (Box 13.1) by increasing alpha N and alpha I. The probability of tumor increases as alpha N increases (Figure 13.3), with gradual increases throughout the two-year period. For this example, N and I cells were equally affected by the toxic compound. Other descriptions might have differential susceptibility of N and I cells. Such a difference might arise if metabolizing enzymes creating a toxic metabolite were absent or present at lower concentrations in I than in N cells. Another observation from this mode of action is the continuing decrease in p(tum) when the background proliferation rate falls below the basal

Modeling Multiple Modes of Action for Carcinogens

275

Figure 13.3 TSCGM Simulations for probability of tumor in the rat liver for varying cell birth rate constants. The birth rate constants for N and I cells were altered over a range of values using a batch run in Berkeley Madonna. The legend box in the figure notes the values of alpha N for each run. The third line from the bottom corresponds to the basal rate.

rate. This behavior, alteration in background tumor rate, could arise for reduced nutrition where cell turnover is reduced. Reduced calorie intake within limits is known to enhance longevity.

13.3.2

Receptor-Mediated Cell Proliferation

Some carcinogens act as mitotic agents when present in liver at sufficiently high concentrations. This group of chemicals includes enzyme inducers, such as phenobarbital, dioxin, and peroxisome proliferating agents. These compounds act by interacting with receptors in liver and initiating a battery of cellular responses that upregulate various proteins and cause liver enlargement in treated rats and mice. This mode of action was described as shown in Box 13.2 with a compound that can bind to a receptor to form a receptor–ligand complex. The proportionate occupation of the receptor by the ligand increases the birth rate constant of I cells. The pulse command introduces a one hour input pulse of magnitude 1.0 at 10 hours and repeats the input every 24 hours. This mode of action leads to more rapid increases in I cell populations and enhances carcinogenicity through greater transition rates to M cells because of the increase in the I cell populations (Figure 13.4). In this case compared to Figure 13.3, the mitogenic action is limited to the I cell population. It could include both N and I cells.

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Two-Stage Clonal Growth Modeling of Cancer

Box 13.2: Additions for Tumor Promotion With Receptor Occupancy Affecting alpha I k on = 1000 ;2nd order rate constant for formation of ligandreceptor complex k off = 100 ;first order rate constant for dissociation of ligand-receptor complex ;binding maximum A receptor total = 1 flux on = k on*dose *A receptor free flux off = k off*A receptor ligand complex A receptor ligand complex’ = flux on - flux off A receptor free = A receptor total - A receptor ligand complex alpha I = alpha I basal*exp(-A receptor ligand complex) + alpha I max*(1-exp(-.... A receptor ligand complex)) beta I = alpha I init A receptor ligand complex = 0. dose = PULSE(1,10,24) ;every 24 hr

Figure 13.4 TSCGM Simulations for probability of tumor in the rat liver for tumor promotion. In this structure (Box 13.2) the carcinogenic chemical interacts with a receptor and the receptor-chemical complex increases the birth rate of intermediate cells. This family of curves was obtained with a batch run varying the dissociation constant for the chemical-receptor complex over seven orders of magnitude.

Modeling Multiple Modes of Action for Carcinogens

13.3.3

277

DNA Reactive Modes of Action

Reactive compounds may directly react with DNA to form adducts. When these adducts are present during DNA synthesis, they have the ability to increase the likelihood of mutation during cell division, that is, to increase u N and u I. This mode of action is captured in Box 13.3. Here, a compound is introduced via a squarewave pulse of magnitude “conc” for six hours in a pattern that repeats every 24 hours. This input is added to the model as the dose term in the reaction causing adduction of DNA. The adduction occurs with a second-order adduction rate constant, k formation adduct, and a repair rate, k repair DNA. The presence of adduct causes an increase in the mutation probability through a proportionality constant, k adduct pmut. The equation for the increase in mutation rate is: u N = u I = u N basal + k adduct pmut∗ A adduct

(13.8)

This model construct can be used to examine the alterations in tumor probability for different adduction rates, repair rates, and mutation probabilities. The changes in adduct load with respect to time reach a steady repeating pattern after a few days and would have a saw tooth daily pattern (for the current set of adduction parameters) throughout the 18 000 hour simulation (Figure 13.5). The batch run in the right panel here also shows the more rapid appearance of tumors as the mutational probability increases from 1 × 10−5 to 1 × 10−4 . The curves for p(tum) with this DNA reactive mode of action increase more rapidly with time than those for the promotional modes of action (Figures 13.3 and 13.4). Once again, the dose response for p(tum) after two years for various suites of parameters can be visualized with a parameter plot. These dose-response curves for various values of the probability of mutation, k-adduct-pmut, are parallel and displaced increasingly to the left as k adduct pmut increases (Figure 13.6).

Box 13.3: Model Additions for DNA-Reactivity Simulations conc = 1.0 ;inhaled concentration input1 = 1.0 ;creates square wave pulse of size-input1 tinput = 6.0 ;h, duration of each input input2 = IF MOD(TIME, 24) < = tinput THEN input1 ELSE 0 ; input2 is the squarewave input dose = conc*input2 ;multiplies pulse by conc to give dose input below k formation adduct = 0.0002 k repair DNA = 0.1 k adduct pmut = 0.0002 A adduct’ = k formation adduct*dose - A adduct*k repair DNA u N = u N basal + k adduct pmut*A adduct ;probability of mutation per division uI = uN

Figure 13.5 TSCGM Simulations for probability of tumor in the rat liver for DNA Reactivity Model. The left panel shows the time course for the adduct load over the first eight days of the simulation; these daily peaks then repeat throughout the 18 000 hours. In the right panel, curves show the p(tum) expected for different values of the efficacy of the adduct for causing mutation, that is, k adduct pmut. Model equations for DNA reactivity appear in Box 13.3. Batch results could also be generated for rate of adduction and rates of repair to see their influence on the shape of the curves.

Figure 13.6 TSCGM Simulations for probability of tumor in the rat liver for varying doses in the DNA reactivity mode of action for cancer. In this view, the p(tum) at 18 000 hours is plotted for different conc inputs using a parameter plot function in Berkeley Madonna. Individual curves are generated for various values of k adduct pmut, from 0.01, 0.001, 0.0001 0.000 01. The curve to the right has the lowest value and the curves shift sequentially to the left as the value is increased.

Modeling Multiple Modes of Action for Carcinogens

13.3.4

279

Multiple Modes of Action for Carcinogens

Reactive compounds are likely to have the capacity both to kill cells and increase replication, and to interact with DNA to increase mutation probability per division. There may also be “conditional” aspects of the interaction of these two mechanisms of carcinogenicity. For instance, adduct repair may be adequate to clear all adduct in the absence of overt cellular toxicity. However, with toxicity, cell death and replication, the cell environment, and the cell DNA repair processes are likely to function differently from low, non-toxic doses. In this case, it might be necessary to include dose dependencies for the mutation probability depending on the level of cytotoxicity and cell replication. These mixed mode of action carcinogens could give rise to even steeper time- and dose-dependencies of p(tum) than with either mode of action alone. The last example (Box 13.4) provides a simple method to code for two modes of action, including a complex dose-dependence of cell replication. Here, a potency term enhances the mutational probability for the N and I cells as dose increases (Equation 13.9) and the cell replication rate is a quadratic function of dose (Equation 13.10). u N = 2 × 10−7 ∗ (potency ∗ dose + 1)

(13.9)

alpha N = 0.00015 − b ∗ dose + a ∗ doseˆ2

(13.10)

This model generates a U-shaped tumor dose-response (Figure 13.7) when the rate of cell division (alpha N) is a U-shaped function of dose and the probability of mutation per cell division (u N) is constant with dose (i.e., potency is 0.0). When u N increases with dose, the tumor dose-response curves change from U-shape to become monotonically increasing. This example shows that dose linear increases in the probability of mutation may in some cases not increase the tumor response above its baseline level. Compounds that produce these complex dose-response behaviors include caffeic acid and formaldehyde (Lutz et al., 1997; Conolly et al., 2003). With these various modules as templates, the interested reader can generate mixed mode of action hypotheses for carcinogens and evaluate their expected time- and dose-dependent behaviors through simulations with this TSCGM in Berkeley Madonna or similar software packages that solve simple differential equations.

Box 13.4: Additions for Including Two Modes of Action dose = 1 potency = 0 u N = 2.e-7 * (potency * dose * 1) uI = uN per division a = 0.0001 b = 0.0002 alpha N = 0.00015 -b*dose + a*doseˆ2

;probability of mutation

280

Two-Stage Clonal Growth Modeling of Cancer 1

ptum(final)

0.3162

0.1

0.03162

0.01 0

0.5

1

1.5

2

2.5

3

dose

Figure 13.7 TSCGM Simulations for two modes of action with varying potency values. This simulation shows the parameter plots for a situation where the birth rate constants are represented by a quadratic function, equivalent to two different mechanisms of action on promotion. Potency, which varies for the five curves (increasing from 0.0, 0.5, 1.0, 2.0, and 3.0), reflects increasing mutational probability with increasing dose. The upper curve has the highest potency value. As potency decreases, the curves drop and move to the right respectively.

13.4

Conclusion

Compelling evidence from histopathological, epidemiological, and molecular biological studies indicates that malignant transformation is the end result of an accumulation of alterations in the cellular genome and that the process of accumulating these alterations is profoundly affected by changes in cell proliferation kinetics (Gaylor and Zheng, 1996; Lutz and Kopp-Schneider, 1999). The TSCGM is the simplest mathematical model of carcinogenesis to incorporate explicitly both genomic alterations and cell proliferation kinetics. However, Moolgavkar et al. (1999) emphasized that the model should not be interpreted to mean that carcinogenesis results from two rate-limiting mutations. Indeed, for most cancers, the number of rate-limiting mutations is not known. Rather, the model can be interpreted within the framework of the initiation-promotion progression paradigm of chemical carcinogenesis. Initiation, which typically confers a growth advantage, is a rare event that may involve one or more mutations. Promotion consists of the clonal expansion of these initiated cells. Finally, one of the initiated cells may be converted into a malignant cell.

References

281

This step may also involve more than a single mutation. The two-stage clonal expansion model is thus best thought of as a biologically motivated model, as opposed to a mechanistic model of cancer. Use of this model does not avoid uncertainty about the actual mechanism, and the structure and parameters of the model might not have a one-to-one correspondence with specific cellular or biochemical entities. Nonetheless, the TSCGM can be applied to evaluate the influence of different biological processes on expected tumor probability and can be used to simulate different mechanistic classes of chemical carcinogenesis. The examples here provide starting points for looking broadly at these modes of action. Interestingly, the basic outline for implementation of the TSCGM, using the Hoogenveen correction, requires just three differential equations – for N cells, I cells, and hazard rate. Other examples included equations to track time-dependent changes in adducts and the ligand–receptor complexes, but the TSCGM basics are just the three state equations. These cancer models move the usual PK models for concentrations of chemicals or amounts of adducts and concentration of ligand–receptor complex to a second stage asking about the consequences of these interactions for behavior of individual cells. The examples here provided only rudimentary PK inputs into the TSCGM. However, the linkages for specific problems could be as detailed as required by the knowledge of the kinetics of chemical disposition and the interactions with biological processes that affect parameters in the TSCGM. The example of using a TSCG model for cancer risk assessment with formaldehyde introduced a very detailed model for delivery of formaldehyde to various regions in the nose to produce alterations in cell proliferation and mutation (Conolly et al., 2003).

References Clewell, H.J. III, Quinn, D.W., Andersen, M.E., and Conolly, R.B. (1995) An improved approximation to the two-stage clonal growth model of cancer. Risk Anal., 15, 467–473. Conolly, R.B., Kimbell, J.S., Janszen, D., et al. (2003) Biologically motivated computational modeling of formaldehyde carcinogenicity in the F344 rat. Toxicol Sci., 75, 432–447. Conolly, R.B., Kimbell, J.S., Janszen, D.J., et al. (2004) Human respiratory tract cancer risks of inhaled formaldehyde: Dose-response predictions derived from biologically-motivated computational modeling of a combined rodent and human dataset. Toxicol. Sci., 82, 279–296. Crump, K.S., Hoel, D.G., Langley, C.H., and Peto, R. (1976) Fundamental carcinogenic processes and their implications for low dose risk assessment. Cancer Res., 36, 2973–2979. Dewanjii, A., Venzon, D.J., and Moolgavkar, S.H. (1989) A stochastic two-stage model for cancer risk assessment. II. The size and number of premalignant clones. Risk Anal., 9, 179–187. Dragan, Y., Teeguarden, J., Campbell, H., et al. (1995) The quantitation of altered hepatic foci during multistage hepatocarcinogenesis in the rat: transforming growth factor alpha expression as a marker for the stage of progression. Cancer Lett., 93, 73–83. Gaylor, D.W. and Zheng, Q. (1996) Risk assessment of nongenotoxic carcinogens based upon cell proliferation/death rates in rodents. Risk Anal., 16, 221–225. Hoogenveen, R.T., Clewell, H.J., Andersen, M.E., and Slob, W. (1999) An alternative exact solution of the two-stage clonal growth model of cancer. Risk Anal., 19, 9–14. Kodell, R.L. and Turturro, A. (2004) Risk-assessment implications of mechanistic model’s prediction of low-dose nonlinearity of liver tumor risk for mice fed fumonisin b(1). Nonlinearity Biol. Toxicol. Med., 2, 35–43. Knudson, A.G. (1971) Mutation and cancer: Statistical study of retinoblastoma. Proc. Natl. Acad. Sci. USA, 68, 820–823.

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Little, M.P. and Wright, E.G. (2003) A stochastic carcinogenesis model incorporating genomic instability fitted to colon cancer data. Mathematical Biosciences, 183, 111–134. Lutz, W.K. and Kopp-Schneider, A. (1999) Threshold dose response for tumor induction by genotoxic carcinogens modeled via cell-cycle delay. Toxicol Sci., 49, 110–115. Lutz, U., Lugli, S., Bitsch, A., et al. (1997) Dose response for the stimulation of cell division by caffeic acid in forsestomach and kidney of the male F344 rat. Fundam. Appl. Toxicol., 39, 131–137. Moolgavkar, S.H. and Knudson, A.G. Jr. (1981) Mutation and cancer: A model for human carcinogenesis. J. Natl. Cancer Inst., 66, 1037–1052. Moolgavkar, S.H. and Venzon, D.J. (1979) Two-event models for carcinogenesis: Incidence curves for childhood and adult tumors. Math. Biosci., 47, 55–77. Moolgavkar, S.H., Luebeck, E.G., Turim, J., and Hanna, L. (1999) Quantitative assessment of the risk of lung cancer associated with occupational exposure to refractory ceramic fibers. Risk Analysis, 19, 599–611. Portier, C.J., Sherman, C.D., and Kopp-Schneider, A. (2000) Multistage, stochastic models of the cancer process: A general theory for calculating tumor incidence. Stochastic Env. Res. Risk Assess., 14, 173–179.

14 Statistical and Physiological Modeling of the Toxicity of Chemicals in Mixtures* Hisham A. El-Masri1 , Michael A. Lyons2 , and Raymond S. H. Yang2 1

Integrated Systems Toxicology Division, National Health and Environmental Effects Research Laboratory, US Environmental Protection Agency, USA 2 Qunantitative and Computational Toxicology Group, Colorado State University, USA

14.1 Introduction Toxicological interactions modulate pharmacokinetic (absorption, distribution, metabolism, and excretion) and/or pharmacodynamic (e.g., receptor binding, cellular replication, etc.) mechanisms of single chemicals. In some cases interactions between chemicals may take place before they are introduced into a biological system; for example, more toxic nitrosamines are formed by the reaction between nitrites and amines as they are being introduced into biological tissues. Once present in exposure pathways, chemical components of a mixture can enhance or retard their individual absorption rates into tissues. For example, some organochlorine pesticides and polychlorinated biphenyls possess estrogenmimicking properties and have been measured in human breast adipose tissue and in human milk. These chemicals enter breast tissue from varied environmental contamination of food,

∗ The research described in this article has been reviewed by the National Health and Environmental Effects Research Laboratory, US Environmental Protection Agency and approved for publication. Approval dose not signify that the contents necessarily reflect the views and policies of the agency nor does the mention of trade names or commercial products constitute endorsement or recommendation for use.

Quantitative Modeling in Toxicology  C 2010 John Wiley & Sons, Ltd

Edited by Kannan Krishnan and Melvin E. Andersen

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Statistical and Physiological Modeling of the Toxicity of Chemicals in Mixtures

water, and air, and due to their lipophilic properties can accumulate in breast fat. However, in many situations, breast tissue is also exposed to a range of estrogenic chemicals applied as cosmetics. When these cosmetics are left on the skin, they facilitate a more direct dermal absorption route for breast exposure to the estrogenic chemicals (Darbre, 2006). Interactions can also take place during distribution, metabolism, and excretion of chemicals. Examples of pharmacokinetic interactions have been given by Mumtaz and Hertzberg (1993). An example of a clear synergistic pharmacodynamic interaction is the increased lethality of rats exposed to combinations of carbon tetrachloride and chlordecone (Kepone) (Mehendale, 1990). The mechanism of this interaction is not well established but it is thought that Kepone retards the ability of the liver to repair injured and/or regenerate dead cells caused by carbon tetrachloride liver toxicity. Limitations of available resources make it unlikely that experimental toxicology will provide health risk information about all the possible mixtures to which humans may be exposed. Using the combinational notation (n Ci ) for the number of (i) experiment combinations taken from the total number of components in the mixture (n), the overall number of experiments needed to cover all possible combinations in a mixture is equal to n C1 + n C2 + n C3 + n C4 +. . . n Ci . . .+ n Cn . This summation adds up to 2n − 1. For example, a mixture consisting of four components (A, B, C, D) would require four (4 C1 ) individual experiments (A, B, C, and D) plus six (4 C2 ) binary experiments (AB, AC, AD, BC, BD, and CD) plus four (4 C3 ) tertiary experiments (ABC, ACD, ABD, and BCD) plus one (4 C4 ) ternary experiment (ABCD). For one dose level of each component, the total number of experiments in this ternary mixture is fifteen. For several dose levels and a large number (n) of mixture components, it is easy to see the need for more efficient and economical experimental designs. These designs can be used with computational methods (predictive toxicology) to simulate dose-response relationships of mixtures and estimate the significance of the presence or absence of interactions. The purpose of this chapter is to present common methods used for investigating toxicology of chemical mixtures with emphasis on the role of mechanistically based computational methods in identifying interaction mechanisms and thresholds.

14.2

Experimental and Statistical Methods to Investigate Toxicological Interactions

Methods for the analysis of toxicological interactions are either devised to identify the presence or absence of interactions, and/or to investigate the mechanisms of interactions if they exist. Toxicological studies of mixtures employ either a whole mixture concept or more detailed formulated fractions of a whole mixture. Whole mixture studies involve exposing test systems, in vitro and/or in vivo, to the intact mixture and conducting dose-response studies to evaluate the nature and magnitude of the hazard associated with exposure. This approach is applied to study real-life mixtures, such as tobacco smoke, jet fuels, or specially designed mixtures (Mauderly, 1993). Formulated mixtures employ either full factorial design encompassing the whole dose-response region of the mixtures, or subsets of it. Figure 14.1 is an illustration of designs used to study effects of mixtures of two chemicals.

Experimental and Statistical Methods to Investigate Toxicological Interactions

285

(b)

Dose B

Dose B

(a)

Dose A

Dose A

(d)

Dose B

Dose B

(c)

Dose A Dose A

Figure 14.1 Common experimental designs used to study the joint effect of binary mixtures. (a) Factorial design encompasses all dose combinations of both chemicals. (b) Simplex design for two chemicals consisting of dose combinations that lie in a straight line. Simplex designs are usually useful in screening, but require follow up for identifying interaction paramters. (c) Ray designs consisting of experimental points lying on straight lines stemming from origin. Each line is a collection of experiments where the ratio of doses is fixed. Ray designs are ideal for studying the additivity of chemical mixtures (Gennings, 1995; Meadows et al., 2002). (d) Central composite design. This design requires the minimum number of experiments while combing features of other designs.

In general, statistical methods applied to chemical mixtures are conducted to detect interaction based on changes of dose-response relationship slopes from additivity (Gennings et al., 2005). If the slope of the dose-response curve of one chemical does not significantly change in response to the presence of other chemicals, then there is no interaction between the first chemical and the rest of the mixture’s components. Using data from individual and mixtures toxicology studies, statistical analysis of interaction is then used for detecting any significant changes of the dose-response slope. Absence of toxicological interaction is then tested against the possibility of additive response when the chemicals are co-administered to test animals. Central to the application of statistical methods in mixtures toxicology is the definition of additivity as provided by Berenbaum (1985; 1989): c
xi =1 E i i=1

(14.1)

286

Statistical and Physiological Modeling of the Toxicity of Chemicals in Mixtures

where xi is the concentration of chemical i in a mixture of c chemicals, and Ei is the concentration of chemical i at the predetermined response (e.g., LD50) when administered alone. Detection of interaction is then based on statistically significant deviation of the sum (given by the left-hand side of the above equation) from unity. If the sum is less than one, then a greater than additive response is claimed of the mixture at the doses given. When the left-hand side of the above equation is greater than unity, then less than additive response is assumed. Berenbaum’s (1985; 1989) definition of additivity is related to doses of chemicals individually and in a mixture at specific dose-response regions (Gennings et al., 2005). Hence, application of the above additivity equation does not require the presence of parallel individual dose-response curves, a usual assumption for similarity in toxicological mechanism used, for example, in the Toxicity Equivalency Factor (TEF) method. Gennings et al. (2005) provided an algebraic equivalent of the Bernebaum’s definition of additivity to statistical additivity models using an approximation of the dose-response function based on Taylor’s series expansion. Their analysis starts by assuming g(µ) to be a known function of the mean response of interest in an analysis of a mixture of c components. This function can be thought of as a mathematical transformation fitted to the response of chemicals in the mixture (µ). If g(µ) is a function of the exposure concentrations of the mixture’s components, and it is a differentiable and continuous function over the range of doses used in the mixture, then a Taylor’s series approximation of g(µ) is approximated by Gennings et al. (2005) as follows: (1) (1) g(µ) = f (0, 0, 0, . . . 0) + f 1 (0, 0, 0, . . . 0) + f 2 (0, 0, 0, . . . 0)

+...

f 1(c) (0, 0, 0,

. . . 0) +

c−1
c


f i(2) j (0, 0, 0 . . . 0)

i=1 j=i+1

+

c−2
c−1
c


f i(3) jk (0, 0, 0, . . . 0)

i=1 j=i+1 k=i+2 (c) + . . . f 1,2,...c (0, 0, 0, . . . 0)

xi x j 2!

xi x j xk 3!

xi x j xk , . . . xc c! (14.2)

(n) (0, 0, 0, . . . 0) is the nth partial derivative of f with respect to variables where f variables evaluated at (0, 0, 0, . . . 0). If each of the derivative terms can be represented as an unknown constant β (·) , where the subscript (· ) denotes that variables used in the derivative and β 0 = f (0, 0, 0, . . . 0), β 1 = f 1(1) (0, 0, 0 . . . 0), β 2 = f 2(1) (0, 0, 0 . . . 0), . . . β c = (2) f c(1) (0, 0, 0 . . . 0), β 12 = f 12 (0, 0, 0 . . . 0), and so on. Equation 14.2 can be rewritten as:

g(µ) = β0 + β1 x1 + β2 x2 + β3 x3 + . . . . βc xc +

c−1
c


βi j xi x j

i=1 j=i+1

+

c−2
c−1
c
i=1 j=i+1 k=i+2

βi jk xi x j xk + . . . .. β12..c xi x j ..xc + . . .

(14.3)

Experimental and Statistical Methods to Investigate Toxicological Interactions

287

Equation 14.3 can be truncated to approximate g(µ) as: g(µ) ≈ β0 + β1 x1 + β2 x2 + β3 x3 + . . . . βc xc +

c−1
c


βi j xi x j

i=1 j=i+1

+

c−2
c−1
c


βi jk xi x j xk + . . . .. β12..c xi x j ..xc

(14.4)

i=1 j=i+1 k=i+2

Equation 14.4 is a mathematical approximation of the response surface of the mixture as a function of varying doses of each chemical individually or in combinations. Graphical representations for binary mixtures of fixed response contours of the response surface equation are defined as isoboles. Reviews for the application of response surface methodology and isobole based analyses in investigating toxicological interactions of chemical mixtures are given by Greco, Bravo, and Parsons, (1995), el-Masri, Reardon, and Yang, (1997), and Cassee et al., (1998). The response surface equation (Equation 14.4) is the basis for statistical analysis to test the presence of interaction among chemicals in mixture. The statistical strategy starts by assuming additivity, which reduces Equation 14.4 to: g(µ) = β0 +

c


βi xi

(14.5)

i

The parameters in the additivity equation above can be estimated using single chemical dose-response data only. For instance, the method of iteratively reweighted least-squares is used to estimate the unknown parameters in the additivity model. Once the parameters are estimated and the goodness of fit is ascertained, the estimated additivity model is used to construct a prediction interval of the specified combination of interest. Comparison of the measured responses in mixtures with the predicted additive interval provides criteria to identify the presence and direction of the toxicological interaction. Details and application of the above statistical procedure to investigate interactions in a chemical mixture are given by Gennings (1996). Similarly, Carter and Carchman (1988) provided a statistical methodology to test for the presence and direction of interaction using the approximation equation for the response surface of a mixture. It is easier to illustrate their methodology for a binary mixture starting with the following equation for the response surface: g(µ) = β0 + β1 x1 + β2 x2 + β12 x1 x2

(14.6)

The above equation can be rearranged to: 1−

x2 β12 x1 x2 x1 + = (g(µ0 ) − β0 ) (g(µ0 ) − β0 )/β1 (g(µ0 ) − β0 )/β2

(14.7)

When the cross-product constant β 12 is not significantly different from zero, no interacβ12 x1 x2 ) is greater than one when tion is detected. If β 12 is less than zero, then (1 − (g(µ 0 )−β0 ) g(µ0 ) > β 0 , indicating less than additive interaction. If β 12 is more than zero, then β12 x1 x2 ) is less than one when g(µ0 ) > β 0 , indicating greater than additive interaction. (1 − (g(µ 0 )−β0 )

288

Statistical and Physiological Modeling of the Toxicity of Chemicals in Mixtures

Therefore, a statistical methodology to test the deviation of β 12 from zero is used to assess the significance and direction of interaction. Efficient experimental design is needed to yield estimates of the measured response in mixture experiments to be used in statistical comparisons with additivity models. A classical design in the statistical literature for studying toxicological interaction is a factorial design where each of the chemicals in the mixture is studied at all levels of the other chemicals. Generally, the levels of each chemical component are evenly spaced, so as to cover symmetrically the dose region of interest (Gennings, 1996). The logic of a factorial design, as well as of many others, is to support efficiently the estimation of a response surface that includes the interaction parameters, which is usually described by the response surface equation (Gennings, 1996; Gennings et al., 2005):

g(µ) ≈ β0 + β1 x1 + β2 x2 + β3 x3 + . . . . βc xc +

c−1
c


βi j xi x j

i=1 j=i+1

+

c−2
c−1
c


βi jk xi x j xk + . . . .. β12..c xi x j ..xc

(14.8)

i=1 j=i+1 k=i+2

An example of a full factorial design was the study of developmental toxicity in Fischer 344 rats caused by combinations of trichloroethylene (TCE), di(2-ethylhexyl)phthalate (DEHP), and heptachlor (HEPT) (Narotsky et al., 1995). This study consisted of a 53factorial design resulting in 125 dose experimental groups. As the number of chemicals in a mixture increases, factorial designs become prohibitive in cost and resources. A more economical design is a ray design (Gennings, 1996). In ray designs, mixtures of the chemicals under study are evaluated along rays of fixed ratios. One of the primary advantages to using fixed-ratio ray designs is the savings in terms of experimental resources required to test hypotheses of additivity using the mathematical and statistical analyses provided earlier. Selection of mixture points in regions of environmental or biological relevance (defined by fixed-ratio mixtures of the chemicals in mixtures) results in economical and practical designs for use in testing for interactions when the number of components of the mixture is large (Gennings, 1995) Meadows et al. (2002) developed optimal experimental design strategies for tests of interactions using fixed-ratio ray designs. An example of the fixed-ratio ray design was a study using a mixture of five organophosphorus (OP) pesticides (chlorpyrifos, diazinon, dimethoate, acephate, and malathion) in both adult and pre-weanling rats (Moser, Simmons, and Gennings, 2006). Cholinesterase inhibition and behavioral changes (motor activity, gait, and tail-pinch response) were measured in 17-day-old Long-Evans male rats following acute exposure to the OPs. Dose-response data collected for each OP were used (alone or in conjunction with the mixture data) to build an additivity model to predict the effects of the pesticide mixture along a ray of increasing total doses, using the same fixed ratio of components. Analysis of the full ray revealed significant greater-than-additive responses for all endpoints.

Biologically Based Modeling of Toxicological Interactions of Chemical Mixtures

14.3

289

Biologically Based Modeling of Toxicological Interactions of Chemical Mixtures

Mechanistic models incorporate mathematical description of biological processes to describe tissue disposition, metabolism, excretion, and/or physiological and biochemical effects of mixtures. Physiologically based pharmacokinetic/pharmacodynamic (PBPK/PD) models are examples of mechanistic models used in mixtures’ research. Because they include explicit mathematical description of biological processes related to mechanisms of interactions, PBPK models represent a potentially useful framework for investigating mixtures of increasing complexity (Krishnan et al., 2002). A schematic of a general PBPK model is given in Figure 14.2. One of the first examples that used PBPK model to investigate kinetic interactions was developed for trichloroethylene (TCE) and 1,1-dichloroethylene (1,1-DCE) (Andersen et al., 1987). The binary interaction PBPK model was used to quantitatively distinguish between different types of enzyme inhibition interactions between TCE and 1,1-DCE: competitive, uncompetitive, and noncompetitive. Applying the appropriate equations describing each inhibition mechanism into the interaction PBPK model and comparing the model prediction to experimental results from gas uptake studies, Andersen et al. (1987) were able to identify competitive inhibition as the mechanism of interaction between TCE and 1,1-DCE. Following similar mechanistic hypotheses of enzymatic interactions, a methodology involving several PBPK models can be used to estimate the overall interaction in complex mixtures. For instance, all component PBPK models in a mixture can be interconnected at the binary level, such that the overall PBPK framework simulates the kinetics of all mixture

Lungs

Adipose tissue Slowly perfused tissues Richly perfused tissues Liver metabolism & competition

Figure 14.2 A generic PBPK model consisting of five compartments. Each compartment represents a set of tissues that are biochemically and physiologically relevant to the chemical being modeled.

290

Statistical and Physiological Modeling of the Toxicity of Chemicals in Mixtures

components, accounting for the enzymatic interactions occurring at various levels in more complex mixtures (Krishnan et al., 2002). An example of this methodology was used for m-xylene, toluene, ethyl benzene, dichloromethane, and benzene in mixtures of varying composition and complexity (Haddad et al., 1999). Another example using similar methodology investigated the interactions of alkyl benzenes mixture in rats and humans (Tardif et al., 1997). A different approach to using PBPK modeling for complex mixtures was based on the chemical engineering concept of lumping. This approach was applied to a mixture of gasoline hydrocarbons (Dennison et al., 2004). Despite being comprised of hundreds of components, the lumped components of a gasoline mixture were described using a single set of chemical parameters (such as volatility-weighted fractions) that depended on the blend of gasoline. Treating the lumped gasoline components as a single chemical, the PBPK model successfully accounted for enzymatic competitive inhibition binary interactions between the lumped component and five other chemical components (benzene, toluene, ethylbenzene, xylene, and hexane). This type of modeling approach served as a first example of how the engineering concept of chemical lumping can computationally be used in pharmacokinetics. PBPK/PD models are developed when PBPK models are mathematically linked to a physiological or biochemical response at target tissues. Few examples in the literature illustrate the application of PBPK/PD models for analyzing toxicological interactions. One example was the quantitative investigation of the interaction mechanism between Kepone and carbon tetrachloride using a PBPK/PD models (el-Masri et al., 1996b). Carbon tetrachloride (CCl4 ) lethality in Sprague–Dawley rats is greatly amplified by pretreatment of Kepone (Mehendale, 1990). This increase in lethality was attributed to the obstruction of liver regenerative processes after toxic insult by CCl4 . Based on the available mechanistic information of Kepone/CCl4 interaction, such as inhibition of regenerative proliferation and reduction of repair mechanism rates, a PBPK/PD model was constructed where effects of Kepone on CCl4 toxicity were incorporated (Figure 14.3). Subsequently, the PBPK/PD model, coupled with Monte Carlo simulation, was used to predict lethality of rats treated with CCl4 alone and CCl4 in combination with Kepone. PBPK/PD-Monte Carlo model simulations estimated lethality rates which were not significantly different from the observed mortality, with the exception of CCl4 application at very high doses (e.g., 6000 microliters/kg, p = 0.014) (el-Masri et al., 1996b). Deviation of the predicted mortality from the observed ones at very high doses may be attributed to extrahepatic systemic toxicities of CCl4 , or solvent effects on tissues at high concentrations, which were not included in the model. Based on Monte Carlo simulations, which were used to run electronically 1000 lethality experiments for each dosing situation, the LD50 estimates for CCl4 toxicity with and without Kepone pretreatment were 47 and 2890 µl/kg, respectively. However, much of this amplification of CCl4 lethality with Kepone pretreatment was probably due to pharmacokinetic factors, because when target tissue dose (i.e., model estimated amount of CCl4 metabolites) was used to evaluate lethality, this amplification was reduced to fourfold.

14.4

Interaction Thresholds

Dose-dependent changes in toxicity mechanisms of single chemicals can possibly take place along the full dose-response spectrum. At high doses, the possibility exists for some steps

Interaction Thresholds

291

{Set of physiological Parameters} One set of parameters Kepone Interaction representing one animal CCl4 PBPK Model

Cell division/death submodel

Animal survival/Death 1000 Monte-Carlo Simulations

Animal LD50

Figure 14.3 A schematic of the Monte Carlo pharmacodynamic modeling of Kepone and CCl4 to predict LD50 in rats (el-Masri et al., 1996b).

in the principal mechanism of toxicity to shift to other mechanisms. Some case studies illustrating these phenomena are given for acetaminophen, butadiene, ethylene glycol, formaldehyde, manganese, methylene chloride, peroxisome proliferator activated receptor (PPAR), progesterone/hydroxyflutamide, propylene oxide, vinyl acetate, vinyl chloride, vinylidene chloride, and zinc (Slikker et al., 2004). The possibility of mechanism shifts for single chemicals can also be observed for interaction mechanism of chemical mixtures. For instance, interactions (synergism or antagonism) taking place at high individual doses of a mixture may not be significant at low levels. One of the early experiments indicating a change of the mechanism of interaction with dose was conducted using chloral hydrate and ethanol (Gessner and Cabana, 1970). The binary mixture was investigated using a fixed response of 50% of the mice losing the righting reflex (ED50). The authors compared the experimentally determined ED50s at 19 different dose combinations to lines of additivity formed by connecting the upper and lower confidence limits of the ED50s of the individual drugs. Evidence for a departure from additivity was provided whenever the confidence bounds for the experimentally determined ED50 for a combination did not overlap with the additivity confidence region. The isobologram of Gessner and Cabana associated with the empirical ED50s of ethanol and chloral hydrate is consistent with the existence of an interaction threshold. Inspection of the isobologram shows additivity to be prevalent for a combination of chloral hydrate less than 125 mg/kg and ethanol greater than 1200 mg/kg for the ED50 response. When chloral hydrate exceeds 125 mg/kg and ethanol is less than 1200 mg/kg in combination, there is a synergistic interaction (Figure 14.4) (Hamm, Carter, and Gennings, 2005). This suggests the possibility of an interaction threshold when the chemicals are combined. The dose region where interactions signaling deviation from additivity are not significant is described as the interaction threshold dose region. The boundary that separates the dose space into regions of interaction and additivity, called the interaction threshold boundary, is of interest to locate (Hamm, Carter, and Gennings, 2005). The interest in defining this region is important because it signifies the need to include or exclude interactive effects in the calculations of health risks of the mixtures, specifically at low environmentally relevant

292

Statistical and Physiological Modeling of the Toxicity of Chemicals in Mixtures

Synergy

Chloral Hydrote (mg/kg I.P)

250

200

150

100

50

Additivity 0

0

400

800

1200

1600

2000

2400

2800

Ethonol (mg/kg I.P)

Figure 14.4 Isobolgram for the chloral hydrate and ethanol interaction copied with modifications from Gessner and Cabana (1970). The isobole is a graphical representation of the combined doses of both chemical resulting in righting reflex loss in 50% of tested animals (ED50). No significant interaction is observed at dose levels below ≈ 125 mg/kg for chloral hydrate and above ≈ 1200 mg/kg for ethanol.

doses. The interaction threshold boundary may take a variety of different shapes, and the shape of this boundary is not likely to be known. Hamm, Carter, and Gennings (2005) developed a general procedure to accommodate various potential shapes for this boundary. Their analysis defined the interaction threshold, based on the isobologram concept, as the dose region where departure from additivity among components in a mixture exists. Statistical methods can be useful in identifying a threshold when existing data cover a wide enough range of experiments along the dose-response continuum, specifically in the low-dose region. However, estimation of these low-dose interaction thresholds experimentally is economically costly and challenging because of the need to use a large number of laboratory animals. For instance, the chloral hydrate/ethanol experiments used a total of 1681 animals in 21 treatment groups (Gessner and Cabana, 1970; Hamm, Carter, and Gennings, 2005). In view of the experimental and computational difficulties, exact estimations of interaction threshold levels may not be feasible for health risk assessments of mixtures. Identifying a set of exposure levels for components in a mixture where interactions are not observed may not necessarily be an interaction threshold. Instead, studies can be conducted to test the presence of “no interaction” at low environmentally relevant doses. An example of such studies was conducted to find out whether simultaneous administration of nine chemicals (dichloromethane, formaldehyde, aspirin, di(2-ethylhexyl)phthalate, cadmium

Interaction Thresholds

293

chloride, stannous chloride, butyl hydroxyanisol, loperamide, and spermine) at a concentration equal to the “no-observed-adverse-effect level” (NOAEL) for each of them would result in a NOAEL for the combination (Groten et al., 1997a). A four-week oral/inhalation study in male Wistar rats was performed in which the toxicity (clinical chemistry, hematology, biochemistry, and pathology) of combinations of the nine compounds was examined. It was concluded that simultaneous exposure to these nine chemicals does not constitute an evidently increased hazard compared to exposure to each of the chemicals separately, provided the exposure level of each chemical in the mixture is at most similar to or lower than its own NOAEL (Groten, Girthofer, and Probster, 1997b). Mechanistic modeling (such as PBPK/PD models) along with mode-designed experiments provides an efficient methodology for the identification of interaction thresholds. Based on mechanistic consideration of enzyme inhibitions, prediction of the presence of an interaction threshold between binary chemicals was performed using PBPK modeling for two different sets of chemicals: volatiles (TCE and 1,1-DCE), and pesticides (chlorpyrifos and parathion). In the first example, earlier interaction PBPK model showed competitive inhibition to be the mode of interaction between TCE and 1,1-DCE (Andersen et al., 1987). To predict the range at which the interaction threshold was determined, the PBPK model was modified to include mathematical descriptions of the percentage of enzyme sites occupied by either chemical in the presence or the absence of the other (el-Masri, Tessari, and Yang, 1996a). By comparing the percentage of sites occupied by one chemical in the presence and absence of the second chemical, the binary PBPK model simulations were used to predict a range of concentrations (100 ppm or less) of either chemical where the competitive inhibition interaction would not be observed. These findings were further verified using model-designed gas uptake experiments. In another example, a binary interaction PBPK model was developed to estimate an interaction threshold for the joint toxicity between chlorpyrifos and parathion in the rat (el-Masri, Mumtaz, and Yushak, 2004). Initially, individual PBPK models were developed for parent chemicals and their oxon metabolites to estimate the blood concentrations of their respective metabolite. The metabolite concentrations in blood were then linked to the acetylcholinesterase kinetics submodel. The resulting overall PBPK model described interactions between these pesticides at two levels: (1) competitive inhibition of the P450 enzymatic reactions, and (2) competition to binding of acetylcholinesterase sites. Using the overall model, a response surface was constructed at various dose levels of each chemical to investigate the mechanism of interaction and to calculate interaction threshold doses. Investigations of interaction thresholds of three common volatile organic solvents, trichloroethylene (TCE), perchlorate (PERC), and methylene chloride (MC) under different dosing conditions were performed using PBPK modeling (Dobrev, Andersen, and Yang, 2001; 2002). Briefly, an interactive PBPK model was built where PERC and MC are competitive inhibitors for TCE. The model was developed and tested against gas uptake pharmacokinetic data in F344 rats at relatively high doses of single chemicals, binary mixtures, and the ternary mixture. Computer simulations were used to extrapolate from high to low concentrations to investigate the toxicological interactions at occupational exposure levels, specifically at threshold limit value/time weighted average (TLV/TWA). Using a 10% elevation in parent compound blood level as a criterion for significant interaction, interaction thresholds were predicted with two of the three chemicals held at constant concentrations.

294

14.5

Statistical and Physiological Modeling of the Toxicity of Chemicals in Mixtures

Conclusions and Future Directions

Ideally, all the components of the mixture need to be identified and their toxicity experimentally determined or obtained from the literature. Several testing protocols can be used to obtain appropriate information. Experimental design depends on the number of chemical components of the mixture and the need to assess different possibilities for interactions between chemical components in a mixture. Several experimental approaches can be used to evaluate the toxicity of chemical mixtures. Whole mixture testing through the tier or screening approach is usually used to identify toxic effects and risks posed by a defined mixture. Bioassay-directed fractionation experiments are used when a causative agent(s) is to be determined to relate exposures to the active ingredient of a mixture or to identify the source of pollution. Once causative agents are identified, experiments can be conducted to test the presence and direction of possible toxicological interactions using statistical methods based on significant changes of dose-response slopes. In general, statistical methods for the analysis of interactions are based on comparisons between experimental results and what is expected when additivity is assumed. Statistical methods are useful in identifying the presence of interactions, and the direction of interaction within the range of data to which they are applied. Advances in experimental and computational methodologies for the investigation of chemical mixtures toxicity are focused towards generating most information with the least number of experiments. Experimentally, recent advances in functional genomics technologies allow the monitoring of many gene profiles, increasing the likelihood for the identification of mechanisms where synergistic or additive effects can be expected, specifically when similar molecules or pathways are targets of different components of the mixture. Toxicogenomic methods were used to provide insights into the combined action of the food additives butylated hydroxytoluene, curcumin, propyl gallate, and thiabendazole in liver (Stierum et al., 2005). Gene expression profiling of individual additives experiments using cDNA arrays provided novel biological information, including changes in drug metabolism, proliferation of peroxisomes, and p53 metabolism. Results of the individual studies were used to generate hypotheses on possible interactions at the mechanistic levels. Toxicogenomics can also be informative when changes occur in different, specific biological pathways for different single components of a mixture indicating lack of interactions. For instance, cDNA microarray technology was used to identify changes in gene expression that influence differences in human keratinocyte cell line responses to arsenic and a mixture of arsenic, lead, cadmium, and chromium (Bae et al., 2002). The study showed unique multiple genes expression patterns, indicating the possibility of independent action between the mixture components at the molecular level. Another study tested mixtures of arsenic [As(V)], cadmium [Cd(II)], chromium [Cr(III, VI)], and lead [Pb(II)] to identify metalresponsive promoters and to determine whether the pattern of gene expression changed with a mixture of these metals (Mumtaz et al., 2002). The study used commercially developed assay system employing a battery of recombinant HepG2 cell lines to test the transcriptional activation capacity of xenobiotics in any of 13 different signal-transduction pathways. Singly, As(V), Cd(II), Cr(III, VI), and Pb(II) produced complex induction profiles in these assays. However, no evidence of synergistic activity was detected with a mixture of Cd(II), Cr(III), and Pb(II). Toxicogenomic methods provide insights into complex interactions that

Conclusions and Future Directions

Interaction Hypothesis

295

Physiological Biochemical Parameters

Interaction Quantitative Model Disagree

Model Verified

{ Agree

Model Simulations (tissue levels)

Model-Designed Experiments

Experimental Data

Figure 14.5 Mechanistic models are used to generate predictions related to an interaction hypothesis. The predictions can then be tested in experiments. Deviation of experimental results from model predictions can then be used to refine the model parameters or test the interaction hypothesis.

occur in cellular systems and could be used to identify biomarkers of exposure to other environmental chemicals. Interaction hypotheses generated from toxicogenomic studies can be used to generate mechanistic models which are used to simulate results that can be tested by model-designed experiments. Whenever possible, evaluation of individual components, in various combinations, is conducted to gain knowledge about toxicological mechanisms as well as about mechanisms of interactions between the components within the mixture. The knowledge gained from investigating mechanisms of interactions can be used in developing predictive computational models. In general terms, the purpose of these models is to interpret data for the entire range of the dose-response surface based on a mathematical/statistical description of interaction hypotheses. These hypothesis-driven mechanistic models can also be used for the development of efficient experimental design by considering the cycle of model and experiments for optimal use of resources (Figure 14.5). For example, PBPK/PD models can be combined with statistical methods to identify interaction based on a hypothesized interaction mechanism. In this manner, the results from PBPK/PD simulations are introduced as g(µ) into the general dose-response surface function: g(µ) ≈ β0 + β1 x1 + β2 x2 + β3 x3 + . . . . βc xc +

c−1
c


βi j xi x j

i=1 j=i+1

+

c−2
c−1
c


βi jk xi x j xk + . . . .. β12..c xi x j ..xc

i=1 j=i+1 k=i+2

Statistical fitting of the model-generated simulations with the above equation will generate response surfaces to which targeted experiments can be designed. For example, an interaction PBPK/PD-Monte Carlo model simulation for Kepone and CCl4 was coupled

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Statistical and Physiological Modeling of the Toxicity of Chemicals in Mixtures

with a second order regression equation to predict lethality response-surface in rats. The results of the model-calibrated regression equation were the derivation of lethality-generated isoboles for the interaction between Kepone and CCl4 at different responses (el-Masri, Reardon, and Yang, 1997).

References Andersen, M.E., Gargas, M.L., Clewell, H.J. III, and Severyn, K.M. (1987) Quantitative evaluation of the metabolic interactions between trichloroethylene and 1,1-dichloroethylene in vivo using gas uptake methods. Toxicol. Appl. Pharmacol., 89, 149–157. Bae, D.S., Hanneman, W.H., Yang, R.S., and Campain, J.A. (2002) Characterization of gene expression changes associated with MNNG, arsenic, or metal mixture treatment in human keratinocytes: application of cDNA microarray technology. Environ. Health Perspect., 110 (Suppl. 6), 931– 941. Berenbaum, M.C. (1985) The expected effect of a combination of agents: the general solution. J. Theor. Biol., 114, 413–431. Berenbaum, M.C. (1989) What is synergy? Pharmacol. Rev., 41, 93–141. Carter, W.H. Jr. and Carchman, R.A. (1988) Mathematical and biostatistical methods for designing and analyzing complex chemical interactions. Fundam. Appl. Toxicol., 10, 590–595. Cassee, F.R., Groten, J.P., van Bladeren, P.J., and Feron, V.J. (1998) Toxicological evaluation and risk assessment of chemical mixtures. Crit. Rev. Toxicol., 28, 73–101. Darbre, P.D. (2006) Environmental oestrogens, cosmetics and breast cancer. Best Pract. Res. Clin. Endocrinol. Metab., 20, 121–143. Dennison, J.E., Andersen, M.E., Clewell, H.J., and Yang, R.S. (2004) Development of a physiologically based pharmacokinetic model for volatile fractions of gasoline using chemical lumping analysis. Environ. Sci. Technol., 38, 5674–5681. Dobrev, I.D., Andersen, M.E., and Yang, R.S. (2001) Assessing interaction thresholds for trichloroethylene in combination with tetrachloroethylene and 1,1,1-trichloroethane using gas uptake studies and PBPK modeling. Arch. Toxicol., 75, 134–144. Dobrev, I.D., Andersen, M.E., and Yang, R.S. (2002) In silico toxicology: simulating interaction thresholds for human exposure to mixtures of trichloroethylene, tetrachloroethylene, and 1,1,1trichloroethane. Environ. Health Perspect., 110, 1031–1039. el-Masri, H.A., Mumtaz, M.M., and Yushak, M.L. (2004) Application of physiologically-based pharmacokinetic modeling to investigate the toxicological interaction between chlorpyrifos and parathion in the rat. Environmental Toxicology and Pharmacology, 16, 57–71. el-Masri, H.A., Reardon, K.F., and Yang, R.S. (1997) Integrated approaches for the analysis of toxicologic interactions of chemical mixtures. Crit. Rev. Toxicol., 27, 175–197. el-Masri, H.A., Tessari, J.D., and Yang, R.S. (1996a) Exploration of an interaction threshold for the joint toxicity of trichloroethylene and 1,1-dichloroethylene: utilization of a PBPK model. Arch. Toxicol., 70, 527–539. el-Masri, H.A., Thomas, R.S., Sabados, G.R., et al. (1996b) Physiologically based pharmacokinetic/pharmacodynamic modeling of the toxicologic interaction between carbon tetrachloride and Kepone. Arch. Toxicol., 70, 704–713. Gennings, C. (1995) An efficient experimental design for detecting departure from additivity in mixtures of many chemicals. Toxicology, 105, 189–197. Gennings, C. (1996) Economical designs for detecting and characterizing departure from additivity in mixtures of many chemicals. Food Chem. Toxicol., 34, 1053–1058. Gennings, C., Carter, W.H. Jr., Carchman, R.A., et al. (2005) A unifying concept for assessing toxicological interactions: changes in slope. Toxicol. Sci., 88, 287–297. Gessner, P.K. and Cabana, B.E. (1970) A study of the interaction of the hypnotic effects and of the toxic effects of chloral hydrate and ethanol. J. Pharmacol. Exp. Ther., 174, 247–259.

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Greco, W.R., Bravo, G., and Parsons, J.C. (1995) The search for synergy: A critical review from a response surface perspective. The American Society for Pharmacology and Experimental Therapeutics, 47, 331–385. Groten, J.P., Schoen, E.D., van Bladeren, P.J., et al. (1997a) Subacute toxicity of a mixture of nine chemicals in rats: detecting interactive effects with a fractionated two-level factorial design. Fundam. Appl. Toxicol., 36, 15–29. Groten, M., Girthofer, S., and Probster, L. (1997b) Marginal fit consistency of copy-milled all-ceramic crowns during fabrication by light and scanning electron microscopic analysis in vitro. J. Oral Rehabil., 24, 871–881. Haddad, S., Tardif, R., Charest-Tardif, G., and Krishnan, K. (1999) Physiological modeling of the toxicokinetic interactions in a quaternary mixture of aromatic hydrocarbons. Toxicol. Appl. Pharmacol., 161, 249–257. Hamm, A.K., Carter, W.Hans Jr., and Gennings, C. (2005) Analysis of an interaction threshold in a mixture of drugs and/or chemicals. Stat. Med., 24, 2493–2507. Krishnan, K., Haddad, S., Beliveau, M., and Tardif, R. (2002) Physiological modeling and extrapolation of pharmacokinetic interactions from binary to more complex chemical mixtures. Environ. Health Perspect., 110 (Suppl. 6), 989–994. Mauderly, J.L. (1993) Toxicological approaches to complex mixtures. Environ. Health Perspect., 101 (Suppl. 4), 155–165. Meadows, S.L., Gennings, C., Carter, W.H. Jr., and Bae, D.S. (2002) Experimental designs for mixtures of chemicals along fixed ratio rays. Environ. Health Perspect., 110 (Suppl. 6), 979–983. Mehendale, H.M. (1990) Potentiation of halomethane hepatotoxicity by chlordecone: a hypothesis for the mechanism. Med. Hypotheses, 33, 289–299. Moser, V.C., Simmons, J.E., and Gennings, C. (2006) Neurotoxicological Interactions of a FivePesticide Mixture in Preweanling Rats. Toxicol. Sci., 92, 235–245. Mumtaz, M.M., and Hertzberg, R.C. (1993) The Status of Interactions Data in Risk Assessment of Chemical Mixtures, Taylor and Francis, Washington, DC. Mumtaz, M.M., Tully, D.B., el-Masri, H.A., and De Rosa, C.T. (2002) Gene induction studies and toxicity of chemical mixtures. Environ. Health Perspect., 110 (Suppl. 6), 947–956. Narotsky, M.G., Weller, E.A., Chinchilli, V.M., and Kavlock, R.J. (1995) Nonadditive developmental toxicity in mixtures of trichloroethylene, Di(2-ethylhexyl) phthalate, and heptachlor in a 5 × 5 × 5 design. Fundam. Appl. Toxicol., 27, 203–216. Slikker, W. Jr., Andersen, M.E., Bogdanffy, M.S., et al. (2004) Dose-dependent transitions in mechanisms of toxicity: case studies. Toxicol. Appl. Pharmacol., 201, 226–294. Stierum, R., Heijne, W., Kienhuis, A., et al. (2005) Toxicogenomics concepts and applications to study hepatic effects of food additives and chemicals. Toxicol. Appl. Pharmacol., 207, 179–188. Tardif, R., Charest-Tardif, G., Brodeur, J., and Krishnan, K. (1997) Physiologically based pharmacokinetic modeling of a ternary mixture of alkyl benzenes in rats and humans. Toxicol. Appl. Pharmacol., 144, 120–134.

15 (Q)SAR Models of Adverse Responses: Acute Systemic Toxicity Mark T.D. Cronin, Yana K. Koleva, and Judith C. Madden School of Pharmacy and Chemistry, Liverpool John Moores University, United Kingdom

15.1 Introduction Acute toxicity is usually associated with death and other organ specific effects after a short (and usually high dose) exposure to a chemical agent. Testing for acute (systemic) toxicity aims to provide information on the effects of (usually) a single dose of a chemical given during a 24-hour period and then to provide any observations for a subsequent 21-day period (Gennari et al., 2004). The most common assay for acute toxicity is the classic LD50 test. This was introduced in the 1920s and has undergone a number of revisions to reduce animal use and suffering (Botham 2004). The animals of choice are usually the mouse or rat, and one of the fundamental pieces of information the test provides is a 50% lethal dose (LD50) value, that is the concentration that will cause lethality in 50% of a group of animals after 24 hours. A well performed assay will not only provide an LD50 value, but also identify target organs and other clinical manifestations of acute toxicity, determine whether the toxic effects are reversible, and provide dose-response guidance for other studies. There are a number of routes of administration – oral, intravenous, intraperitoneal, dermal, and so on. An acute mammalian toxicity test is possibly one of the commonest assays performed worldwide and is often the first in vivo toxicity test performed on a chemical. In many ways it is considered a standard assay for product safety evaluation and assessment. Despite, and because of, its widespread use, there are considerable efforts to apply the 3Rs principles (replacement, refinement and reduction) to the acute mammalian toxicity tests. These efforts

Quantitative Modeling in Toxicology
C 2010 John Wiley & Sons, Ltd

Edited by Kannan Krishnan and Melvin E. Andersen

300

(Q)SAR Models of Adverse Responses: Acute Systemic Toxicity

include the use of in silico techniques, which are based around the use of (quantitative) structure-activity relationships ((Q)SARs) (Tsakovska et al., 2006; 2008). The aim of a (Q)SAR is to provide a model that allows the user to make a prediction of toxicity (Bassan and Worth 2008). To achieve this, toxicological information and data are required. In terms of modeling acute toxicity, these are usually LD50 data, as the more subtle organ effects are both more difficult to model and the information tends to be less openly available. A reasonable number of LD50 data are openly available for modeling, and probably much more confidential information available in businesses. The greatest problem with modeling this endpoint, however, is the availability of high quality data. Many of the historical data used for modeling are occasionally of debatable quality (i.e., from different and non-standard endpoints) and this will impact on the subsequent quality of the model. The ability to be able to predict toxicity rapidly from structure means that developing models of mammalian LD50 is very attractive, not only to provide rapid assessment of toxicity but also to reduce animal testing. There are, however, many problems in addition to data quality associated with its modeling. In most cases, the LD50 is brought about by a single administration and, hence, is it unlikely to reach a steady state. This makes QSAR modeling more difficult due to variations in pharmacokinetic properties. It is also considered that lethality in this context is a crude endpoint, and putting an exact concentration onto it is misleading. There are also differences between the routes of administration and species, and different data must be considered separately. Despite the difficulties in the in silico modeling of acute toxicity (LD50), a number of studies have been performed. There are a number of good, detailed reviews that will assist the reader to obtain more information, for example, Cronin and Dearden (1995), Philips et al. (1990), and Tsakovska et al. (2006; 2008).

15.2 Predicting Acute Mammalian Toxicity There is a wide variety of methods to predict acute mammalian toxicity from structure. Methods are described briefly below and range from relatively simple to more multivariate and, hence, complex. 15.2.1

Category Formation and Read-Across

The premise of in silico methods for the prediction of toxicity is that similar compounds will have similar toxicity. At its simplest level this approach allow for the grouping of similar compounds together. This process of identifying similar compounds is often termed “category formation.” Once compounds are grouped together, it is possible to interpolate or read toxicity across the list, hence this simplistic approach is termed “read-across.” Grouping of chemicals and read-across to facilitate toxicity prediction has been accepted for many years for regulatory submissions of chemicals. It is now becoming of broader interest to tackle many toxicological problems including submissions made under the European Union Registration, Evaluation, Authorization and restriction of Chemical substances (REACH) legislation. The concept is straightforward for a qualitative toxicity endpoint, for example, whether a compound is “similar” to other compounds classified as being toxic. The key to this process is determining what a similar compound is. If one is fortunate to

Predicting Acute Mammalian Toxicity

301

have a series of structural analogues, then making a read-across prediction for a missing analogue is straightforward. Much recent work has aimed to determine whether compounds can be grouped together in terms of mechanisms of action. This approach is one of the cornerstones of the OECD (Q)SAR Application Toolbox (Section 15.2.3). The next challenge for read-across following the formation of a category is the quantitative prediction of toxicity. Enoch et al. (2008a) have outlined a strategy for the quantitative prediction of toxicity within a category. This has been applied successfully in the quantitative prediction of the potency of skin sensitizers. The approach is reliant on identifying electrophilic mechanisms of toxic action (which is obviously not appropriate for all areas of acute mammalian toxicity). The approach can be summarized as follows: r The mechanisms and modes of toxic action are identified – these may be related to a particular endpoint as required. Currently these have been identified for mechanisms/modes such as narcosis, uncoupling, electrophilic interaction, receptor-mediated toxicity, and so on. r The structural boundaries of the mechanisms are defined. For instance, Enoch, Madden, and Cronin (2008b) have defined the structural boundaries of the classic electrophilic mechanisms of action. r For a chemical for which a prediction is required, it should be placed within an appropriate category. Chemicals that also fall within that category with associated toxicity data should be obtained. r (Qualitative) read-across can be performed within the category. r Quantitative read-across can be performed following the calculation of appropriate descriptors and identification of the most similar compounds. This is best illustrated through the use of an example. To predict the toxicity of 2,4hexadienal (Table 15.1), this can first be assigned to a category, and then similar compounds with toxicity data found. In the case of 2,4-hexadienal, the mechanism was assumed to be that of a Michael acceptor (Roberts et al. 2007). The rat oral LD50 toxicity of other Michael acceptors was obtained from the United States National Library of Medicine (2008). Descriptors can be calculated for these data. All calculations on chemical structure were performed using the Gaussian03 package of programs using the B3LYP/6-31G(d) level of theory (Frisch et al., 2003). All structures were drawn using the GausView application within Gaussian03; chemical structures were then optimized using the following criteria: Maximum force < 0.000 450, rms (root-mean-square) force < 0.000 300, maximum displacement < 0.001 800, and rms displacement < 0.001 200. The global electrophilicity parameter (ω) was then calculated for each optimized chemicals as described in Equations 15.1–15.3 below. The index is derived from chemical potential (µ) and chemical hardness (η), which in turn have been shown to be related to the energies of the highest molecular orbital and the lowest unoccupied orbital (Parr, Szentpaly, and Liu, 1999): Electrophilicity index (ω) = µ2 /2 η

(15.1)

µ = (E HOMO + E LUMO )/2 η = E LUMO − E HOMO

(15.2) (15.3)

where:

CAS no.

126-99-8

142-83-6

78-85-3

Name

Chloroprene

2,4-Hexadienal

Methacrylaldehyde

H3C

H2C

H2C

CH3

Cl

Structure

O

O

O

140

300

450

Experimental LD50 [mg/kg]

0.30

0.49

0.71

Experimental log LD50 [mmol/kg]

0.53 (log mmol/kg); 324.09 mmol/kg

Predicted LD50 by ω

1.706

1.980

2.195

ω [eV]

Table 15.1 Chemicals and associated data illustrating the concept of read-across of LD50 within a well defined toxicologically meaningful category.

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303

Where: EHOMO is the energy of the highest occupied molecular orbital, ELUMO is the energy of the lowest unoccupied molecular orbital. For the compounds considered, the results of the calculations for ω are shown in Table 15.1. Following calculation of ω for the compounds with toxicity data in the Michael acceptor domain, two compounds, chloroprene and methacrylaldehyde, were found to be the most similar structurally, as well as having the closest ω values on either side of the ω value for 2,4-hexadienal. According to the methodology of Enoch et al. (2008a), a trivial extrapolation can be made between the two values for ω. The predicted toxicity value of 0.53 is very close to the observed value of 0.49. Read-across of toxicity following the formation of a category is a very simple approach, and if used correctly may be immensely powerful. It is reliant, however, on the correct and appropriate formation of a category, and the availability of supporting toxicity data.

15.2.2 15.2.2.1

Quantitative Structure-Activity Relationships (QSARs) for the Prediction of Acute Systemic Toxicity QSARs for the Prediction of the Acute Toxicity of Narcotics

The concept of narcosis is established for many (non-mammalian) acute toxicities, and the formulation of the relationships with physicochemical properties can be traced back to the nineteenth century and the work of Richet (1893), Overton (1901) and Mayer (1899). In many aquatic systems the acute toxicity of narcotic chemicals is known to form good relationships with hydrophobicity (Cronin 2006). QSARs can be developed for the toxicity data from these systems, usually linear relationships with the logarithm of the octanol–water partition coefficient (log P) are found. These hydrophobicity based QSARs are useful for industrial chemicals as a high proportion of them are narcotic in nature, and also because they provide a prediction of a “baseline” or “minimum” toxicity. Compounds with more specific effects have a toxic potency in excess of this minimum toxicity. There is a good rationale for acute aquatic narcotic effects to show a strong relationship with hydrophobicity. For compounds with reasonable water solubility, it can be assumed that the compound will achieve an equilibrium, or steady state, with the organism. The hypothesis raises the intriguing possibility that a baseline effect may be observed in non-aquatic based systems. It does seem possible that a minimum toxicity with narcotic chemicals is observed, for instance, in cell lines and in vitro systems (Escher et al., 2008). There is also a possibility that, to a limited and carefully defined extent, there may be a relationship between lethal potency to mammals and hydrophobicity. The process of extrapolating between species – the formation of so called “inter-species relationships” is fundamental in toxicology. There has been particular interest in understanding the relationship between species within a mechanistic framework. In particular, Delistraty (2000) described the possible correlation between rat inhalation LC50 and rainbow trout LC50. The inhalation route (for rat) is of interest as the air and water exposures correspond to the respiratory medium of the test system. Such extremes of inter-species relationships are not new (Cronin and Dearden 1989; Hodson 1985) but must be treated with obvious caution and with an appreciation of their limitations.

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Following on from an understanding of the concept of baseline toxicity, and that there is some relationship between the toxicity of chemicals to mammalian and non-mammalian species, it is worth considering available QSARs for known narcotic chemicals. Narcosis itself covers a range of mechanisms of action, the most common of which is non-polar narcosis. The domain of non-polar narcosis is becoming better defined, and includes saturated aliphatic alcohols, ketones and ethers (Ellison et al., 2008). There are inevitably many differences between acute toxic potency as considered in rats and mice, and that to aquatic organisms. Mammalian toxicity studies are unlikely to reach any form of steady state (indeed, this is not the purpose of such an assay). In addition, mechanisms and metabolism will be much more complex and less predictable in mammalian systems. Despite the inevitable problems with modeling acute mammalian toxicity data, there have been successes in developing simple and robust QSARs. To illustrate the hypothesis that there may be a strong relationship between mammalian the acute toxicity of narcotics and log P, Jeppsson (1975) found the following relationships for mouse intravenous LD50 (LD50M-IV ). For the toxicity of ethers: Log(1/LD50M-IV ) = 0.79 log P − 0.09 (log P)2 + 1.38 n = 5, r = 0.99, s = 0.10.

(15.4)

Where: log P is log n-octanol–water partition coefficient, n is the number of compounds, r is the correlation coefficient, s is the standard error. For the toxicity of alkanes: Log(1/LD50M-IV ) = 0.94 log P − 0.11 (log P)2 + 0.56 n = 6, r = 0.98, s = 0.10.

(15.5)

For the toxicity of ketones: Log(1/LD50M-IV ) = 0.93 log P − 0.14 (log P)2 + 1.56 n = 4, r = 0.99, s = 0.10.

(15.6)

It should be noted that the numbers of compounds (4–6) in each of these relationships are very low for a QSAR. In addition, Jeppsson (1975) did provide further relationships with molecular weight. No attempt was made to combine all three classes of compounds together to form a single QSAR. However, this may not have been successful, as while the coefficients on the log P terms in Equations 15.4 to 15.6 are similar, there is a significant difference in the slope suggesting increased sensitivity to the ethers and ketones compared to the alkanes. While not reported by Jeppsson (1975), di Paolo (1978) did find a significant relationship through the use of two molecular connectivity values. To confirm the development of QSARs for congeneric series, Tichy et al. (1985) indicated strong relationships with carbon number and molecular connectivity indices (and hence, by

Predicting Acute Mammalian Toxicity

305

analogy, hydrophobicity) and the acute toxic potency of a series of aliphatic alcohols. Strong relationships were also seen between species, but not necessarily route of administration. These structure–activity and species–species relationships suggest the same mechanism of action and consistency of these narcotic effects between species. While there has been success in the development of linear QSARs for the relationship between acute mammalian toxicity and log P, there is also considerable evidence that the relationship may be bilinear. This would represent the distribution of the toxicant within the mammal. The bilinear approach for modeling the toxicity of narcotics was proposed by Lipnick and co-workers (Lipnick et al., 1985, 1987; Lipnick, 1991). For instance, the following bilinear relationships are reported (Lipnick et al. 1987): For the toxicity of monohydric ketones: Log(1/LD50M-O ) = 0.56 log P − 0.91 log(0.049.β 10 P + 1) + 1.20 n = 13, r = 0.96, s = 0.076, F = 36.5.

(15.7)

where LD50M-O is the mouse oral LD50 and F is Fisher’s statistic. For the toxicity of monohydric alcohols: Log(1/LD50M-IPR ) = 0.82 log P − 23.6 log(0.00045.β 10 P + 1) + 1.38 (15.8) n = 11, r = 0.99, s = 0.11, F = 106. where LD50M-IPR is the mouse intraperitoneal LD50. For the toxicity of both monohydric alcohols and ketones: Log(1/LD50M-INV ) = 0.86 log P − 1.20 log(0.0067.β 10 P + 1) + 1.44 n = 22, r = 0.99, s = 0.10, F = 307.

(15.9)

where LD50M-INV is the mouse intravenous LD50. Log(1/LD50R-O ) = 0.81 log P − 0.97 log(0.080.β 10 P + 1) + 0.98 n = 54, r = 0.82, s = 0.21, F = 35.3.

(15.10)

where LD50R-O is the rat oral LD50. Log(1/LD50R-IPR ) = 0.85 log P − 0.90 log (0.035.β 10 P + 1) + 1.24 (15.11) n = 7, r = 0.99, s = 0.04, F = 238. where LD50R-IPR is the rat intraperitoneal LD50. Lipnick (1991) later described Equation 15.10 for rat oral LD50 as a baseline model. It is noted that electrophilic compounds had toxicity in excess of this model. Regrettably, this concept has not been expounded upon, for instance with the toxicity data described in the next section. It should be noted that other attempts have been made to model the mammalian acute toxicity of alcohols. For instance, Guilian and Naibin (1998) described a decision tree type approach to predict the rat and mouse oral LD50 of 95 alcohols. The tree is developed on six descriptors for substructural factors, numbers of hydroxy groups and carbon atoms. There is no evidence of a baseline effect, but this study included a heterogeneous group of compounds

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that included unsaturated alcohols and diols, which are known to be electrophilic in nature (and hence have excess toxicity above baseline).

15.2.2.2

QSARs for Groups, Chemical Classes and Potential Mechanisms Other Than Narcosis

A number of QSARs have been developed for the acute mammalian toxicity for several chemical classes which fall outside of the “traditional” domain of non-polar narcosis. For instance, Casida et al. (1976) found a significant relationship between the mouse intraperitoneal LD50 and a measure of molecular size (the van der Waals volume of a substituent, VolvdW ) and the hydrophobicity substituent constant π , for a series of 2,6,7trioxabicyclo [2.2.2]-octanes and related compounds: Log(1/LD50M-IPR ) = 3.29 VolvdW − 0.662 (VolvdW )2 + 2.14 π − 4.89 n = 11, r = 0.96.

(15.12)

It should be noted that the units of toxicity for Equation 15.12 are mg/kg, and that this equation should be re-formulated in mol/kg. Unfortunately, units of mg/kg also appear to have been used by Mundy et al. (1978) who found the following relationship for a series of O,O-dimethyl O-(p-nitrophenyl) phosphorothioates and their O-analogues: Log(1/LD50M-O ) = −0.35 log P − 0.99 f + 0.5 E s − 0.89 n = 12, r = 0.94, s = 0.23.

(15.13)

where f is the Swain and Lupton’s Field constant and Es is Taft’s steric substituent constant. It should be noted that Equation 15.13 contains a negative correlation with log P; a factor that may require further investigation. J¨ackel and Klein (1991) extended the concept of the bilinear approach to predict rat oral LD50 but required further descriptors to mode the toxicity of anilines. These were the (MV) and energy of the lowest unoccupied molecular orbital (ELUMO ), which may represent the reduced toxicity of larger compounds and influence of electrophilicity respectively: Log(1/LD50R-O ) = 1.06 log P − 0.21 (log P)2 − 0.30 E LUMO − 0.038 MV + 2.46 n = 29, r = 0.90, s = 0.11, F = 25.6. (15.14) Isayev et al. (2006) studied the rat oral LD50 of some nitroaromatic compounds which are known to be electrophilic in nature. Due to their capability to act by electrophilic mechanisms of action, compounds such as the nitroaromatic compounds are known to have acute toxicity greatly in excess of narcosis in many species. This “reactive” toxicity has been shown to be difficult to model by traditional QSAR methods (Cronin, Gregory, and Schultz, 1998). The QSAR developed by Isayev et al. (2006) includes a number of topological parameters; the more reactive nature of these compounds probably explains the lack of hydrophobic descriptors. The topological descriptors are difficult to explain in mechanistic or physicochemical terms, but may relate to molecular features that are

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Table 15.2 A summary of QSAR studies for acute systemic toxicity Species

Type of compounds

Descriptors

Reference

Mouse oral LD50

Mono- and dinitrile compounds

Tanii and Hashimoto (1984, 1985a; 1985b)

Mouse oral LD50 Rat oral LD50

Acyrlates and methacrylates Phenylureas

Hydrophobicity (both linear and bilinear relationships) Hydrophobicity

Mouse oral LD50

Procaine analogues

Rat oral LD50

Organophorous compounds

Mouse intraperitoneal LD50

Pyridines and bi-pyridines

Hydrophobicity and ionization Hydrophobicity Seven miscellaneous descriptors in a neural network Hydrophobicity and electrophilicity

Tanii and Hashimoto (1982) Nendza (1991) do Amaral et al. (1997) Eldred and Jurs (1999)

Cronin et al. (2002)

important for toxicity: Log(1/LD50R-O ) = −103 X5Av − 0.157 PCD + 0.291 C−026 + 5.21 (15.15) n = 28, r = 0.924, s = 0.253, F = 46.6. where X5Av and PCD are topological descriptors describing the presence of heteroatoms and bond types, and C-026 is a fragment descriptor. There are excellent reviews by Phillips et al. (1990) and Tsakovska et al. (2006; 2008) with further comprehensive compilations of QSARs for acute mammalian toxicity. A small selection of QSAR studies (illustrating a range of endpoints and modeling approaches for acute toxicity) is summarized in Table 15.2. The use of QSARs for (structurally) restricted classes of chemicals is, of course, very limited in its applicability. The success of modeling in this area does, however, suggest that small, local, models for mammalian toxicity may be a profitable approach. A number of models use hydrophobicity. There are a number of possible reasons for this, including similarity in mechanism of toxic action and compounds with similar log P values have similar pharmacokinetic properties, hence equivalent amounts of the toxicant may accumulate at the active site (regardless of mechanisms of action). As with the development of QSARs for many biological effects, the use of hydrophobicity descriptors should be the first method of investigating an acute toxicity data set. 15.2.2.3

QSARs for Larger, Chemically Heterogeneous Data Sets

There are fewer published QSARs available for larger and/or more structurally diverse datasets of mammalian toxicity values. This may reflect both the difficulty in obtaining

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such data and also the problems of their modeling. One of the first attempts to model a significant number and diversity of rat oral LD50 was published by Enslein and Craig (1978). They compiled data for 425 compounds (although the data were not published) and developed a relationship with 29 descriptors (including log P, molecular weight, and structural fragments). The statistical fit of the model was at best moderate (r = 0.70), indicating the possible problems of attempting to model such a compilation of data for chemicals with complex and varied mechanisms of action, as well as highly variable data quality. The model developed by Enslein and Craig (1978) went on to form the basis of some of the models available in the TOPKAT software (Section 15.2.3). A model for the prediction of the acute mammalian (mice and rats) toxicity of a number of drugs was presented by Quinones-Torrelo et al. (2001). This is based on retention indices from biopartitioning micellar chromatography, which are effectively a surrogate for hydrophobicity. Again, this could be useful application of QSAR, and shows that by combining relatively restricted series of molecules, simple and powerful models for toxicity can be created. Lessigiarska et al. (2006) considered a small set of compounds, with reasonable structural diversity, for which rat oral LD50 data were available. A number of models based on a variety of descriptors was found to be significantly correlated to toxicity.

15.2.3

Expert Systems and Other Approaches to Predict Toxicity

A number of QSAR approaches have been formalized into expert systems. Such systems allow for the input of a chemical structure and usually supply the user with an automatic prediction of toxicity. Such systems are favored by many users as, in many cases, they allow a “non-expert” user to make predictions of toxicity. Such non-expert use of these methods is seldom to be recommended, however, and while these methods may provide a prediction easily, the interpretation of the predicted value would require more expert knowledge. Table 15.3 summarizes the main expert systems that may be used to predict mammalian toxicity. This is a fast moving area of research and it is unlikely to remain as a comprehensive listing. Of these software packages, the majority (i.e., TOPKAT, MC4PC, ToxFilter, TerraQSAR, and ToxBoxes) are commercial programmes that automate a range of QSAR approaches to predict a variety of endpoints. Brief methodological details of the expert systems are given below, and details on suppliers, and so on given in Table 15.3. As ever, the interested reader is recommended to contact the vendor for up-to-date information: r TOPKAT – a series of regression based QSARs derived from 2-D descriptors such as atom counts and electrotopological state (e-state) values derived from the original models of Enslein and Craig (1978). r MC4PC, CASETox (MultiCASE) – use a probability assessment to determine whether a structural fragment is associated with toxicity. Models are created by including structural fragments in regression analyses. r Tox Filter – QSARs developed from recursive partitioning using molecular descriptors for size and hydrophobicity and other physicochemical parameters. r TerraQSAR – a probabilistic neural network methodology using molecular fragments.

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309

Table 15.3 Summary of the main properties of expert (and other) systems used to predict and assist in the prediction of acute mammalian toxicity. Expert system name
R

TOPKAT

MC4PC, CASETox (MultiCASE)

Supplier and web site

Endpoint

Accelrys Inc., http:// Rat Oral accelrys.com/products/ LD50 discovery-studio/ toxicology/ Rat Inhalation LC50 MultiCASE Inc., http://www. multicase.com/

FDA NTP WHO Rat LD50

NTP Maximum tolerated dose – Mice NTP Maximum tolerated dose – Rats FDA Maximum tolerated dose Male Rat – non-toxic dose FDA Maximum tolerated dose Female Rat – non-toxic dose FDA Maximum tolerated dose Male Mouse – non-toxic dose FDA Maximum tolerated dose Female Mouse – non-toxic dose FDA Maximum tolerated dose Male Rat – lethal dose FDA Maximum tolerated dose Female Rat – lethal dose FDA Maximum tolerated dose Male Mouse – lethal dose FDA Maximum tolerated dose Female Mouse – lethal dose

Number of compounds in the model Data not available at time of writing

Data not available at time of writing 7920

321 321 1014

1020

939

951

1015

1020

939

951

(Continued)

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(Q)SAR Models of Adverse Responses: Acute Systemic Toxicity

Table 15.3 (Continued) Expert system name Tox Filter

TerraQSARTM – OMAR TerraQSARTM – RMIV ToxBoxes

OECD (Q)SAR Application Toolbox

LeadScope Toxicity Database

Supplier and web site

Endpoint

Pharma Algorithms http://pharmaalgorithms.com/tox filter.htm

Intraperitoneal administration in mice. LD50

TerraBase Inc. http://www.terrabaseinc.com/tq-4omar.htm TerraBase Inc. http://www.terrabaseinc.com/tq-4rmiv.htm Pharma Algorithms http:// pharma-algorithms. com/acutetox.htm

Organisation for Economic Co-operation and Development Toolbox is downloadable from www.oecd.org/env/ existingchemicals/qsar LeadScope Inc http://www.leadscope. com/

Mouse, intravenous LD50 Mouse, oral LD50 Mouse, subcutaneous LD50 Rat, intraperitoneal LD50 Rat, oral LD50 Rat and mouse, oral LD50

Rat and mouse, intravenous LD50

Number of compounds in the model (database – 30 000 compounds and a validation set – 3300); 18 925 17 150 7066 3471 5826 Approximately 10 000 2457 compounds

Mouse and rat oral, Analysis of over intraperitoneal, 100 000 intravenous, compounds subcutaneous Oral Acute Toxicity Hazard Categories (OECD Ranges) High acute toxicity in rodent Currently limited in terms of acute mammalian toxicity data

Information on over 160 000 compounds. The precise number with acute toxicity is not stated.

Conclusions

311

r ToxBoxes – QSARs derived from molecular fragments. Predicted log LD50 values are converted to the probability of a compound having a LD50 value in defined range by binomial regression. Probabilities were further corrected according to the presence of known “toxicophores” and to provide a reliability index for LD50 prediction. This provides a knowledge based expert system that identifies hazardous fragments that may be responsible for the high acute toxicity of compounds in rodents. There are 86 “hazardous fragments” in ToxBoxes v2.9. r OECD (Q)SAR Application Toolbox – The software does not make predictions per se, but allows the user to form toxicologically meaningful categories and to search available data. r LeadScope Toxicity Database – this is a database product only. A different approach to the prediction of toxicity is made available through the OECD (Q)SAR Application Toolbox. As noted above, this software will allow for the formation of categories of compounds. From this it may be possible to perform (qualitative or quantitative) read-across, as illustrated in Section 15.2.1. This software (which is freely downloadable) is under development, although at the time of writing a fully function version (ver 1.0) is available for use. This software is limited only by the availability of data and grouping approaches. LeadScope has made available a database product and possibly presents the user with the capability of combining these data with chemical grouping and category formation.

15.3

Integration of (Other) Non-Test Data into Strategies to Predict Acute Toxicity

It is always ambitious to assume that a single prediction of toxicity, from any of the methods described in this chapter, will be entirely successful. However, if one considers a scenario where similar predictions are made by a number of techniques, one may have greater confidence in the predictions. If these predictions could be supported by other non-test data, such as the results from in vitro assays, and supporting animal test data for “similar” compounds, then a wholly convincing argument can be made for the 3Rs in acute toxicity. There are a number of possibilities for refining acute toxicity testing in the broadest context including (Q)SARs and in vitro data. Botham (2004) has discussed the prospects for tiered testing strategies. Other strategies have been put forward by Gubbels-van Hal et al. (2005) and Combes et al. (2008). There are also a number of international projects to promote and develop strategies to replace animal testing for acute systemic toxicity. These include, for instance, the European Union ACuteTox Project (Clemedson, Kolman, and Forsby, 2007; www.acutetox.org)

15.4

Conclusions

There is a long history of the use of acute systemic data to develop QSARs. For successful application of these technologies a number of approaches can be taken. The formation of toxicologically meaningful categories using tools such as the OECD (Q)SAR Application

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Toolbox will become increasingly important. There are intriguing possibilities to combine category formation with the use of the “baseline effect” to increase the confidence that may be placed in a prediction. There are numerous local QSARs and a small number of expert systems to predict LD50 endpoints. These must be used with caution and an appreciation of their limitations including the applicability domains. For the most successful application of these alternatives, they must not be used in isolation but combined with other non-test data and information and formulated into strategies to increase the confidence and utility associated with predictions.

Acknowledgment The funding of the EU FP6 InSilicoTox Marie Curie Project (MTKD-CT-2006-42328) is gratefully acknowledged.

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Parr, R.G., Szentpaly, L.V., and Liu, S. (1999) Electrophilicity index. J. Am. Chem. Soc., 121, 1922–1924. Phillips, J.C., Gibson, W.B., Yam, J., et al. (1990) Survey of the QSAR and in vitro approaches for developing non-animal methods to supersede the in vivo LD50 test. Fd Chem. Toxicol., 28, 375–394. Quinones-Torrelo, C., Sagrado-Vives, S., Villanueva-Camanas, R.M., and Medina-Hernandez, M.J. (2001) An LD50 model for predicting psychotropic drug toxicity using biopartitioning micellar chromatography. Biomed. Chromatog., 15, 31–40. Richet, M.C. (1893) Not´e sur le rapport entre la toxicit´e et les propri´et´es physiques des corps. Compt. Rend. Soc. Biol. (Paris), 45, 775–776. Roberts, D.W., Aptula, A.O., Cronin, M.T.D., et al. (2007) Global (Q)SARs for skin sensitisation – assessment against OECD principles. SAR QSAR Environ. Res., 18, 343–365. Tanii, H. and Hashimoto, K. (1982) Structure–toxicity relationship of acrylates and methacrylates. Toxicol. Lett., 11, 13–17. Tanii, H. and Hashimoto, K. (1984) Studies on the mechanism of acute toxicity of nitriles in mice. Arch. Toxicol., 55, 47–54. Tanii, H. and Hashimoto, K. (1985a) Structure–acute toxicity relationship of dinitriles in mice. Arch. Toxicol., 57, 88–93. Tanii, H. and Hashimoto, K. (1985b) Structure–toxicity relationship of mono- and dinitriles, in QSAR in Toxicology and Xenobiochemistry, vol. 8 (ed. M. Tichy), Pharmacochem, Library, Elsevier, Amsterdam, pp. 73–82. Tichy, M., Trcka, V., Roth, Z., and Krivucova, M. (1985) QSAR analysis and data extrapolation among mammals in a series of alphatic alcohols. Environ. Health Persp., 61, 321–328. Tsakovska, I., Lessigiarska, I., Netzeva, T., and Worth, A.P. (2006) Review of (Q)SARs for mammalian toxicity. EUR 22846 EN, Available from http://ecb.jrc.it/qsar/publications/ (accessed 22 August 2008). Tsakovska, I., Lessigiarska, I., Netzeva, T., and Worth, A.P. (2008) A mini review of mammalian toxicity (Q)SAR models. QSAR Combin. Sci., 27, 41–48. United States National Library of Medicine (2008) available from: http://chem.sis.nlm.nih.gov/ chemidplus/ (accessed 22 August 2008).

Section 5 Model application and evaluation

16 Modeling Exposures to Chemicals From Multiple Sources and Routes Panos G. Georgopoulos1 , Sastry S. Isukapalli1 , and Kannan Krishnan2 1

2

16.1

Environmental and Occupational Health Sciences Institute (EOHSI), USA D´epartement de sant´e environnementale et sant´e au travail, Facult´e de m´edicine, Universit´e de Montr´eal, Canada

Introduction

All humans are exposed either continuously or intermittently to a variety of chemicals that are present in multiple environmental and microenvironmental media (e.g., air, water, soil, airborne dust, food, medications, cosmetics, etc.), through multiple routes (e.g., oral, inhalation, dermal) and pathways (e.g., drinking water, bathing, diet, hand-to-mouth, etc.). These chemicals can originate from many types of sources, both local and distant (e.g., releases from industrial facilities into air or to surface waters, air emissions from vehicles, leaching from landfills or storage facilities to soil and groundwater, contaminants in food and in tap water, indoor releases from building materials, consumer products, cooking, etc.). Exposures can take place in a variety of indoor and outdoor settings (occupational, residential, recreational, commuting, etc.) and the actual intake and subsequent uptake of chemicals of concern by each individual depends not only on the environmental and microenvironmental levels of these chemicals but also on various interrelated behavioral and biological factors that include age (developmental stage) and health status. Activity and energy expenditures by individuals, as well as her/his physiology, will influence inhalation rates, food and water consumption rates, and so on, as well as rates of transformation and elimination from the body. In general, complex interactions of human (micro)environment, behavior and biology (including genetics) determine Quantitative Modeling in Toxicology
C 2010 John Wiley & Sons, Ltd

Edited by Kannan Krishnan and Melvin E. Andersen

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Modeling Exposures to Chemicals From Multiple Sources and Routes Source-to-dose modeling

Source/Stressor Formation Chemical Physical Microbial Magnitude Duration Timing

Dose-to-response analysis

Altered Structure/Function

Transport/Transformation Dispersion Kinetics Thermodynamics Distributions Meteorology

Emission Inventories

Environmental/ Microenvironmental Characterization Air Water Diet Soil & Dust

Environmental Databases

Disease

Early Biological Effect: Biomarkers

Exposure Pathway Route Duration Frequency Magnitude

Demographic & Activity Databases

Molecular Biochemical Cellular Organ Organism

Toxicokinetics: Biomarkers

Dose Absorbed Target Internal Biologically Effective

Urine Hair Blood Nails etc.

Cancer Asthma Infertility etc.

Edema Arrhythmia Enzymuria Necrosis etc.

Bionomic Databases

Biomarker (exposure, effect, susceptibility) Databses

Physiology Databases

Individuals(s) Population Statistical Profile Community of Concern Reference Population Susceptible Individual Susceptible Sub-Populations Population Distributions

Figure 16.1 Schematic depiction of a general framework for exposure and dose assessment. Modeling can be performed in either a prognostic mode or a diagnostic mode. This bi-directional approach takes into account interactions among different exposure/dose subsystems in the context of important biological effects, in order to determine appropriate metrics of exposure and dose (Georgopoulos (2008); adapted with kind permission from Springer Science + Business Media, Copyright 2008).

exposures and biologically effective dose of environmental contaminants (Harris and Mattes, 2008; Georgopoulos, 2008). However, a more detailed discussion of these interactions is beyond the scope of this chapter. Various mathematical models of human exposure exist; they typically provide estimates of “aggregate” exposures (for one contaminant from multiple routes) or of “cumulative” exposures (for multiple contaminants usually present in one medium, such as inhaled air or drinking water). Exposure modeling forms a critical component in the study of processes in the source-to-dose-to-effect continuum (Figure 16.1); it establishes linkages to environmental information for single or multiple media, linkages to patterns of human behavior and activities, and linkages to information associated with the properties and mechanisms of biological action of single or multiple toxicants. Exposure modeling has evolved in recent years from simple, screening or case specific analysis, to an integrative area of research and application. However, it is also still one of the weakest links in most health risk assessments, especially when involving multiple contaminants in multiple media, due to the complexity of the processes involved. A so-called “Completed Exposure Pathway” (CEP) (Georgopoulos and Lioy, 1994; Georgopoulos and Lioy, 2006; Williams and Paustenbach, 2002) occurs when five elements are present: a source of contamination, an environmental medium and transport mechanism, a route of exposure, a point of exposure, and a receptor or a population of receptors. The sequence of events leading from the emission or formation of a toxicant to health effects (or a biological endpoint in general) represents a “chain” of coupled processes. Figure 16.1 depicts schematically a general, multistep modeling framework for exposure, dose, and environmental health risk assessment, that has evolved over recent years, in

Introduction

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both academic/research and regulatory settings. The left side of this scheme represents the realm of exposure modeling, consisting of various elements in the “source-to-dose” sequence. Characterization of exposures to multimedia chemicals requires a consistent linking of multiple models that describe processes occurring in the source-to-dose part of the framework. These models need to be linked not only with each other, but also with various databases relevant to releases of the chemicals of concern, their levels in multiple environmental and biological media, and with data on activities and demographics of potentially exposed individuals and populations. It should be noted that Physiologically based pharmacokinetic (PBPK) and toxicokinetic modeling plays an increasingly integral part in exposure modeling, both for estimating uptakes, doses, and biomarkers resulting from exposures to chemicals and for assessing (“reconstructing”) exposures from available biomarker data. This chapter presents an overview of exposure modeling, including current practices and advances, focusing on a comprehensive methodological framework applicable to a wide range of situations. It also presents step-by-step demonstration of case studies illustrating specific applications of this framework. 16.1.1

Types of Exposure Modeling and Related Terminology

Models of human exposure to environmental pollutants can be classified according to a variety of attributes. Examples of classification schemes include: r Population Based Exposure Models (PBEMs) versus “specific” Individual Based Exposure Models (IBEMs). r Deterministic versus probabilistic (or “statistical”) exposure models. r Prognostic versus diagnostic exposure models. r Observation-driven (“phenomenological”) versus mechanism-driven models (or “hybrid” models, combining both). r Screening (typically conservative) models versus detailed models of “actual” exposure. Estimation of exposures can be performed through predictive (or “prognostic”) exposure modeling, through statistical (“diagnostic”) analyses of data from field studies, or through a combination of both. Prognostic assessment of exposure and dose is based on estimating contaminant emissions in the environment and relevant microenvironments, modeling ambient transport and fate, modeling individual or population time–location–activity patterns, modeling the intake and subsequent uptake of contaminants, and modeling the absorption, distribution, metabolism and elimination of the contaminant from the bodies of the exposed subjects. Diagnostic assessment of exposure and dose in principle combines measurements of environmental and microenvironmental indicators with biomarker information, either through statistical methods or via more detailed analyses using Bayesian approaches for model-data fusion (Georgopoulos et al., 2009). Before discussing exposure modeling approaches in more detail, certain issues should be considered: r Firstly, it should be mentioned that there is significant variation in the definitions of many of the terms used in the exposure modeling literature; indeed, the science of exposure modeling is a rapidly evolving field and the development of a “standard” and commonly

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accepted terminology is an ongoing process (ATSDR, 2008; Lioy et al., 2005; Zartarian, Bahadori, and Mckone, 2005). r Secondly, one should note that, very often, procedures that are called “exposure modeling,” “exposure estimation,” and so on, in the scientific literature, may in fact refer to only a limited subset of the “complete” set of the steps required for a comprehensive exposure assessment (e.g., contaminant transport, fate, microenvironmental accumulation, etc.), that are schematically depicted in Figure 16.1. Though such procedures, and related application studies, provide useful information, in the present chapter they are treated as specific components of a complete exposure assessment. r Finally, the concept of microenvironments is critical in developing procedures for exposure modeling. In the past, microenvironments have typically been associated with inhalation exposures to airborne contaminants and have been defined as individual or aggregate locations (and sometimes even as activities taking place within a location) where homogeneous concentrations of the pollutants of concern are encountered. Thus a microenvironment was often identified with an “ideal” (i.e., perfectly mixed) compartment of classical compartmental modeling. More recent and general definitions view the microenvironments as “control volumes,” either indoors or outdoors, that can be fully characterized by a set of either mechanistic or phenomenological governing equations, when appropriate parameters are available, given necessary initial and boundary conditions. The boundary conditions typically would reflect interactions with the “background” and with other microenvironments. The parameterizations of the governing equations generally include information on attributes of “sources” and “sinks” within each microenvironment. This type of general definition allows for the concentration within a microenvironment to be non-homogeneous (non-uniform), provided its spatial profile and mixing properties can be fully predicted or characterized. By adopting this definition, the number of microenvironments used in a study is kept manageable, while existing local variabilities in concentrations of chemicals of concern can still be taken into account. Microenvironments typically used to determine inhalation exposures include indoor residential microenvironments, other indoor locations (such as occupational and recreational microenvironments), outdoors near roadways, other outdoor locations, and invehicles. Outdoor locations near roadways are segregated from other outdoor locations (and can be further classified into street canyons, vicinities of intersections, etc.) because emissions from automobiles alter local concentrations significantly compared to background outdoor levels. Indoor residential microenvironments (kitchen, bedroom, living room, etc. or an aggregate “home” microenvironment) are typically separated from other indoor locations because of the time spent there and potential differences between the residential environment and various work/public environments. Traditional definitions of exposure start with the concept of “integrated exposure” (during the period from time t0 to t1 ):
t1 ∈¯ m (t0 , t1 ) =

cm (t) dt t0

(16.1)

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321

where cm (t) is the contact concentration experienced by individual m of an exposed population at time t. This is often simplified using approximations of the form: ∈¯ = Σn ∆∈¯ m = Σn ∆tn c¯mn

(16.2)

where the concentration experienced by individual m is (approximately) constant during the time interval ∆tn as denoted by c¯mn . Application of Equations 16.1 or 16.2 requires measurements (or modeled estimates) of cm (t) or the sequence of cmn values. When observations are used, a concern not always addressed by Equation 16.1 is the use of concentrations below the detection limits of the measuring instrument. A further complication is that of detectable but low background concentrations that can be a critical factor in determining both the duration and overall magnitude of integrated exposures. This issue is especially important when aggregate multimedia exposures from multiple pathways result from low concentrations in each medium, each of which may be below the detection limit, but the combined exposures can result in significant amounts of dose. When the concentration estimates reflect an average over a period, actual information may be lost because the time averaging process serves as a low-pass filter. This can be critical if fast and/or nonlinear phenomena are present somewhere in the exposure sequence (e.g., in environmental transformations). Therefore, it is essential for model formulations that preliminary estimates of appropriate numerical measures for the nonlinearity and the stiffness (the ratios of characteristic time scales for mixing/dispersion and chemical transformation, environmental half-times of chemicals, etc.) of an exposure system are calculated at the onset of the assessment process. Many averaging/filtering and lumping/approximation methods commonly used to assess exposures through measurement and modeling, or a combination of both, may introduce substantial errors in this assessment. These include, for example: volumetric and temporal discretization and integration; use of pseudostationarity and similarity assumptions for treating stiffness in model equations; assumptions of independence or of weak coupling for parallel physical and chemical processes; certain types of chemical lumping (i.e., representing a chemical mixture through certain “representative” components of it); use of independence assumptions and neglect of higher order auto- and cross-correlation terms of stochastic variables; and so on. Although these procedures cannot be avoided in many analyses of practical situations, it is essential that their effects be considered, at least via an order of magnitude analysis, prior to conducting an exposure assessment. This will ensure that the exposure characterization is not driven by invalid assumptions. Various complex issues are “hidden” inside the simple formulation of Equation 16.1. (∈¯ m ) is actually a stochastic function of three variables: cm (t), t0 , and t1 , that may not be independent. This representation cannot explicitly reveal the fact that cm (t) obeys a more complicated probability density than the random environmental or microenvironmental concentration, cx (t), observed at a fixed location, x: the probability of cm (t) = Cm (t) is actually given by the conditional probability density of cx (t) given that the position vector of the individual m at time t is actually ym (t) = x. Prob [cm (t) = Cm (t)] = Prob [cx (t) = Cm (t) |ym (t) = x]

(16.3)

Therefore, exposure assessment should focus explicitly on individuals (“Person Oriented Modeling”) and not on exposure locations (points, areas, microenvironments, etc.) per se.

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This represents a major challenge, as very few studies measure “personal concentrations”, cm (t). What is routinely monitored is cx (t); indeed, numerous databases are available that archive information from “fixed location” monitors and this information must be used to derive, via modeling, the personal exposure concentration profile, cm (t). Human exposures to toxicants result in tissue dose; depending on the properties of the toxicant, metrics such as instantaneous, time profile, or accumulated dose may be relevant to the biological effect. The actual concentration levels of toxicants or their metabolites in the target organ determine reaction rates and potential effects. Although these levels are related to exposure, they are also affected by ADME (Absorption, Distribution, Metabolism, and Elimination) processes in the body. The associated kinetic rates may provide the overall limiting step to the dynamics of each biological system. For example, in the presence of a fast elimination rate, a prolonged exposure to low concentration levels may not result in a significant accumulated target tissue dose while a short exposure to high concentration, although resulting in a much lower integrated exposure, may lead to high target tissue dose and significant biological effects. Therefore, the metric of exposure has to be defined to reflect the significance of potentially harmful exposures. Averaging times, threshold limits of concentration, and so on, should therefore be defined “backwards,” starting from considerations of the time scales involved in the processes of the dose/response component of the exposure system.

16.2 Developments in Exposure Modeling Modeling frameworks for exposure assessment in the past have typically focused on subsets of the pathways/routes and sources of exposure relevant to multimedia contaminants, potentially neglecting significant contributions from remaining pathways/routes or sources. This is especially true when multiple routes that are ignored, individually contribute a small amount to the total exposures, but together can make a significant impact. In recent years, the focus of environmental risk analysis, performed by both the research community and regulatory agencies, has been shifting from (a) single contaminant and pathway analysis, to (b) multiple contaminants and pathway analysis, to (c) integrated systems analysis, as shown in Table 16.1. However, many of the advancements in multimedia contaminant transport, fate, and exposure modeling have not been incorporated yet in common practices of risk assessment for multimedia contaminants. During the past two decades an extensive number of modeling tools has been developed by various organizations to support quantitative exposure analyses and assessments. Representative comprehensive exposure models that consider multiple components of the source-to-dose sequence are the NEM/pNEM (National Exposure Model and Probabilistic National Exposure Model) (Whitfield, Richmond, and Johnson, 1997); HAPEM (Hazardous Air Pollutant Exposure Model) (Rosenbaum, 2005); APEX (Air Pollution Exposure) Model (USEPA, 2006b) – a component of TRIM (Total Risk Integrated Methodology) modeling system (USEPA, 1999, 2006b); SHEDS (Stochastic Human Exposure and Dose Simulation) (Burke, Zufall, and Ozkaynak, 2001; Zartarian et al., 2006, 2000); and MENTOR (Modeling ENvironment for TOtal Risk studies) (Georgopoulos and Lioy, 2006; Georgopoulos et al., 2005, 2008; Isukapalli, Lioy, and Georgopoulos, 2008). Various other models (such as Lifeline (Price et al., 2003), CARES (ILSI, 2009), Calendex (Exponent,

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Table 16.1 Evolution of modeling approaches for integrated environmental assessments. PAST: Single Pathway Analysis of Risk

PRESENT: Multiple Pathway Analysis of Risk

Single contaminant

Multiple contaminants

Multiple contaminant sources

Multiple contaminant sources

Single medium environmental fate and transport

Linked fate and transport in different environmental media

Single exposure route

Multiple exposure routes

Phenotype-based toxicity

Phenotype-based toxicity with susceptibility considerations Chemical and exposure-route specific risk for “standard individuals” Quantitative uncertainty

Primary human health criteria for individual contaminants Qualitative uncertainty

FUTURE: Integrated “Person-Oriented” Systems Analysis of Risk Mixtures of contaminants with environmental and biological interactions Multiple co-occurring chemical and non-chemical stressors affecting an individual Dynamically integrated multimedia fate and transport in the environmental and biological systems Aggregate/cumulative exposure and dose analysis Mechanistic linkage of phenotype with genotype Aggregated Risk for Diverse Human Populations (with Susceptible Subpopulations) Quantitative uncertainty and variability resolved for specific environmental and biological processes

(adapted from NUREG, 2002; Whelan and Laniak, 1998).

2009), etc.) are discussed in Price and Chaisson, 2005. Major attributes of these models are summarized in Table 16.2 (it should be noted that extensive research and development work is currently ongoing for many of these systems; therefore the attributes listed in Table 16.2 are expected to change and be enhanced with time). From these models, pNEM is included in the table to represent an “older generation” of models (“cohort based”) that have been or are being replaced by “Person Oriented Models” that employ a “bottom-up” approach to develop estimates of exposures from activity information of individual “persons,” either real or “virtual.” Along with pNEM, HAPEM and APEX have primarily a regulatory focus; on the other hand, SHEDS and MENTOR are “research oriented” and various implementations of these systems are available for application to specific type of “real world” situations. For example, the MENTOR-1A (MENTOR in a “One Atmosphere” setting) (Georgopoulos et al., 2005) implementation, focusing on inhalation exposures, provides a platform for simulating inhalation exposures for multiple co-occurring, chemically reactive, criteria pollutants and air toxics, while MENTOR-2E (MENTOR for “Emergency Events”) (Isukapalli, Lioy, and Georgopoulos, 2008) allows simulation of emergency events

A year/one hour

Ranging from urban to national/Census tract level Season; 3 hours

Urban areas/Census tract level

Temporal Scale/Resolution

No

Yes

Characterization of the High-End Exposures Typical Spatial Scale/Resolution

Top-down approach

Top-down approach

Behavior/Activity Patterns

Annual averaged Inhalation

Hourly averaged Inhalation

HAPEM

Exposure Estimate Exposure Routes

pNEM

Table 16.2 Essential attributes of various exposure models.

Weeks to year; hour/minutes

Urban area/Census tract level

Yes

Bottom-up approach (person oriented)

Hourly/minutes Inhalation

APEX

MENTOR

Weeks to year; hour/minutes

Urban areas/Census tract level

Weeks to year; hour/minutes

Urban areas/Census tract level

Hourly/minutes Hourly/minutes Inhalation, Ingestion, Inhalation, Ingestion, Dermal Absorption Dermal Absorption Bottom-up approach Bottom-up approach (person oriented) (person-oriented); can be directly applied to individual based modeling Yes Yes

SHEDS

Additive terms for sources Yes No No No

Yes (gas stove, tobacco smoking)

Yes Yes

No

Yes

Specification of Indoor Source Emissions Commuting Patterns Potential Dose Calculation Physiologically Based Dose Variability/ Uncertainty

Point estimates

Random samples from probability distributions

Microenvironmental (ME) Factors

Empirical indoor/outdoor ratios

Non-steady-state and steady-state mass balance equations (hard coded)

Microenvironment Concentration Estimation (µEs) Mass balance (steady-state); empirical ratios; dynamically generated µEs Random samples from probability distributions

Yes

No

Yes

No

Yes (multiple sources Yes (gas stove, defined by the user) tobacco smoking, other sources) Yes Yes Yes Yes

Random samples from probability distributions

Mass balance; empirical ratios; fixed µEs

Yes (various “tools”)

Yes

Yes Yes

Mass balance; empirical ratios; indoor chemistry; dynamically generated µEs Case specific or random samples from probability distributions Yes (multiple sources defined by the user)

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involving releases/spills of hazardous materials. A multimedia implementation of MENTOR, MENTOR-4M (MENTOR for Multiple co-occurring contaminants and Multimedia, Multipathway, Multiroute exposures) (Georgopoulos et al., 2008), as well as MENTOR-1A and MENTOR-2E are now part of the United States Environmental Protection Agency’s (USEPA) list of the Council for Regulatory Environmental Models (CREM) (USEPA, 2008a). 16.2.1

Elements of Comprehensive Exposure Modeling for Individuals and Populations

Major factors that need to be considered in studying human exposures to multimedia contaminants are shown in Figure 16.2. For assessing exposures to multimedia environmental chemicals, the “Person Oriented” framework, summarized schematically in Figure 16.3, provides a comprehensive approach consisting of the following seven “steps” that consider inhalation outdoors, indoors, and in vehicles, drinking water consumption, food intake, non-dietary ingestion, dermal contact, and so on. These steps are general in nature and can together be considered to provide a “universal template” for conducting prognostic exposure modeling for multimedia chemicals, for both individuals and populations. A summary description of each step follows: Step 1. Estimation of the multimedia background levels of multimedia environmental contaminants (air, water, soil, food, etc.), for the area/locations where the exposed individuals or populations of interest reside, through extraction/processing of information from the outcomes of selected comprehensive environmental models and/or from field studies. Several widely used environmental models exist for studying the fate and transport of chemicals in different media (such as Models-3/CMAQ CB4 and CBTOX versions (USEPA, 1999; Georgopoulos et al., 2005; Luecken, Hutzell, and Gipson, 2006), CAMx (ENVIRON, 2004), AERMOD (USEPA, 1998), CALPUFF (Scire, Strimaitis, and Yamartino, 2000), MM5 (NCAR, 2004), RAMS/HYPACT (Walko and Tremback, 2001; Walko, Tremback, and Bell, 1999) for air pollutants; EPANET2 (Rossman, 2000) for water-borne contaminants in municipal networks; MODFLOW (Guiguer and Franz, 1996), FACT (Hamm and Aleman, 2000) for groundwater contaminant transport; CATS (Fascineli, Hunter, and De Grava Kempinas, 2002; Traas et al., 1996) for food-web simulations; FRAMES/3-MRA (USEPA, 2003) for multimedia fate and transport simulations, etc.) For exposure assessment purposes, ambient pollutant concentration information available at a local level (such as census tract or neighborhood) may be needed as an input to microenvironmental models for the estimation of population or individual exposures. However, typical field monitoring networks, as well as regional environmental quality models, provide spatial characterizations of concentration fields that often are too coarse for exposure characterization; so there is a need to further characterize local variability. This can be accomplished through Spatio-Temporal Random Field (STRF) theory (Christakos and Vyas, 1998a, 1998b), as well as Bayesian Maximum Entropy (BME) (Christakos and Serre, 2000; Serre, 1999) interpolation methods available in conjunction with the MENTOR system (Georgopoulos et al., 2005). Step 2. Estimation of multimedia levels (indoor air, drinking water, soil/dust, food, etc. concentrations) and temporal profiles of environmental contaminants in various

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Microenvironmental/exposure/dose modeling system human demographics land use and ecology watersheds and topography

water bodies base grid and subsurface properties

Figure 16.2 Person oriented modeling: Spatio-temporal environmental characterization is coupled with microenvironmental dynamics, physiological characteristics, and time–location–activity patterns to develop estimates of exposures and doses ([top left] USEPA (2003); [top right] Georgopoulos et al. (1997), adapted with permission, Copyright 1997 American Chemical Society; [bottom] Chrisman (2001), reprinted with permission from John Wiley & Sons, Inc., Copyright 2001).

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Figure 16.3 The MENTOR framework for assessing cumulative/aggregate exposures and doses for multiple multimedia contaminants (from Georgopoulos et al. (2008); reprinted by permission from Macmillan Publishers Ltd, copyright 2007). See Table 16.3 for definitions of acronyms.

microenvironments, such as residences, offices, restaurants, vehicles, and so on. These levels can be calculated through microenvironmental steady-state or dynamic mass balance model simulations, supplemented by information from empirical databases. Step 3. Development of behavioral (activity, diet, etc.) data specific to the exposed subjects (for individual based modeling) or selection of a fixed-size sample population of “virtual individuals” (for population based modeling) in a way that statistically reproduces essential demographics (age, gender, race, occupation, education) of the population unit used in the assessment. For example, a sample of 500 “virtual individuals” is typically used to represent the demographics of a given census tract. The population attributes, such as the distributions of age, gender, employment, and housing, can be developed from available census data (e.g., from the US Census Bureau (US Census Bureau, 2007); American Housing Survey (USHUD, 2009) or from study-specific definitions). Sometimes, relevant databases are available as components of other modeling systems, as in the case of the Air Pollution Exposure Model (APEX) (Glen, 2002) which provides databases for housing as well as for commuting profiles. Step 4. Development of activity event (or exposure event) sequences for each member of the study group or of the sampled population of virtual individuals for the exposure period. In the case of population based modeling, this can be accomplished through retrieval of matching time–activity diary records from existing databases of past studies (e.g., from the USEPA’s Consolidated Human Activity Database (CHAD) (McCurdy

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Table 16.3 Acronyms used in the MENTOR flowchart of Figure 16.3. AERMOD AIRS APEX ASPEN CATS CEP CMAQ DEEM DEPM EMAP FACT GMS HAPEM ICRP ISCST MODFLOW NAWQA NGA NHANES NHAPS REMSAD RIOPA SDWIS/FED STORET WMS WQN

AMS/EPA Regulatory Model Improvement Committee Model Aerometric Information Retrieval System Air Pollution Exposure Model Assessment System for Population Exposure Nationwide Contaminants in Aquatic and Terrestrial ecoSystems Cumulative Exposure Project Community Multiscale Air Quality model DEpendability Evaluation of Multiple-phased systems Dietary Exposure Potential Model Environmental Monitoring and Assessment Program Flow And Contaminant Transport Groundwater Modeling System Hazardous Air Pollutants Exposure Model International Commission on Radiological Protection Industrial Source Complex Short Term Dispersion Model MODular three-dimensional finite-difference ground-water FLOW model National Water Quality Assessment National Geochemical Atlas National Health and Nutrition Examination Survey National Human Activity Pattern Survey Regional Modeling System for Aerosols and Desposition Relationships among Indoor, Outdoor and Personal Air Safe Drinking Water Information System/Federal Version Storage and Retrieval database Watershed Modeling System Water Quality Network

et al., 2000; Stallings et al., 2002)), based on the demographic characteristics of each “virtual individual.” CHAD contains over 30,000 person days (diary records) of activity patterns developed from pre-existing human activity studies. Each diary record provides a basis for simulating the movement of the “virtual individual” through geographic locations and microenvironments during the simulation period. Each event is defined by geographic location, start time, duration, microenvironment visited, and an activity performed. The attributes of CHAD records include age, gender, employment status, and smoking status of each individual, and they can be used to match attributes of each sampled “virtual individual.” Step 5. Estimation of multimedia levels (indoor air, drinking water, and food concentrations) and temporal profiles of multimedia chemicals in various microenvironments (residences, offices, restaurants, vehicles, etc.): Residential indoor air concentrations can be calculated using microenvironmental mass balance modeling with inputs from Step 2. For non-residential microenvironments (office, school, restaurant, etc.), it can be developed either through mass balance modeling or through linear regression equations developed from analysis of concurrent indoor and outdoor measurement data available for the multimedia chemicals in these microenvironments. The Stochastic Human Exposure and Dose Simulation (SHEDS) model (Burke, Zufall, and Ozkaynak, 2001) provides

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distributions of air exchange rates for different types of residential microenvironments, while other models and databases provide distributions for air exchange rates for general non-residential microenvironments (Turk et al., 1989) and vehicle microenvironments (Hayes, 1991). Drinking water concentrations can be obtained from regulatory monitoring databases (such as SDWIS/FED) (USEPA, 2008b) or field study measurements (such as NHEXAS) (Pellizzari and Clayton, 2006; Thomas, Pellizzari, and Berry, 1999). If such data are not available, the drinking water distributions can be modeled using water network models such as the EPANET2 model (Rossman, 2000) with treatment plant data to obtain drinking water concentrations (Maslia et al., 2000). Food concentrations (“residues” of chemical of concern) can be obtained from survey studies such as the US Food and Drug Administration’s (USFDA) Total Diet Study (TDS) (Tao and Bolger, 1999), the Pesticide Data Program (PDP) (USDA, 2009) and the National Human Exposure Assessment Survey (NHEXAS) (Pellizzari and Clayton, 2006; USEPA, 2006a). Step 6. Calculation of inhalation and ingestion intake (drinking water, dietary, and nondietary) rates for the members of the study group or the sample population of virtual individuals, reflecting/combining the physiological attributes of the study subjects and the activities pursued during the exposure events. For population based modeling, the drinking water and food intake rates can be estimated by extracting appropriate survey records from, for example, the Continuing Survey of Food Intake by Individuals database (CSFII) (Tippett, Enns, and Moshfegh, 1999), that match the demographic characteristics of the “virtual individual,” and from other literature sources (Harris and Mattes, 2008). These rates include: (1) consumption of tap water directly for drinking, (2) amount of tap water used in food and home-prepared cold beverages (e.g., lemonade mixes), and (3) hot beverages (e.g., coffee, tea). It should be noted that currently available literature studies on drinking water intake are based on short-term survey data and may have certain limitations, especially with respect to upper percentile values. The CHAD diary records also provide information on energy expenditure, which can be used to estimate water intake rates. The inhalation rate can be calculated based on the age and gender of each person in conjunction with the Metabolic Equivalent of Tasks (METs) value associated with the activity pursued (Georgopoulos et al., 2005). The energy expenditure information from CHAD diary records can be used directly to estimate inhalation rates. Alternatively, probability distributions or tables describing age-specific inhalation rates of humans can also be used (Allan and Richardson, 1998; Brochu, Ducre-Robitaille, and Brodeur, 2006a, 2006b). For population based modeling, dietary intake of multimedia chemicals for each virtual individual can be estimated by using the following information: food consumption rates, composition of food item (recipe file), and contaminant residue data in food. The US Department of Agriculture (USDA) CSFII database provides information on food consumption rates for the general United States population, covering 1994–1996 and 1998. Recipe files for specific types of food intakes can be developed and linked to the CSFII and TDS databases to generate the estimates of dietary intakes of different chemicals. Data on appetite and intake can be obtained through relevant literature (Harris and Mattes, 2008). The magnitude of non-dietary intake of specific chemicals from incidental soil/dust ingestion can be estimated using age-specific empirical intake rate distributions fitted to available tracer element mass balance study results. The distributions of estimated soil and dust ingestion rates can be obtained from surveys

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such as those from Buck et al., 2001. These estimates can then be apportioned by using time spent outdoors versus indoors into corresponding soil and dust ingestion exposures. Step 7. Combination of inhalation and ingestion intake rates for each study subject (for individual based modeling) or for each “virtual individual” of the representative sample (for population based modeling) with corresponding microenvironmental concentrations of contaminants, for each activity event and location, to assess exposures and estimation of target tissue doses of contaminants through PBPK modeling. The use of PBPK modeling overcomes many limitations associated with commonly used assumptions that employ linear approximations to relate internal dose to cumulative exposure through a given exposure pathway. In the past, it was common practice to employ “Simple Pathway Exposure Factors” to relate ambient concentration to dose as a result of this assumption (USEPA, 1991). However, this practice is often not applicable due to nonlinear processes of metabolic elimination, saturation effects, and so on. Furthermore, the internal and target tissue doses due to exposure to the same agent via different routes (e.g., ingestion and inhalation) are not necessarily additive and care must be taken in defining total dose due to multiroute exposures. Thus, the scientifically sound approach for relating exposure to internal dose is provided through PBPK modeling that can account for the distribution and metabolism of the chemical in the various organs. Use of PBPK models in exposure assessment allows evaluation of assumptions regarding the relationship of exposure and dose, physiological damping of exposure, and so on, because they treat explicitly the effect of temporal variation of exposure on total and target tissue dose. It must be noted that the above seven steps can be used in a “nested manner” in order to characterize both uncertainty and variability involved in exposure and dose assessment. Variability is both intra-individual and inter-individual (in the case of population based modeling). In order to characterize variability for a given set of exposure modeling options, the seven steps can be run with appropriate inputs to estimate the intra-individual and population variabilities. However, in order to characterize the uncertainty in estimates of distributions of exposures, these calculations have to be run multiple times by sampling the corresponding parameter distributions that represent the uncertainties. In the following, two demonstration case studies, one for individual based and one for population based modeling, are presented. For simplicity, the focus is on a single, extensively studied chemical, benzene, and the route of inhalation. However, the approaches are general and can be extended to mixtures and multiroute exposures. The interested reader can find multicontaminant and/or multiroute applications in Georgopoulos and Lioy, 2006 and Georgopoulos et al., 2005, 2008.

16.3 16.3.1

Case Study: Subject-Specific Individual Based Exposure Modeling Potential Benzene Exposures Due to Volatilization from Soil Contaminated by Underground Storage Tank Leak

The demonstration examples presented here describe inhalation exposure due to benzene contamination of soil near a home (Figure 16.4). Two different scenarios are considered here: (1) volatilization of benzene from the soil and (2) volatilization of benzene due to use

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Figure 16.4 Schematic description of the underground leak of heating oil tank. A contaminant of concern is benzene. Two types of exposures to benzene are examined in demonstration case studies: (a) exposure due to inhalation of benzene volatizing from the soil, and (b) exposure due to inhalation of benzene volatilizing from benzene-contaminated shower water used from a private well on the property.

of contaminated groundwater. In the case of underground contamination from tank leaks, significant time often elapses before the leak is discovered, and a retrospective exposure and risk assessment is required. Furthermore, since the amount of the chemical leaking into the ground (i.e., “source term”) is often unknown, and since the properties of the soil are highly variable, probabilistic exposure modeling is typically performed. The individual based exposure modeling for this case study employs analytical equations developed by Jury et al. (1990) to describe volatilization of organic chemicals from below the soil surface. Using this approach, potential exposure to contaminants evaporating from soil can be calculated based on information on the following: Source term: This includes data on the depth at which contaminated soil is located from the surface (L), the thickness of the contaminated soil layer (W; i.e., contamination is present from a depth of L to L + W from the surface), and the bulk concentration of the chemical in the soil (C0 ). Soil properties: These include soil porosity (φ), soil bulk density (ρb ), water content of the soil (Θ), and air content of the soil (a). Transport and transformation properties: Gas diffusion coefficient (Dga ), liquid diffusion coefficient (Dlw ), Henry’s Coefficient (KH ), chemical half-life (τ ; or decay rate

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constant, µ), organic partition coefficient (Koc ), surface wind speed (u), thickness of the air layer perpendicular to wind speed (B), height of the mixing layer (H), and the thickness of a thin, near ground, stagnant air boundary layer (d). Data on these quantities can be used to estimate the extent of volatilization of the chemical into the atmosphere through the following equations: C Tb (z, t) = C T (z, t; L + W ) − C T (z, t; L)

(16.4)

where

     (z − L − VE t) (z − VE t) 1 Co exp (−µt) erfc − erfc 2 (4D E t)1/2 (4D E t)1/2    + 1 + VE H E           (z + L + VE t) (z + VE t) · exp VE z D E erfc − erfc + 2 + VE H E 1/2 1/2 (4D E t) (4D E t)  

  [z + (2HE + VE ) t] · exp [HE (HE + VE ) t + (HE + VE ) z] D E erfc (4D E t)1/2      [z + L + (2HE + VE ) t] − exp HE L D E erfc (16.5) (4D E t)1/2

C T (z, t; L) =

h = Dga /d (boundary layer transfer coefficient)  HE = h K H (ρb f oc K oc + Θ + a K H )  

 10/3 a Dg K H + Θ 10/3 Dlw φ 2 (ρb f oc K oc + Θ + a K H ) DE = a (effective diffusion coefficient)  VE = Jw (ρb f oc K oc + Θ + a K H ) (effective solute velocity)

(16.6) (16.7) (16.8) (16.9)

When KH is large, the transport is insensitive to the thickness of the boundary layer, resulting in a simplified equation for calculating the flux at the soil surface:   1/2     

 exp −L 2 4D E t − exp −(L + W )2 4D E t (16.10) Jsb = −Co e−µt D E πt This flux can then be used in conjunction with a “box-model” type approximation for estimating airborne concentrations using the equation: Jsb (16.11) uB H It must be noted that this simplification avoids computational errors (round off and overflow errors) associated with calculation of the error function (i.e., calculating erfc(x) for large values of x). For many environmental exposures, the approximation is adequate. However, uncertainties in various quantities, such as the soil properties, necessitate a probabilistic analysis of the potential exposures. In this case study, the soil is assumed to be contaminated with a uniform concentration of heating oil. Contaminant is found in a 60 cm (W) deep layer of soil that is located 150 cm (L) from the surface. The horizontal (areal) extent of contaminated soil is assumed to be 10 m (B) in a direction perpendicular to the wind flow. The atmospheric boundary layer Cair =

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Figure 16.5 Left: Estimates of flux from volatilization of benzene from an underground leak. The volatilization is a result of heating oil leak (containing 25% mass concentration of benzene). The shaded area shows the 90th percentile confidence interval for estimated flux. Right: Corresponding potential exposure concentrations for an individual residing in the house.

mixing height (H) is assumed to be 10 m. Benzene volatilization is assumed to start at time t = 0 (corresponding to the start of year 2004). Figure 16.5 shows results from a Monte Carlo analysis of the emissions flux and potential exposure concentrations. Uncertainties in three major soil properties, soil porosity (φ), soil bulk density (ρb ), and water content of the soil (Θ), are considered, and quantified in terms of uniform distributions around the mean values. The impact of these parameters on the estimates of benzene fluxes and corresponding potential exposure concentrations is shown in Figure 16.5. The contribution of the leaking tank to airborne concentrations outside the house in this example is less than 10−2 µg/m3 . This can be compared to the national background ambient benzene concentration estimate of 0.43 µg/m3 (from National Air Toxics Assessment (NATA), USEPA, 2009), leading to the conclusion that the contribution of volatilization from the underground leak to potential inhalation benzene exposure is not significant in this example.

16.3.2

Potential Benzene Exposures and Doses Due to Volatilization from Groundwater Contaminated by Underground Storage Tank Leak

In the previous example, inhalation exposures associated with volatilization of benzene from the soil were calculated and found to be insignificant. In the second example here (adapted from Georgopoulos et al., 1997), benzene present in groundwater establishes a pathway of indoor exposure through usage of contaminated well water in the house for showering and bathing. In such a scenario, the contamination can have a substantial contribution to total benzene exposures, mainly due to volatilization of benzene from shower water. In this case, the exposures resulting from volatilization from tap water use are studied using an activity-location based exposure model, and a physiologically based toxicokinetic model for uptake and metabolism within the body.

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The indoor air is assumed to comprise four well-mixed compartments, representing the shower, bathroom, bedroom, and the rest-of-the-house. The model is used to estimate potential inhaled and dermal benzene dose to residents. The scenario involves indoor exposure to benzene following a 20 minute shower with contaminated water (with a benzene concentration of 300 µg/l in the water). Inhalation and dermal exposure are assumed to occur in the shower for 20 minutes, followed by inhalation-only exposure of five minutes in the bathroom, 35 minutes in the bedroom, and five hours in the living room. Data sources for air exchange rates, and so on, are described in Georgopoulos et al., 1997. 16.3.3

Basic Equations for the Microenvironmental Model

Concentrations of benzene in indoor air are calculated through a multicompartmental mass balance model. The general lumped parameter mass balance equation for a single chemical species in a well mixed compartment is: Vi

N N N      dCi K i j ai j Ci∗j − Ci + Q ji C j − Q i j Ci + Si (t) ; = dt j=1 j=1 j=1

(16.12)

where Ci is the concentration of the chemical in a microenvironment, i, at time t. Here, Vi is the volume of microenvironment, Ci∗j is the chemical concentration in compartment i in equilibrium with that in j, Kij is the mass transfer coefficient from compartment i to j, Qji is the volumetric flow rate from compartment j to i, aji is the interfacial area between compartments i and j, and Si (t) is rate of release of the contaminant in compartment i. The indoor source term due to volatilization from tap water use is given by   Ii φi Γ t, τi0 , τi∗ Cw , (16.13) Si (t) = τi∗ − τi0 where:

 φi = φiRn

2.5 2/3

Dw

+

RT



2/3

Da H

2.5 2/3

Rn

Dw

+

RT 2/3

Da H

(16.14)

0 Here, the subscript i indicates compartment i, I is the total amount of water consumed,  0 τi ∗and  ∗ τi denote the times at which water activity starts and ends, respectively, and Γ t, τi , τi = 1 if there is water activity during time t in compartment i (otherwise 0), Cw is the concentration of the contaminant in water, φ Rn is the water-to-air transfer efficiency for radon (Rn), Dw and Da are effective diffusivities in water and air (for the contaminant and radon, depending on the subscript for the equation), respectively. R is the universal gas constant, H is the Henry’s law constant, and T is the air temperature. Numerical solution of the differential equation here provides estimates of the concentrations of the contaminant in each compartment.

16.3.4

Basic Equations for the Toxicokinetic Model

The basic lumped parameter perfusion limited PBPK model equations are as shown below.

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Mass balance in PBPK compartment j:  cj dc j = Q j carterial − − Rj + Sj Vj dt P j /blood

(16.15)

where the subscript j indicates compartment j, Vj is the volume, cj is the tissue concentration, Pj/blood is the partition coefficient of chemical between tissue j and blood. The reaction term is given by: Rj =

m  V maxi, j c j f u, j K mi, j + c j f u, j i=1

(16.16)

where Vmaxi,j is the maximum rate of metabolism of the contaminant through enzyme i in tissue j, Km is the Michaelis–Menten affinity coefficient for enzyme i in tissue j, and fu,j is the unbound fraction of the contaminant in tissue j. The source terms for the contaminant in the body are as follows:   (16.17) Slung = Q alveolar Cair(inhaled) − Cair(exhaled)  cskin (16.18) Sskin = K media,skin Askin Cmedia − Pskin/media Skidney = f GFR Q kidney ckidney f u,blood (16.19) Here, Q represents the blood flow rate into compartment j and f GFR is the glomerular filteration fraction of kidney blood flow. Additional details on the PBPK modeling are given in Georgopoulos et al., 1997 and Isukapalli, Roy, and Georgopoulos, 2007. Figure 16.6 shows the model predicted microenvironmental concentrations and doses. Airborne concentrations over 100 µg/m3 can result due to the volatilization from showering. The model predictions were in close agreement with corresponding measurements of indoor levels of benzene.

16.4 Case Study: Numerical Probabilistic Modeling; Population Exposure Modeling This case study focuses on studying the impact of outdoor and indoor sources of benzene on population exposures and doses in a large urban area. It involves estimating year-long exposures for the population residing in the 498 census tracts in urban Philadelphia, PA, and the Camden, NJ, region in the United States. The geographic region and the census tracts are described in Georgopoulos et al., 2005; this region has a total residential population of about 2.1 million, based on Census 2000 data. In this study, MENTOR-1A was employed for modeling hourly exposures to benzene for the general population in the urban Philadelphia, PA, and Camden, NJ, areas for the entire year of 2001, using available databases for characterizing outdoor emissions, demographic characteristics of the population under study, housing characteristics, indoor sources, time–activity diaries, and physiological properties. In this study, a total of

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Figure 16.6 Estimates of exposures of a hypothetical individual to benzene due to volatilization of contaminated tap water. Shown are estimates of indoor air benzene-time concentration profiles in different rooms of the house following a “shower event,” and corresponding total dose and amount metabolized, as calculated by an integrated microenvironmental and PBPK model.

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249,000 “virtual individuals” were simulated (using 500 “virtual individuals” for each census tract) to represent the corresponding residential population. In the simulation, the activity patterns of each virtual individual were simulated throughout the day, for the entire year. A brief summary of the implementation of each step of the general framework described earlier is provided here. Step 1: Background atmospheric benzene concentrations were estimated using simulations from an air toxics version of CMAQ (Luecken, Hutzell, and Gipson, 2006); performed by the USEPA for the entire calendar year of 2001 using a nested grid with 36, 12, and 4 km horizontal grid resolution over successively smaller domains, with the finest scale grid covering the Philadelphia, PA, and Camden, NJ, regions. The simulations provided the hourly-averaged concentrations of multiple air pollutants across the nested grid. Surface-level concentrations were used for exposure calculations. Further details on the emission inventory and the simulation procedure can be found in Luecken, Hutzell, and Gipson, 2006. Step 2: Local outdoor concentrations were estimated through the use of spatio-interpolation schemes, specifically, the “Spatio-Temporal Random Field” (STRF) theory (Christakos and Vyas, 1998a). The STRF approach interpolates monitor data simultaneously in space and time. This method can thus analyze information on “temporal trends,” which cannot be incorporated directly in purely spatial interpolation methods, such as standard kriging. Regional scale air quality modeling predictions were interpolated to the scale of census tracts to prepare the input concentrations for the population exposure model using the STRF technique, as described in Georgopoulos et al. (2005). Step 3: The attributes of the population under study were retrieved from the 2000 US Census Survey (US Census Bureau, 2002). A statistical sample of 500 “virtual individuals” was sampled for each of the 498 census tracts under study to statistically reproduce essential demographics distributions of age, gender, housing type and employment status. The sampling process involved assigning essential demographics attributes from the corresponding distributions. In this application, the age and gender were assigned first, based on the corresponding fractions for the census tract, and employment was assigned based on the age and gender and the census tract data. Other attributes were assigned from either regional or national distributions. Step 4: A 24-hour activity diary for each “virtual individual” of the simulated population was selected from the Consolidated Human Activity Database (CHAD) (McCurdy et al., 2000) diaries, so as to match the demographic characteristics of the “virtual individual” with respect to age, gender, employment, and smoking status. In order to generate the longitudinal exposure sequence for the entire year, different activity diaries were sampled for each “virtual individual” to represent the weekday/weekend variability as well as the different seasons. These were then aggregated to establish a year-long activity sequence for each “virtual individual.” Step 5: Since available data and estimates of indoor sources of air toxics are sparse, the indoor levels of benzene were estimated via distributions that characterize the relationships between indoor and outdoor concentration levels. These relationships are often dependent on multiple factors (e.g., in case of benzene, the presence of an attached garage, cigarette smoking, or wood parquet flooring). Probabilistic input distributions for indoor/outdoor ratios of benzene levels were obtained from Graham and Burke (2003).

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Step 6: For each activity event of a “virtual individual,” inhalation rates were calculated using a combination of age- and gender-dependent body mass, basal metabolic rate, activity-specific energy expenditure, and Metabolic Equivalent of Tasks (METs). (METs are described in detail in Georgopoulos et al., 2005). Step 7: Using the inhalation rate in conjunction with the microenvironmental concentrations, the benzene uptake for each “virtual individual” was calculated using the basal inhalation rate and METs values. Step 8: A flow-limited PBPK model for benzene was used, based on the structure described in Isukapalli, Roy, and Georgopoulos, 2007, to calculate total and tissue doses for the “virtual individuals” representing the population of concern. The estimated exposures were significantly different for each season, as shown in Figure 16.7. Cumulative distribution functions (CDFs) of daily doses for the simulated population are shown in Figure 16.8. This type of population exposure modeling can provide insight into identifying susceptible subpopulations based on different demographic and physiological attributes. The PBPK model was applied to study the inter-individual variability for a subset of the population. Figure 16.9 shows the variability in the amount of benzene metabolized by different individuals that have similar physiological characteristics and same ambient levels of benzene. This calculation characterizes the contribution of demographic factors and activities to the variability in population doses.

16.5

Diagnostic Modeling for Assessing Exposure: Estimating Exposures from Biomarkers

Assessing exposures from concentrations or estimating biological doses and their effects using exposure measurements constitutes a “forward” mode of analysis, whereas estimating or reconstructing exposures from biomarkers requires an “inverse” mode of analysis. As described in the earlier sections, the forward analysis can be accomplished through the direct application of environmental (microenvironmental) exposure and toxicokinetic models, either empirical or mechanistic (i.e., physically and biologically based). The reconstruction analysis requires application of numerical model inversion techniques to toxicokinetic (and possibly toxicodynamic) models in conjunction with biomarker data; “complementary” environmental data will typically be needed for interpretation of the reconstruction results. It is widely recognized now that biomonitoring data can be used not only as early indicators of a biological effect for assessing health risks but that, under certain circumstances, but may also be used to identify contributors to exposures, which can be used to assess health risks (NRC, 2006). PBPK and Biologically Based Dose Response (BBDR) models in conjunction with numerical inversion techniques and optimization methods form major components of a framework for inverse modeling, as shown in Figure 16.10. The methodology for effectively assessing exposures from biomarker data involves multiple steps: Available supporting or complementary exposure data can be used to develop prior estimates of exposures for individuals and populations. These estimates can then be improved by using PBPK modeling and inversion techniques along with corresponding biomarker data. Exposure reconstruction can be formulated as a problem with the objective to identify the specific input combinations or distributions that best explain the observed

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Figure 16.7 Calculated estimates of the 90th percentile of seasonal averages of hourly local (census tract) personal exposure benzene concentrations resulting from outdoor sources for 2001 for the urban population of the Philadelphia, PA, region.

outputs while minimizing an “error metric.” The inputs typically involve spatial and temporal information on microenvironmental media concentrations of contaminants as well as corresponding information on human activities that result in intakes of these contaminants, whereas the outputs are observed biomarkers, and the error metric can be defined in terms of population variation, random error, and so on. Computational inversion/optimization techniques can be broadly classified into “deterministic” and “stochastic” (Moles, Mendes, and Banga, 2003). These methods in general use a systematic exploration of the input space

Diagnostic Modeling for Assessing Exposure: Estimating Exposures from Biomarkers 104

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Figure 16.8 Calculated distributions (cumulative) of daily average doses of benzene for the urban population of Philadelphia, PA, region (see map of the area in Figure 16.7) for year 2001. Contributions of outdoor sources only (left) and combined contribution of indoor and outdoor sources (right).

Ambilent conc (ppm)

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Figure 16.9 Intra-individual variability in ambient concentrations of benzene (top), and interindividual variability in doses experienced by an urban population (Philadelphia, PA, for Year 2001). A subset of “virtual individuals” with similar physiological characteristics experiencing the same outdoor concentrations was considered for studying inter-individual variability. The variation of over a factor of three in outdoor contributions to cumulative annual dose is attributed solely due to variation in microenvironmental factors and activity patterns.

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Figure 16.10 Major components required for a general prognostic/diagnostic framework of exposure modeling using combinations of environmental, behavioral, and biological (including biomarker) data.

to identify the “global” minimum of the error metric and the corresponding values of inputs (Georgopoulos et al., 2009). Several computational techniques have been used for exposure reconstruction from biomarkers, including: Maximum Likelihood Estimation (Rigas, Okino, and Quackenboss, 2001; Roy and Georgopoulos, 1998), Exposure Conversion Factor Method (Tan et al., 2006), Discretized Bayesian methods (Sohn, Mckone, and Blancato, 2004; Tan, Liao, and Clewell, 2007). Novel methods for exposure reconstruction and model parameter estimation include the Markov Chain Monte Carlo (MCMC) technique (Allen, Hack, and Clewell, 2007; Bois et al., 2007; Covington et al., 2007; Gilks, Richardson, and Spiegelhalter, 1998). Case studies focusing on comparative advantages of traditional methods and a review of novel methods are provided in Georgopoulos et al., 2009. Figure 16.11 presents an example involving reconstruction of exposure to chlorpyrifos (a pesticide that was widely used in the past) from measured biomonitoring data (concentrations in blood of 3,5,6-trichloro-2-pyridinol, TCPy, a metabolite of chlorpyrifos). Details of the biomarker databases, assumptions regarding exposures and inversion methods used are discussed in Georgopoulos et al., 2009. In this example, multiple exposure reconstruction techniques were evaluated, along with different assumptions regarding activity patterns (frequency of intake of food that contained chlorpyrifos). As shown in Figure 16.11, different assumptions regarding frequencies of intake resulted in widely varying estimates of calculated intake doses. The results are also sensitive to the inversion approach employed. In general, several major factors influence the feasibility and efficacy of exposure reconstruction from biomarkers. The specificity and the sensitivity of the biomarker with respect to the exposure metric of interest (e.g., concentration of the agent of concern) are two of the most important such factors. Biochemical properties of absorption, distribution, metabolism, and elimination (ADME) impact the types of exposures that can be estimated from the biomarker data (Hays et al., 2007). One of the major factors affecting the accuracy of exposure reconstruction is the half-life of a chemical in the body. The “residence time” or “age” of an “observed” (i.e., measured) biomarker molecule can be defined as the time

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Figure 16.11 Estimated average intake doses of chlorpyrifos (CPF) through exposure reconstruction from biomarkers based on assumptions of activity patterns (frequency of dietary intake of chlorpyrifos). For simplicity, dietary exposure is assumed to represented by a bolus dose. Different assumptions in frequencies of intake (1 or 7 times per week) result in widely varying estimates of intake doses calculated through inversion of biomarker data. The results are also sensitive to the inversion approach used (steady-state, Bayesian, and exposure conversion factor methods are discussed in the text).

elapsed since it entered (or was generated in) the body. The observed biomarker levels (molecules of either a chemical or its metabolites, potentially involving multiple exposures across multiple timescales) represent an “integration” over molecules of different “ages,” dependent on the time each molecule entered or was generated in the system, and on elimination kinetics. As an example, for chemicals and metabolites with relatively short half-lives, only the exposure history of the previous days or weeks can be estimated. For those with longer half-lives, larger timescales of exposure history have to be considered, and the influence of confounding sources creates additional uncertainties. In the simplest case of a steady, continuous exposure, and of toxicokinetics that can be described adequately by a single-compartment PK model, b (t) = x  e−kt , R (t) = ke−kt , and F (t) = 1 − e−kt , where x  is a known exposure concentration, and the elimination rate k is related to half-life, t1/2 , as k = log2 /t1/2 . These equations for age distribution also represent the output versus time function from a bolus input. In the case of discrete repeated (“cyclical”) exposures of time period, ∆t, assuming that the biomarkers are collected at a time λ∆t after the end of the last exposure (0 < λ ≤ 1), and that all exposure concentrations are equal to x  , the relative contribution of exposures that occurred at different times can be expressed in terms of “cycles” of exposure, as follows: ∞ n n     −k(i+λ)∆t −ik∆t xe and F (n) = e e− jk∆t (16.20) b (n) = i=0

i=0

j=0

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Figure 16.12 Impact of half-life on the relative contributions of different timescales of exposures to observed chemical biomarker levels. The example shown above is based on a one-compartment PK model (linear decay); the biomarker represents the level of chemical in the compartment. This provides an insight into the types of exposures that can be reconstructed from biomarkers based on the biological properties of the contaminant Georgopoulos et al., 2009; Reprinted by permission from Macmillan Publishers Ltd, Copyright 2008).

Figure 16.12 shows, as a function of different half-lives, the relative contributions of different timescales of continuous, steady exposures to observed chemical biomarker levels in a single-compartment system. These calculations are an extension of the approach presented in NRC, 2006.

16.5.1

Deterministic Numerical Inversion

The exposure reconstruction problem can be formulated as a global minimization problem that involves finding a set of possible exposures x by minimizing a “cost function,” J, based on observed biomarker data b (ti ) at each time point ti (a total of N meas measurements), and a forward model for estimating biomarkers: b = m(x,ti ). Additionally, constraints can be included in the form of bounds on possible exposures (x L ≤ x ≤ xU ), equality constraints on the model ( f (x,b,t) = 0), and inequality constraints (g (x,b,t) ≤ 0). Typical examples of J include: J=

N meas  i=1



T    b (ti ) − m (x,ti ) b (ti ) − m (x,ti )

[least square minimization] (16.21)

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and N meas     f x b (ti ) |x,m (x,ti ) J = −L m,x,b = −

[maximum likelihood estimation]

i=1

(16.22) 16.5.2

Stochastic Inversion/Bayesian Approach

A general probabilistic framework for inverse problem solution is provided by the Bayesian approach, which is based on Bayes’ Theorem: p (x | b) = 

p (b | x) p (x) , p (b | x) p (x) dx

(16.23)

If prior knowledge on exposure attributes is represented by pprior (x), the theoretical (“model”) knowledge of the relation between x and b represented by ptheory (b|x), and the prior information about exposure represented by pprior (x), then for a specific set of biomarker measurements, b :       (16.24) pprior x,b = pinferred x | b pprior b ; for fixed b Overall, if pmodel (m,x) denotes the probability density of the “true” model output being m for inputs x:   (16.25) ptheory b | x = perror (b | m) pmodel (m | x) dm, where perror (b | m) is the probability of measuring b when the true value is m; that is, it is the distribution of “measurement error” and not “model error:”  p (x) perror (b | m) pmodel (m | x) dm   p (x,b) = (16.26) p (x) perror (b | m) pmodel (m | x) dmdx r For a “deterministic” model, Pmodel (m | x) is a delta function centered on m(x). r For a “deterministic” model with “model error” (or uncertainty), Pmodel (m | x) represents the distribution of uncertainty in m(x). r For a “stochastic” model, P model (m | x) represents the distribution of predictions that can be obtained for a specific (fixed) set of inputs x. 16.5.3

Bayesian Markov Chain Monte Carlo (MCMC) Technique

The MCMC approach provides a means for sampling from the “posterior probability distribution” without having to sample the entire range of the prior distribution. The method requires defining the prior distributions, available biomarker data, and a likelihood function defining the likelihood of the data given a set of forward model parameters; then the MCMC approach involves marching in the sample space based on acceptance criteria that consider the likelihood of the data given the parameters. The estimation of population parameters (i.e., one distribution that is representative of “all” individuals) with the MCMC technique quite often results in an artificial fit of a single parameter and, thus, results in a large “error

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term.” These errors will be substantial when there are large inter-individual variabilities with regard to exposure patterns. There is a need for “optimal” exposure reconstruction using PBPK models, and this need derives from the fact that incorporating optimization approaches in the inverse modeling process can result in faster convergence and more robust solutions (Georgopoulos et al., 2009). Though typical PBPK models can be run quickly on modern computers, the computational demands can become challenging when hundreds of thousands of simulations are used in the inverse modeling on desktop computers. Likewise, complex PBPK modeling scenarios (e.g., mixtures of metals or pesticides with large half-lives) may need significantly more computational time for a single simulation. Therefore, the use of Fast Equivalent Operating Models (FEOMs) (Balakrishnan et al., 2003; Li et al., 2002; Wang et al., 2005) may be necessary in order to achieve reasonable computational performance. Figure 16.13 presents the conceptual framework depicting the steps involved in using optimization techniques in conjunction with inverse modeling for faster convergence that incorporates the use of FEOMs for faster simulation times. This framework is not limited to exposure reconstruction. It can also be used for estimating distributions of physiological and biochemical PBPK model parameters for individuals and populations that are consistent with available biomarker data (typically study specific data where exposures are adequately characterized) by combining the data with prior estimates of the parameters. Furthermore, the framework

Figure 16.13 Exposure reconstruction process using optimization-aided approach with a full PBPK model or a Fast Equivalent Operational Model (FEOM). The coupling with optimization techniques reduces the number of simulations significantly, and the use of FEOMs reduces the time required for each run (Georgopoulos et al. (2008); reprinted by permission from Macmillan Publishers Ltd, Copyright 2008).

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can be used to select appropriate PBPK model structures when alternative formulations are available.

16.6

Conclusion

Exposure modeling is an essential component of the health risk assessment process. Recent years have seen a transformation from location-specific exposure modeling with artificial screening scenarios to more realistic “person-oriented” modeling. PBPK modeling has become a central component in exposure modeling both for forward source-to-dose exposure assessment, and is increasingly finding more applications in reverse “exposure assessment” or “exposure reconstruction” from biomarkers. The approaches for individual and population based exposure modeling presented here are general in nature and can be applied to complex exposure scenarios involving mixtures of chemicals. The example case studies demonstrate how prognostic exposure modeling can be applied to study individual-specific exposures for assessing the relative importance of different routes of exposures, as well as to study, in a statistical sense, exposures to the general populations and susceptible subpopulations. Overall, a major shift has been taking place through the development of “person oriented” approaches and models that aim to account for total exposures of individuals and of populations to co-occurring stressors. These new “systems based” approaches focus on individual persons, real or “virtual,” with well defined physiological, socioeconomic, and so on, attributes, and take into account how the detailed activities of these persons in space and time affect their “microenvironments” and their corresponding exposures to stressors, as well as how they affect the physiological processes determining biologically relevant dose. Proceeding a step further, person oriented approaches are starting to take advantage of information on genetic and other factors that influence individual susceptibility to environmental stressors. The current explosion in toxicoinformatic (genomic and epigenomic, transcriptomic, proteomic, metabonomic, etc.) data is expected with time to enhance the understanding of inter-individual variability in both exposure and effect dynamics, develop linkages to environmental, behavioral and biological factors that determine disease susceptibility, and eventually establish a framework for “personalized” environmental health risk assessments.

16.7

Acknowledgments

This work was primarily supported by the USEPA-funded Environmental Bioinformatics and Computational Toxicology Center (ebCTC), Grant # GAD R 832721-010. Additional support was provided by the NIEHS sponsored UMDNJ Center for Environmental Exposures and Disease, Grant #: NIEHS P30ES005022.

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17 Probabilistic Reverse Dosimetry Modeling for Interpreting Biomonitoring Data Yu-Mei Tan and Harvey J. Clewell III The Hamner Institutes for Health Sciences, USA

17.1 Introduction A major challenge in human health risk research is to establish an accurate relationship between the levels of exposure to environmental chemicals and the degrees of disruptions at various biological endpoints. Except for a few cases in which human kinetic data are available, such dose-response relationships are often inferred from animal toxicity studies or in vitro data. Since these data often do not cover the low exposure region that humans encounter, the dose-response relationship determined based on animal data needs to be extrapolated to relevant human region. To reduce the uncertainty in the process of extrapolations, a computational model that describes the biological mechanism of disposition and responses, and is calibrated with high dose experimental data, could be used to evaluate the low dose effect in humans. For some chemicals, simple pharmacokinetic modeling is adequate to describe the dose-response relationship. For example, an estimate of the volume of distribution and clearance of a chemical will suffice to convert a steady-state blood concentration to an equivalent daily dose rate. For most chemicals, more sophisticated descriptions of distribution and metabolism are required to incorporate nonlinear biochemical processes in a biological approach context. In these cases, physiologically based pharmacokinetic (PBPK) modeling can assist high-to-low dose, route-to-route, and interspecies extrapolations necessary for estimating human risk on the basis of animal toxicity studies

Quantitative Modeling in Toxicology
C 2010 John Wiley & Sons, Ltd

Edited by Kannan Krishnan and Melvin E. Andersen

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or in vitro data (Clewell and Andersen, 1985; Clewell, Andersen, and Barton, 2002; Clewell and Clewell, 2008). These calibrated models can predict internal tissue dose for assessing human health risk based on the assumption that similar tissue response arises from equivalent target tissue dose across species. In addition, their ability to link external exposures to internal tissue doses has allowed them to be applied in interpreting biomonitoring data.

17.2

Biomonitoring, Exposure, and Human Health Risks

The term biomonitoring refers to the measurement of chemicals or their metabolites in human tissues or specimens (NRC, 2006). Biomonitoring identifies the presence of chemicals, both natural and synthetic, in human populations and has long been used in the workplace to identify workers with excessive exposure or evidence of early toxic effects in workers. It plays an important role in recognizing and preventing toxic hazards in the workplace, especially when baseline measurements are available and a series of specimen samples are collected on the same individual over time. In recent years, more biomonitoring studies have been conducted to evaluate exposures to environmental chemicals for members of general public. These studies have been mainly brought about by improved analytical capabilities that allow more chemicals to be detected at ever lower concentrations in the human body. The US Centers for Disease Control and Prevention (CDC), for example, measures chemicals and/or their metabolites in blood and urine samples from participants in the National Health and Nutrition Examination Survey (NHANES) and publish results from these studies biennially. While the purpose of these reports is “to provide unique exposure information to scientists, physicians, and health officials to help prevent disease that result from exposure to environmental chemicals” (CDC, 2005), they noticeably increase public awareness of the term “biomonitoring” and enhance concerns, or even exacerbate anxiety, regarding daily chemical exposures. While biomonitoring is widely used to detect chemicals in the human body, it has several limitations. Biomonitoring data are measures of the internal exposure to a chemical, but they do not have a direct relation with exposures or effects. They are complexly related to the nature of exposures and the mechanisms of clearance of substance from the body. By themselves, biomonitoring data cannot be used to distinguish the relative contributions of different sources (e.g., air vs food) or routes (e.g., dietary vs inhalation). Also, they cannot be used to differentiate whether a substance in the human body comes from exogenous sources or is endogenously produced. Acetone, formaldehyde, methanol, and ethylene oxide are all examples of environmental chemicals that can also be generated from normal metabolism. Another limitation that occurs with large-scaled biomonitoring studies is that the observed biomarker level is only a snapshot of chemical concentrations in tissues or specimens at a single point in time. What is measured may reflect recent exposure, exposure over a longer period, or neither. Even in an occupational setting where the collection of biological samples is recorded in detail and exposures are monitored constantly, biomonitoring may still be done at a time which fails to provide useful information regarding exposure. Besides the limitations associated with linking biomonitoring results with exposures, limitations also exist when establishing the relationship between biomonitoring results and health effects. Often, the selection of a biomarker is based on characteristics such as

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specificity, sensitivity, accessibility, and available methods of measurement and/or analysis, rather than considering biomarkers that are associated with the biological effects. Some biomarkers provide a better surrogate for target tissue dose than others. Blood concentration data usually serve as a relatively good surrogate for target tissue dose when the parent compound is toxic. But if the toxicity is produced by metabolism, the relationship of target tissue dose to parent chemical blood concentration may be complex and route dependent. For example, the liver toxicity of chloroform results from the metabolic production of phosgene (Pohl, Martin, and George, 1980). The relationship of chloroform blood concentrations to the rate of metabolism in the liver is quite different for inhalation exposure, where only 25% of the arterial blood flow from the lung perfuses the liver, as compared to oral exposure, where all of the portal blood flow from the gastrointestinal (GI) tract goes to the liver directly. Samples other than blood, such as exhaled air, milk, or hair, can also serve as surrogates for target tissue dose, to the extent that they can be related to blood concentrations or total body burden. One example is the case of using hair concentrations of mercury as a biomarker for methylmercury exposure, based on the measured hair:blood partition coefficient (Shipp et al., 2000). Urinary data can also serve as a measure of intake; at steady state, the total daily amount excreted in the urine can be used as a surrogate for the bioavailable fraction of the daily environmental exposure rate (Yager et al., 1999). Urine data alone, however, are not informative regarding internal concentrations. In that situation, pharmacokinetic modeling can be used to relate urine concentrations to blood concentrations. Similarly, data on milk concentrations, together with estimates of suckling rate, can serve as an estimate of intake for a nursing infant. But in the absence of information on the pharmacokinetics of the compound in the infant, milk concentrations do not directly relate to the infant’s internal exposure (Clewell and Gearhart, 2002). Due to the limitations discussed (Figure 17.1), biomonitoring studies should not be considered a substitute for exposure or risk assessment. Exposure assessment identifies the sources, pathways and routes of exposure, as well as measures or estimates the intensity, frequency, and duration of exposure. It also includes analyses on human activity patterns and behavioral variations in individuals or populations to better characterize the uncertainty inherent in exposures. Risk assessment uses information collected from animal toxicity studies, in vitro studies, epidemiological studies, or clinical studies to determine probability of health effects caused by exposure to environmental substances. Biomonitoring appears to be the missing link between these two assessments, since it evaluates the amount of environmental substances that actually enter the human body. But, to properly connect biomonitoring data with exposures requires information on the pharmacokinetics of the substance in relation to the tissue or specimen that is sampled, as well as the time-dependent nature of the exposure in relation to time of sampling. Linking biomonitoring data to human health risks is even more challenging due to the limited amount of human toxicity data. The CDC has estimated that over three-quarters of the chemicals it has reported to be present in human blood have no human toxicity values (CDC, 2005). In such a case, biomonitoring data may be of use to identify temporal exposure trends or highly exposed subpopulations as an extension of exposure assessment, but they will not be of use to evaluate the potential health implications of the exposures as part of risk assessment. In the case when toxicity values are available on a chemical, several approaches may be used to place biomonitoring data in a health risk context.

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Biomonitoring Data

Biomonitoring data alone do not fully reflect the nature of exposure (i.e., routes, activities)

Biomonitoring data may be complexly related to the biological effective dose at the site of action

Biomonitoring data alone do not provide information on health effects or risk

EXPOSURE

TARGET TISSUE DOSE

ADVERSE HEALTH EFFECTS

Figure 17.1 The Role of Biomonitoring in the “Exposure–Target Tissue Dose–Adverse Health Effects” Continuum. Human biomonitoring data are of value from a qualitative perspective in identifying chemicals to which humans have been exposed. They provide an impetus for future evaluation of the nature of exposures and potential health implications. Interpretation of health implications of human biomonitoring data is more problematic, requiring additional analyses to relate biomarker levels to exposures associated with adverse health effects in toxicity studies.

17.3 Approaches for Interpreting Biomonitoring Data The most direct use of a biomarker of internal exposure is when the relationship of the biomarker to the health effect of concern has been characterized in humans. An example of this case is methylmercury, where human epidemiological studies of maternal ingestion of methylmercury in contaminated fish have identified the relationship between cord blood concentrations of mercury and effects on childhood performance in neurological testing. CDC (2005) compared the cord blood mercury level that is associated with a 5% increase in the prevalence of an abnormal Boston Naming Test with blood concentrations of mercury measured in women of child-bearing age in the United States to provide a risk characterization. Unfortunately, there are few cases in which human data are available to directly relate a biomarker of internal exposure to biological effects. It is, however, possible to estimate potential human health effects using the relationship of the biomarker level to concentration at which toxic effects are observed in animal studies. Such approach is referred to as “Forward Dosimetry,” which is used to estimate internal exposures based on external exposures that characterize the toxicity of a chemical. In conventional forward dosimetry, the relationship between external exposures and measured biomonitoring data is established statistically by direct measurement. A common practice in the workplace is to relate biomarker concentrations with time-weighted average measurements of exposure levels obtained from personal monitoring. Forward dosimetry can also be done by indirect inference, such as using centralized monitoring of community water or measurement of food contamination levels to estimate internal exposures for comparison with biomonitoring data collected from the consumer population. With the use of activity diaries, questionnaires, and computational models, these biomonitoring data may

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also be interpreted at an individual level. Another way to conduct forward dosimetry is to exercise PBPK models to estimate internal tissue concentrations in relation to some specific exposure levels, such as an exposure guidance value. Hays et al. (2007) proposed that a Biomonitoring Equivalent (BE), a biomarker concentration associated with continuous exposure at a given exposure guidance value, could be used as a basis for determining whether a particular biomonitoring result presents a cause of concern. For example, the BE blood concentration associated with the Reference Dose (RfD) for a compound would be obtained by running the pharmacokinetic model for continuous exposure at the RfD and setting the BE to the predicted steady-state blood concentration. If the margin of safety between the BE and the biomonitoring results is low, this compound may become the candidate for additional epidemiologic or exposure pathway evaluation (Hays et al., 2007). Another approach for linking biomonitoring data to health outcomes is to estimate external exposures that would be consistent with the measured biomonitoring data. Such approach is referred to as “Reverse Dosimetry.” Similar to forward dosimetry, reverse dosimetry also uses pharmacokinetic models to link external exposure to biomarker concentration. The term “reverse,” however, does not imply that the model input (i.e., administered dose or exposure) and output (i.e., internal tissue concentrations) are reversed. Instead, reverse dosimetry uses other statistical and computational tools to reverse the relationship of external-to-internal measures of exposures. This additional manipulation from forward dosimetry allows the estimated levels of external exposures to be compared to some “safe” exposure concentrations (e.g., regulatory guidance values), since the traditional risk assessment paradigm and the resulting estimates of safe exposures are often based on measures of administered dose or exposure concentration (Figure 17.2). At the individual level, reverse dosimetry is referred to as dose or exposure reconstruction. At the population level, reverse dosimetry is incorporated with probabilistic data regarding exposure patterns and pharmacokinetics; it is referred to as “probabilistic reverse dosimetry.” A number of examples can be found in the literature that applies pharmacokinetic models in reverse dosimetry for compounds ranging from persistent to non-persistent: r Persistent compounds (half-lives in the order of years) – Dioxin (Lorber, 2002; Aylward et al., 2005a, 2005b) r Intermediate-persistence compounds (half-lives in the order of days to months) – Methylmercury (Clewell et al., 2000; Shipp et al., 2000; Stern, 2005; Allen, Hack, and Clewell, 2007) r Non-persistent compounds (half-lives in the order of hours) – Chloroform (Georgopoulos, Roy, and Gallo, 1994; Roy et al., 1996; Tan et al., 2006) – Benzene (Weisel et al., 1996; Roy and Georgopoulos, 1998) – Trichloroethylene (Sohn, McKone, and Blancato, 2004) – Trihalomethanes (Tan, Liao, and Clewell, 2007) – Chlorpyrifos (Bouchard et al., 2005) – Triclopyr (Gosselin et al., 2005) While forward dosimetry, such as the BE approach, is particularly attractive for persistent and intermediate-persistence compounds where the impact of time-varying exposure is damped, the application of forward dosimetry on non-persistent compounds is more problematic. For non-persistent compounds, where half-lives are in the order of hours, measured biomarker concentrations are dominated by recent exposures. A random biomarker sample

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Human Exposure (Chemical Concentrations in the environment)

Forward dosimetry

Pharmacokinetic Modeling

Chemical Concentration in human blood from biomonitoring studies

Reverse dosimetry

Margin of safety

Chemical Concentrations in animal blood from toxicity studies

Animal exposures (Administered doses in toxicity studies)

Traditional risk assessment

Figure 17.2 Interpretation of Biomonitoring Data. To be put in a health risk context, the relationship of human biomonitoring data to animal toxicity data must be determined. Biomonitoring provides a measure of tissue concentration. Traditional risk assessment is based on measures of external exposures, such as mg/kg/day ingested. In forward dosimetry, pharmacokinetic studies in experimental animals can be used to support a direct comparison of internal doses, providing an estimate of margin of safety. Alternatively, reverse dosimetry can be conducted to estimate the external exposure in humans for comparison with an animal-based health standard, such as a Reference Dose (RfD).

from an intermittent exposure could be well above or below the time-weighted average value that would be achieved by an equivalent continuous exposure, depending on the relationship of the peak exposures and the time of sampling. Thus, reconstructing exposures from these compounds becomes an ill-posed problem technically because there is not a unique solution. For example, in the case of a single inhalation exposure to a non-persistent compound, several potential exposure scenarios could achieve the same blood concentration at a single time point (Figure 17.3): r a short duration exposure to a high concentration; r a long duration exposure to a low concentration; r a long duration exposure to a high concentration, followed by a delay before measuring the blood concentration; r multiple short duration exposures; r and many other possibilities. Over the years, a number of human PBPK models of volatile organic compounds (VOCs) have been developed specifically to estimate internal exposures from complex

Compound concentration in blood

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100 80 60 40 20 0 0

5

10

15

20

25

30

Time (h)

Figure 17.3 Issues with Exposure Reconstruction for Non-Persistent Compounds. For nonpersistent compounds, measured biomarker concentrations are dominated by recent exposures. For example, several exposure scenarios could achieve the same blood concentration at the single time point (marked by the arrow): a short-duration exposure to a high concentration (solid line); a long-duration exposure to a low concentration (dotted line); a long-duration exposure to a high concentration, followed by a delay before measuring the blood concentration (dashed line); multiple short-duration exposures (dash-dot line).

environmental exposures (Blancato and Chiu, 1993; Chinery and Gleason, 1993; Levesque et al., 2000, 2002; Adams et al., 2005; Haddad, Tardif, and Tardif, 2006), and several studies have attempted to perform exposure reconstruction (Georgopoulos, Roy, and Gallo, 1994; Roy et al., 1996; Weisel et al., 1996; Roy and Georgopoulos, 1998). The difficulties associated with reconstructing exposures to non-persistent compounds have been illustrated in a study by Sohn, McKone, and Blancato, (2004). In this study, data on controlled inhalation exposures of human subjects to trichloroethylene were analyzed as if the data were random samples from a large population with unknown exposure conditions. The actual exposures were conducted at a concentration of 100 ppm for four hours. The exposure onset, concentration, and duration were reconstructed using Bayesian analysis. Overall, posterior estimates were close to the actual exposure conditions but the confidence intervals were fairly broad. In the case of the reconstructed air concentrations, the 95% confidence interval for the posterior estimate ranged from less than 100 ppm to more than 250 ppm. These results reflect both the potential and the limitations of performing exposure reconstruction for compounds with a short half-life. Rather than attempting to identify the specific exposure producing an individual’s biomarker value, a probabilistic approach provides a distribution of exposures that are consistent with the measured biomarker. When it is used at the population level, the results of a probabilistic analysis can be considered to be an estimate of the distribution of exposures in the population that is consistent with population based biomonitoring results. In the next section a “probabilistic reverse dosimetry” approach is introduced; it incorporates probabilistic information regarding chemical pharmacokinetics and possible exposure patterns to infer external measures of exposure from internal measures of exposure.

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17.4

Probabilistic Reverse Dosimetry Modeling for Interpreting Biomonitoring Data

Probabilistic Reverse Dosimetry

A probabilistic reverse dosimetry approach involves a suite of computational tools to estimate a distribution of exposures likely to have produced the observed biomarker concentrations in a population. The core of this approach is using PBPK modeling to describe the tissue dosimetry – from external exposures to internal tissue concentrations. To “reverse” this “forward dosimetry,” other computational tools are used, including Monte Carlo analysis and Bayesian statistics. Exposure modeling and quantitative structure property relationships (QSPRs) may also be used to better characterize exposures or estimate chemical-specific parameters in a PBPK model. A brief description of each tool is presented below.

17.4.1

Exposure Modeling

Characterizing exposure pattern and its relationship to time of sampling is critical, especially for non-persistent compounds. While exposure pattern can simply be a series of inputs (e.g., inhale for 20 minutes once daily) into a PBPK model, sometimes an exposure model is required to aggregate all major exposure contributing factors. These factors may include spatial and temporal profiles of chemical transportation, as well as human activities/behaviors. The complexity of an exposure model is dependent upon the nature of the chemical and common exposure scenarios. For example, a one-compartment model can be used to represent a household appliance, describing mass transfer of volatile compounds from tap water to indoor air when this appliance is in use (Shepherd, Corsi, and Kemp, 1996; Howard and Corsi, 1998; Reed, Corsi, and Moya, 1999). In other cases, multiple compartments are required to characterize exposures. For example, a common multicompartment household model incorporates information on volumes of residential zones (e.g., rooms), ventilation characteristics of each zone, and human activities, such as the amount of time individuals spend in each zone, or water device usage to estimate the temporal profile of exposures to volatile compounds received by individuals (McKone, 1987; Weisel et al., 1999; Wilkes, 1999; Kim, Little, and Chiu, 2004). In an exposure model, environmentalrelated parameters can usually be measured directly and behavioral-related parameters may be obtained from questionnaires or self-recorded diaries. When the primary sources of time/activity data are not available, secondary data from surveys may be used to estimate human activities in a population. The 1997 Exposure Factors Handbook (USEPA, 1997) is one of the databases that contains summary data obtained from various questionnaires, diary surveys, and other sources. The Handbook includes most scenarios and factors that are commonly used in exposure assessments, including consumption of drinking water, fruits, vegetables, meat, grain products, dairy products, and fish; soil ingestion; inhalation rates; skin surface area; breast milk intake; soil adherence; lifetime; activity patterns; body weight; consumer product use; and the reference residence (USEPA, 1997). More specifically on activity patterns, information is available on time spent in various activities and in various microenvironments. Some examples are frequency and duration of taking baths or showers; time spent in heavy traffic either running, walking, standing, or in a vehicle; time spent in various indoor and outdoor

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locations; and time spent in an activity or microenvironment related to tobacco smoking. Activity factors are available for both adults and children under 12 years old. Another commonly used database is the US Environmental Protection Agency’s Consolidated Human Activity Database (CHAD), which contains data obtained from pre-existing human activity studies that were collected at city, state, and national levels. CHAD refers to two separate items: the CHAD database and the CHAD application. The CHAD database contains data either in the original raw data form or modified according to predefined format requirements; and the CHAD application is downloadable software used to manipulate the database. The CHAD database output is a sequence number that indicates an individual of certain demographic background in a day when this person starts and ends an activity in a specific location. CHAD is typically used to provide input data for simulation models such as the Stochastic Human Exposure and Dose Simulation (SHEDS) Model or the Air Pollutants Exposure (APEX) Model. It can be applied to provide input data for PBPK models as well. Besides mass balance compartmental models, other types of exposure model deal with cumulative and/or aggregate exposures. Cumulative exposure refers to exposures to multiple chemicals from a common-mechanism group. For example, N-methyl carbamate and organophosphorus pesticides both are inhibitors of acetylcholinesterase. The inhibition can cause an accumulation of acetylcholine at nerve synapses, leading to prolonged stimulation of acetylcholine receptors on postsynaptic cells and consequent neurotoxic effects. Thus, exposure to both N-methyl carbamate and organophosphorus pesticides may pose a health risk even if the individual compounds are each present at levels below their respective “safe levels.” Aggregate exposure refers to exposures to a single chemical from multiple sources and routes. An example would be that people are exposed to polychlorinated biphenyl (PCB) through food (e.g., fish, ducks, frogs), water, air, skin contact with dust particles, and products that contain PCB (e.g., additives in paints, inks, electrical equipment). Exposure models that simulate cumulative and/or aggregate exposures often contain a database and a program that provides a user interface for accessing and manipulating the database. CalendexTM is an aggregate and cumulative exposure model that estimates human exposure to single and multiple compounds in food, residues in or around the residence, and/or residues from occupational exposures. This calendar based model can estimate exposures for various periods, from daily to chronic (up to one year) exposures. CalendexTM also includes temporal and spatial variances in each assessment, such as chemical degradation over time or types of pest control used in different geographic locations. Another similar exposure model is the Cumulative and Aggregate Risk Evaluation System (CARES) model that estimates exposure to pesticides from all sources. CARES is also calendar based and provides temporal, spatial, and demographic specificity. Besides a stochastic, population based exposure calculation, CARES has a toxicity module that can calculate risk deterministically or probabilistically using Monte Carlo simulation. Rather than being calendar based, LifeLineTM is developed to characterize aggregate exposures and risks from pesticide residues in diet, residential uses, and tap water related sources by simulating an individual’s lifetime exposures. LifeLineTM allows the user to examine the patterns of exposure for a population over time, or the distribution of exposure across a population at different age and season. It can also be used to estimate the corresponding risks for non-cancer toxic effects or lifetime cancer risks associated with these exposures.

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17.4.2

Probabilistic Reverse Dosimetry Modeling for Interpreting Biomonitoring Data

Monte Carlo Analysis

Monte Carlo analysis is used to handle interindividual variability and uncertainty in pharmacokinetics and exposure patterns. The first step in conducting Monte Carlo analysis is to define distributions for both pharmacokinetic and exposure parameters in a model. Distributions for physiological parameters can often be found in the literature, while distributions for chemical-specific parameters are often estimated from in vitro studies or rely on the researcher’s professional judgment. Distributions for exposure parameters may be obtained from direct measurements (e.g., air ventilation rate) or large surveys (e.g., chromium concentrations in drinking water). Databases such as The 1997 Exposure Factors Handbook (USEPA, 1997) or CHAD may also be useful resources. After the distributions are defined for all parameters in a model, the Monte Carlo algorithm randomly samples from each of the distributions, runs the model, and saves the resulting output (such as blood concentrations). Each run of the model represents a randomly selected individual who is exposed to a randomly selected exposure scenario. The process is repeated a large number of times to obtain a stable distribution of the output. 17.4.3

Bayesian Statistics

Biomarker concentrations are affected by not only the exposure levels but also by other factors, such as the time between exposure and sampling, as well as variability among individuals with respect to their exposure patterns and pharmacokinetics. Thus, an approach that explicitly recognizes and accounts for these sources of variation is preferred when estimating exposures based on observed biomarker levels. The Bayesian approach has this desired feature, so it can be used in the probabilistic reverse dosimetry approach to infer a distribution of external exposure based on the prior knowledge of pharmacokinetics or a PBPK model, potential exposure patterns, and observed biomarker levels. The paradigm that forms the basis of this approach is based on Bayes’ formula: P (e|b) =


P (b|e) · P(e) P(b|e) · P(e) · de

(17.1)

where e indicates the exposure of interest and b is the biomarker levels. The above equation indicates that the probability that the exposure level is e, given a biomarker measurement, b, depends on how likely it is to get the biomarker level b given exposure e, the probability of having had exposure e, and the overall likelihood of observing biomarker level b. In probabilistic reverse dosimetry, the P(b|e) term in Equation 17.1 represents the model predictions of the biomarker level as a function of the exposure level, and is estimated by running Monte Carlo simulations of the PBPK model. Operationally, the computation of P(e|b) and P(e) would be extremely computationally intensive if Equation 17.1 is to be evaluated for all possible biomarker measurements and exposure levels. To lessen this computational burden, both P(b|e) and P(e) can be “rounded” to some desired precision, essentially creating bins into which both the exposure and the predicted biomarker results can be categorized. The result of this process is a distributional expression of the likelihood that the exposure level is e when the biomarker is b, P(e|b). A simple example below will demonstrate the process of “reversing” a forward dosimetry using the Bayesian approach.

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Table 17.1 Monte Carlo generated probabilities of blood concentrations at given exposures. Blood concentration

Water concentration = 10 ppm Water concentration = 20 ppm

1 ppb

5 ppb

0.7 0.2

0.3 0.8

Assumptions in the example are: 1. A population of 100 individuals is exposed to a compound in tap water. 2. These individuals are exposed to the compound at one of the two possible concentrations, 10 or 20 ppm; P(e = 10 ppm) + P(e = 20 ppm) = 1. 3. The probability of water concentration is uniformly distributed; P(e = 10 ppm) = P(e = 20 ppm) = 0.5. 4. From a recent biomonitoring study, the blood concentrations of the compound in these 100 individuals are either 1 or 5 ppb; P(b = 1 ppb) + P(b = 5 ppb) = 1. 5. Sixty individuals have a blood concentration of 1 ppb (P(b = 1 ppb) = 0.6); and the other 40 individuals have a blood concentration of 5 ppb (P(b = 5 ppb) = 0.4). 6. By running a Monte Carlo simulation of a PBPK model for this compound, the probability of blood concentrations at a given water concentration is shown in Table 17.1. The probabilities shown in Table 17.1 represent the term P(b|e) in Equation 17.1. For example, the probability of having a blood concentration of 1 ppb given the exposure is 10 ppm is 0.7. With P(b|e) in Table 17.1 and P(e) in the third assumption, P(e|b) (Table 17.2) can be calculated using Equation 17.2. For example, the probability of being exposed to 10 ppm given that the blood concentration is 1 ppb is 0.78. P (e = 10 ppm|b = 1 ppb) =

P (b = 1 ppb|e = 10 ppm) · P(e = 10 ppm) P(b = 1 ppb|e = 10 ppm) · P(e = 10 ppm) + P(b = 1 ppb|e = 20 ppm) · P(e = 20 ppm)

=

0.7 × 0.5 = 0.78 0.7 × 0.5 + 0.2 × 0.5

(17.2)

Table 17.2 Probability of exposure levels at a given blood concentration. Blood concentration

Water concentration = 10 ppm Water concentration = 20 ppm

1 ppb

5 ppb

0.78 0.22

0.27 0.73

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Next, P(e|b) results shown in Table 17.2 and the biomonitoring results (see assumption 5 above) are used to estimate the distribution of exposures likely to have produced the biomonitoring results in this population. Given that 60% of the population has a blood concentration of 1 ppb and 40% has a blood concentration of 5 ppb, it is estimated that 57.6% of the population is exposed to 10 ppm (0.6 × 0.78 + 0.4 × 0.27 = 0.576), and 42.4% is exposed to 20 ppm (0.6 × 0.22 + 0.4 × 0.73 = 0.424).

17.4.3.1

“Exposure Conversion Factor”

The Bayesian approach for transforming from forward to reverse dosimetry requires a fair amount of statistical manipulation. This approach can be simplified in the case where the PBPK model behaves linearly in the region of application, that is, low exposure scenarios. The simplified inversion method first uses the Monte Carlo technique to estimate the corresponding distribution of biomarker levels resulting from a reference exposure level, such as 1 ppm or 1 µg/l. Next, the reference exposure is divided by the output distribution from the Monte Carlo analysis to obtain an “Exposure Conversion Factor” (ECF) distribution, which has a unit equivalent to (unit of exposure level)/(unit of biomarker level). The ECF distribution can then be multiplied by an observed biomonitoring result to reconstruct the probability distribution of concentrations to which an individual might have been exposed. The ECF distribution can also be convoluted with the distribution of population based biomonitoring results to obtain an estimate of the distribution of exposures in that population (Figure 17.4).

Figure 17.4 Schematic of the Exposure Conversion Factor Approach to Reconstruct Exposure from Biomonitoring Data. The model is first run repeatedly at an assumed exposure level (e.g., 1 mg/l in drinking water), but with randomly selected exposure patterns and pharmacokinetics parameters, simulating a population of individuals with different daily exposures and sampling times. The resulting distribution of blood concentrations at the time of sampling is then inverted to obtain an Exposure Conversion Factor (ECF) distribution. Multiplying the ECF distribution by a measure biomarker concentration results in a distribution of exposures (e.g., drinking water concentration) that would be consistent with that biomarker concentration, for comparison with a health standard such as Reference Dose (RfD).

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The application of both the Bayesian approach and the Exposure Conversion Factor method in probabilistic reverse dosimetry has been evaluated in a study on estimating complex household exposures to trihalomethanes (THMs) (Tan et al., 2006; Tan, Liao, and Clewell, 2007). The THMs are chloroform, bromodichloromethane (BDCM), dibromochloromethane (DBCM), and bromoform (TBM). Apart from occupational exposure, the most likely source of exposure to THMs is from residential usage of chlorinated water. Due to the high volatility of these compounds, inhalation of THMs transferred from tap water to air represents a major fraction of these residential exposures. In particular, showering contributes significantly to inhalation and dermal exposure to THMs (Wallace, 1997). Among the four THMs, chloroform toxicity and kinetics are best characterized and more data are available on human exposures to chloroform. In addition, a PBPK model already exists for chloroform (Corley, Gordon, and Wallace, 2000). Based on this published model, a generic PBPK framework was developed for all THMs (Tan, Liao, and Clewell, 2007) and then the four individual models were linked as one mixture model to evaluate the residential exposure to THMs simultaneously. Next, the PBPK mixture model was combined with a mass transfer model (an exposure model) for showering (Weisel et al., 1999). In the combined exposure–PBPK model, values of human physiological parameters were obtained from the literature and values of chemical-specific parameters were estimated by allometric scaling of published rodent values or application of published QSPR algorithms. To define the inhalation, ingestion, and dermal exposures associated with residential use of water containing THMs, the following time-dependent parameters were included in the exposure model: (1) THMs concentration in tap water; (2) background THMs concentration in ambient air; (3) drinking water intake amount; (4) shower duration; (5) the mass transfer coefficient for the volatile emission of THMs during showering; (6) shower flow rate; and (7) shower stall dimensions (Tan et al., 2006; Tan, Liao, and Clewell, 2007). Typical values of these parameters, obtained from large-scale survey reports (USEPA, 1996, 2000, 2001; Wallace, 1997; Mayer et al., 1999), were used as inputs for the PBPK model. After parameterizing the model, Monte Carlo simulations were performed to generate distribution of THMs concentrations in blood. The results suggested that the variability in the estimated biomarker levels comes mostly from the variability in exposure conditions (e.g., showering, drinking water ingestion) rather than from the variability in pharmacokinetics (e.g., body weight, fat content). Next, the Monte Carlo generated distributions were applied in both the Bayesian approach and the Exposure Conversion Factor method for conducting probabilistic reverse dosimetry. Exposures that are likely to have produced the blood concentrations of chloroform reported in NHANES III (CDC, 1996) were estimated. The Exposure Conversion Factor method resulted in a slightly higher estimate of the distribution of water concentrations, but not significantly different from the distribution of exposures estimated using the Bayesian approach.

17.4.4

QSPR

A major challenge associated with interpreting biomonitoring data is the large number of compounds for which such data are currently being collected. Developing and validating a PBPK model for each of these compounds is not a feasible choice. Therefore, a generic

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PBPK framework may be used to conduct a preliminary screening of the available biomonitoring data to identify the exposures of greater concern before resources are allocated for developing more complete PBPK descriptions. For a generic PBPK model, values for physiological parameters can be obtained from the literature, but values for chemical-specific parameters are often unavailable for most chemicals. For these poorly characterized compounds, chemical-specific parameters may be estimated using QSPR technique to correlate a compound’s chemical structure with biological activity (e.g., metabolism) when sufficient information on the physical and biochemical properties of the compound is accessible. The application of the QSPR technique in probabilistic reverse dosimetry has been demonstrated in a recent effort focused on interpreting blood or exhaled air concentrations of poorly characterized VOCs (Liao, Tan, and Clewell, 2007). This study was conducted to develop a generic PBPK model framework for screening biomonitoring data of VOCs. To represent a wide range of physicochemical properties, seven VOCs were selected: trichloroethylene (TCE), vinyl chloride (VC), styrene, dichloromethane (DCM), perchloroethylene (PERC), isopropanol (IPA), and acetone. The PBPK model, which has the structure based on work with TCE and IPA/acetone (Clewell et al., 2000, 2001a, b), includes five tissue compartments and addresses inhalation, oral, and dermal routes of exposure. To simulate dermal exposure, the model has a skin-surface compartment with diffusion-limited transport of VOCs across the skin. This model simulates the concentrations of parent compounds in blood and exhaled breath, as well as total amount of compounds metabolized. Parameters in a PBPK model can be categorized into four types: experimental, physiological, partitioning, and metabolism. Experimental parameters are determined solely by the characteristics of the exposures and most physiological parameters are available from the literature. Partitioning and metabolism parameters are chemical specific and need to be estimated for poorly characterized compounds. Liao, Tan, and Clewell (2007) estimated these chemical-specific parameters using QSPR or bounding analyses, since most QSPR models are developed for estimating partitioning parameters but not for metabolism parameters. An example of using bounding analyses to estimate metabolism parameter is that blood flow to the liver can provide a physiological limit on the metabolic extraction of compounds cleared by liver metabolism (between 0 and 100%). Liao, Tan, and Clewell (2007) were able to demonstrate the use of QSAR and bounding techniques to implement a generic PBPK model to estimate the pharmacokinetics of TCE without the use of any TCEspecific pharmacokinetic data. The probabilistic reverse dosimetry using the QSAR-derived PBPK model produced an estimated population exposure distribution somewhat broader than, but similar to, an analysis using a model developed on the basis of TCE-specific data, demonstrating the potential of this approach (Liao, Tan, and Clewell, 2007).

17.5

Conclusion

Probabilistic reverse dosimetry incorporates probabilistic information on pharmacokinetics and exposure patterns to estimate distributions of exposures likely to have produced the observed biomarker levels in a population. This approach uses several computational tools, including PBPK modeling, exposure modeling, Monte Carlo analysis, Bayesian statistics,

References

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and QSPR. Developing and improving the pharmacokinetic tools along with studies to monitor a variety of exogenous compounds in the human body would allow biomonitoring data to be interpreted in relation to risk, helping regulators and informed public to place the observations in context.

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Georgopoulos, P.G., Roy, A., and Gallo, M.A. (1994) Reconstruction of short-term multiroute exposure to volatile organic-compounds using physiologically-based pharmacokinetic models. J. Expo. Anal. Environ. Epidemiol., 4, 309–328. Gosselin, N.H., Brunet, R.C., Carrier, G., and Dosso, A. (2005) Worker exposures to triclopyr: Risk assessment through measurements in urine samples. Ann. Occup. Hyg., 59, 415–422. Haddad, S., Tardif, G.-C., and Tardif, R. (2006) Development of physiologically based toxicokinetic models for improving the human indoor exposure assessment to water contaminants: Trichloroethylene and trihalomethanes. J. Toxicol. Environ. Health A, 69, 2095–2136. Hays, S.M., Becker, R.A., Leung, H.W., et al. (2007) Biomonitoring equivalents: A screening approach for interpreting biomonitoring results from a public health risk perspective. Regul. Toxicol. Pharmacol., 47, 96–109. Howard, C. and Corsi, R. (1998) Volatilization of chemicals from drinking water to indoor air: the role of residential washing machines. J. Air Waste Manage. Assoc., 48, 907–914. Kim, E.Y., Little, J.C., and Chiu, N. (2004) Estimating exposure to chemical contaminants in drinking water. Envion. Sci. Technol., 38, 1799–1806. Levesque, B., Ayotte, P., Tardif, R., et al. (2000) Evaluation of the health risk associated with exposure to chloroform in indoor swimming pools. J. Toxicol. Environ. Health A, 61, 101–119. Levesque, B., Ayotte, P., Tardif, R., et al. (2002) Cancer risk associated with household exposure to chloroform. J. Toxicol. Environ. Health A, 65, 489–502. Liao, K.H., Tan, Y.-M., and Clewell, H.J. (2007) Development of a screening approach to interpret human biomonitoring data on volatile organic compounds (VOCs). Risk Anal., 27 (5), 1223– 1236. Lorber, M. (2002) A pharmacokinetic model for estimating exposure of Americans to dioxin-like compounds in the past, present, and future. Sci. Total Environ., 288, 81–95. McKone, T.E. (1987) Human exposure to volatile organic compounds in household tap water: The indoor inhalation pathway. Environ. Sci. Technol., 21, 1194–1201. Mayer, P.W., DeOreo, W.B., Optiz, E.M., et al. (1999) Residential End Uses of Water, AWWA Research Foundation, Denver. National Research Council (NRC) (2006) Human Biomonitoring for Environmental Chemicals, The National Academies Press, Washington, DC, pp. 316. Pohl, L.R., Martin, J.L., and George, J.W. (1980) Mechanism of metabolic activation of chloroform by rat liver microsomes. Biochem. Pharmacol., 29, 3271–3276. Reed, C., Corsi, R., and Moya, J. (1999) Mass transfer of volatile organic compounds from drinking water to indoor air: the role of residential dishwashers. Environ. Sci. Technol., 33, 2266–2272. Roy, A. and Georgopoulos, P.G. (1998) Reconstructing week-long exposures to volatile organic compounds using physiologically based pharmacokinetic models. J. Exp. Anal. Environ. Epidemiol., 8, 407–422. Roy, A., Weisel, C.P., Gallo, M., and Georgopoulos, P. (1996) Studies of multiroute exposure/dose reconstruction using physiologically based pharmacokinetic models. J. Clean Technol., Environ. Toxicol. Occup. Med., 5, 285–295. Shepherd, J.L., Corsi, R.L., and Kemp, J. (1996) Chloroform in indoor air and wastewater: the role of residential washing machines. J. Air Waste Manage. Assoc., 46, 631–642. Shipp, A.M., Gentry, P.R., Lawrence, G., et al. (2000) Determination of a site-specific reference dose for methylmercury for fish-eating populations. Toxicol. Indust. Health, 16 (9–10), 335–438. Sohn, M.D., McKone, T.E., and Blancato, J.N. (2004) Reconstructing population exposures from dose biomarkers: inhalation of trichloroethylene (TCE) as a case study. J. Expo. Anal. Environ. Epidemiol., 14, 204–213. Stern, A.H. (2005) A revised estimate of the maternal methyl mercury intake dose corresponding to a measured cord blood mercury concentration. Environ. Health Perspect., 113, 155–163. Tan, Y.-M., Liao, K.H., Conolly, R.B., et al. (2006) Use of a physiologically based pharmacokinetic model to identify exposures consistent with human biomonitoring data for chloroform. J. Toxicol. Environ. Health, Part A, 69, 1727–1756. Tan, Y.-M., Liao, K.H., and Clewell, H.J. (2007) Reverse dosimetry: interpreting trihalomethanes biomonitoring data using physiologically based pharmacokinetic modeling. Journal of Exposure Science & Environmental Epidemiology, 17 (7), 591–603.

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18 Quantitative Modeling in Noncancer Risk Assessment Q. Jay Zhao1 , Lynne Haber2 , Melissa Kohrman-Vincent2 , Patricia Nance2 , and Michael Dourson2 1

US Environmental Protection Agency, Office of Research and Development, National Center for Environmental Assessment, Cincinnati, OH, USA 2 Toxicology Excellence for Risk Assessment, Cincinnati, OH, USA

18.1

Introduction to Dose-Response Analysis in Noncancer Risk Assessment

Noncancer risk assessment is an assessment of any noncancer human health effect(s) related to the exposure of a chemical. This assessment approach is based on the risk assessment paradigm developed by the National Research Council of the National Academy of Sciences (NAS, 1983). This paradigm breaks down the process of human health risk assessment into four components. These four components include: 1. Hazard Identification – The determination of whether a particular chemical is or is not causally linked to particular health effects. 2. Dose-Response Assessment – The determination of the relation between the magnitude of exposure and the probability of occurrence of the health effects in question. 3. Exposure Assessment – The determination of the extent of human exposure before or after application of regulatory controls. 4. Risk Characterization – The description of the nature and often the magnitude of human risk, including attendant uncertainty. Hazard identification involves the review of relevant scientific data to determine if exposure to a chemical substance is causally related to increased incidence of adverse health effects Quantitative Modeling in Toxicology
C 2010 John Wiley & Sons, Ltd

Edited by Kannan Krishnan and Melvin E. Andersen

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in humans, the nature of those effects, as well as the biological significance and relevance of those observed effects. The dose-response assessment involves determination of the doses at which various effects are seen, with the goal of identifying the critical effect, and estimating the quantitative relationship between the amount of exposure and the risk of particular adverse effect at that dose. The exposure assessment involves identifying the routes of exposure by which the substance reaches an individual (i.e., oral, inhalation, dermal), quantitatively estimating the amount the individual is exposed to, and estimating the number of individuals likely to be exposed. An exposure assessment may be specific to a site or scenario, or broadly characterize an entire population. The risk characterization integrates the dose-response and the exposure assessment to determine the likelihood of a response under specific exposure conditions, and identifies limitations and uncertainties in the derived risk values to provide a comprehensive estimate of potential risk to exposed populations. In order to conduct the dose-response assessment, the results of the hazard identification step are reviewed to identify the relevant effects, and the doses at which these effects occur. This can be done by plotting the dose and response on an XY-graph, in which the X-axis charts dose or concentration, and the Y-axis charts the response (Figure 18.1a). Visual inspection of this dose-response plot not only can provide a comparison of dose-response relationships among various endpoints, it also provides a way to identify a threshold for the most sensitive adverse response. The first adverse effect (or its precursor changes in

B

A

Gamma Multi-Hit Model with 0.95 Confidence Level

Fraction Affected

Response

1

Gamma Multi-Hit BMD Lower Bound

0.8 0.6 0.4 0.2 0

NOEL

NOAEL

LOAEL

Dose or Concentration

FEL

BMDL 0

50

BMD 100 dose

150

200

Serum Enzyme Change Minimal Lymphocyte Infiltration Fatty Liver (Critical Effect) Convulsion

Figure 18.1 (A) An example of dose-response curves for various effects. (B) An example of a BMD calculation. The BMD shown in this example is more appropriately labeled a BMDL, since it is calculated using the lower statistical limit of the dose-response model.

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373

structure or function) relevant to humans that occurs as the dose increases is then identified as the critical effect. Protecting exposed individuals from the critical effect would imply that other adverse responses are also prevented. Adverse effects are presumed to either exhibit a threshold or a non-threshold doseresponse curve. Depending on the chemical’s mode of action, different approaches are used to estimate the potential risk posed by a chemical substance. For example, regulatory organizations usually assume that noncarcinogenic and nonmutagenic effects have a threshold, a dose level below which an empirically observable response is unlikely because homeostatic compensation and adaptive mechanisms in the exposed tissue protect against toxic effects. In contrast, chemicals that cause cancer by a mutagenic mode of action are assumed not to have a threshold. The assumption of threshold noncarcinogenic response leads such organizations to estimate an “acceptable level of exposure” for human generally based on an estimated response level that marks the beginning of a low-dose extrapolation (i.e., the point of departure [POD]), derived from well-conducted human toxicity studies if they are available, or more commonly, animal toxicity studies with application of uncertainty factors (UF). Traditionally, a No-Observed-Adverse-Effect-Level (NOAEL) or a LowestObserved-Adverse-Effect Level (LOAEL) is used as the POD. Recently, dose-response modeling (i.e., calculating a benchmark dose, or BMD, as discussed in the next section) has been used to identify the POD in the place of NOAEL. Once the POD is identified, uncertainty factors are used to account for uncertainty and variability in the extrapolation from available data to estimates of doses that would be considered an “acceptable level of exposure” over a lifetime in sensitive human populations. While there are modest differences in specific application between organizations, all organizations have factors to account for differences between average humans and sensitive humans, and differences between experimental animals and humans. The other factors address lack of knowledge (uncertainty), and may be addressed separately or holistically. For example, the US Environmental Protection Agency (EPA) has separate factors for (1) the lack of a NOAEL, (2) extrapolation to lifetime exposure, and (3) gaps in the database, while IPCS and Health Canada consider these three areas holistically as data gaps (Table 18.1). For each of these areas, the preference is to base the factor on the available understanding of the chemical’s mode of action and toxicity (e.g., whether there is information suggesting an increased toxicity when exposure duration increases, or gaps in the database could be supplemented by the database for a similar compound); default values are used in the absence

Table 18.1 Areas of uncertainty considered by various organizations, and the default values for the uncertainty factor for these areas. UFs Intraspecies Interspecies Subchronic to chronic LOAEL to NOAEL Database Modifying Factor

Health Canada

IPCS

10 10 1–100

10 10 1–100

1–10

1–10

RIVM

ATSDR

EPA

10 10 10 10 NA NA

10 10 NA 10 NA NA

10 ≤10 ≤ 10 ≤ 10 ≤ 10 0 to ≤ 10 (discontinued)

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Table 18.2 Acceptable Level of Exposure Terminology Agency

Terminology

Agency for Toxic Substance and Disease Registry (ATSDR) Health Canada

Minimum Risk Level (MRL) Tolerable Daily Intake (TDI) Tolerable Concentation (TC) Tolerable Intake (TI) Reference Dose (RfD) Reference Concentration (RfC) Acceptable Daily Intake (ADI)

International Program for Chemical Safety (IPCS) United States Environmental Protection Agency (US EPA) World Health Organization (WHO)

of such data. The total uncertainty factor is determined as the product of the individual uncertainty factors. To determine the “acceptable level of exposure,” the POD (NOAEL, LOAEL, or BMD) is divided by the product of the appropriate uncertainty factors. The resulting equation is: Acceptable level of exposure =

POD (NOAEL, LOAEL, or BMD) (Total uncertainty factor)

A variety of terms are used to refer to “acceptable level of exposure.” Some examples are provided in Table 18.2.

18.2 18.2.1

Application of Benchmark Dose Modeling Introduction to Benchmark Dose Method

The benchmark dose or concentration (BMD for oral exposure or BMC for inhalation exposure) is defined by the US EPA (1995a) as “a statistical lower confidence limit for a dose (or concentration) that produces a predetermined change in response rate of an adverse effect (called the benchmark response or BMR) compared to background.” This method was developed by Crump (1984) and Dourson et al. (1985) as an improvement over the NOAEL/LOAEL method for developing noncancer risk values. The goals were to provide flexibility and to give more weight to sample size and dose-response characteristics (Crump 1984, 1995; Dourson et al., 1985; Haber et al., 2001; Kimmel and Gaylor, 1988; US EPA 1995a, 2010a,b). The BMD/BMC is calculated by first fitting one or more flexible mathematical model(s) to the observed dose-response data. This model is used to identify the dose corresponding to the BMR, the BMD (see Figure 18.1b). Often, a statistical confidence lower bound (usually the 95% lower bound on the dose) is used instead of the actual dose-response at that point to account for statistical uncertainty and to ensure a health-protective result; this bound is referred to as the BMDL. Older literature referred to this lower bound as the BMD, describing the central tendency as the maximum likelihood estimate (MLE) (Crump 1984). BMD modeling has a number of advantages over the NOAEL/LOAEL approach for developing noncancer risk values (US EPA, 1995a, 2010a,b; Crump, 1984, 1995; Haber

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et al., 2001). First, the BMD is not limited to being one of the experimental doses. The BMD uses all the information provided by the dataset and is much less dependent on dose spacing than is the NOAEL/LOAEL approach, and the BMD can give a much better estimate of the toxicological threshold when the dose spacing is large. A second advantage of the BMD approach is that it uses more of the dose-response data, unlike the NOAEL, which is based on a single dose. This means that the BMD can incorporate information about the slope of the dose-response curve. In addition, a BMD can be calculated even if a study did not identify a NOAEL, removing the need for extrapolation from a LOAEL. A limitation of the NOAEL is that it is based on a combination of scientific judgment and statistical analysis, and the role of scientific judgment is often a source of controversy. In contrast, the BMD is based on a defined response level, which can lead to increased consistency across endpoints. However, the use of the BMD does not remove all controversy or the need for scientific judgment, since judgment plays an important role in the definition of the BMR, and a given BMR (e.g., 10% change in organ weight) may have very different biological implications depending on the target (e.g., liver vs. brain weight). Another advantage of BMD modeling is that it appropriately reflects uncertainty and variability, particularly uncertainty associated with sample size. All other things being equal, smaller sample size results in reduced statistical power, and therefore wider confidence limits. Because NOAELs are often identified based on statistical significance, a smaller (less powerful) study would tend to result in larger, less conservative, NOAELs as the POD than experiments with a larger sample size (since it would be less likely that smaller changes are statistically significant). In contrast, a conservative approach would be to use a lower POD when there is more uncertainty in the toxicity data. Using the BMD approach, a smaller sample size would tend to result in wider confidence limits, and a lower (more conservative) BMDL, corresponding to the greater uncertainty with the smaller study. Unlike cancer modeling, BMD modeling for noncancer endpoints is used to estimate a response in the range of the observed data, rather than extrapolating well below the observed range. This avoids uncertainties and non-biologically plausible results associated with low-dose extrapolation (Crump 1995), and reduces the model dependence if the model fit the data in the observable range. Thus, the BMR should be chosen at the lower end of the experimentally detected responses. A series of papers that compared NOAELs and BMDs using several different definitions of BMRs for a large database of developmental toxicity studies (Allen et al. 1994a,b; Kavlock et al. 1995), has aided in evaluating the impact of the BMR definition. Though there are many advantages to using a BMD to calculate Reference Doses (RfDs) and reference Concentrations (RfCs), there are also a number of limitations, some of which are shared with the NOAEL/LOAEL approach. First, the results are limited by the quality of data available, and some studies do not report data in a form appropriate for modeling (see the following section). The data also need to exhibit a dose-related trend, ideally containing data point(s) at the lower end of dose-response range. Toxicological judgment still plays a critical role, and proper identification of the studies and endpoints to be used for modeling must be done to ensure a useful BMD is derived (Haber et al. 1998). Without good quantitative data or quality data reporting, there may be substantial uncertainty in the resulting BMD (and therefore the estimate of risk or an acceptable level of exposure), despite the apparent precision resulting from modeling. Finally, conducting BMD modeling increases the amount of effort needed for an analysis.

376

18.2.2

Quantitative Modeling in Noncancer Risk Assessment

Data requirements for BMD modeling

The first step in benchmark dose analysis is to determine whether the data are adequate for modeling. First, each study should be evaluated for overall study and data quality, using criteria similar to that used for the NOAEL approach. This includes determining whether the study was well-conducted, used appropriate controls, evaluated appropriate endpoints, and whether the appropriate duration and route of exposure were used. The endpoints should be evaluated to determine whether they identify potential critical effects. After this initial evaluation, the next step is to choose the endpoints to be modeled. The ultimate goal is to identify the most sensitive threshold for an adverse effect or known precursor. Because the BMD is a reflection of the shape of the dose-response at any given point, the data set with the lowest NOAEL may not necessarily have the lowest BMD. Therefore, it is necessary to model multiple data sets. Ideally, one could model all responses that are biologically and statistically significant. Choice of data sets to model requires some judgment and consideration of the slope of the line, since shallower slope below the LOAEL means a smaller BMD. However, a reasonable approach is to model only those endpoints for which the LOAELs are within a 10-fold range of the lowest LOAEL of the database. In addition to choosing the endpoints for modeling, the data need to be available in certain formats and conform to certain quantitative requirements. The data to be modeled should generally contain a significant dose-related trend. In addition, most in the field believe that there should be at least two dose groups with response levels in excess of the control response so that a dose response can be adequately modeled. Thirdly, it is preferred that there be at least one dose with a response in the range of the BMR, so that no extensive extrapolation is needed to estimate a BMDL. However, many data sets do not have any data points in the range of the BMR, and this is not necessarily a reason to exclude the data from modeling. For such data sets, it is important to consider the distance of the data from the BMR, the slope of the line in the region of the data points closest to the BMR, and the implications of the resulting uncertainties. Data requirements for modeling also depend on the type of endpoint modeled. Dichotomous data (also called quantal data) reflect the presence or absence of a defined response in each subject. For such data, modeling requires both the number of animals evaluated and the number affected (or the percent affected). Continuous data are the measured parameters in the subjects, such as body weights or serum enzyme activities. The response might be reported as an actual measurement (e.g., absolute organ weight), or a contrast (e.g., absolute or relative change from control). For continuous data, modeling requires either individual measurement data or summarized group data including the number of subjects evaluated, the mean response, and a measure of variability (i.e., standard deviation, SD; or standard error, SE).

18.3

Procedures in Conducting Benchmark Dose Modeling

Currently, the most commonly used BMD modeling software for chemical risk assessment is the US EPA BMD Software (BMDS). This software package was developed by US EPA, Office of Research and Development, National Center for Environmental Assessment, and is available for free download at the US EPA website http://www.epa.gov/ncea/bmds/. In

Procedures in Conducting Benchmark Dose Modeling

377

addition to the BMD software, this website also provides online training. Prior to the develR R and ToxTools
) opment of BMDS, there were some proprietary models (e.g., THRESH
available for BMD modeling. In addition, experienced programmers can conduct similar R . Although the concepts analyses using spreadsheet programs such as Microsoft EXCEL
are general, this chapter focuses on BMDS, as a user-friendly, freely-available program that is accepted for regulatory use. All screen shots presented in this chapter were generated with BMDS version 1.4.1c. Although developed in the US, BMDS is used by regulatory agencies internationally, including in Canada and Europe. European groups also use Proast, software developed by RIVM, the National Institute of Public Health and the Environment in the Netherlands. Proast currently can be downloaded for free from the RIVM web site (http://www.rivm.nl/en/foodnutritionandwater/foodsafety/proast.jsp). Running BMDS involves three steps: data and model selection, model parameter selection, and modeling result evaluation. The result of the BMDS modeling is a text output file containing information on model parameters, modeling results, and detailed statistics on model fit, as well as a plot of the data and the fitted curve. The following sections present detailed step-by-step directions for the BMD modeling.

18.3.1 18.3.1.1

Data and Model selection Data Format and Data Entry

To begin BMD modeling, click on “New/Create” or “Open” from the “File” pull-down menu in the initial BMDS window. This will open the first BMDS screen (see Figure 18.2): “Create/Edit Dataset Screen.” The selection of “New/Create” allows the user to manually enter data, and the selection of “Open” allows the user to open a previously saved data file or R spreadsheet file. to enter data from other data sources, such as from a Microsoft EXCEL

R In addition to entering data directly from an EXCEL spreadsheet file, one can also use R “copy and paste” function to transfer data. However, it is important the regular Windows
R to note that in order to use the “copy and paste” function to transfer data from an EXCEL
spreadsheet into the “Create/Edit Dataset Screen”, one needs to highlight the data in the spreadsheet that needs to be transferred, copy the contents into the clipboard, and close R spreadsheet file before the final “paste” into the BMDS “Create/Edit Dataset the EXCEL
Screen.” This “paste” function is found on the “Edit” pull-down menu of BMDS. Column headers in the “Create/Edit Dataset Screen” may be renamed by right-clicking on the header, or columns can be identified by column number. The next step is to choose the model type. BMDS provides three sets of mathematical models for data modeling: (1) dichotomous models for incidence data; (2) continuous models (for measurements); and (3) nested dichotomous models (for litter data). After one chooses the model type from a pull-down menu, BMDS modifies the screen to request the input data required for that model type, and pull-down menus are used to identify which column of data corresponds to which data element. BMDS allows input of dichotomous data either as incidence data (e.g., 11/50 animals showed a particular effect) or as a percentage (of 50 animals, 20% showed the effect). Figure 18.2 shows an example of data entry in BMDS for incidence data. When percent response is used instead of the number of responders, the column with percentage information should be assigned to the “% Positive” instead of the “Incidence” as shown in the lower middle part of Figure 18.2.

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Quantitative Modeling in Noncancer Risk Assessment

Figure 18.2

Dichotomous Data Entry.

BMDS allows input of continuous data as either group data or individual data. Figure 18.3 shows an example of data entry for summarized group data (i.e., the N column is for sample size in each dose group, the Mean column is for group mean, and the SD column is for standard deviation of that group data). Because BMDS requires that variability be provided in terms of the SD, variability reported in terms of the SE needs to be converted to the SD. This is done by multiplying the SE by the square root of the sample size of that group (i.e., SD = SE × square root [N]). When individual data are available for direct input (i.e., dose column and response column only), BMDS will automatically calculate the mean and SD for each dose group based on the data entered for individual doses and responses. Both dichotomous and continuous responses mentioned above are observed from each individually exposed animal. The third type of data that BMDS can model is nested dichotomous data, such as those obtained in reproductive or developmental toxicity studies (e.g., the proportion of affected fetuses per litter). In this case, the mother is exposed to the chemical, but experimental observations are made on fetuses or pups, and findings may be reported for such effects as percent of fetuses in each litter that were resorbed or malformed. This type of data provides greater sensitivity for detecting a positive response than regular data due to a larger sample size in each dose group. Version 1.4.1c of BMDS provides

Procedures in Conducting Benchmark Dose Modeling

Figure 18.3

379

Continuous Data Entry.

options for modeling nested dichotomous data. The same principles used in running dichotomous data also apply to the nested model, except that there are two extra parameters employed in the nested models. These two parameters are: (1) the litter-specific covariate, which accounts for potential confounding effects due to the mother’s physiological condition; and (2) intralitter correlations, which accounts for similarity in response among littermates. A detailed training presentation on using a nested model can be found on the US EPA’s BMDS website http://www.epa.gov/ncea/bmds/.

18.3.1.2

Model Type and Model Selection

The goal of the mathematical modeling in benchmark dose computation is to fit a model to dose-response data, especially at the lower end of the observable dose-response range. Thus, the criteria for final model selection are often based mainly on how well various models describe the data. In BMD dose-response analysis, it is a common practice to run all of the available models for each model type (e.g., Gamma, Logistic, Probit, Multi-stage, Weibull, and Quantal-Linear models under the dichotomous model type) to fit a particular set of data, and evaluate the modeling results to make a final selection of BMD or BMDL. Model selection is accomplished by selecting a model from the pull-down menu for the

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Quantitative Modeling in Noncancer Risk Assessment

Figure 18.4 Dichotomous Type Model Run Window. This window shows that a BMR of 10% extra risk and restricted betas are chosen for this Gamma BMD modeling. In addition, the checks on BMD Calculation and BMDL Curve Calculation indicate that the modeling results should include a BMD calculation and showing an additional BMDL curve on the dose-response curve.

“Model” choice as shown in the Figure 18.2 for dichotomous models and in the Figure 18.3 for continuous models. 18.3.2

Model Parameter Selection

After data entry and model selection, clicking on the “Proceed” button will lead to step 2: “Type Model Run” screen. In the “Type Model Run” screen, the user can define the BMR and other parameters for doing the modeling, as described in the following paragraphs. 18.3.2.1

Setting the Benchmark Response

Because BMD modeling is used to estimate a toxicological threshold, the “benchmark response” or BMR should be chosen so that it is close to a biological response level that

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can be reliably identified in a similar type of toxicology study. While the exact choice of the BMR for different study types is open to scientific judgment, consistency in the approach across analyses is important, with aim of the BMR reflecting a similar degree of response. For comparing potencies across chemicals or endpoints for dichotomous data, a 10% response has been commonly used as a BMR because it is generally at or near the limit of sensitivity (i.e., statistical power to detect a significant response) in most cancer bioassays and in some noncancer bioassays. Please note that US EPA commonly uses a 95% lower confidence limit on the dose estimated to result in a BMR (e.g., BMDL10 ) as the POD for calculating risk values, and Health Canada typically uses the central tendency estimate for a BMR (e.g., BMD05 ). For example, reproductive and developmental studies having nested study designs easily support a BMR of 5% because they often provide greater sensitivity due to the larger sample size. Allen et al. (1994a,b) provided some perspective on this issue. The BMR for dichotomous data can be presented as either added risk or extra risk (see Figure 18.4). Added risk is defined as an additional proportion of total animals that respond to a treatment, i.e., Added risk AR(d) = P(d) – P(0). Extra risk is the fraction of animals that are available to respond to a treatment (at a dose, d) among animals that did not respond at the control treatment level, i.e., the extra risk ER(d) = [P(d) – P(0)]/[1 – P(0)]. When the background response, P(0), is low and close to zero, the added risk will be close to extra risk. When the background response is high, the same level of response in the treated group will correspond to a much higher extra risk than the added risk calculated for the same dataset. Here, P(d) is the probability of response at dose d, and P(0) is the probability of response in the absence of exposure (d = 0). US EPA usually defines BMRs in terms of extra risk, as the more conservative approach. For continuous data, the response is a measured value in the treated and control groups, and can be expressed in several different ways. The level of change can be expressed as a difference in mean responses from the control [i.e., mean(d) – mean(0)], a change normalized by the background mean response {i.e., [mean(d) – mean(0)]/mean(0)}, or a change relative to the variability of control group {i.e., [mean(d) – mean(0)]/SD(0)}. Here, mean(d) is the mean value of the response at dose d, and mean(0) is the mean value in the control group. Thus, the continuous BMR can be an absolute change (e.g., decreased mean body weight of 50 g), a relative change (e.g., 10% body weight decrease), or a change relative to standard deviation (e.g., 1.0 SD from the control mean), corresponding to the three equations listed earlier in this paragraph. If there is a minimum level of change in the continuous endpoint that is generally considered to be biologically significant (for example, a decrease in average adult body weight of 10%), then that amount of change can be used to define the BMR. In the absence of information regarding the level of response considered to be adverse, one can use a change in the mean equal to one control standard deviation from the control mean as a definition of the BMR. This BMR based on 1.0 SD corresponds to an excess risk of approximately 10% in incidence responding to the treatment compared to the controls, assuming a normal distribution in the data with a 2% background effect in the controls (Crump, 1995). Thus, using a BMR of a 1.0 SD provides consistency between the BMR definitions for continuous and dichotomous data, with both being based on an effect in an estimated 10% of the exposed population. BMDS also allows the user to directly enter a response value as a cutoff point for the BMR.

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Figure 18.5 Continuous Type Model Run Window. This window shows that a BMR of 1.0 SD for this BMD modeling. Similar to the dichotomous model run, the check on BMD calculation indicate that the modeling results should include a BMD calculation but without showing an additional BMDL curve on the dose-response curve. Rel. Dev.: [m(d) − m(0)]/m(0) or [n% of m(d)]; Abs. Dev.: m(d) − m(0); Std. Dev.: [m(d) − m(0)]/SD(0) or [n of SD(0)]; Point: a direct assigned BMR value.

Because the BMR for continuous data can be presented in different formats, the BMR value entered in the “BMR” window of the “Type Model Run” screen in the BMDS (v. 1.4.1) actually means a factor which will be used to calculate the real BMR (see Figure 18.5). This calculated BMR is then used to calculate the BMD and BMDL. For example, to define a 10% decrease in body weight change as the BMR, one needs to select “Rel. Dev.” under “BMR Type” and enter 0.1 in the “BMR” window. To define an absolute body weight change of 50 g from the control mean as the BMR, one needs to select “Abs. Dev.” and enter 50 in the “BMR” window. If one decides to use a one standard deviation difference from the control mean as the BMR, one needs to select “Std. Dev.” and enter 1.0 in the “BMR” window. Finally, BMDS also allows setting a cutoff point directly as the BMR (e.g., the modeler may decide that body weight less than 180 g is considered adverse). In this case, one needs to select “Point” and enter the cutoff value of 180 directly in the “BMR” window.

Procedures in Conducting Benchmark Dose Modeling A

B Multistage Model

Gamma Multi-Hit Model with 0.95 Confidence Level 1

Gamma Multi-Hit BMD Lower Bound

Multistage

0.8

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Fraction Affected

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383

0.6 0.4 0.2 0 BMDL

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0.6

50

100 dose

150

200

0

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Figure 18.6 (A) A fitted Gamma model produced an infinite slope at the beginning of the dose response curve which results in a zero BMDL estimate. (B) A fitted multistage model results in a non-monotonic dose response curve.

18.3.2.2

Setting Model Parameters

The purpose of the model fitting process is to find values for all of the model parameters so that the resulting fitted model predicts the input data as well as possible. BMDS provides two ways to specify or restrict certain parameters in each model. The “Standard User Mode” is the most commonly used mode for BMD modeling and it is also a default mode for BMDS. It allows restriction on some key model parameters such as slope, power or signs of coefficients, depending on the type of model selected. The “Advanced User Mode” can be chosen when the “Type Model Run” screen is active, using the pull-down “Options” menu at the top of the main BMDS window. The “Advanced User Mode” provides more flexibility in running the model by allowing the user to manually specify any or all of the parameters (e.g., initial value or final parameter values) to further improve the model fit. Our discussion will only focus on using the “Standard User Mode.” The choice of whether to restrict a parameter when running a BMD model depends on the behavior of that particular model with the dataset of interest. In certain cases, a fitted unrestricted model takes an unrealistic form. For example, an infinite slope in a Gamma model at the beginning of the dose response curve (see Figure 18.6a) might not be consistent with a threshold biological response for a particular endpoint, and it could result in an estimated BMD and BMDL of zero. Another example is a non-monotonic curve generated by an unrestricted multistage model (see Figure 18.6b). In this case, unrestricted polynomial coefficients (betas) allow the fitted model to result in a wavy curve that is not consistent with most toxicological dose responses. When a fitted model results in an unrealistic form, a restriction on the model parameters, such as slope, power or coefficient, could prevent such problems. As a rule of thumb, the user can first try to run a BMD model with a parameter restriction whenever it is available. If the restricted model does not provide a satisfactory fit to the data, a model run with unrestricted parameters or using manually-specified parameters might provide a better fit to the data, as long as a fitted model does not take an unrealistic form. It is extremely important to carefully evaluate the

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shape of the dose-response curve, especially in the low-dose range, when an unrestricted model is used. This is usually accomplished by a visual inspection of the dose-response plot. An important function of BMD modeling is that the software provides not only the best estimate for a dose response curve, but also the corresponding confidence limit on the curve, which then forms the basis for the estimate of the BMDL. The confidence limit in the dichotomous models is estimated based on the sample size and incidence data in each dose group. In contrast, in the continuous models, the confidence limit is estimated based on variance data (e.g., SD at each data point). A BMD model needs not only to describe the mean response, but also to describe the variance at each data point. The variance is important both in estimating the confidence limit on the BMD curve, and the determination of the BMD, in the form of determining the BMR. The BMDS continuous models allow the user to model the data with a constant variance or with variance modeled as a power function of the response {Var(i) = α[mean(i)]ρ } at each data point. The “Type Model Run” screen provides a choice of “Constant Variance (Rho = 0)?” (see Figure 18.5). When constant variance is selected, rho is set to zero; otherwise, rho is modeled using the expression presented above. BMDS provides test results in the text output file to assist in the selection of this parameter. The “Test 2” result (p value) in the output file (see Appendix 2) suggests whether variance needs to be modeled for the particular dataset. If the “Test 2” result suggests a homogenous variance in the data set (p > 0.1), a constant variance model is appropriate. Otherwise, the model should be rerun with a non-constant variance setting. The “Test 3” result will indicate whether the variance is modeled successfully with the power function in a non-constant variance model. If a non-constant variance model still fails to model the variance data, this means that the only available variance model in the current version of BMDS (the power function of the response) could not provide a reliable estimate for the confidence limit for the data. In such cases, a good estimate of the variance is not possible with BMDS, and the user needs to take extra caution in evaluating the estimated BMD and the BMDL from the model.

18.3.3

Evaluation of BMD Modeling Results

Once the model parameter selection is done, running BMDS will produce a text output file containing all of the detailed statistics of the model fit and BMD modeling results, and a dose-response plot for visual inspection. An important criterion for evaluation of BMD model results is that the fitted model should describe the data, especially in the low dose region close to the BMR. Thus, the evaluation of a BMD model includes evaluation of global fit to the data points overall, local data fit close to the range of the BMR, and visual inspection of the dose-response plot. The BMDS text output contains information for evaluation of a global goodness-of-fit measure (p-value) and local data fit (scaled residual at each data point). BMDS will produce a plot from each model run. By visually inspecting the dose-response plot, the user can examine the overall model fit to the data points, the model fit to the low dose area, any data point(s) with poor fit, and any unrealistic curve shapes. The visual inspection of the plot is especially helpful for identifying issues such as infinite slope at the zero dose, and non-monotonic curves; these issues might not be easily identified from the goodness-of-fit p value and scaled residual data from the text output file.

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385

The goodness-of-fit p value is reported in both the dichotomous and continuous model output. In the dichotomous model output, it is reported as the Chi square p value listed under the “Goodness of Fit” table (see Sample dichotomous data BMD model output in Appendix 1). In the continuous model output, it is the Test 4 p value (see Sample continuous data BMD model output in Appendix 2). When assessing global model fit, larger p values indicate a better fit, and a perfectly fitted model would have a goodness-of-fit p value of 1.0. A global goodness of fit p value greater than 0.1 is commonly used for risk assessment purpose (US EPA 2010a,b). For local measures of model fit at each data point, BMDS reports scaled residuals in the “Goodness of Fit” table. Since it is critical that the model fit the data in the low dose range, the scaled residuals in the low dose region provide a measurement of local model fit. The smaller (in absolute value) the scaled residual, the better the model fit to the data point. The scaled residuals should generally be below 2.0 in absolute value, and any scaled residual exceeding 2.0 in absolute value warrants further examination of the model. BMDS provides a suite of models for each type of data. Some models may fit a particular range better than others. Therefore, it is recommended that several models or model options be employed, testing a variety of flexible mathematical expressions with the aim of fitting the data. In addition, modeling the data with all of the available models also provides insight into the uncertainty in the estimated BMD/BMDL. When there is a lack of fit in the low dose range due to characteristics of the dose-response data at the high doses, the data may be adjusted by eliminating the high dose group in order to improve the model fit at the low dose region. This makes sense biologically, because high-dose phenomena such as saturation of metabolism may result in a different shape of the dose-response curve in the low-dose region. At the expense of estimating an extra “asymptote” parameter, some models such as the Hill model are capable of modeling data that “flatten out” in the high dose region. Version 1.4.1 of BMDS contains a Hill model for the evaluation of continuous data and the recently-released version 2.1 of BMDS also contains a Hill model for the evaluation of dichotomous data.

18.3.4

Choosing Models Among Multiple Acceptable Models

Often more than one model will result in an acceptable fit to the data. If the model BMD(L) estimates from a set of acceptable models (usually those with a goodness-of-fit p ≥ 0.1) are widely divergent, this would be an indication there is a great deal of model dependency. In this case, the user needs to identify the best fitted model(s) among all of the acceptable models available based on global model fit, local model fit and visual inspection of the doseresponse plot as discussed before. In addition, biological considerations, such as whether a model is biologically tenable considering the mode of action of the chemical for causing the particular chemical endpoint, may also lead one to prefer one model over another. For example, a Hill model might be preferred for modeling a receptor mediated dose response. Once the acceptable model(s) have been identified, the BMD(L) for that endpoint is chosen based on consideration of both the model fit (accounting for model complexity), and the magnitude of the BMD(L); the exact approach used is a science policy decision. If the model estimated BMDLs from a set of acceptable models are not sufficiently close, this indicates model dependency and the lowest BMDL should be used, as a conservative

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approach. If the BMDLs are sufficiently close, the Akaike’s Information Criterion (AIC, described in the next paragraph) should be evaluated. One can then choose the BMDL for the model with the lowest AIC. Alternatively, if several models have the same AIC, the BMDL for that endpoint can be based on the average of the BMDLs from all models with the same AIC. Conversely, one could argue that if BMDLs differ by more than 3-fold, this indication of model dependency would be a reason to focus more strongly on the best fitting model. The AIC provides a relative overall evaluation of model fit to a particular data set considering the number of parameters employed in the model (Akaike, 1973; Linhart and Zucchini, 1986; Stone, 1998). AIC1 can be used to compare models from different families that use a similar fitting method (for example least squares or a binomial maximum likelihood) as well as within the same family. Within a family of models, model fit will improve (increase in log-likelihood at the maximum likelihood estimates for parameters or increase in goodness-of-fit p value) as the number of parameters increases. However, there is a trade-off between adding additional parameters and improving fit. For a similar degree of fit, the AIC rewards the less complex model. A smaller AIC value represents a better fit considering the number of parameters employed. 18.3.5 18.3.5.1

Examples of Using BMD Modeling to Identify a Point of Departure Dichotomous BMD Models

An example of dichotomous data set is presented here. The data set includes dose, group sample size (n) and incidence in each dose group. Dose (mg/kg-day) Sample size Incidence 0 50 100 150

100 100 100 100

0 5 30 65

To model these data, they could be entered into the “Create/Edit Dataset” window as shown in Figure 18.2 by clicking the “New/Create” button or clicking “New” on the “File” pull-down menu. After selecting the model type (i.e., Dichotomous) and specific model (e.g., Gamma model), and assigning the dose, sample size and incidence data columns to the “Dose”, “Subjects in Dose Group” and “Incidence” entries, clicking the “Proceed” button will advance to the “Dichotomous Type Model Run” screen (see Figure 18.4). Here, a BMR of 10% extra risk and restriction on Power are applied to this Gamma BMD model run. In addition, it is requested that the text output reports the calculated BMD and the dose-response plot shows the BMDL curve, by checking boxes for “BMD Calculation” and 1

Akaike’s Information Criterion (AIC) (smaller number is better) AIC = −2 × LL + 2 × P LL = log-likelihood at the maximum likelihood estimates for parameters P = number of model degrees of freedom

Procedures in Conducting Benchmark Dose Modeling A

B Hill Model with 0.95 Confidence Level

Gamma Multi-Hit Model with 0.95 Confidence Level 0.8

Gamma Multi-Hit BMD Lower Bound

0.7

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Hill

1.72 Mean Response

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Figure 18.7 (A) Dose-response curve for sample dichotomous data. (B) Dose-response curve for sample continuous data.

“BMDL Curve Calc.” Clicking on the “Run” button will execute the BMD modeling, and BMDS will produce a dose-response plot (Figure 18.7a), and an output text file (Appendix 1). Table 18.3 summarizes BMD results obtained from running all of the dichotomous models against this data set. Based on the goodness-of-fit p values, the Quantal-linear model does not provide an adequate fit overall (p = 0), and has a poor data fit in the range of the BMR (scaled residual at 5% = −3.69). The Multistage model (degree of poly of 2) overestimates responses at the middle-range of the dose-response curve (scaled residual at 5% = −1.545). As an estimate of the model fit in the range of the BMR, we used the scaled residue at the low dose data point, for which the response is 5%. The Logistic and Probit models overestimate the control response (scaled residuals at 0 dose = −0.996 and −0.628, respectively) which may have resulted in an overestimate of the BMD and BMDL. This is because the BMR used to calculate the BMD and BMDL is based on the estimated control value, not the measured control value.

Table 18.3 Summary of dichotomous data BMD modeling results

Model

p value

AIC

Scaled Residual at 0

Gamma Logistic Log-Logistic Multistage Probit Log-Probit Quantal-Linear Weibull

0.9032 0.3317 0.8851 0.2520 0.6543 0.6513 0 0.9912

295.6 298.5 295.6 297.9 296.6 296.2 324.4 295.4

0 −0.996 0 0 −0.628 0 0 0

Scaled Residual at 5%

BMD (mg/kg-day)

BMDL (mg/kg-day)

0.230 −0.246 0.287 −1.545 −0.077 0.443 −3.69 −0.083

64.3 70.5 65.1 51.3 67.8 63.7 24.1 64.3

54.5 61.8 55.3 45.7 58.9 54.9 20.5 53.7

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Based on these considerations, the Gamma, Log-Logistic, Log-Probit and Weibull models provide good model fitting to this dataset. BMDs and BMDLs obtained from these four models range from 53.7 to 55.3 mg/kg-day which are sufficiently close. Thus, based on US EPA BMD modeling procedure, we would next look at the AIC values from these models. The model with the lowest AIC is the Weibull model, suggesting that the fit with a relatively simpler model is comparable to that with the more complex models. Thus, the BMD of 64.3 mg/kg-day and BMDL of 53.7 mg/kg-day obtained from this model are considered appropriate estimates for this sample dichotomous data.

18.3.5.2

Continuous BMD Models

An example of continuous data set is presented here. The data set includes dose, group sample size (n), group mean and corresponding standard deviation in each dose group.

Dose (mg/kg-day) Sample size Mean 0 35 105 316

10 10 10 10

1.61 1.67 1.7 1.72

SD 0.037 0.022 0.037 0.031

To model these data, they could be entered into the “Create/Edit Dataset” window as shown in Figure 18.3 by clicking the “New/Create” button. After selecting the model type (i.e., Continuous) and specific model (e.g., Hill model), and assigning the dose, sample size, mean and standard deviation data columns to the columns headed “Dose”, “Subjects in Dose Group”, “Mean”, and “Std. Dev.”, clicking the “Proceed” will advance BMDS to the “Continuous Type Model Run” screen (see Figure 18.5). Here, a BMR of one standard deviation, and no restriction on the parameter of Power in the Hill model are applied. In addition, it is requested that a constant variance model is used, the text output reports the calculated BMD, and the dose-response plot shows the BMDL curve, by checking boxes for “Constant Variance (Rho=0)?”, “BMD Calculation?” and “BMDL Curve Calc.?” Clicking on the “Run” button will execute the BMD modeling, and the BMDS will produce a dose-response plot (Figure 18.7b), and an output text file (Appendix 2). Table 18.4 summarizes BMD results obtained from running all of the continuous models against this data set. Based on the goodness-of-fit p values, only the Hill model provides an adequate fit to the data (p = 0.9341), while neither the Polynomial nor Power models provide adequate fit. As shown in Appendix 2, the Test 2 p value is 0.3673, indicating that a homogeneous variance model appears to be appropriate. Therefore, the constant variance model shown in the Appendix 2 is adequate for estimating a BMD and BMDL for this dataset. A low scaled residual of 0.037 at low dose (see Table 18.4) and reasonable model fit to the data (see Figure 18.7b) also indicate a satisfactory BMD model. Thus, the BMD of 12.3 mg/kg-day and BMDL of 5.8 mg/kg-day obtained from this model are considered appropriate estimates for this set of continuous data.

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Table 18.4 Summary of continuous data BMD modeling results Model

p value

AIC

Polynomial <0.001 −309.4 Power <0.001 −278.7 Hill 0.9341 −230.7

18.4 18.4.1

Scaled Residual Scaled Residual BMD1SD BMDL1SD at control at low dose (mg/kg-day) (mg/kg-day) −2.72 −2.72 −0.0059

1.38 1.38 0.037

N/A 140 12.3

N/A 104 5.8

The Future of Noncancer Dose-Response Modeling Epidemiology Data

BMD modeling is also used frequently in evaluating epidemiological data. Several regulatory limits have been derived using BMD modeling of epidemiology data, including Health Canada’s tolerable concentration (TC) and US EPA’s RfC for carbon disulfide (Health Canada, 1999; US EPA, 1995b), the US EPA RfDs for methylmercury (US EPA, 2001) and benzene (US EPA, 2003), and the US EPA RfC for 1,3-butadiene (US EPA, 2002). BMD modeling of epidemiology data has also been used in published assessments of such chemicals as cadmium (Kobayashi et al., 2006; Shao et al., 2007) and manganese (Clewell et al., 2003). The advantages of the BMD approach for epidemiology data are similar to those for modeling of animal data, particularly the improved reflection of uncertainty and the BMD(L) not being limited to the exposure groupings. This latter consideration is of particular relevance to epidemiology data, since each individual may have been exposed to a different dose. Published epidemiology studies often group data for dose-response analysis into categories (e.g., low, medium, and high exposure), but using different definitions of categories (e.g., different cutpoints separating low, medium and high exposure) would result in a different NOAEL and LOAEL. When BMD modeling is done for categorized data, the results are still influenced by the authors’ determination of breakpoints between categories. However, BMD modeling using individual exposure levels and responses makes it possible to include all of the data in the dose-response analysis without using arbitrary categories. The uncertainties associated with epidemiology data also present some additional challenges in applying the BMD approach to such data. Because the BMR is defined relative to the control group, uncertainties in estimating the response in the control group affect the determination of the BMD(L) (Budtz-Jorgensen et al. 2001; Budtz-Jorgensen 2006). Of course, the absence of a “true” control group also makes it problematic to identify a NOAEL, if all comparisons are with a “low” exposure group, rather than an unexposed group. Another concern is the wide variation in responses observed in epidemiology studies. This variation can create “noise” in the data, which reduces the power to distinguish between dose-response functions that have different shapes in the observed dose range (Budtz-Jorgensen et al. 2001). This “noise” may mean that markedly different models will fit the data, but will yield very different BMDLs, making the determination of the BMDL dependent on model choice. Finally, large variation in exposure levels can lead to nondifferential measurement error, resulting in an overestimation of the BMD and BMDL (Budtz-Jorgensen et al. 2004; Fuller 1987; Carroll 1998). These considerations mean that additional care is needed in applying BMD methods to epidemiology data, but many of these factors also affect the confidence and accuracy of the NOAEL/LOAEL method.

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BMD Modeling of Genomics Data

As toxicology becomes more of a mechanistic science and more focused on data at the molecular level, quantitative interpretation of “omics” data, such as genomics, using powerful informatics tools will become increasingly important. Several investigators have begun to apply benchmark modeling approaches to omics data. In an early application of benchmark dose modeling to gene expression data, Schlecht et al. (2006) modeled the change in gene expression related to estrogenic activity in rats exposed to benzophenone-2. Because the expression of individual genes was monitored (via reverse transcription-polymerase chain reaction, RT-PCR), this analysis was less data-intensive than one using microarrays to evaluate a broad range of genes. In addition, while modern microarray methods and related computational approaches evaluate families of related genes (gene ontology) to strengthen the analysis, Schlecht and colleagues could not conduct such an analysis, since they only evaluated selected genes, and not all related genes in a family represent a specific response. Two research groups have developed software to facilitate the analysis of microarray data, taking into account gene ontology data. Yang et al. (2007) described a Java application that combines BMD methods with gene ontology classification. After fitting flexible mathematical models to the gene expression data, and estimating BMDs for individual genes (based on significant change from expression in control animals), the software categorizes the genes into gene ontology categories and calculates the central tendency and variability of the BMD and BMDL for genes within a category. The software is freely available at http://sourceforge.net/projects/bmdexpress/ and is distributed under the MIT Public License; the source code was modified from BMDS application developed by the US EPA. Thomas et al. (2007) used this software to calculate BMDs for changes in gene expression data in nasal epithelium following acute formaldehyde exposure. Burgoon and Zacharewski (2008) described ToxResponse Modeler, a cross-platform Java application for streamlining BMD analysis of gene expression or other “omics” data. To date, risk assessment applications of genomics data has been limited, primarily to hazard identification. Use of genomics data in dose-response analyses has been limited by the significant uncertainty in linking genomic data to adverse outcomes, or otherwise quantitatively integrating the data into the risk assessment paradigm. However, a number of initiatives are underway to characterize and validate genomics data and other early effect biomarkers, particularly in light of the NRC report on Toxicity Testing in the 21st Century (NRC, 2007). As more information about these biomarkers is collected and validated, the application of dose-response modeling methods, such as BMD modeling, to these endpoints will grow rapidly.

18.4.3

New Version of EPA BMDS

Recently, the US EPA released a new version of BMDS (version 2.1). While maintaining all the features of BMDS version 1.4.1c, the new version provides significant enhancements in the user interface, batch run setting and group result summary. The batch run setting is called session run (see Figure 18.8) in the new version BMDS where a data set can be modeled with a group of models simultaneously. It also can automatically summarize all modeling results in the form of a spreadsheet for documentation (Figure 18.9). These enhancements

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Figure 18.8 Session Window (i.e., batch model run) from the new version of BMDS (v. 2.1) where data are saved as a “.dax” file and model options (equivalent to the “type model run” window in BMDS 1.4.1) are saved as a “.opt” file for each particular model.

Figure 18.9 A summary table produced by the new version BMDS (v. 2.1) which combines model statistics selected by user into a spreadsheet for documentation.

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significantly increase the efficiency in conducting BMD modeling and documentation. In addition to the improvement in modeling efficiency, the new version also provides new model capabilities, such as: (1) The addition of a dichotomous Hill model; (2) New sets of background dichotomous models that will allow the user to specify background response in BMD modeling; and (3) Exponential models for continuous data, which are often used by European Risk Assessors. BMDS 2.1 is available from the US EPA’s website: http://www.epa.gov/ncea/bmds. For the latest development and details about the BMDS, users should refer to this website.

18.5 Disclaimer The views expressed in this paper are those of the authors and do not necessarily reflect the views and policies of the US Environmental Protection Agency or Toxicology Excellence for Risk Assessment. Mention of trade names or commercial products does not constitute endorsement or recommendation for use.

Appendix 1. Sample Dichotomous Data BMD Model Output ================================================================== Gamma Model. (Version: 2.7; Date: 01/18/2007) Input Data File: C:\BMDS\DATA\CONT.(d) Gnuplot Plotting File: C:\BMDS\DATA\CONT.plt Thu Oct 02 17:06:16 2008 ================================================================== BMDS MODEL RUN ˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜ The form of the probability function is: P[response]=background+(1-background)∗ CumGamma[slope∗ dose, power], where CumGamma(.) is the cummulative Gamma distribution function Dependent variable = response Independent variable = Dose Power parameter is restricted as power >=1 Total number of observations = 4 Total number of records with missing values = 0 Maximum number of iterations = 250 Relative Function Convergence has been set to: 1e-008 Parameter Convergence has been set to: 1e-008 Default Initial (and Specified) Parameter Values Background = 0.0049505 Slope = 0.0407766 Power = 5.53371

Disclaimer

393

Asymptotic Correlation Matrix of Parameter Estimates (∗∗∗ The model parameter(s) -Background have been estimated at a boundary point, or have been specified by the user, and do not appear in the correlation matrix) Slope Power Slope 1 0.99 Power 0.99 1

Parameter Estimates 95.0% Wald Confidence Interval Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit Background 0 NA Slope 0.0341206 0.0085439 0.0173748 0.0508663 Power 4.6581 1.01495 2.66882 6.64737 NA - Indicates that this parameter has hit a bound implied by some inequality constraint and thus has no standard error. Analysis of Deviance Table Model Log(likelihood) Test d.f. P-value Full model -145.683 Fitted model -145.784 2 0.9035 Reduced model -224.934 3 <.0001 AIC:

# Param’s 4 2 1

Deviance

0.20301 158.503

295.568 Goodness of Fit

Scaled Expected Observed Size Residual Dose Est. Prob. ----------------------------------------------------------------0.0000 0.0000 0.000 0 100 0.000 50.0000 0.0452 4.522 5 100 0.230 100.0000 0.3156 31.565 30 100 -0.337 150.0000 0.6407 64.074 65 100 0.193 Chiˆ2 = 0.20

d.f. = 2

Benchmark Dose Computation

P-value = 0.9032

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Specified effect Risk Type Confidence level BMD BMDL

= = = = =

0.1 Extra risk 0.95 64.2825 54.5448

Appendix 2. Sample Continuous Data BMD Model Output ================================================================== Hill Model. (Version: 2.11; Date: 01/18/2007) Input Data File: C:\BMDS\DATA\CONTINOUS.(d) Gnuplot Plotting File: C:\BMDS\DATA\CONTINOUS.plt Tue Oct 28 11:09:29 2008 ================================================================== BMDS MODEL RUN ˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜ The form of the response function is: Y[dose] = intercept + v*doseˆn/(kˆn + doseˆn)

Dependent variable = MEAN Independent variable = dose rho is set to 0 Power parameter restricted to be greater than 1 A constant variance model is fit Total number of dose groups = 4 Total number of records with missing values = 0 Maximum number of iterations = 250 Relative Function Convergence has been set to: 1e-008 Parameter Convergence has been set to: 1e-008

Default Initial Parameter Values alpha = 0.00104575 rho = 0 Specified intercept = 1.61 v = 0.11 n = 0.738328 k = 37.9167 Asymptotic Correlation Matrix of Parameter Estimates (

∗∗∗

The model parameter(s) -rho -n have been estimated at a boundary point, or have been specified by the user, and do not appear in the correlation matrix )

Disclaimer

alpha intercept v k

alpha 1 1.7e-007 -7.7e-008 1.5e-007

intercept 1.7e-007 1 -0.5 0.37

v -7.7e-008 -0.5 1 0.49

395

k 1.5e-007 0.37 0.49 1

Parameter Estimates 95.0% Wald Confidence Interval Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit alpha 0.000941336 0.000210489 0.000528785 0.00135389 intercept 1.61006 0.00968468 1.59108 1.62904 v 0.122427 0.0164341 0.0902171 0.154637 n 1 NA k 36.9236 17.6951 2.24181 71.6055 NA - Indicates that this parameter has hit a bound implied by some inequality constraint and thus has no standard error.

Table of Data and Estimated Values of Interest Dose ---0 35 105 316

N Obs Mean -- ----10 1.61 10 1.67 10 1.7 10 1.72

Est Mean -------1.61 1.67 1.7 1.72

Obs Std Dev ----------0.037 0.022 0.037 0.031

Est Std Dev ----------0.0307 0.0307 0.0307 0.0307

Scaled Res. ----------0.0059 0.0378 -0.0653 0.0334

Model Descriptions for likelihoods calculated Model A1:

Model A2:

Model A3:

Yij = Mu(i) + e(ij) Var{e(ij)} = Sigmaˆ2

Yij = Mu(i) + e(ij) Var{e(ij)} = Sigma(i)ˆ2

Yij = Mu(i) + e(ij) Var{e(ij)} = Sigmaˆ2 Model A3 uses any fixed variance parameters that were specified by the user Model R: Yi = Mu + e(i) Var{e(i)} = Sigmaˆ2

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Likelihoods of Interest Model A1 A2 A3 fitted R

Log(likelihood) 119.367629 120.948767 119.367629 119.364212 98.542208

# Param’s 5 8 5 4 2

AIC -228.735259 -225.897533 -228.735259 -230.728423 -193.084417

Explanation of Tests Test 1:

Do responses and/or variances differ among Dose levels? (A2 vs. R) Test 2: Are Variances Homogeneous? (A1 vs A2) Test 3: Are variances adequately modeled? (A2 vs. A3) Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) (Note: When rho=0 the results of Test 3 and Test 2 will be the same.)

Tests of Interest Test Test Test Test Test

1 2 3 4

-2∗ log(Likelihood Ratio) 44.8131 3.16227 3.16227 0.0068354

Test df 6 3 3 1

p-value <.0001 0.3673 0.3673 0.9341

The p-value for Test 1 is less than .05. There appears to be a difference between response and/or variances among the dose levels It seems appropriate to model the data The p-value for Test 2 is greater than .1. A homogeneous variance model appears to be appropriate here The p-value for Test 3 is greater than .1. variance appears to be appropriate here

The modeled

The p-value for Test 4 is greater than .1. The model chosen seems to adequately describe the data Benchmark Dose Computation Specified effect = 1 Risk Type = Estimated standard deviations from the control mean Confidence level = 0.95 BMD = 12.3478 BMDL = 5.79806

References

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References Akaike, H. (1973) Information theory and an extension of the maximum likelihood principle. In Proceedings of the Second International Symposium on Information Theory, B. N. Petrov and F. Csaki, eds. Akademiai Kiado, Budapest, pp. 267–281 Allen, B., Kavlock, R., Kimmel, C. and Faustman, E. (1994a) Dose-response assessment for developmental toxicity II. Comparison of generic benchmark dose estimates with no observed adverse effect levels, Fund. Appl. Toxicol., 23, 487–495. Allen, B., Kavlock, R., Kimmel, C. and Faustman, E. (1994b) Dose-response assessment for developmental toxicity III. Statistical models, Fund. Appl. Toxicol., 23, 496–509. Budtz-Jorgensen, E., Keiding, N. and Grandjean, P. (2001) Benchmark dose calculations from epidemiological data, Biometrics, 57, 698–706. Budtz-Jorgensen, E., Keiding, N. and Grandjean, P. (2004) Effects of exposure imprecision on estimation of the benchmark dose, Risk Analysis, 24 (6), 1689–1696. Budtz-Jorgensen, E. (2006) Estimation of the benchmark dose by structural equation models, Biostatistics, 8 (4), 675–688. Burgoon, L. and Zacharewski, T. (2008) Automated quantitative dose-response modeling and point of departure determination for large toxicogenomic and high-throughput screening data sets, Tox. Sci., 104 (2), 412–418. Carroll, R. (1998) Measurement error in epidemiologic studies, in Encyclopedia of biostatistics, P. Armitage & T. Colton (Eds.), Chichester: John Wiley & Sons, 2491–2519. Clewell, H., Lawrence, G., Calne D. and Crump, K. (2003) Determination of an occupational exposure guideline using the benchmark method, Risk Analysis, 23 (5), 1031–1046. Crump, K. (1984) A New method for determining allowable daily intakes, Fund. Appl. Toxicol., 4, 854–871. Crump, K. (1995) Calculation of benchmark doses from continuous data, Risk Anal., 15, 79–90. Dourson, M., Hertzberg, R., Hartung, R. and Blackburn, K. (1985) Novel methods for the estimation of acceptable daily intake, Toxicol. Ind. Health, 1 (4), 23–33. Fuller, W. (1987) Measurement error models, John Wiley & Sons, Hoboken, NJ. Haber, L., Allen, B. and Kimmel, C. (1998) Non-cancer risk assessment for nickel compounds: Issues associated with dose response modeling of inhalation and oral exposures, Toxicol. Sci., 43, 213–229 Haber, L.T., Dollarhide, J.S., Maier, A. and Dourson, M.L. (2001) Noncancer Risk Assessment: Principles and Practice in Environmental and Occupational Settings. In: Patty’s Toxicology, Fifth edition. Bingham, E., B. Cohrssen, and C.H. Powell, ed. Wiley and Sons, Inc. Health Canada (1999) Priority substances list assessment report: carbon disulfide. Ottawa. Ministry of Public Works and Government Services. Available at http://www.hc-sc.gc.ca/ewh-semt/ pubs/contaminants/psl2-lsp2/index e.html. Kavlock, R., Allen, B., Faustman, E. and Kimmel, C. (1995) Dose-response assessment for developmental toxicity: IV. Benchmark doses for fetal weight changes, Fundam. Appl, Toxicol., 26, 211–222. Kimmel, C. and Gaylor, D. (1988) Issues in qualitative and quantitative risk analysis for developmental toxicity, Risk. Anal., 8 (1), 15–20. Kobayashi, E., Suwazono, Y., Uetani, M., et al. (2006) Estimation of benchmark dose for renal disfunction in a cadmium non-polluted area in Japan, J. Appl. Toxicol., 26, 351–355. Linhart, H. and Zucchini, W. (1986) Model Selection. Wiley, New York. National Academy of Science (NAS) (1983) Risk assessment in federal government: managing the process. National Academy press, Washinton, DC. NRC (2007) Toxicity testing in the 21st Century: Vision and Strategy. Available at http://books.nap.edu/catalog.php?record id=11970 Schlecht, C., Klammer, H., Wuttke, W. and Jarry, H. (2006) A Dose-response study on the estrogenic activity of benzophenone-2 on various endpoints in the serum, pituitary and uterus of female rats, Arch. Toxicol., 80, 656–661.

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Shao, B., Jin, T., Wu, X., Kong, Q. and Ye, T. (2007) Application of benchmark dose (BMD) in estimating biological exposure limit (BEL) to cadmium, Biomed. Environ. Sci., 20 (6), 460–464. Stone, M. (1998) Akaike’s Criteria. in Encyclopedia of Biostatistics, Armitage, P. and Colton, T., eds. Wiley, New York. Thomas, R., Allen, B., Yang, L., et al. (2007) A Method to integrate benchmark dose estimates with genomic data to assess the functional effects of chemical exposure, Tox. Sci., 98 (1), 240–248. US EPA (United States Environmental Protection Agency) (1995a) The use of the benchmark dose approach in health risk assessment, EPA/630/R-94/007, USEPA, Office of Research and Development, Risk Assessment Forum, Washington DC. US EPA (1995b) Carbon Disulfide, Integrated Risk Information System, Available at: http://www. epa.gov/ncea/iris/subst/0217.htm. US EPA (2001) Methylmercury, Integrated Risk Information System, Available at: http://www.epa .gov/ncea/iris/subst/0073.htm. US EPA (2002) 1,3-Butadiene, Integrated Risk Information System, Available at: http://www.epa .gov/ncea/iris/subst/0139.htm. US EPA (2003) Benzene, Integrated Risk Information System, Available at: http://www.epa .gov/ncea/iris/subst/0276.htm. US EPA (2010a) Integrated Risk Information System, IRIS Guidance Documents, Available at: http://www.epa.gov/ncea/iris/. US EPA (2010b) Benchmark Dose Software (BMDS) Training, Available at: http://www.epa .gov/ncea/bmds/. Yang, L., Allen, B. and Thomas, R. (2007) BMDExpress: a software tool for the benchmark dose analyses of genomic data, BMC Genomics, 8, 387–395.

19 Application of Physiologically Based Pharmacokinetic Modeling in Health Risk Assessment Harvey J. Clewell III The Hamner Institutes for Health Sciences, USA

19.1 Introduction The process of assessing the health risks associated with human exposure to toxic environmental chemicals inevitably relies on a number of assumptions, estimates, and rationalizations. Some of the greatest challenges result from the necessity to extrapolate from the conditions in the studies that provide evidence of the toxicity of the chemical to the anticipated conditions of exposure in the environment or workplace. For risk assessments based on animal data, the most obvious extrapolation which must be performed is from the tested animal species to humans. However, others are also generally required: from high dose to low dose, from one exposure route to another, and from one exposure time frame to another. Physiologically based pharmacokinetic (PBPK) modeling provides a powerful method for increasing the accuracy of these extrapolations (Clewell and Andersen, 1985, 1989; Clewell, 1995a; Clewell, Andersen, and Blaauboer, 2008). The inherent capabilities of PBPK modeling are particularly advantageous for crossspecies extrapolation: the physiological and biochemical parameters in the model can be changed from those for the test species to those which are appropriate for humans to provide a biologically meaningful animal-to-human extrapolation (Andersen, Clewell, and Krishnan, 1995). However, it is important to recognize that a full PBPK model may not always be necessary to support a pharmacokinetic risk assessment. In some cases only a

Quantitative Modeling in Toxicology
C 2010 John Wiley & Sons, Ltd

Edited by Kannan Krishnan and Melvin E. Andersen

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simple compartmental pharmacokinetic description is needed; an excellent example has been published for the case of cadmium (Oberdorster, 1989, 1990). Simple pharmacokinetic approaches have sometimes been used by regulatory agencies in cancer risk assessment; for example, the use of metabolized dose for trichloroethylene by the United States Environmental Protection Agency (USEPA, 1991; 1987a). However, the first case where an agency has used a full PBPK approach was in the USEPA’s revision of its inhalation risk assessment for methylene chloride (USEPA, 1987b). The decision to use the PBPK approach in this case was made only after a period of considerable controversy, including a workshop sponsored by the National Academy of Sciences at which the usefulness of PBPK modeling for chemical risk assessment was discussed. The scientific consensus following the workshop was that “relevant PBPK data can be used to reduce uncertainty in extrapolation and risk assessment (NRC, 1987).” In 1989, after a detailed multi-agency evaluation of the available PBPK information and a review by the USEPA Scientific Advisory Board, the USEPA revised the inhalation unit risk and risk-specific air concentrations for methylene chloride in its Integrated Risk Information System (IRIS) database, citing the PBPK model of Andersen et al. (1987a). The resulting risk estimates were lower than those obtained by the default approach by nearly a factor of ten. More recently, an adaptation of the same PBPK model was used by the Occupational Safety and Health Administration (OSHA) in its rulemaking for methylene chloride (OSHA, 1997). The advantages of applying PBPK modeling in risk assessment have been discussed both for cancer (NRC, 1987; USEPA, 1989; Frederick, 1993; Clewell, 1995b, 1995c; Clewell et al., 1995; Clewell and Andersen, 2004; Clewell et al., 2005) and noncancer endpoints (Reitz et al., 1988; Frederick et al., 1992; Beck et al., 1993; Clewell and Jarnot, 2008; Clewell, Gentry, and Gearhart, 1997a; Barton and Clewell, 2000; Gentry et al., 2002, 2003; Clewell et al., 2007). In addition, the use of PBPK modeling has been recommended to improve route-to-route extrapolation (Gerrity and Henry, 1990) and the estimation of risk for chemical mixtures (Mumtaz et al., 1993). Recently, there has been an increasing focus on harmonization of the cancer and noncancer risk assessment paradigms used by regulatory agencies. Although the specific details of applying PBPK modeling within these two paradigms differ, it is possible to identify important elements common to both (Barton, Andersen, and Clewell, 1998). In the following discussion, an attempt is made to describe the key elements of the approach for applying PBPK modeling in risk assessment in a format which is equally applicable to both cancer and noncancer endpoints.

19.2

Dose Metric Selection

The ultimate aim of using pharmacokinetic modeling in risk assessment is to provide a measure of dose which better represents the “biologically effective dose”; that is, the dose which causally relates to the toxic outcome. The improved dose metric can then be used in place of traditional dose metrics (such as concentration or absorbed dose) in an appropriate dose-response model to provide a more accurate extrapolation to the human exposure conditions of concern. Implicit in any application of pharmacokinetics to risk assessment is the assumption that the toxic effects in a particular tissue, referred to as the target tissue, can be related in some way to the concentration of an active form of the substance in that tissue.

Dose Metric Selection

401

Moreover, except for pharmacodynamic differences between animal species, it is expected that similar responses will be produced at equivalent tissue exposures regardless of species, exposure route, or experimental regimen (Andersen, 1981; Monro, 1992; AndersenClewell, and Krishnan, 1995). The motivation for applying pharmacokinetics in risk assessment is the expectation that the observed effects of a chemical will be more simply and directly related to a measure of target tissue exposure than to a measure of administered dose (Clewell and Andersen, 1985; Andersen et al., 1987b). The specific nature of the relationship between target tissue exposure and response depends on the chemical mechanism of toxicity, or mode of action, involved. Many short-term, rapidly reversible toxic effects, such as acute skin irritation or acute neurological effects, may result primarily from the current concentration of the chemical in the tissue. In such cases, the likelihood of toxicity from a particular exposure scenario can be conservatively estimated by the maximum concentration (CMAX ) achieved in the target tissue (Jarabek, 1995; Bushnell, 1997; Benignus et al., 1998). On the other hand, the acute toxicity of highly reactive chemicals, as well as many longer-term toxic effects such as tissue necrosis and cancer, may be cumulative in nature, depending on both the concentration and duration of the exposure. A simple metric for such cases is the area under the concentration curve (AUC) in the tissue, which is defined mathematically as the integral of the concentration over time (Collins, 1987; Andersen et al., 1987b; Voisin et al., 1990). This mathematical form implicitly assumes that the effect of the chemical on the tissue is linear over both concentration and time. The use of the AUC represents an extension of “Haber’s Law,” a concept developed from observations of the effects of chemical warfare gases (Haber, 1924), that toxicity is proportional to the product of the concentration and time of exposure (C × T). For developmental effects, the chemical time course may also have to be convoluted with the window of susceptibility for a particular gestational event (Young et al., 1996). Another complicating factor in describing the relationship between chemical concentration and tissue response is the need to determine the toxicologically active form of the chemical. In some cases, a chemical may produce a toxic effect directly, either through its reaction with tissue constituents (e.g., ethylene oxide) or its binding to cellular control elements (e.g., dioxin). Often, however, it is the metabolism of the chemical that leads to its toxicity. In this case, toxicity may result primarily from reactive intermediates produced during the process of metabolism (e.g., chlorovinyl epoxide produced from the metabolism of vinyl chloride) or from the toxic effects of stable metabolites (e.g., trichloroacetic acid produced from the metabolism of trichloroethylene). The selection of the dose metric, that is, the active chemical form for which tissue exposure should be determined and the nature of the measure to be used, for example, peak concentration (CMAX ) or area under the concentration-time profile (AUC), is the most important step in applying pharmacokinetics in risk assessment. Whether intended or not, any dose metric will be consistent with the modes of action for some chemicals, and not for others. The USEPA (1992), in a joint effort with scientists from several other agencies, prepared a review paper on cross-species extrapolation in cancer risk assessment, which concluded that “. . .tissues experiencing equal average concentrations of the carcinogenic moiety over a full lifetime should be presumed to have equal lifetime cancer risk.” The use of the term “carcinogenic moiety” in this statement reflects the concern that the dose metric should be representative of the active form of the chemical. For example, the use of the lifetime average daily concentration for the parent chemical might be appropriate for a directly genotoxic chemical such as ethylene oxide, which is

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detoxified by metabolism. However, it would not be appropriate for a chemical like vinyl chloride, which requires metabolic activation to be genotoxic. In the latter case, increasing metabolism would increase the exposure to the genotoxic species but would decrease a dose metric based on parent chemical concentration. In such a case, where a reactive species produced during the metabolism of a chemical is responsible for its carcinogenicity, an appropriate cancer dose metric would be the lifetime average daily amount of metabolism in the target tissue divided by the volume of the tissue, as was used in the pharmacokinetic risk assessment for methylene chloride (Andersen et al., 1987a). Similar considerations apply in the case of noncancer risk assessment, except that the dose metrics are only averaged over the duration of the exposure (acute, subchronic, or chronic), not over a full lifetime (Jarabek, 1995).

19.2.1

The Ratio Concept in Risk Assessment

Although it is crucial that the dose metric properly represents the biologically effective dose, it is often possible to simplify the actual dose metric calculation by recognizing that quantitative risk assessment is fundamentally based on a ratio; specifically, the ratio of the dose metric value for the exposure of concern to the value for the exposure (or exposures) defining the toxicity. Typically, the exposures defining the toxicity might be the no observed adverse effect level (NOAEL) in an animal experiment or the doses in a cancer bioassay, while the exposure of concern might be a lifetime continuous human exposure. Any factors which do not change across the conditions of these exposures will not affect the ratio of the dose metrics, and thus will not impact the risk assessment. The dose metric just described for a reactive metabolite is an example of the use of this ratio concept: the amount of metabolism divided by the volume of the tissue is used as a surrogate for the average concentration of the reactive species, on the assumption that the ratio of these two quantities is constant; that is, that the stoichiometric yield of the reactive species and its reaction rate are invariant across species and over the exposure conditions being modeled. As another example of the use of the ratio concept, while the ultimate dose metric for a particular toxicity might be based on the chemical’s concentration in the target tissue, an acceptable dose metric might be based on the chemical’s blood concentration as long as the relationship between the blood concentration and target tissue concentration could be expected to be the same in both the animal toxicity study and the human exposure. In fact, this is probably a reasonable assumption across different exposure conditions in a given species; namely, that the concentrations would be related by the brain:blood partition coefficient. However, while tissue:air partition coefficients for volatile lipophilic chemicals appear to be similar in dog, monkey, and man (Fiserova-Bergerova, 1975), human blood:air partition coefficients appear to be roughly half of those in rodents (Gargas et al., 1989). Therefore, the human brain:blood partition would probably be about twice that in the rodent. Thus, if the model were to be used for extrapolation from rodents to humans, this twofold difference could be factored into the analysis as an adjustment to the blood concentration dose metric. Use of the ratio concept can greatly simplify risk assessment applications of pharmacokinetic modeling for developmental toxicity or teratogenicity studies. While it might seem necessary to use a model which includes compartments for the developing fetus, this might

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not always be the case. For many chemicals, the maternal blood or plasma concentration profile can provide an adequate surrogate for the fetal exposure (Gearhart et al., 1995; Clewell et al., 1997b). An important point to be aware of in this regard is the fact that symmetric diffusion limitation, such as might be expected for placental transport of many environmental contaminants, does not affect the AUC in the tissue. That is, while diffusion limited transport across the placenta might delay the achievement of the maximum concentration in the fetus as compared to the maternal blood, the AUC in the fetus will bear the same relationship to the AUC in the blood as it would in the case of flow-limited transport. Moreover, for exposures of sufficient duration to reach steady state, the steady-state fetal concentration will be completely determined by partitioning and will not be affected by diffusion limited transport. For many chemicals, the only important complication of fetal development is the resulting increase in the total volume of distribution for the chemical. This complication can often be ignored for risk assessment purposes, since the effect will be similar in both the toxicity study and the human exposure of concern (Still another use of the ratio concept.). 19.2.2

Other Metrics

Finally, it should be noted that although CMAX and AUC are the most commonly applied metrics for tissue exposure, other dose metrics might sometimes be more appropriate, particularly for chemicals whose mode of action is related to some aspect of their interaction with a receptor. In such cases, time above a critical concentration (TACC) or average receptor occupancy might actually be more appropriate (Dedrick, 1975; Andersen et al., 1993). Unfortunately, the more an attempt is made to include pharmacodynamic processes into a dose metric, the more difficult it becomes to collect the data necessary for its use. Of the many possible dose metrics, typically only CMAX , AUC, and TACC can be estimated from the kinds of data currently available on chemicals.

19.3

Impact of Pharmacokinetics in Risk Assessment

The standard paradigm for noncancer risk assessment rarely considers chemical-specific pharmacokinetic information. Typically, a NOAEL or lowest observed adverse effect level (LOAEL) derived from data for the exposure route of interest is simply adjusted by the application of generic uncertainty factors (UFs) to obtain reference concentrations (RfCs) or reference doses (RfDs):

Source of uncertainty

Factor

Use of LOAEL Short duration to long Animal to human Human variability Inadequate database Total (maximum)

up to 10 up to 10 up to 10 up to 10 up to 10 3000

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In this paradigm, little attention has been given to incorporating knowledge of the mode of action or of dosimetry of the active chemical form in target tissues in these calculations. The selection of UFs has also generally failed to consider chemical-specific mechanistic information or pharmacokinetic data. One exception is the focus in the revised RfC process on delivered dose adjustments for inhaled materials (USEPA, 1994). In the traditional paradigm for cancer risk assessment, dose-response modeling is used to calculate a carcinogenic potency based on tumors observed in animal bioassays or human epidemiology studies. In the case of animal studies, “body surface area” (BSA) scaling (multiplying by the cube root of the ratio of the animal and human body weights) is used to obtain a human equivalent dose (HED). Dose-response modeling is then performed on the HEDs using the linearized multistage model (Crump, 1984a). For inhalation studies, conversion from inhaled concentration to “absorbed dose” is performed by a rudimentary calculation involving the ventilation rate, body weight, and “fraction absorbed.” As mentioned earlier, chemical-specific pharmacokinetic information has occasionally been used in this process, with the calculation of metabolized dose in the risk assessment for trichloroethylene (USEPA, 1985, 1987a) and the use of a PBPK model in the risk assessment for methylene chloride (USEPA, 1987b) serving as examples. The recent USEPA (2005) guidelines for carcinogen risk assessment would appear to provide the flexibility necessary to move forward in this area. Under the new guidelines, multiple options are available for performing a carcinogenic dose-response assessment: (1) a linear approach which is similar to the traditional cancer paradigm, and (2) a margin of exposure (MOE) approach which is more similar to the noncancer paradigm. The selection of the dose-response approach to be used with a particular chemical is determined on the basis of the information available on the carcinogenic mode of action of the chemical, which considers both pharmacokinetic and mechanistic information.

19.3.1

Cross-Species Extrapolation

In the traditional default risk assessment approaches, all chemicals are implicitly treated as if the observed toxicity is produced directly by the parent chemical itself (Andersen, Clewell, and Krishnan, 1995). This implicit assumption that the parent chemical is directly toxic is true even of the RfC dosimetry guidelines (USEPA, 1994), which differentiate respiratory effects from extra-respiratory effects and include different defaults for chemicals based on their solubility and reactivity. However, a risk assessment which considers pharmacokinetics must necessarily also consider the mode of action, at least to the extent of identifying the active form of the chemical for which the dosimetry should be performed. To demonstrate the importance of considering pharmacokinetics and mode of action in noncancer risk assessment, PBPK models for methylene chloride (MC), trichloroethylene (TCE), and vinyl chloride (VC) were exercised to determine general expectations for the cross-species dosimetry for one class of chemicals, the volatile lipophilic solvents (Clewell, Gentry, and Gearhart, 1997a). All three of these chemicals would be considered Category 3 gases (relatively water-insoluble chemicals which achieve a steady state during inhalation exposure) in the USEPA (1994) dosimetry guidelines. In a standard risk assessment, the animal-to-human dosimetry adjustment for each of these chemicals would be performed in exactly the same way, based on time-weighted average (TWA) exposure concentration for

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Table 19.1 Alternative metrics for cross-species equivalence.

Route

Basis

Inhalation

Default: 1986 USEPA Cancer Guidance New USEPA Cancer Guidance USEPA Noncancer Guidance Allometric: Parent Chemical Reactive Metabolite Stable Metabolite PBPK:a Parent Chemical Reactive metaboliteb Stable Metabolite Default: 1986 USEPA Cancer Guidance New USEPA Cancer Guidance USEPA Noncancer Guidance Allometric: Parent Chemical Reactive metaboliteb Stable Metabolite PBPK:a Parent Chemical Reactive Metabolite Stable Metabolite

Oral

a b

Metric

Human/Animal equivalence ratio

Inhaled dose ∗ BW1/3 TWA Conc. (PD : UF=1-10) TWA Conc. (PD : UF=3)

0.15–0.3 1 1

TWA Conc. TWA Conc/BW1/4 TWA Conc.

1 4–7 1

Parent AUC Tmet/Vt Metabolite AUC

0.6–1.7 5–25 0.1–1

Dose ∗ BW1/3 Dose ∗ BW1/4 Dose (PK+PD: UF=10)

0.08–0.16 0.15–0.25 0.3

Dose ∗ BW1/4 Dose Dose ∗ BW1/4

0.15–0.25 1 0.15–0.25

Parent AUC Tmet/Vt Metabolite AUC

0.01–0.1 1–2 0.02–0.07

Based on PBPK modeling of methylene chloride, trichloroethylene, and vinyl chloride. Total metabolite formed during a defined period/Tissue volume.

inhalation and on mg/kg/day administered dose for oral exposure, regardless of the nature of the toxic endpoint or the mechanism of toxicity. In contrast to the simplicity and uniformity of the default approaches, a pharmacokinetic approach requires the application of scientific judgment to select the appropriate option for each toxic effect of a chemical. A comparison of the default and PBPK based approaches, as a function of the type of toxicity and the exposure route, for MC, VC, and TCE is provided in Table 19.1. For the purpose of this comparison, the acute, reversible neurological effects of these chemicals were assumed to result from the direct toxicity of the parent chemical, and an appropriate dose metric would therefore be either the CMAX or AUC of the parent chemical in the brain or, as discussed above, in the blood as a surrogate for the brain. For the calculations used to prepare Table 19.1, the AUC was selected, since it is more analogous to the TWA calculation typically used for duration adjustment. On the other hand, the production of reactive species during metabolism was assumed to be responsible for the chronic liver toxicity of MC and VC, so the average daily amount of metabolism divided

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by the volume of the liver was chosen as the dose metric. Finally, the development of liver toxicity from TCE was assumed to result from the activity of the stable metabolite, trichloroacetic acid (TCA); therefore, the average daily AUC for TCA in the liver was used as the dose metric. To obtain the comparison shown in Table 19.1, the PBPK models were exercised for a typical exposure scenario in the mouse and rat. The models were then rerun for the same exposure scenario but with human parameters, and the concentration or dose was varied until the human dose metric was the same as that obtained for the mouse and rat. These two PBPK human equivalent concentrations (HECs) or doses (HEDs), one for the mouse and one for the rat, were then compared to the corresponding HECs or HEDs obtained by the default methodology. No animal-to-human UFs were applied in this comparison. As shown in Table 19.1, the correct relationship for cross-species dosimetry depends on whether the toxicity is due to the parent chemical or a metabolite, and in the case of toxicity from a metabolite, whether the metabolite is reactive or stable. Moreover, the nature of the cross-species relationship for each of these possibilities is different for oral exposure than for inhalation. Therefore, pharmacokinetic modeling is required to provide accurate cross-species extrapolation that considers the nature of the toxic entity. Default noncancer risk assessments apply a UF of 10 for uncertainty regarding animal-tohuman extrapolation. This UF is applied to consider the possibility of both pharmacokinetic and pharmacodynamic differences between rodents and humans which could put the human at greater risk (i.e., result in toxicity at lower exposures), and is reduced to three when inhalation dosimetry is used to consider pharmacokinetic differences (USEPA, 1994). A reduced factor of three has also sometimes been applied for data from species which are considered physiologically “closer” to humans, such as dogs or monkeys. This UF plays the same role, and is roughly the same magnitude, as the traditional use of BSA scaling in cancer risk assessment (which resulted in a factor of about seven for rats and 13 for mice). In both cases the concern that the human might receive a relatively greater exposure, and hence be at relatively greater risk, than smaller animals receiving the same nominal dose reflects years of experience with data on chemical toxicities which, for the most part, reflect oral exposure to chemicals which are themselves toxic (Andersen, Clewell, and Krishnan, 1995). As can be seen from Table 19.1, the human would be at greater risk for oral exposures to chemicals which are directly toxic due to the effect of pharmacokinetic scaling. For oral exposures to a toxic chemical which must be cleared by metabolism or urinary excretion, the internal exposure (AUC) in the human would be greater than in smaller animals at the same administered dose because the clearance of chemicals, both metabolic and urinary, tends to decrease relative to body weight as the animal becomes larger (O’Flaherty, 1989). In fact, the allometric scaling of clearance appears to follow body weight raised to the threequarters power, producing slightly less of a difference across species than that predicted by BSA scaling, which is body weight raised to the two-thirds power (USEPA, 1992). Indeed, based on a multi-agency analysis of the evidence for cross-species scaling factors, the USEPA (1992) changed from its default BSA cross-species scaling for cancer to a new scaling approach based on body weight raised to the three-quarters power. In both cancer and noncancer risk assessment, there is continuing controversy regarding the appropriate cross-species default for pharmacodynamics. As discussed above, the origin of the default scaling/UF actually applied in either case rests on observations of relationships across species which are completely consistent with pharmacokinetics alone (Andersen,

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Clewell, and Krishnan, 1995). Nevertheless, the use of pharmacokinetics in a cancer or noncancer risk assessment has never been considered to fully replace the default scaling/UF. Table 19.1 shows that, in the case of noncancer risk assessment, the default approach is not necessarily conservative in all cases, even with the application of the full animal-to-human UF of 10. That is, in some cases, the cross-species differences in pharmacokinetics alone may exceed the default factor applied for both pharmacokinetics and pharmacodynamics. A similar result would be obtained for cancer risk estimates. Particularly in the case of toxicity due to a stable metabolite, the default dosimetry and scaling/UF may sometimes underestimate the human risk (overestimate the HEC/HED). 19.3.2

Cross-Route Extrapolation

Another important use of pharmacokinetics in risk assessment is for extrapolation from one exposure route to another. In default noncancer risk assessment approaches, no provision is made for the use of toxicity data from a different route than the human exposure of concern. Thus, for example, in performing an inhalation risk assessment for a chemical, data from animal studies performed by the oral route could not be included in the quantitative doseresponse calculations. Except in the case of exposure-route-specific, portal-of-entry effects, the use of pharmacokinetic modeling makes it possible to combine data from different routes in a quantitative risk assessment. Specifically, the pharmacokinetic model can be used to predict the target tissue dose associated with an animal toxicity study conducted by one route, and then can be exercised to predict the equivalent human exposure by another route that would result in the same target tissue dose (Gerrity and Henry, 1990). 19.3.3

Dose Extrapolation

A third use of pharmacokinetics in risk assessment is to incorporate dose-dependent pharmacokinetics and metabolism into the dose-response calculations for a chemical. For example, the observed dose-response relationship between the exposure concentration and resulting toxicity of vinyl chloride in animal studies is highly nonlinear due to the saturation of metabolism. When a pharmacokinetic model is used, however, and the exposure is expressed in terms of total metabolism, the dose-response for toxicity becomes linear, improving the accuracy of dose-response modeling. 19.3.4

Time Extrapolation

In some cases, pharmacokinetic modeling provides a more accurate method for extrapolating across exposure time frames than default methods such as the use of the TWA exposure concentration or average daily dose. For example, exposure to vinyl chloride at 100 parts per million (ppm) for eight hours will not be equivalent to exposure at 800 ppm for one hour, due to saturation of metabolism at the higher concentration and rapid post-exposure clearance of unmetabolized chemical by exhalation. Total metabolism in the latter exposure will be significantly lower than in the former, while the AUC for the parent chemical will be greater. However, for a highly lipophilic chemical with similar high affinity, low capacity metabolism, post-exposure metabolism of chemical stored in

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fat tissues could result in nearly the same amount of metabolism from an exposure of a few hours as from a continuous exposure at the same concentration. In cases such as these, a pharmacokinetic model which incorporates a realistic description of the dose-response for metabolism is necessary to determine the correspondence between exposures over different durations (Clewell and Andersen, 1989, 1994). The nature of time extrapolation performed by a pharmacokinetic model will also be determined to a large extent by the dose metric selected. For example, the two dose metrics described for acute toxicity, CMAX and AUC, respond very differently to changes in exposure duration. In the case of a constant concentration inhalation exposure, the concentrations in the blood and tissue quickly rise to a steady state and then remain constant until the exposure is terminated, at which time they rapidly return to zero (except, perhaps, in the fat). Thus CMAX will be relatively invariant for exposures ranging from tens of minutes to years. In contrast, for the same exposure scenario the AUCs in the tissues will be roughly proportional to the length of exposure. It should be recognized, however, that pharmacokinetic modeling is generally not very useful for extrapolating across widely different time frames, for example, from acute to subchronic or from subchronic to chronic exposure durations. The principal determinants of the relationship between the effects of shorter-term and longer-term exposure are, to a large extent, pharmacodynamic factors such as damage accumulation, repair, and compensation. Therefore, the default approach in noncancer risk assessment, in which UFs are applied to account for uncertainty regarding the effect of significant differences in the duration of exposure, is still appropriate when pharmacokinetics is considered. For this reason, the dose metrics calculated with pharmacokinetic models for noncancer risk assessments are usually calculated as average daily values, where the average is taken over the total duration of the exposure. For example, instead of calculating the total AUC over a 90-day exposure, the average daily AUC (which is equivalent to a daily average concentration) is calculated by dividing the total AUC by the total duration of the exposure in days (90 in this case).

19.4

Application of Pharmacokinetic Modeling in Risk Assessment

The application of pharmacokinetic modeling in risk assessment is both chemical- and endpoint-specific. Therefore, it is not possible to completely describe the approach which should be taken under all possible circumstances. The application of pharmacokinetics in a particular case requires the use of scientific judgment and an understanding of the risk assessment process. Nevertheless, a number of steps can be described which will generally be required regardless of the details of the application. These common steps in the process are described in the following sections.

19.4.1

Step 1: Selection of Critical Studies

The first step in performing a risk assessment using pharmacokinetic modeling is essentially the same as in the default approach: evaluation of the available toxicological and mechanistic data for the chemical and selection of potential critical studies. The principal difference is that, since the cross-species equivalence for different toxicological endpoints may vary, as

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described above, it is not always possible to determine from a comparison of the animal exposure data which study will predict effects at the lowest human exposures.

19.4.2

Step 2: Selection of Pharmacokinetic Model

Once the exposure scenarios and endpoints of concern have been selected, the requirements for a pharmacokinetic model can be determined. The key elements of this determination are the animal species and exposure conditions that the model must be able to simulate, and the target tissue dose metrics that the model must be able to calculate. Of course, it is also necessary to determine whether the model has been adequately validated to ensure its reliability for the intended purpose (Clewell, 1995a; Clewell and Clewell, 2008). In particular, the reliability of the model predictions for each of the dose metrics should be carefully evaluated (Clewell, 1995c; Allen, Covington, and Clewell, 1996; Loizou et al., 2008).

19.4.3

Step 3: Calculation of Dose Metrics for Toxicity Studies

For each study and endpoint selected in step 1, the pharmacokinetic model is used to calculate the appropriate dose metrics for the endpoint of concern. In some cases, it may be possible to postulate more than one reasonable dose metric. In such cases, all of the candidate metrics should be calculated. The final decision regarding which metric to use should be made only after the calculations have been completed for each metric, and should consider both the plausibility and conservatism of the various options, as will be discussed later. To calculate the dose metrics, the model parameters are set to those for the species represented in the study, whether an experimental animal study or a human study. In the case of developmental studies, it may be necessary to estimate parameters for a young animal or pregnant female rather than an average adult. To the extent possible, data from the study on animal strain, body weights, age, and activity should be used in selecting parameters for the model. The experimental parameters in the model are then set to reproduce the exposure scenario performed in the study, and the model is run for a sufficient period to characterize the animal exposure to the chemical and, if necessary, its metabolites. There are often a number of options regarding the way in which the model should be run to characterize the exposure. Usually, the desire is to estimate an average daily exposure, although in some cases the total exposure over the duration of the experiment is used. As mentioned earlier, while the averaging period in the case of cancer is typically taken to be the lifetime, the averaging period in the case of noncancer risk assessment is considered to be the duration of the exposure. For acute or short-term exposures, this is most easily done by running the model for the total duration of the exposure (or exposures, for repeated exposure studies), plus an adequate post-exposure period to ensure that the chemical has been completely metabolized and cleared from the body. In the case where a dose metric is based on a metabolite, the post exposure period should also be long enough to ensure the complete clearance of the metabolite. The resulting dose metric obtained for the total duration of the exposure can then be divided by the number of days over which the exposure was conducted (not including the post-exposure period) in order to derive the average daily value.

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The same approach (running the model for the total duration of the study) can be used to calculate the dose metric for longer-term exposures. However, an alternative approach, which is often attractive for modeling of chronic exposures, is to estimate the steady-state dose metric. There are two principal methods for calculating a steady-state estimate. In the first, the model is run until steady state is reached and then the dose metric is calculated by subtraction. For example, in the case of a chronic inhalation exposure conducted five days per week, the model can be run consecutively for one week, two weeks, three weeks, and so on. To calculate the average daily AUC for a given week, the value at the end of the previous week is subtracted from the value at the end of the current week and the result is divided by seven. This process is repeated until the change in the dose metric from one week to the next is insignificant. For continuous exposures, the comparison can be made on a daily basis instead of weekly. The other method for estimating the steady-state dose metric is to run the model for a single-day exposure, plus an adequate post-exposure period as described above, and modifying the single-day dose metric by the necessary factors to obtain an average daily value (e.g., by multiplying by five-sevenths in the case of the fiveday per week exposure just described). This method, which is faster but only approximate, is sufficiently accurate for estimating average daily AUC in many cases. It can be checked against the first method described to determine its accuracy in a particular case. If the NOAEL/UF method is being used in a noncancer risk assessment, a dose metric only needs to be calculated for the NOAEL or LOAEL exposure for a particular study and endpoint. On the other hand, if dose-response modeling is going to be performed, such as in the Benchmark Dose approach (Crump, 1984b, 1995), dose metrics must be calculated for all exposure groups. The dose metrics are then used in the dose-response model in place of the usual exposure concentrations or administered doses. It is important to remember that when this is done, the result of the dose-response modeling will also be in terms of a value of the dose metric rather than an exposure concentration or administered dose. If it is desired to convert the resulting dose metric to the equivalent exposure concentration or administered dose, the pharmacokinetic model must be run “backwards”; that is, the model must be run repeatedly, varying the exposure concentration or administered dose until the desired dose metric value is obtained. Note that this conversion can be accomplished either using the parameters for the test species and experimental exposure, to obtain the result of the dose-response modeling in terms of the exposure conditions, or using those for the human exposure of concern, to obtain the HEC or HED. Alternatively, the HEC or HED for each exposure group could be obtained by the “backwards” modeling just described, and the HECs or HEDs could be used in the dose-response model instead of the dose metrics. However, dose-response modeling is more properly conducted on the dose metrics, since it is expected that the observed effects of a chemical will be more simply and directly related to a measure of target tissue exposure than to a measure of administered dose.

19.4.4

Step 4: Application of Uncertainty Factors

In the default noncancer risk assessment approach, animal exposure concentrations are converted to HECs before applying any necessary UFs. In a pharmacokinetic risk assessment approach, on the other hand, it is more proper to divide the dose metrics obtained from the toxicity studies by the necessary UFs rather than the HECs or HEDs. The

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rationale for applying the UFs to the dose metrics is the same as for using the dose metrics in dose-response modeling: it is expected that the observed effects of a chemical will be more simply and directly related to a measure of target tissue exposure than to a measure of administered dose. The dose metrics are specifically chosen to provide more useful measures of the biologically effective dose. Therefore, it is the dose metrics which should be adjusted to assure that the biologically effective dose is reduced to the extent desired. As a counter-example, consider the case where toxicity has been observed for exposure to a chemical at a concentration well above the point where saturation of the metabolism of the chemical occurs, and where the metabolism of the chemical is responsible for the toxicity. In this case, applying the UF to a dose metric based on total metabolism would ensure that the extent of metabolism would be reduced by the same factor. However, if the concentration at which the effect was observed were sufficiently higher than the concentration at which metabolism is saturated, applying the UF to the exposure concentration might not actually reduce the extent of metabolism to any appreciable extent. The selection of UFs in a pharmacokinetic risk assessment is essentially the same as for the default noncancer process, described earlier, except that the UF for uncertainty in animal-to-human extrapolation should be reduced to reflect the use of pharmacokinetic modeling. By analogy to the USEPA (1992) approach for inhalation dosimetry, reduction of the default animal-to-human UF from 10 to 3 would seem to be reasonable for both inhalation and oral risk assessments. The remaining factor of three is then considered to represent uncertainty regarding pharmacodynamic differences across species, and could be modified on the basis of other information for the chemical. The UFs will generally vary from one study to another, as well as from one endpoint to another, as dictated by the nature of the study (e.g., if only a LOAEL was identified) and the information associated with the endpoint (e.g., if there is evidence regarding the relative sensitivity of humans compared to the experimental species).

19.4.5

Step 5: Determination of Human Exposures

As described previously, in order to convert a dose metric to an exposure concentration or administered dose, the pharmacokinetic model must be “run backwards”; that is, the model must be run repeatedly, varying the exposure concentration or administered dose until the desired dose metric value is obtained. In the case of calculating the acceptable human exposure corresponding to a given toxicity study, the physiological and biochemical parameters in the model are set to appropriate human values and the model is iterated until the dose metric obtained for the human exposure of concern is equal to the dose metric obtained for the toxicity study divided by the UFs. The dose metric should be calculated in an analogous way to the dose metric for the toxicity study; that is, if the dose metric in the toxicity study was expressed in terms of an average daily value, the dose metric used for calculating the associated human exposure should also represent an average daily value. For short-term exposures, where the model has been run for the total duration of the toxicity study and the total dose metric value has been calculated, the dose metric used for calculating the associated human exposure should usually be obtained for an exposure over the same period. An exception to this rule is the case where it is anticipated that the acute exposure of concern for the human may represent a short-term excursion against

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a background of chronic exposure. In this case, a more conservative approach may be preferred, in which a steady-state dose metric calculation is used for the human. When a steady-state dose metric is used in both an experimental animal and the human, it should be noted that the calculation of a steady-state dose metric in the human generally requires running the model for a much longer period than in the animal. In fact, the time required to reach steady state in the human can be estimated by multiplying the time to steady state in the animal by the ratio of human to animal body weights raised to the one-quarter power. This concept of the allometric scaling of equivalent times is referred to as “physiological time” (Lindstedt, 1987).

19.4.6

Step 6: Selection of Preferred Dose Metric/Study/Endpoint

After calculations have been performed for each of the candidate studies and endpoints, the most appropriate of the alternatives must be selected. There are two principal criteria for this selection: plausibility and conservatism. For each endpoint, priority should be given to the dose metric which, on the basis of the available evidence, appears to provide most plausible basis for estimating the biologically effective dose. The plausibility of a given dose metric is determined primarily by two factors: (1) its consistency with available information on the mode of action (mechanism of toxicity), and (2) the consistency of its dose-response with that of the endpoint of concern. The first factor has been discussed earlier; the second refers both to evaluating the dose metric’s ability to linearize the dose-response for the associated endpoint within a study (internal consistency), as well as its ability to demonstrate a consistent quantitative relationship of dose metrics for positive versus negative exposures, regardless of differences in exposure scenario, route, and species (external consistency). The other criterion for the selection of the appropriate dose metric is conservatism. Where there is an inadequate basis for giving priority to one dose metric over another, the most conservative (the one producing the highest risk or lowest acceptable exposure) should be used. After selecting the most appropriate dose metric for each endpoint, the results across the various studies and endpoints should be evaluated using the same criteria, plausibility (i.e., internal and external consistency of dose-response) and conservatism, to arrive at the final recommendation. When a risk assessment is based on an endpoint in an animal experiment, it may sometimes be possible to evaluate data from human exposures as a test of the plausibility of the result, even though the data might not be adequate to serve as the basis for calculating an alternative value. Another useful exercise is to vary the physiological and biochemical parameters used in the model to determine the effect of human pharmacokinetic variability on the dose metric (Clewell and Andersen, 1996). In particular, the model can be used to evaluate the potential for sensitive subpopulations (women, children, the obese, etc.).

19.5

Case Study: Vinyl Chloride

The risk assessment for vinyl chloride provides a useful example of the application of a PBPK model in risk assessment. The PBPK model in this case was initially developed

Case Study: Vinyl Chloride

413

Vinyl Chloride

P450 H2O

Chloroethylene Epoxide

CO2

GSH Glutathione Conjugates

DNA Adducts

Epoxide Hydrolase

GSH Chloroacetaldehyde

Tissue Adducts

Abbreviations: P450 – Cytochrome P450 (CYP); GSH – glutathione.

Figure 19.1

Diagram of the metabolism of vinyl chloride (VC).

to support a cancer risk assessment for vinyl chloride (Clewell et al., 1995, 2001), but was eventually applied for both cancer and noncancer assessments (USEPA, 2000). Vinyl Chloride (VC) is a gas that is used primarily as a chemical precursor in the production of plastics and resins. It is a trans-species carcinogen, producing tumors in a variety of tissues, from both inhalation and oral exposures, across a number of species. In particular, exposure to VC has been associated with a rare tumor, liver angiosarcoma, in a large number of studies in mice, rats, and humans. The mode of action for the carcinogenicity of VC appears to be a relatively straightforward example of DNA adduct formation by a reactive metabolite, leading to mutation, mistranscription, and neoplasia. As shown in Figure 19.1, the primary route of metabolism of VC is by the action of the mixed function oxidase (MFO) system, now referred to as Cytochrome P450 or CYP, to form chloroethylene oxide. The metabolism of VC is a dose-dependent, saturable process. Chloroethylene oxide (CEO) is a highly reactive, short-lived epoxide that rapidly rearranges to form chloroacetaldehyde (CAA), a reactive α-halocarbonyl compound; this conversion can also be catalyzed by epoxide hydrolase. The main detoxification of these two metabolites is conjugation with glutathione. CAA has been associated with the cytotoxicity of VC; CEO is responsible for its carcinogenicity. The carcinogenicity of VC is related to the production of reactive metabolic intermediates. The most appropriate pharmacokinetic dose metric for a reactive metabolite is the total amount of the metabolite generated divided by the volume of the tissue in which it is produced (Andersen et al., 1987a). In the case of VC, a reasonable dose metrics for angiosarcoma would be the total amount of metabolite formation divided by the volume of the liver (RISK). The PBPK model for VC is shown in Figure 19.2. For a poorly soluble, volatile chemical like VC, only four tissue compartments are required in the PBPK model (Figure 19.2): a rapidly perfused tissue compartment which includes all of the organs except the liver; a slowly perfused tissue compartment which includes all of the muscle and skin tissue; a fat

414

Application of Physiologically Based Pharmacokinetic Modeling QP

CI

CX

Lungs CVF

Fat

CVR

Rapidly Perfused Tissues

CVS

Slowly Perfused Tissues

CVL

Liver VMAX1 KM1

CO2

KCO2

QC

QF CA QR CA QS CA QL CA

VMAX2 KM2

Reactive Metabolites

KZER KA

KGSM

KFEE Tissue/DNA Adducts

Glutathione Conjugate KGSM GSH KS

KB

KO

Abbreviations: QP – alveolar ventilation; CI – inhaled concentration; CX – exhaled concentration; QC – cardiac output; QF, CVF – blood flow to, and venous concentration leaving, the fat; QR, CVR – blood flow to, and venous concentration leaving, the richly perfused tissues (most organs); QS, CVS – blood flow to, and venous concentration leaving, the slowly perfused tissues (e.g., muscle); QL, CVL – blood flow to, and venous concentration leaving, the liver; VMAX1,KM1 – capacity and affinity for the high affinity oxidative pathway enzyme (CYP 2E1); VMAX2,KM2 – capacity and affinity for the lower affinity oxidative pathway enzymes, (e.g., CYP 2C11/6); KZER – zero-order rate constant for uptake of VC from drinking water; KA – first-order rate constant for uptake of VC from corn oil; KCO2 – first-order rate constant for metabolism of VC to CO2 KGSM – first-order rate constant for reaction of VC metabolites with GSH; KFEE – first-order rate constant for reaction of VC metabolites with other cellular materials, including DNA; KB – first-order rate constant for normal turnover of GSH; KO – zero-order rate constant for maximum production of GSH; KS – parameter controlling rate of recovery of GSH from depletion.

Figure 19.2

Diagram of the PBPK model of VC.

compartment which includes all of the fatty tissues; and a liver compartment. All metabolism was described in the liver, which is a good assumption in terms of the overall kinetics of VC, but which would have to be revised to include target-tissue-specific metabolism if a serious attempt were to be made to perform a VC risk assessment for a tissue other than the liver (Andersen et al., 1987a). The model also assumes flow-limited kinetics, or venous equilibration; that is, that the transport of VC between blood and tissues is fast enough for steady state to be reached within the time it is transported through the tissues in the blood. Metabolism of VC is modeled by two saturable pathways: one high affinity, low capacity (with parameters VMAX1C and KM1); and one low affinity, high capacity (with parameters VMAX2C and KM2). Subsequent metabolism is based on the metabolic scheme shown

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415

in Figure 19.1; the reactive metabolites (whether CEO, CAA, or other intermediates) may then either be metabolized further, leading to CO2 , react with GSH, or react with other cellular materials, including DNA. Because exposure to VC has been shown to deplete circulating levels of GSH, a simple description of GSH kinetics was also included in the model. The parameters for the model are documented in Clewell et al. (2001) and in the model code (QMT model library folder CLEWELL). The physiological parameters are USEPA reference values (USEPA, 1988), except for the alveolar ventilation (QPC) in the human, which was calculated from the standard USEPA value for the ventilation rate in the human, 20 m3 /day, assuming a 33% pulmonary dead space (USEPA, 1988). The value for the cardiac output (QCC) in the human was selected to correspond to the same workload as the standard USEPA ventilation using data from Astrand and Rodahl (1970). For modeling of the closed chamber studies with human subjects, more typical resting values of 15 for cardiac output (QCC) and 18 for alveolar ventilation (QPC) were used. In some cases, it was also necessary to slightly vary the alveolar ventilation and cardiac output of the animals in the closed chamber studies in order to obtain acceptable simulations of those experiments. The partition coefficients for Fisher-344 (F344) rats were taken from Gargas et al. (1989), and those for Sprague–Dawley rats were taken from Barton et al. (1995). The Sprague–Dawley values were also used for modeling of Wistar rats. Blood/air partition coefficients for the other species were obtained from Gargas et al. (1989), and the corresponding tissue/blood partition coefficients were estimated by dividing the Sprague–Dawley rat tissue/air partition coefficients by the appropriate blood/air value. The affinity for the 2E1 pathway (KM1) in the rat, mouse, and hamster was set to 0.1 on the basis of studies of the competitive interactions between CYP2E1 substrates in the rat (Barton et al., 1995; Andersen et al., 1987b). The affinity used for the non2E1 pathway (KM2) in the mouse and rat was set during the iterative fitting of the rat total metabolism, glutathione depletion, and rate of metabolism data, described below. The capacity parameters for the two oxidative pathways (VMAX1C and VMAX2C) in the mouse, rat, and hamster were estimated by fitting the model to data from closed-chamber exposures with each of the species and strains of interest (Barton et al., 1995; Bolt et al., 1977; Clement, 1990; Gargas, Clewell, and Andersen, 1990), holding all of the other model parameters fixed and requiring a single pair of values for VMAX1C and VMAX2C to be used for all of the data on a given sex/strain/species. Figures 19.3 and 19.4 show examples of the results of this fitting process for the male B6C3F1 mouse and male Wistar rat, respectively. Initial estimates for the subsequent metabolism of the reactive metabolites and for the glutathione submodel in the rat were taken from the model for vinylidene chloride (D’Souza and Andersen, 1988). These parameter estimates, along with the estimates for VMAX2C and KM2, were then refined for the case of VC in the Sprague–Dawley rat using an iterative fitting process which included the closed chamber data for the Sprague–Dawley and Wistar rat (Barton et al., 1995; Bolt et al., 1977; Clement, 1990) along with data on glutathione depletion (Jedrychowski, Sokal, and Chmielnicka, 1985; Watanabe et al., 1976), total metabolism (Gehring, Watanabe, and Park, 1978), and CO2 elimination (Watanabe and Gehring, 1976). Since this last dataset was obtained for oral dosing with VC in corn oil, a value for KA, the oral uptake rate from corn oil, was estimated from fitting of separate data on blood concentrations following dosing of rats with VC in corn oil (Withey, 1976).

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Chamber Concentration (ppm)

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100 340 ppm 525 ppm 1100 ppm 3100 ppm 10 0

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Figure 19.3 Model predictions (lines) and experimental data (symbols) for the chamber concentration during exposure of male B6C3F1 mice to VC in a closed, recirculated chamber (Data taken from Clement, 1990).

Chamber Concentration (ppm)

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Figure 19.4 Model predictions (lines) and experimental data (symbols) for the chamber concentration during exposure of male Wistar rats to VC in a closed, recirculated chamber (Data taken from Bolt et al., 1977).

Case Study: Vinyl Chloride

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Figure 19.5 Model predicted (lines) and experimentally determined (symbols) glutathione concentrations (as percentage of control animal levels) 0, 20, and 44 hours following four hour inhalation exposures to VC at concentrations of (top to bottom) 15, 50, 150, 500, and 15 000 mg/m3 (Data taken from Jedrychowski , Sokal, and Chmielnicka, 1985).

The results of this iterative process are illustrated in Figures 19.5 to 19.8. The parameters obtained for the rat were used for the other species with appropriate allometric scaling (e.g., body weight to the −1/4 for the first order rate constants). Parameterization of the P450 metabolism pathways in the human was accomplished as follows: There is no evidence of high capacity, low affinity P450 metabolism for chlorinated ethylenes in the human based on the results of occupational kinetic studies for another chemical, TCE; therefore, VMAX2C in the human was set to zero. The ratio of VMAX1C to KM1 could be estimated by fitting the model to data from closed chamber studies with two human subjects (Buchter et al., 1978), in a manner entirely analogous to the method used for the animal closed chamber analysis. The result of fitting the data on one of the two subjects is shown by the upper curve in Figure 19.9a, and the model prediction using the value estimated from this subject is compared with the data from the second subject in Figure 19.9b. The precision of the estimate of VMAX1C/KM1 can be evaluated by a comparison of the two model runs shown in these figures, for KM1 = 1.0 and KM1 = 0.1. It can be seen that the ratio of VMAX1C/KM1 varies between the two subjects. This variability of CYP2E1 activity in the human is not surprising; several studies have demonstrated a variability of human CYP2E1 activity of roughly an order of magnitude (Reitz, Mendrala, and Guengerich, 1989; Sabadie et al., 1980). Much lower variability is observed in the inbred strains typically used in animal studies; for example, the coefficient of variation (standard deviation divided by the mean) for CYP2E1 activity in rats in one study of rodents was only 14% (Sabadie et al., 1980). The wide variability in human CYP2E1 activity is an

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Glutathione (percent of control)

200

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Figure 19.6 Model predicted (lines) and experimentally determined (symbols) glutathione concentrations (as percentage of control animal levels) immediately following six hour inhalation exposures to VC (Data taken from Watanabe et al., 1976). 10000

Total Amount Metabolized (mg)

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Figure 19.7 Model predicted (lines) and experimentally determined (symbols) total amount metabolized during six hour inhalation exposures to VC (Data taken from Gehring, Watanabe, and Park, 1978).

Case Study: Vinyl Chloride

419

Percent of Metabolism / Dose Expired as CO2

20

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5 CO2P CO2PM 0 0.01

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Figure 19.8 Model predicted (lines) and experimentally determined (symbols) total expired CO2 , as a percentage of total metabolism (upper line and symbols) and as a percentage of dose (lower line and symbols), following oral dosing with VC in corn oil (Data taken from Watanabe and Gehring 1976).

important consideration for estimating the potential difference between average population risk and individual risk in a human cancer risk assessment for materials like VC, whose carcinogenicity depends on metabolic activation. In order to obtain separate estimates of VMAX1C and KM1 in the human, a higher exposure concentration closer to metabolic saturation would be required. Fortunately, cross-species scaling of CYP2E1 between rodents and humans appears to follow allometric expectations for metabolism very closely; that is, the metabolic capacity scales approximately according to body weight raised to the 3/4 power (Andersen et al., 1987a). Support for the application of this principle to VC can be obtained from data on the metabolism of VC in non-human primates (Buchter et al., 1980). Based on data for the dose-dependent metabolic elimination of VC in the rhesus monkey, the maximum capacity for metabolism can be estimated to be about 50 µmol/h/kg. This equates to a VMAX1C (the allometrically scaled constant used in the model) of approximately 4 mg/h for a 1 kg animal, a value which is in the same range as those estimated for the rodents from the closed chamber exposure data. The similarity of VMAX1C in humans and rats is also supported by an in vitro study which found the activity of human microsomes to be 84% of the activity of rat microsomes. Based on these comparisons, the human VMAX1C was set to the primate value and KM1 was calculated using this value of VMAX1C and the ratio of VMAX1C/KM1 obtained from the closed chamber analysis. The ability of the resulting human model to reproduce constant concentration inhalation exposure data (Buchter et al., 1978) is shown in Figures 19.10a and b. From a comparison of the model predictions for KM1 = 1.0 and

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10 KM1=0.1

Chamber Concentration (ppm)

KM1=1.0

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Figure 19.9 Model predictions (lines) and experimental data (symbols) for the chamber concentration during exposure of human subjects to VC in a closed, recirculated chamber (Data taken from Buchter et al., 1978). (a) Subject A – the lines show the model predictions for (top to bottom) KM1 = 1.0 and 0.1; (b) Subject B – the lines show the model predictions for (top to bottom) KM1 = 1.0 and 0.1.

Case Study: Vinyl Chloride

421

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Figure 19.10 Model predictions (lines) and experimental data (symbols) for the exhaled air concentration during and following inhalation exposure of human subjects to a constant concentration of 2.5 ppm VC (Data taken from Buchter et al., 1978). (a) Subject A – the lines show the model predictions for (top to bottom) KM1 = 1.0 and 0.1; (b) Subject B – the lines show the model predictions for (top to bottom) KM1 = 1.0 and 0.1.

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Application of Physiologically Based Pharmacokinetic Modeling

KM1 = 0.1, it can be seen that the reproduction of parent chemical concentrations in a constant concentration inhalation exposure is not a particularly useful test of the accuracy of the metabolism parameters in a PBPK model of a volatile compound. Based on the results of the Monte Carlo Analysis, the discrepancies or agreement between the model and the data are primarily due to details of the physiological description of the individual, such as fat content, ventilation rate, blood/air partition, and so on, rather than rate of metabolism.

19.6

Comparison of Risk Estimates for Human VC Inhalation

The model was used to calculate the pharmacokinetic dose metric for angiosarcoma (RISK) in the most informative of the animal bioassays (Maltoni et al., 1981, 1984; Maltoni and Cotti, 1988; Feron et al., 1981), as well as for human inhalation exposure. These RISK dose metric (milligrams metabolized per liter liver per day assuming the density of the liver is 1 kg/l) were then used to estimate the 95% upper confidence limit (UCL) on the human risk for lifetime exposure to one part per billion (ppb) VC from each of the sets of animal bioassay data. As shown in Table 19.2, the resulting risk estimates for lifetime human exposure to 1 ppb VC, based on the RISK dose metric, range from 1.52 × 10−6 to 15.7 × 10−6 . It should be noted that although the animal studies represent both inhalation and oral exposure, the risk predictions in each case are for human inhalation exposure. There are no consistent differences between risk estimates based on male and female animals, with the female based risks being higher than the male based risks in some studies, and lower in others, but generally agreeing within a factor of two to three. The risk estimates based on inhalation studies with mice (0.5 × 10−6 to 4.3 × 10−6 /ppb) agree very well with those based on inhalation studies with rats (1.46 × 10−6 to 5.94 × 10−6 /ppb), demonstrating the ability of pharmacokinetics to integrate dose-response information across species. The risks estimated from the dietary administration of VC (0.94 × 10−6 to 3.13 × −6 10 /ppb) are also in good agreement with those obtained from the inhalation bioassays, showing good route-to-route correspondence of potency based on the pharmacokinetic dose metric. However, the estimates based on oral gavage of VC in vegetable oil (6.58 × 10−6 to 16.3 × 10−6 /ppb) are about sixfold higher than either dietary or

Table 19.2 Human risk estimates (per million) for lifetime exposure to 1 ppb vinyl chloride in air based on the incidence of liver angiosarcoma in animal bioassays. 95% UCL Risk/million/ppb Animal bioassay study

Males

Females

Maltoni et al. (1981, 1984) – Mouse Inhalation Maltoni et al. (1981, 1984) – Rat Inhalation Feron et al. (1981) – Rat Diet Maltoni et al. (1981, 1984) – Rat Gavage

1.52 5.17 3.05 8.68

3.27 2.24 1.10 15.70

Comparison of Risk Estimates for Human VC Inhalation

423

inhalation exposure. It has previously been noted in studies with chloroform that administration of the chemical in corn oil results in more marked hepatotoxic effects than observed when the same chemical is provided in an aqueous suspension (Bull et al., 1986). Corn oil alone leads to an increase in peroxisomal oxidative enzyme activity in rats (DeAngelo et al., 1989). The toxicity and oxidative environment created in the liver by continual dosing with large volumes of vegetable oil could serve to potentiate the effects of genotoxic carcinogens in the liver. In support of this suggestion, Newberne, Weigert, and Kula (1979) found that incorporation of corn oil into the diet increased the yield of aflatoxin B1 -induced tumors in rats. A similar phenomenon could be responsible for the apparently higher potency of VC when administered by oil gavage compared to incorporation in the diet. 19.6.1

Epidemiological Analysis of Vinyl Chloride Carcinogenicity

In order to evaluate the plausibility of the risks predicted on the basis of the animal data, risk calculations were also performed on the basis of available epidemiological data (Clewell et al., 2001). A comparison of the results of the analyses of the three sets of data, shown in Table 19.3, gives some indication of the consistency of the human results. The lifetime risk of liver cancer per ppb VC exposure estimated from the three studies only ranges over about one order of magnitude: from 0.4 × 10−6 to 4.2 × 10−6 . Moreover, these estimates are in excellent agreement with the estimates based on animal data shown in Table 19.2. The agreement of the pharmacokinetic animal based risk estimates with the pharmacokinetic human based risk estimates provides strong support for the assumption used in this study: that cross-species scaling of lifetime cancer risk can be performed on a direct basis of lifetime average daily dose (without applying a body surface area adjustment) when the risks are based on biologically appropriate dose metrics calculated with a validated PBPK model. The consistency of this conclusion likely depends on the characteristics of the carcinogen, that is, trans-species carcinogens with common target organs across species. The pharmacokinetic cancer risk assessment for vinyl chloride demonstrates all of the attributes of an effective target tissue dose metric. Firstly, the form of the metric (total daily metabolism divided by the volume of the liver) was consistent with the mode of action for the endpoint of concern (liver tumors), which involves DNA adduct formation by a highly reactive chloroethylene epoxide produced from the metabolism of vinyl chloride. Secondly, while the dose-response for liver tumors versus exposure concentration of vinyl chloride is highly nonlinear, with a plateau at several hundred ppm, the dose-response for liver tumors

Table 19.3 Human risk estimates (per million) for lifetime inhalation of 1 ppb vinyl chloride in air based on the incidence of liver angiosarcoma in human epidemiological studies. Epidemiological study

95% UCL Risk/million/ppb

Fox and Collier (1997) Jones et al. (1987) Simonato et al. (1991)

0.71–4.22 0.97–3.60 0.40–0.79

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versus the metabolized-dose metric is essentially linear from 1 to 6000 ppm. Finally, and most impressively, when the potency of vinyl chloride liver carcinogenicity was expressed in terms of the metabolized-dose metric, essentially the same potency was calculated from both inhalation and oral studies in the mouse and rat, as well as from occupational inhalation exposures in the human. While it is rare to find a case where there is such consistency across widely diverse studies, a dose metric which adequately represents the biologically effective dose should generally have lower values under exposure conditions with no effect and higher values for toxic exposures, regardless of differences in exposure scenario, route, or species.

19.7

Conclusion

Many of the issues described in this chapter with regard to the PBPK based approach are equally applicable to the default risk assessment process. For example, the selection of a dose metric which is appropriate for the chemical and toxicity of concern, while more evident in the PBPK based approach, is just as important in the default approach. A case in point is the question of whether concentration or AUC should be used for short-term exposure guidelines (Jarabek, 1995). Unfortunately, with the exception of the RfC dosimetry guidelines (USEPA, 1994), the selection of dose metric is typically described more as a matter of policy than of scientific judgment. In this regard, the recent USEPA cancer guidelines (USEPA, 2005) represent an important departure from previous guidelines, which identified defaults as policy positions and required substantial justification for departure from the default approach. In contrast, defaults under the new cancer guidelines are described as no-information alternatives, the use of which must be defended on the basis of the lack of chemical-specific information to support a more scientifically appropriate approach. PBPK modeling is one of several new technologies that support the incorporation of chemical-specific information in risk assessment (Clewell, Andersen, and Blaauboer, 2008). There is a continuing interest on the part of regulatory agencies concerning the use of PBPK modeling in chemical risk assessment. Yet, while risk assessments using PBPK models have been proposed for a number of chemicals, for both cancer and noncancer endpoints, there are relatively few cases to date of the actual acceptance of PBPK based risk assessments by the agencies. The slow progress of the application of PBPK modeling in risk assessment may be due in part to the lack of a common expectation regarding the necessary elements of a PBPK based approach. The intent of this chapter was to describe the essential elements of a preferred approach for applying PBPK modeling in a chemical risk assessment, whether for cancer or noncancer endpoints. It is hoped that to the extent that PBPK based risk assessments can adhere to a similar protocol, the familiarity of the agencies with the process may increase and its acceptance may be fostered (Clewell, Andersen, and Blaauboer, 2008). Another issue slowing the acceptance of PBPK models in risk assessment is the lack of a clear consensus on the criteria for model evaluation; this issue is currently being discussed at the international level (Loizou et al., 2008). To a large extent, however, the traditional elements of good modeling practice can be straightforwardly applied to the evaluation of PBPK models for use in risk assessment (Clewell and Clewell, 2008).

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Clewell, H.J. and Andersen, M.E. (1994) Physiologically-based pharmacokinetic modeling and bioactivation of xenobiotics. Toxicol. Ind. Health, 10, 1–24. Clewell, H.J. and Andersen, M.E. (1996) Use of physiologically-based pharmacokinetic modeling to investigate individual versus population risk. Toxicology, 111, 315–329. Clewell, H.J. III and Andersen, M.E. (2004) Applying mode-of-action and pharmacokinetic considerations in contemporary cancer risk assessments: An example with trichloroethylene. Crit. Rev. Toxicol., 34 (5), 385–445. Clewell, H.J. and Jarnot, B.M. (1994) Incorporation of pharmacokinetics in non-carcinogenic risk assessment: Example with chloropentafluorobenzene. Risk Anal., 14, 265–276. Clewell, H.J. III, Gentry, P.R., and Gearhart, J.M. (1997a) Investigation of the potential impact of benchmark dose and pharmacokinetic modeling in noncancer risk assessment. J. Toxicol. Environ. Health, 52, 475–515. Clewell, H.J., Andersen, M.E., Wills, R.J., and Latriano, L. (1997b) A physiologically based pharmacokinetic model for retinoic acid and its metabolites. J. Am. Acad. Dermatol., 36, S77–S85. Clewell, H.J., Andersen, H.J., and Blaauboer, B.J. (2008) On the incorporation of chemical-specific information in risk assessment. Toxicology Lett., 180, 100–109. Clewell, H.J., Gentry, P.R., Gearhart, J.M., et al. (1995) Considering pharmacokinetic and mechanistic information in cancer risk assessments for environmental contaminants: examples with vinyl chloride and trichloroethylene. Chemosphere, 31, 2561–2578. Clewell, H.J., Gentry, P.R., Gearhart, J.M., et al. (2001) Comparison of cancer risk estimates for vinyl chloride using animal and human data with a PBPK model. Sci. Total Environ., 274 (1–3), 37–66. Clewell, H.J., Gentry, P.R., Kester, J.E., and Andersen, M.E. (2005) Evaluation of physiologically based pharmacokinetic models in risk assessment: An example with perchloroethylene. Crit. Rev. Toxicol., 35, 413–433. Clewell, R.A. and Clewell, H.J. (2008) Development and Specification of Physiologically Based Pharmacokinetic Models for Use in Risk Assessment. Regul. Toxicol. Pharmacol., 50, 129– 143. Clewell, R.A., Merrill, E.A., Gearhart, J.M., et al. (2007) Perchlorate and radioiodide kinetics across life-stages in the human: Using PBPK models to predict dosimetry and thyroid inhibition and sensitive subpopulations based on developmental stage. J. Toxicol. Environ. Health, Part A, 70 (5), 408–428. Collins, J.M. (1987) Prospective predictions and validations in anticancer therapy, in Drinking Water and Health, vol. 8, National Research Council, Washington, DC. Crump, K.S. (1984a) An improved procedure for low-dose carcinogenic risk assessment from animal data. J. Environ. Pathol. Toxicol., 5, 339–348. Crump, K.S. (1984b) A new method for determining allowable daily intakes. Fundam. Appl. Toxicol., 4, 854–871. Crump, K.S. (1995) Calculation of benchmark doses from continuous data. Risk Anal., 15, 79–89. DeAngelo, A.B., Daniel, F.B., McMillan, L., et al. (1989) Species and strain sensitivity to the induction of peroxisome proliferation by chloroacetic acids. Toxicol. Appl. Pharmacol., 101, 285–298. Dedrick, R.L. (1975) Pharmacokinetic and pharmacodynamic considerations for chronic hemodialysis. Kidney Intl., 7 (Suppl. 2), S7–S15. D’Souza, R.W. and Andersen, M.E. (1988) Physiologically based pharmacokinetic model for vinylidene chloride. Toxicol. Appl. Pharmacol., 95, 230–240. Feron, V.J., Hendriksen, C.F.M., Speek, A.J., et al. (1981) Lifespan oral toxicity study of vinyl chloride in rats. Food Cosmet. Toxicol., 19, 317–333. Fiserova-Bergerova, V. (1975) Biological-mathematical modeling of chronic toxicity. AMRL-TR75-5, Aerospace Medical Research Laboratory, Wright-Patterson Air Force Base, Ohio. Fox, A.J., and Collier, P.F. (1977) Mortality experience of workers exposure to vinyl chloride monomer in the manufacture of polyvinyl chloride in Great Britain. Br. J. Ind. Med., 34, 1–10. Frederick, C.B. (1993) Limiting the uncertainty in risk assessment by the development of physiologically based pharmacokinetic and pharmacodynamic models. Toxicol. Lett., 68, 159–175. Frederick, C.B., Potter, D.W., Chang-Mateu, M.I., and Andersen, M.E. (1992) A physiologically based pharmacokinetic and pharmacodynamic model to describe the oral dosing of rats with ethyl acrylate and its implications for risk assessment. Toxicol. Appl. Pharmacol., 114, 246–260.

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20 Uncertainty, Variability, and Sensitivity Analyses in Simulation Models Sastry S. Isukapalli1 , Martin Spendiff 2 , Panos G. Georgopoulos1 and Kannan Krishnan3 1

Environmental and Occupational Health Sciences Institute (EOHSI), USA Computational Toxicology Section, Health and Safety Laboratory, United Kingdom 3 D´epartement de sant´e environnementale et sant´e au travail, Universit´e de Montr´eal, Canada 2

20.1 Introduction Analysis of environmental and biological systems through simulation models involves the consideration of several uncertainties and variabilities. In the realm of exposure and risk modeling, uncertainties are often present in the estimates of toxicant emissions, fate and transport, contact with contaminants, and uptake of toxicants by individuals and populations. In the realm of biological modeling, uncertainties are present due to limitations in our knowledge of the ADMET (absorption, distribution, metabolism, excretion, and toxicity) processes associated with different toxicants. Together, these uncertainties impact our estimates of corresponding health risks. Likewise, variability or heterogeneity is present across different population groups and also includes spatial and temporal aspects; this can be quantified but cannot be reduced. The implications of uncertainties and variabilities are particularly important in decision making, e.g., in the assessment of several potential regulatory options. A clear distinction must be made between uncertainty and variability, as their treatment has significant policy implications. Insight into specific variabilities and their impact on risk estimates can help in targeting decision making towards a population based Quantitative Modeling in Toxicology
C 2010 John Wiley & Sons, Ltd

Edited by Kannan Krishnan and Melvin E. Andersen

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goal. In contrast, insight into uncertainties and their impacts can help prioritize resources for reducing uncertainty. This distinction has been widely recognized, as demonstrated by the routine use of sensitivity, uncertainty, and variability analyses in human and ecological health risk assessments (USNRC, 2007; IPCS, 2006; Lester, Green, and Linkov, 2007; Barton et al., 2007). Characterizing uncertainties and variabilities by studying how they impact the final simulation outcomes quantifies the confidence in the model results and helps target future studies for the reduction of overall uncertainties. This will also provide an understanding of the important and unimportant assumptions and quantitative reasoning regarding their importance (USEPA, 1997). This chapter focuses on the types of uncertainties and variabilities encountered in simulation models relevant to toxicological risk assessment, differentiation between uncertainty and variability, differentiation of various types of uncertainties, various methods for characterizing them, how they impact the model outputs, and methods for identifying critical uncertainties and variabilities. These are demonstrated through representative examples covering the areas of exposure, dose and toxicokinetic modeling. Guidelines are also presented for applying sensitivity, uncertainty, and variability analyses in simulation modeling.

20.2

Simulation Models in Toxicology and Risk Assessment

Simulation models are convenient and often essential approximations for estimating quantities that cannot be directly measured, such as time-course concentration of contaminants in various organs following an exposure, for reconstructing past exposures or doses from available biomarkers, and for planning purposes for evaluating alternative remediation strategies. These models can also be used as a basis for “hypothesis testing” that examines multiple “what if” questions. Simulation models necessarily use simplified representations of physical systems and processes, due to trade-offs forced between project resources and the level of detail in modeling, due to the model serving “sufficiently well” in spite of some inaccuracies, and due to the convenient reduction of the analysis efforts (Nilsen and Aven, 2003). A critical component of developing and evaluating simulation models is the judicious choice of model assumptions – a highly simplified model would provide quick results that may not be generalizable, whereas an excessively complex model would be data limited for both model evaluation and for routine use. A major reason for using simpler models in lieu of complex, more realistic models involves the problem of parameter identifiability and estimation. For example, physiologically based pharmacokinetic (PBPK) models with multiple compartments may have identifiability problems that can often be addressed via simplifying reparameterization (Chappell and Gunn, 1998; Yates, 2006). In general, the acceptable level of uncertainty in model estimates depends on the intended purpose of the application of the simulation model. For example, in the case of a PBPK model, for a given exposure level, the corresponding internal dose can range between zero (theoretical minimum) and potential dose (theoretical maximum), depending on the degree of knowledge regarding the key pharmacokinetic determinants (e.g., tissue uptake, metabolic and pulmonary clearance, volume of distribution), each of which has its ranges of uncertainty.

Simulation Models in Toxicology and Risk Assessment

431

Figure 20.1 Steps in the development of simulation models for solving a physical problem, and corresponding simplifications employed in this process.

Figure 20.1 shows the major steps involved in defining a conceptual model and implementing it as a numerical simulation model. Once a model is developed, the next stages include refinement, parameter estimation, and determination of the model’s suitability for specific applications. In addition to underlying randomness of a system and variability in the components of a system, uncertainties in simulation models can arise during various stages of model development.

20.2.1

Integrated Simulation Models

In recent years, the focus of environmental risk analysis performed by both the research community and regulatory agencies has been shifting from (a) single contaminant and pathway analysis, to (b) multiple contaminants and pathway analysis, to (c) integrated systems analysis (Whelan et al., 2001; NUREG, 2002; Ramaswami, Milford, and Small, 2005; Georgopoulos, 2008). Furthermore, the focus has also shifted from deterministic to probabilistic analysis, focusing on characterizing both variability and uncertainty analyses in risk assessment (USNRC, 2007; IPCS, 2006; Drouin et al., 2007). Thus, the state-of-the-science in exposure and risk modeling has been gradually moving from a deterministic “standard reference individual” to studying the general population and susceptible populations (Price and Chaisson, 2005; Georgopoulos et al., 2005, 2008).

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Risk assessments in the past have used highly simplified models mainly due to limitations of available datasets and computational power. Advances in available databases for environmental releases, environmental concentrations, human activity patterns, and so on, provide information necessary for performing improved modeling analysis. Furthermore, advances in computer technology, including inexpensive cluster computing, have made it feasible to perform large scale applications of integrated models (Byun and Ching, 1999; Georgopoulos and Lioy, 2006; Babendreier and Castleton, 2005; Marin, Guvanasen, and Saleem, 2003). The state-of-the art and next generation modeling applications can thus take advantage of elaborate modeling components to describe, in a consistent manner, underlying environmental fate and transport processes in multiple media, human activity patterns, exposures, and dose-response relationships. Uncertainty analysis for integrated models, however, is substantially more complex than for single models (Babendreier and Castleton, 2005; van Asselt and Rotmans, 2002; Oughton et al., 2008). 20.2.2

Tiered Approach for Uncertainty Analysis of Simulation Models

Uncertainties in exposure and risk assessment can be addressed using four tiers of analyses (IPCS, 2006; USEPA, 1999) and this procedure can be generalized to other simulation models used in quantitative risk assessment. Traditionally, when uncertainties are not explicitly characterized, a safety factor (e.g., a typical value of 10, or another type of uncertainty factor) is used for characterizing upper bounds of exposures or risks (Stedeford et al., 2007); this is considered as a Tier 0 analysis. A Tier 1 analysis involves conducting uncertainty analysis in a local manner: a point estimate of risk assessment followed by local sensitivity analysis. A Tier 2 analysis involves probabilistic characterization of uncertainties and global sensitivity analysis. Tier 3 involves separate characterization of uncertainties and variabilities using techniques such as two-dimensional Monte Carlo methods, which are discussed in the following sections.

20.3 Origins and Types of Uncertainties in Exposure, Dose, and Risk Assessment Uncertainties in exposure, dose, and risk assessment models can be broadly classified as natural uncertainty or variability, model uncertainty, and data/parametric uncertainty, depending on their origins and on how they are addressed (Isukapalli and Georgopoulos, 2001). 20.3.1

Natural Uncertainty and Variability

These are often encountered in exposure, dose, and risk assessment models because there is a degree of unavoidable randomness or variability in the processes governing exposures, toxicokinetics, and toxicodynamics. As a practical matter, even quantities that are precisely measurable are often modeled as “random” or “variable” quantities due to cost and effort involved with continuous and precise measurement. Examples of cases where inherent randomness is important include stochastic fate and transport processes (e.g., atmospheric

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turbulence and micro-mixing) that affect levels of toxicants in different media. Examples where variability is important include those in human activity patterns (that affect exposures and intakes), physiological attributes, genetic susceptibility, age/gender variation, and medical conditions. In simulation models, such heterogeneity can be characterized through frequency distributions spanning the dimensions of relevant model parameters. In recent applications of comprehensive exposure models, focus has mainly been on studying population variability in exposures and doses (e.g., estimating the “highly exposed” subpopulation). This involves estimating frequency distributions of exposures by considering variability in population activities, physiological attributes, socioeconomic factors, etc. (Isukapalli, Lioy, and Georgopoulos, 2008; Georgopoulos et al., 2005, 2008). Even when there is no uncertainty in the model parameters considered, population based modeling is applicable only for estimating population distributions of exposures and doses (i.e., it is not applicable for estimating exposures and doses for a specific individual). This has also been referred to as Type A uncertainty (Hoffman and Hammonds, 1994).

20.3.2

Model Uncertainty

Uncertainty in simulation models can arise due to the choices made regarding the logical structure and detail of the model, the computational approach, and the model resolution, as shown in Figure 20.1. Model uncertainty is significant when alternative sets of assumptions and approximations used for developing a model can result in significantly different conclusions. For example, different types of PBPK models can be developed depending on the choice of compartment lumping, assumptions regarding mixing within a compartment (flow limited or diffusion limited), and assumptions regarding transport of the toxicant within a compartment. If representation of uncertainty itself is regarded as part of the model, model uncertainty manifests itself in multiple forms, including inaccurate probability distributions or distribution parameters for inputs/parameters and omission of correlations among inputs/parameters (Nilsen and Aven, 2003; Sander, Bergback, and Oberg, 2006). Uncertainties also arise when models that are developed using assumptions and data appropriate for one set of variables are applied to other, substantially different scenarios (e.g., interspecies extrapolation and high dose to low dose extrapolation). Application of simulation models sometimes requires a trade-off between the computation time (hence cost) and prediction accuracy, thus resulting in uncertainties; this is often manifested in terms of a varying spatial and/or temporal resolution of the model. Another type of model uncertainty arises because the state-of-the-art has not evolved to the point where the real system can be modeled defensibly, or due to factors that have not been identified; this is referred to as completeness uncertainty (Reinert and Apostolakis, 2006). In general, model uncertainties can be reduced through improved understanding of the system being studied and by refining the model. The impact of model uncertainties on output metrics can be generally addressed through several methods (Reinert and Apostolakis, 2006; Barton et al., 2007; Moschandreas and Karuchit, 2002; Linkov and Burmistrov, 2003), including the “adjustment factor approach” along with the application of the best available model, or by assigning degrees of confidence in each of model, and weighting the simulation model outputs accordingly (Zio and Apostolakis, 1996; Nilsen and Aven, 2003).

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Uncertainty, Variability, and Sensitivity Analyses in Simulation Models

Data and Parametric Uncertainty

Uncertainty in simulation models can arise due to incomplete knowledge regarding the values of model parameters or input data (USNRC, 2007). Specifically, they can arise from a variety of sources: random errors due to limitations in the precision and accuracy of measurements, systematic biases, assumptions used to infer an actual quantity of interest from observed readings of a “surrogate” or “proxy” variable, and non-representativeness of data supporting the parameters. Parametric uncertainties can also arise from uncertainties in measurement data used for model evaluation; and can also result when model parameters are estimated from available data using deterministic or stochastic parameter estimation techniques (Moles, Mendes, and Banga, 2003). Data and parameter uncertainty can be reduced mainly by gathering more data (either direct or supporting data). The impact of data and parameter uncertainties on output metrics is typically addressed by “propagating” these uncertainties through the model and identifying significant contributors to overall uncertainty (Isukapalli and Georgopoulos, 2001).

20.3.4

Techniques for Representing Uncertainties

This chapter focuses on characterizing and propagating data/parametric uncertainties and variability and provides guidelines for conducting uncertainty and variability analyses. Overview summaries of different techniques for representing methods and applications of uncertainty analysis in risk assessment have been presented in the literature (Oberg and Bergback, 2005; Lester, Green, and Linkov, 2007; Ionescu-Bujor and Cacuci, 2004; Cacuci and Ionescu-Bujor, 2004; Dorne, Walton, and Renwick, 2005; Isukapalli and Georgopoulos, 2001), and are briefly summarized here. Interval analysis is an appropriate choice when only rough estimates of “bounds” on uncertain parameters are available (i.e., “unknown but bounded”), which happens when studies report only a range for parameters without specifying a distribution (Hickey, Ju, and Van Emden, 2001; Granvilliers, Cruz, and Barahona, 2004). This approach involves estimating the bounds in model outputs of interest based on corresponding bounds in the inputs and model parameters. Several computational toolboxes exist for interval arithmetic Jaulin, 2001; http://www.cs.utep.edu/interval-comp/intsoft.html). The main limitation of this technique is that all the uncertainties are forced into one arithmetic interval and no further insight (e.g., into high percentiles) can be obtained. Furthermore, application of interval arithmetic requires judicious choice of the ordering of equations because of the problem of “overestimation” (e.g., if A = [−1 1] and B = [−1 1], then depending on how the problem is formulated, the answer to A − B can range from [−2 2] to simply 0). Fuzzy Theory facilitates uncertainty analysis of systems where uncertainty arises due to vagueness or “fuzziness” in system attributes rather than due to randomness alone (e.g., when qualitative information is used in modeling). This extends conventional logic to handle “degrees of truth” and maps specific variables from a discrete set to a continuous form. Classical set theory has a “crisp” definition as to whether an element is a member of a set or not. However, certain attributes of systems cannot be ascribed to one set or another. For example, an attribute of a system can be specified as either “low” or “high.” In such a case, uncertainty arises out of vagueness involved in the definition of that attribute. Classical set theory allows for either one or the other value. On the other hand, fuzzy theory allows for a

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gradual degree of membership. This approach was introduced by Zadeh (Zadeh, Klir, and Yuan, 1996; Zadeh, 1965) and has seen some renewed interest in PBPK modeling recently (Seng, Nestorov, and Vicini, 2007; Gueorguieva, Nestorov, and Rowland, 2004), especially as a means to translate between fuzzy logic and probabilistic analysis. Probabilistic Analysis is the most widely used method for characterizing uncertainty in physical systems, especially for estimating the probability distributions of uncertain parameters; this is described in detail here. Other approaches for uncertainty representation include fuzzy measure theory (Wang and Klir, 1992) and fuzzy rough set theory (Klir and Yuan, 1995), possibility theory (Wolkenhauer, 1998), belief measures (Gordon and Shortliffe, 1984), etc. (see, e.g., Halpern, 2003; Parsons, 2001; Buchanan and Shortliffe, 1984).

20.4 Major Steps in Uncertainty Analysis of Simulation Models The major steps in studying data/parametric uncertainty in simulation models include: (a) characterization of uncertainties in model inputs and parameter through available data, expert judgment, or assumptions (input/parameter uncertainty characterization), (b) estimation of the uncertainty in model outputs resulting from the uncertainty in model inputs and model parameters (uncertainty propagation), and (c) identifying important uncertainties that contribute the most to output uncertainties (combined sensitivity/uncertainty analysis or global sensitivity analysis). Related steps include characterization of uncertainties associated with different model structures and model formulations (model uncertainty), and uncertainties arising due to limitations in evaluation data (evaluation data uncertainty). Uncertainty reduction follows uncertainty and sensitivity analysis; it involves incorporation of new data and refinement of models (model-data fusion), using techniques such as Bayesian Markov Chain Monte Carlo methods (Gamerman and Lopes, 2006; Gelman, 2004; Balakrishnan et al., 2003).

20.4.1

Characterization of Input/Parameter Distributions

As described earlier, model inputs and parameters may encompass uncertainty and variability, which can be represented through frequency or probability distributions. These can be developed through available information in the literature, Bayesian parameter estimation from available data, or by using standard distributions such as uniform, normal, lognormal, distributions based on expert opinion (Morgan, Henrion, and Small, 1990; Finley et al., 1994; Clemen and Winkler, 1999; USEPA, 1997) and subsequent distribution fitting. When simulation models are linked in a pipeline manner, results from uncertainty analysis of an upstream model lend themselves as inputs to other models (e.g., outputs of exposure models are input to PBPK models). Fitting of distributions from available data through standard tools is often a primary means for characterizing input/parameter uncertainty. Several toolboxes are available for identifying not only the best distribution to represent a dataset or a variable, but also for

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estimating the parameters of the distribution (Mathworks, 2008; Vose, 2008; Cousineau, Brown, and Heathcote 2004). This process includes selecting candidate distributions, obtaining best fit with the data for each distribution parameter estimation technique, and selecting the best distribution from those. Sometimes, when data cannot be adequately described using a standard distribution, various multimodal distributions can be used through a “mixture distribution” (Everitt and Hand, 1981; Zheng and Frey, 2004). A majority of sensitivity/uncertainty analysis methods can only be applied directly when the inputs are independent. When input variables are correlated (i.e., multiple variables are jointly distributed, for example, in the case of fractional tissue volumes), these can be represented as functions of independent random variables using standard transformation techniques (Devroye, 1986; Isukapalli and Georgopoulos, 2001). The USEPA guidelines document on Monte Carlo methods (USEPA, 1997) presents several questions whose answers help in selecting probability distributions for model parameters. 20.4.2

Uncertainty Propagation

Once the uncertainties in model inputs are characterized through probability distributions, the next step is “propagation” of these uncertainties as shown in Figure 20.2. Except for very simple models, analytical representations of output uncertainties are not possible. The most common way for propagating uncertainties is through traditional Monte Carlo techniques, where the input/parameter values are sampled from their respective distributions, the simulation model is run for each such combination, and model outputs are statistically analyzed. Some improvements in the performance of the uncertainty propagation can be achieved by using efficient sampling techniques, such as the Latin Hypercube Sampling (Helton and Davis, 2003; Rubinstein, 1981). More recent advances in efficient sampling techniques include sequence generators based on methods of Sobol (Bratley and Fox, 1988), of Halton (1960), and of Faure (Kocis and Whiten, 1997). These efficient sampling methods can cover the space of the input distributions in a more “representative” fashion using a smaller number of samples, as shown in Figure 20.3. Efficient sampling is critical when the cost of model runs is high or when a limited number of model simulations is performed. For example, in a two-stage Monte Carlo analysis, the number of variability simulations

Figure 20.2 Uncertainty propagation in a single model. Several sampling techniques and response-surface based methods can be used to estimate the overall uncertainty in model outputs based on uncertainties in model inputs.

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within each uncertainty simulation is set to about 100 to 200 in order to keep the total number of simulations manageable (about 10,000 to 20,000). Once the model simulations are performed, the model outputs corresponding to different sampling points can then be aggregated to obtain relationships between uncertainties in inputs and outputs. Subsequent analysis can use statistical regression of these samples. Sampling of discrete values or records from a dataset is common in population exposure application. The best example is that of activity pattern sampling which cannot be specified as a probability distribution. Instead, for each iteration of a model run, to generate an activity pattern and corresponding microenvironmental location information, a corresponding record is picked from a database, such as the Consolidated Human Activity Database (CHAD) (McCurdy et al., 2000), and the exposure model is run using the corresponding time-dependent activity and location information.

20.4.3

Separate Characterization of Uncertainty and Variability

Separate characterization of uncertainty and variability is important for population exposure modeling. Uncertainty and variability can be characterized separately through the application of “two-stage” or nested Monte Carlo methods (Cohen, Lampson, and Bowers, 1996; Simon, 1999; Frey and Rhodes, 1996). In this approach, each uncertainty simulation consists of a set of Monte Carlo runs that address variability. In the context of exposure modeling, this is typically accomplished as described below (Xue et al., 2006). For each uncertainty simulation, the parameters for distributions for describing population variability are sampled from their corresponding uncertainty distributions. Subsequently, for each variability run, samples are generated from the distributions specified by the parameters in the uncertainty simulation. The uncertainty and variability simulations are tracked separately, so that they can be characterized separately. For each uncertainty simulation, a cumulative distribution function (cdf) can be developed to characterize the

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Figure 20.4 Uncertainty and variability characterization in population exposure modeling by considering “virtual individuals” that statistically represent real individuals. Performing nested Monte Carlo simulations for characterizing uncertainty and variability can be computationally very demanding.

variability. Aggregation over the different uncertainty runs provides a “range of confidence” in the distributions describing the population variability. These steps are shown in detail in Figure 20.4. This approach allows identification of population subgroups or conditions that are highly susceptible by focusing on a specific region (such as the 95th percentile). Likewise, it is possible to investigate the combination of factors that produce such a high output and approaches can be studied to mitigate those factors.

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20.5 Sensitivity and Sensitivity/Uncertainty Analysis The term “sensitivity” refers to the rate of change in the output of a model with respect to changes in model inputs. In a broader sense, sensitivity can refer to how conclusions may change if models, data, or assessment assumptions are changed (USEPA, 1997). Sensitivity Analysis (SA) is the quantitative study of sensitivity and is important for evaluating the applicability of the model, determining parameters for which it is important to have more accurate values, and understanding the behavior of the system being modeled. The choice of a sensitivity analysis method depends to a great extent on the sensitivity measure employed, the desired accuracy in the estimates of the sensitivity measure, and the computational cost involved (Isukapalli and Georgopoulos, 2001). 20.5.1

Screening Level Sensitivity Analysis

To develop a broad picture of which parameters should be included in detailed sensitivity analyses, a screening level variation of parameters or model formulation is useful. In this approach, the model can be run by varying one parameter at a time or for changes in model structure (e.g., in model resolution or selecting one model from a set of alternative models). Using this analysis, estimates of extrema in model outputs can be obtained, which can provide value in risk assessment applications. When the range of variation in parameters is small, simulations using perturbations around a baseline value can provide information on “local sensitivity.” 20.5.2

Local Sensitivity Analysis

In order to estimate how a model behaves within a small range of parameter values and which parameters contribute most to the sensitivity, gradient based local sensitivity analysis can be used. This method estimates model sensitivity to input and parameter variation in the vicinity of a sample point. A typical local measure of sensitivity of a model output yi with respect to a model input xj is the normalized gradient given by
 x j ∂ yi n (20.1) Si j = yi ∂ x j This approach can be useful for obtaining a snapshot of how the model behaves around the baseline or describing general model behavior if the model is linear. When normalized sensitivity of a model output with respect to an input is large, care must be exercised in making decisions based on that output. In some cases, this can even shed focus on the validity of some underlying assumptions. The local sensitivity can be estimated numerically through systematic perturbation in parameters around a baseline value and using central differences using the equation: ∂ yi = ∂x j y j (x1 , x2 , . . . , x j + ∆x j , x j+1 , . . . , xn ) − y j (x1 , x2 , . . . , x j − ∆x j , x j+1 , . . . , xn ) 2∆x j (20.2)

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For a small number of parameters and few baseline points of interest, this approach is computationally inexpensive. However, the results may vary significantly depending on the choice of ∆x j – a very low value can result in errors due to numerical machine precision issues, while a higher value can result in approximations when the model is nonlinear at the baseline. Other techniques for assessing local sensitivity include Automatic Differentiation (Isukapalli, Roy, and Georgopoulos, 2000; Bischof et al., 1996), symbolic differentiation (Sandu, Daescu, and Carmichael, 2003), and the decoupled direct method (Dunker, 1984). If the model is nonlinear, gradient based methods may not be able to capture the impact of an input on an output of interest, since different sensitivity patterns occur in different regions of “input/parameter space” or “input/parameter domain.” Thus, local sensitivity analysis must be performed at a large set of points in the parameter domain (including different combinations of parameter inputs) in order to assess whether an input/parameter xi is more important than an input/parameter xj. For nonlinear models, local methods can only be used to rank the parameters in order of importance for the single set of input values on which the analysis was performed. A global first-order index considers the effect of varying a single parameter for all possible parameter sets. A global total-order index considers the effect of varying a single parameter both individually and in conjunction with all combinations of parameters for all possible parameter sets. An SA that does not consider interactions between input parameters implicitly assumes that the effect of varying two parameters simultaneously is given by the sum of their individual sensitivities. This assumption holds for linear models, but is not valid for PBPK models that incorporate nonlinear expressions (for example, to represent rates of metabolism). The importance of interactions in nonlinear models is illustrated by the surface in Figure 20.5 where, the metabolic clearance rate of a compound is described as a function of K M and V max . An analysis that only considered first-order effects would predict

Figure 20.5 Importance of studying global sensitivity: shown is a plot of surface describing the clearance rate predicted by the Michaelis–Menten equation for kinetics at low substrate concentrations. The slopes of the arrows at A and B represent the local sensitivity coefficients about the points (A): Vmax = 10, KM =1 and (B) Vmax = 2, KM =5. Extrapolating the results from a local sensitivity analysis at Point A to infer model behavior at Point B will lead to erroneous results.

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that a perturbation from point B to point A would result in a change in clearance equal to the sum of changes in clearance given by perturbing B in the of K M and V max directions individually. By ignoring interactions a clearance rate of 3.9 is predicted, rather than the true value of 9.9. The local analysis is only applicable within a small “distance” from the point in the “parameter space” at which the analysis was performed. When a local analysis is carried out with high concentrations of the modeled compound, the analysis may wrongly identify that K M is non-significant – that is, a Type II error (Kriebel et al., 2001). When the analysis is conducted at low concentrations, there is a chance of Type I error if the application of the model is intended for high concentration scenarios.

20.6 Global Sensitivity Analysis To study the system behavior over the entire range of parameter variation, often taking the uncertainty in the parameter estimates into account, a global/domain-wide sensitivity analysis is required; this is known as “global sensitivity analysis” (GSA). However, it must be noted that the results from GSA are not applicable when the distributions of underlying input/parameters change significantly. A wide range of global sensitivity analysis techniques and applications are presented in the literature (Saltelli, 2008; Saltelli, Chan, and Scott, 2000). Sensitivity and uncertainty need to be considered together when studying simulation models. A limitation of typical applications of sensitivity analyses is that the analysis does not require one to assess how likely it is that specific values of the parameters will actually occur (van der Sluijs et al., 2004). A parameter may have large uncertainty, but the output may not be sensitive to the parameter. Likewise, a parameter may have small uncertainty but the output may be highly sensitive to the parameter. The collective impact of uncertainty and sensitivity may also depend on operating conditions and other factors. Figure 20.6 shows the impact of uncertainty in Km on the rate of metabolism for high substrate concentration (five relative units): the impact of low uncertainty in Km results in lower uncertainty in the rate of metabolism (RM; left region, dark gray plot), while a higher uncertainty in Km results in higher uncertainty in RM (right region; light gray plot). Figure 20.7 shows results from similar analysis at low substrate concentration (0.5 relative units). The impact of uncertainties in Km on rate of metabolism is completely reversed (i.e., lower uncertainty in Km results in higher uncertainty in RM whereas higher uncertainty in Km results in lower uncertainty in RM) and the outcomes are not intuitive, thus highlighting the need for combined sensitivity and uncertainty analysis. Techniques for global SA include regression of Monte Carlo or model simulation runs based on efficient sampling (Cullen and Frey, 1999), High Dimensional Model Representation (HDMR) techniques (Li et al., 2001; Rabitz and Alis, 1999), Fourier Amplitude Sensitivity Test (FAST) (McRae, Tilden, and Seinfeld, 1982), Extended FAST method (Saltelli, Tarantola, and Chan, 1999), the method of Sobol (Sobol, 2001), Bayesian Analysis (Jonsson et al., 2007), and Probability Bounds Analysis (Ferson and Tucker, 2006; Nong and Krishnan, 2007). Techniques used for PBPK models need to be numerically efficient, able to deal with non-monotonic output and differential forms. Most of these sensitivity

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Figure 20.6 Combined impact of sensitivity and uncertainty on uncertainty in estimated rate of metabolism for high substrate concentration (five relative units). Intuitively, lower uncertainty in Km results in lower uncertainty in rate of metabolism (RM) [dark gray plot], while higher uncertainty in Km results in higher uncertainty in RM [light gray plot].

analysis methods satisfy these criteria and allow for variance decomposition and estimation of main and interaction effects (Saltelli and Bolado, 1998). Generally, PBPK models have well in excess of 20 input parameters, making an exhaustive quantitative, global method computationally expensive. One solution is to use a global screening method that is computationally less expensive, such as the Morris’ Test (Morris, 1991) described below, in order to determine the most influential parameters and then to run a global quantitative method on only those parameters. This appears to be reasonable since the influence of parameters on output is generally observed to follow a Pareto-like distribution with few parameters accounting for most of the variance. Morris’s Test provides a “one-at-a-time” (OAT) design for screening model inputs that do not have significant impact of model outputs with each factor assumed to be uniformly distributed in [0 1] and later transformed to their respective distributions. For a model with n inputs, this method involves statistical analysis of a set of r trajectories, each containing n + 1 points. Efficient design of these trajectories for better representation of the input space has also been proposed (Campolongo, Cariboni, and Saltelli, 2007). However, the

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Figure 20.7 Combined sensitivity and uncertainty analysis for low substrate concentration (0.5 relative units). In contrast with results in Figure 20.6, lower uncertainty in Km results in higher uncertainty in rate of metabolism (RM) [dark gray plot], whereas higher uncertainty in Km results in lower uncertainty in RM [light gray plot].

number of model simulations is higher than efficient factorial design based techniques, which can be used in conjunction with Morris’s Test (Pujol and Corre, 2007). A global first-order index can be viewed as being analogous to generating a population simulation model where each possible combination of inputs and parameters sampled from their respective distributions can be considered as a member of the population. For any given output metric, its overall variation can be compared with the expected value of the metric as one input varies. In essence, this means that if specifying one input causes a change in the expected value of an output metric that is comparable with the variation found over the set of all parameters, it is influential. This process is illustrated in Figure 20.8. The curve on the left shows the distribution of metabolic rate predicted by the Michaelis–Menten equation for a Monte Carlo simulation with Vmax, Km, Conc (concentration), and Pnip (a noninfluential parameter) independently varying between 1 and 1000. The expected value for the metabolism rate, E(rate), is also shown. The curves on the right show the expected rate given a specific value of Vmax, Km, Conc and Pnip. The non-influential parameter, Pnip, has a random correspondence to metabolic rate (and non-influential variance contribution). First-order sensitivities can be obtained by calculating the variance along each of the curves

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Figure 20.8 Example of systematic sensitivity analysis over the domain of interest through independent, random variation of all parameters over their possible range. Insight can be obtained regarding the parameters that are not influential.

and dividing by the variance of the entire dataset. However, this type of exhaustive screening may not be possible for computationally demanding models and methods such as Morris’s Test or other efficient variants can be used for screening. 20.6.1

Surrogate Based Modeling Techniques for Global Sensitivity Analysis

When a simulation model requires significant computer time per simulation, there is a need for computationally efficient methods for uncertainty propagation. Surrogate based modeling aims to represent the original model in terms of an approximation. This can be an approximation of either the deterministic model or the probabilistic model that encompasses the probability distributions of inputs and parameters. Examples include the Stochastic Response Surface Method (SRSM) (Isukapalli, Roy, and Georgopoulos, 2000; Isukapalli, Roy, and Georgopoulos, 1998) and the High Dimensional Model Representation (HDMR) (Li et al., 2002; Wang et al., 2005). In case of the SRSM, the uncertain model inputs are represented using a basis of standard normal distributions, since there is a direct, one-to-one transformation between any two probability distributions (Devroye, 1986; Isukapalli and Georgopoulos, 2001). The outputs are then approximated in terms of orthogonal series expansions of standard random variables with coefficients that can be calculated from a limited number of model runs. The SRSM provides a set of sample points (combinations of different inputs) for running the model. Once the model is run at these points, the model outputs can be used to estimate the coefficients of the orthogonal series expansions. Then a statistically equivalent polynomial approximation of the model outputs is produced; this can be used to estimate statistical properties of the outputs as well as correlations among outputs and among outputs and inputs. One additional advantage of the SRSM is that the coefficients of the

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series expansions provide sensitivity information of model outputs with respect to the inputs. In case of the HDMR method, there are several variants possible. The Cut-HDMR method (Li et al., 2001) aims to reduce a complex model in terms of look-up tables based on a limited number of model simulations. The reduced models are fast models that can be used then to perform Monte Carlo type analyses. The Random-Sampling HDMR method (Wang et al., 2003; Li et al., 2002), on the other hand, relies on a set of random samples of model outputs in order to decompose the variance in terms of individual contributions. Both the SRSM and the HDMR method use orthogonal series expansions that allow for relatively straightforward global sensitivity analyses. The orthogonal expansions can also be considered as “reduced” or “surrogate” models that can be used for subsequent applications when using the original model can be computationally expensive (e.g., for Bayesian Markov Chain Monte Carlo analysis) (Balakrishnan et al., 2003). The number of model simulations required for sampling based sensitivity and uncertainty varies widely. However, for surrogate based modeling, the number of model runs is primarily dependent on factors such as the number of inputs and order of approximation, and so on. In the case of SRSM, for a model with n uncertain inputs, the first-order approximation requires about 2n runs, whereas a second-order approximation requires about n2 runs. Likewise, for the Cut-HDMR, with m cuts for each input, the first-order approximation requires n × m runs, whereas the second-order method requires about n2 × m2 runs. The number of required simulations can be substantially reduced by using additional information, such as local sensitivities in the form of partial derivatives, when such calculations are computationally efficient (Isukapalli and Georgopoulos, 2001; Isukapalli, Roy, and Georgopoulos, 2000); in such a case, each model run can provide n + 1 data points, one for the model output and n for partial derivative of the model output with respect to each of the inputs. Techniques for obtaining partial derivative information using relatively fewer resources include the Automated Differentiation technique (Bischof et al., 1996; Kharche and Forth, 2006; Isukapalli and Georgopoulos, 2001). Even though sampling based methods may appear to be more efficient when dealing with models involving large dimensions (e.g., a 100 parameter model may require about 10,000 runs with a second-order SRSM, which is comparable to the number of runs used in other sampling techniques), it must be noted that sampling in a large number of dimensions may not always be effective. The number of points to adequately sample from a high-dimensional space increases exponentially because the corresponding sampling space becomes “vastly empty” (Tarantola, 2005).

20.6.2

Use of Results from Global Sensitivity and Uncertainty Analyses

The results from a global sensitivity and uncertainty analysis provide quantitative evaluation of how model parameters or inputs influence model outputs, which parameters are important contributors to the variation in outputs, and which parameters can be deemed non-influential. The uncertainties in the non-influential parameters can be neglected (e.g., by setting values of these parameters to a nominal or reference value). By identifying the most sensitive model parameters/inputs, resources can be focused to reduce uncertainty where it is most appropriate. Furthermore, the identification of non-influential parameters

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helps in calibrating other model parameters (without expending resources on estimating the non-influential parameters). Lack of sensitivity of one output with respect to an input implies that the data gathered for that output should not be used for estimating the parameters for the input. Therefore, sensitivity analysis should be performed before estimating model parameters from available data. This is very critical in the case of Bayesian parameter estimation techniques; the performance of the estimation method can be significantly improved by using the most appropriate combination of data for estimating a given set of input parameters or by iteratively estimating appropriate parameters based on available data and sensitivity information. Based on the results of a global sensitivity analysis, a simulation model can be simplified by removing the non-influential parameters (and corresponding detailed description of noninfluential processes) and providing a simpler model that can be subsequently applied in decision making. This is especially important when the removal of some processes makes the model easy to calibrate, easy to specify, or significantly faster to run. However, caution must be exercised in characterizing non-influential inputs through a global sensitivity analysis. This is especially true when the number of such inputs is large and there is significant uncertainty in their estimates (Jonsson et al., 2007). This caution applies to the processes of parameter estimation and model reduction. Combined sensitivity, uncertainty, and variability analysis provides information on susceptible subpopulations, subregions, and specific operating conditions.

20.7 Example Applications 20.7.1

Model Reduction and Parameter Estimation for a PBPK Model

This example uses two previously constructed models for m-xylene (Loizou et al., 1999) and for ethanol (Loizou and Spendiff, 2004) which were merged to study the interactive effects of ethanol and m-xylene co-exposure and to illustrate methodologies that are applicable to model reduction, parameter fitting, and model corroboration. Model reduction for the PBPK model for m-xylene involved the following steps: 1. Identification of non-important parameters using the Morris Test. This reduced the number of parameters to be estimated from 57 to 15. 2. Calculation of total-order effect sensitivity indices for each of the 15 parameters for which parameters needed to be estimated. 3. Visualization of the total effect of each parameter over the timescale of interest. 4. Assigning typical values to parameters (or freezing the parameters) for which the sensitivity is negligible over the entire time range. If the total index for the parameter is not negligible for all times of interest then that parameter has non-negligible impact, since that parameter has a significant impact at some stages of the model, thus its influence on dose metrics cannot be neglected. The statistics in Table 20.1 describe model output from three population simulations. The first simulation (A) involves the 15 most significant parameters identified by the Morris Test and uses 100,000 model runs. The second simulation (B) has 2 parameters fixed (V max,caa , the limiting rate of metabolism for an isoform of hepatic alcohol dehydrogenase, and V max,C2E1 ,

Example Applications

447

Table 20.1 Descriptive statistics for peak venous concentration of m-xylene for different sensitivity analysis applications with (A) 15 most important variables considered, (B) two input parameters fixed (i.e., Vmax,caa , the limiting rate of metabolism for an isoform of hepatic alcohol dehydrogenase, and Vmax,C2E1 , the limiting rate of metabolism for cytochrome P450 2E1) and (C) two influential parameters fixed (i.e., body weight and breathing rate) Statistical metric

Run A

Run B

Run C

Mean Std. Dev. 1st Quartile 3rd Quartile

0.498 0.249 0.314 0.628

0.499 0.251 0.314 0.628

0.488 0.193 0.346 0.602

the limiting rate of metabolism for cytochrome P450 2E1) and uses one tenth of the number of model evaluations. The third run (C) has two influential parameters fixed (body weight and breathing rate) and, like run B, uses 10,000 model evaluations. Table 20.1 suggests that there is no significant difference between the output distributions given by run A and run B, despite the reduced dimensionality and number of model evaluations. Run C clearly has significantly reduced variance as two driving parameters have been omitted from the Monte Carlo analysis. This could give false confidence if the model is used to assess the maximum blood concentrations occurring across a population. Figure 20.9 illustrates the effect of variation of the tissue:blood partition coefficient (Pka) for the skin on the predicted amount of m-xylene in the liver. Clearly, in the conditions of the model application, the skin:blood partition coefficient has no discernable influence on the amount of m-xylene in the liver. Therefore, parameters such as this can be set to

8

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6

4

2

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30

Figure 20.9 Amount of xylene in the liver (Aliver) with the tissue:blood partition coefficient for the skin removed (set to unity). Symbols and solid line represent model output.

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their nominal values, thus speeding up simulations that involve a large number of model evaluations (such as Monte Carlo and Markov Chain Monte Carlo). More importantly, the number of parameters that need to be assigned realistic distributions is reduced. However, care must be exercised in order to avoid extrapolation of such a reduced model to scenarios that are not addressed in the original model (e.g., scenarios involving only dermal exposures, which are highly impacted by the value of the Pka). The next step involves estimation of parameters whose variation can have a non-negligible impact on model outputs; this is often performed by using experimental data (Dobrev et al., 2003). The process of screening out unimportant parameters is often critical. For example, an analysis of the statistical properties of fitted estimates of the metabolic constants for a model of carbon tetrachloride has shown that the typical use of PBPK models to derive in vivo metabolic constants can be relatively inefficient, providing estimates that differ 100% from the true value (Smith, Evans, and Davidian, 1998). The following discusses some of the major issues associated with parameter estimation. When estimating multiple parameters from data, it is important to consider system identifiability – that is, that there is a unique set of parameters that explains the data. However, for many complex simulation models, this may not be straightforward. In such cases, a global sensitivity analysis can provide information for fine tuning the parameter estimation process, as discussed in the earlier section on use of results from global sensitivity and uncertainty analyses (Section 20.6.2). Parameter estimation based on optimizing model predictions to match experimental data implicitly assumes that the Model Specification Error (MSE) is insignificant or can be characterized by an unbiased “error term,” and so appears to minimize the disagreement between predictions and data, yielding “improved” estimates for real physical quantities. If MSE is small then the validity of optimization of a subset of parameters hinges on the uncertainty associated with the parameters held fixed and the sensitivity indices for the parameters. When an optimization is performed on a subset A of the input parameters, the errors in other parameters are absorbed into estimates of subset A. This results in errors in the optimized parameters which will compensate for the errors in other parameters. It is important to identify the conditions under which experimental data will be most informative for estimating model parameters. For example, in the estimation of parameters for a PBPK model for ethanol, global sensitivity analysis was performed as shown in Figure 20.10 for identifying important parameters. The results indicate that the contribution to variance in model output is negligible for all time points after two hours. Since this is a global method that considers the contribution of parameters over the entire parameter space, we may conclude that variation of kmin over the entire physiologically-feasible range produces negligible variance in the dose metric after two hours; thus kmin can be assigned a nominal value. However, small errors in the dose metric when an insensitive parameter is being estimated will result in large errors in the parameter values, often resulting in problems of lack of convergence of parameter estimation process. Furthermore, dominant input parameters that are absorbed into a sensitive parameter being estimated will result in large errors. Therefore, datasets with measurements concentrated around the region of maximum sensitivity for the quantity of interest are the most appropriate for the purposes of parameter estimation. The importance of using global sensitivity analyses is illustrated further by Figure 20.11. Since the local and global sensitivity indices are significantly different for each parameter,

Example Applications

First-order sensitivity index for ethanol concentration in the brain

0.6

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Drink Time kMin kMax

0.5

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0.3

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Figure 20.10 Global Sensitivity Analysis of ethanol concentration in the brain. The graph shows the changes in the first-order sensitivity indices for the most important model parameters governing model output variance when brain ethanol concentration versus time is the chosen dose metric. An oral dose of 608 mg kg/1 in a 70 kg white male Caucasian was simulated. The Morris method was used to determine the most influential parameters contributing to model output variance. The most influential parameters were then analyzed using the extended FAST.

local sensitivity indices are not sufficient for drawing inference on the contribution of a parameter to output variance. In the context of population PBPK models, the local analysis can be viewed in terms of a single individual, while the global analysis can be viewed in terms of a population. A parameter that can be relatively important at a local scale (e.g., for an individual) may be significantly less important in determining the variability over the population. 20.7.2

Uncertainty and Variability Analysis of an Integrated Exposure-PBPK Model

This example focuses on uncertainty analysis of an integrated exposure-PBPK model that consists of an indoor air quality model linked with a PBPK model. The indoor air quality model was based on Wilkes (1999) and the PBPK model was based on Roy et al. (1996). The indoor air quality model incorporates location and time-activity pattern information and estimates the exposures to water disinfection byproducts (in this case, chloroform) due to water use (in showers, toilets, and faucets). It has five compartments (living room, kitchen, bedroom, bathroom, and rest-of-house). There are 13 uncertain and variable parameters.

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Uncertainty, Variability, and Sensitivity Analyses in Simulation Models

Figure 20.11 Ratios of the total order global sensitivity index and the local sensitivity measure for peak brain concentration of ethanol in the brain using the FAST. The local and global sensitivity indices are not the same, therefore local sensitivity indices are inadequate for drawing inference on parameters’ contribution to output variance. The low values for some of the ratios mean that a local analysis, which shows that a parameter (such as Ka2max) which is relatively important for an individual, is less important in determining the variability over the population.

The variabilities were described by their respective distributions, predominantly consisting of lognormal distributions, and the uncertainties were described by distributions of the geometric means of the variable parameters. The PBPK model for chloroform addresses the multiroute uptake (inhalation, dermal absorption, and ingestion). The input variables such as contact medium concentrations depend upon the location and activity of the individual. A total of 17 uncertain and variable parameters were considered. As with the case of the indoor air quality model, the uncertainties were described by distributions of the geometric means of the each variable parameter. The modeled scenario involves exposure due to volatilization of household water during routine use; the water is assumed to contain 100 µg/L of chloroform. The household consists of two adults and a child, with representative activity patterns for each person. The model estimates the time profiles of concentrations in various microenvironments and these estimates are provided as inputs to the PBTK model. Two methods were used in this analysis for characterizing uncertainty and variability: (a) a two-stage Monte Carlo analysis using 100 uncertainty simulations, each of which consist of 200 variability runs, and (b) the Stochastic Response Surface Method, which tracks the uncertainty and variability separately, while requiring only one set of simulations to study both the uncertainty and variability. Figure 20.12 shows the distributions characterizing the uncertainty in the median estimates of population doses of chloroform. The model predictions obtained employing SRSM (992 model simulations) were similar to those obtained employing standard Monte Carlo simulation (which required 20,000 runs). The integrated model employed here is a simple numerical model, so running a large number of

Guidance on Application of Sensitivity, Uncertainty, and Variability Analyses Inhaled Dose (50th Percentile)

1

Cummulative Probability [mg]−1

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0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

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0.05

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Figure 20.12 Cumulative distribution functions reflecting the uncertainty in the estimates of median of population variability. The SRSM and Monte Carlo method agree well, with the SRSM requiring a significantly smaller number of model simulations.

simulations is not computationally prohibitive. However, in cases where the computational demands of a model are excessive, efficient methods such as the SRSM provide substantial advantages.

20.8 Guidance on Application of Sensitivity, Uncertainty, and Variability Analyses In general, the acceptable level of uncertainty in model estimates depends on the intended purpose of the application of the simulation model. Depending on the complexity of the model, sometimes trade-offs are made with respect to the level of detail in sensitivity, uncertainty, and variability analyses. Prior to performing sensitivity, uncertainty, and variability analyses, some important questions need to be answered with respect to: (a) how a quantitative analysis of uncertainty and variability will improve the risk assessment and whether the effort involved is justified; (b) what the major sources of variability and uncertainty are, and how variability and uncertainty will be kept separate in the analysis; and (c) how the estimates of uncertainty and variability improve a regulatory decision (USEPA, 1997). Once the expected benefits from reducing uncertainty in estimates and anticipated costs are understood, the decision on the optimal and focused use of limited resources on reducing uncertainty in a simulation model is based on the sensitivity of a decision variable to specific parameters and the cost involved in reducing the uncertainty. For example, a screening level method or semi-quantitative characterization of certain parameters (e.g., high, medium or low hepatic extraction) may be sufficient if that parameter does not significantly contribute to the uncertainty in the output. However, when the decision metric is highly sensitive to a specific model input, detailed sensitivity analysis must be performed taking into account interactions amount various inputs and uncertainties in them.

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Uncertainty, Variability, and Sensitivity Analyses in Simulation Models

Preliminary sensitivity analyses can help in identifying model components and parameters that contribute significantly to uncertainty. This can involve an exploratory analysis by varying different model parameters simultaneously, while fixing a majority of them at typical values. When there are uncertainties in the input distributions or model structure, it is recommended that multiple combinations of options be considered in order to obtain bounds on model outputs. At this stage, only rough estimates of parameter values are needed. This process will help in identifying important factors (including options for model structure) that merit further detailed analysis. Preliminary analyses of identifiability of parameters based on available data can help in assessing data adequacy and in reparameterizing the model as needed for accurate estimation of model parameters. This identifiability analysis can also inform design of new experiments. Uncertainty propagation and global sensitivity analysis then involves the identification of the types of distributions that need to be assigned to uncertain parameters using information on prior parameter estimates, experimental data, and expert opinion. This may also involve simple distribution fitting or comprehensive Bayesian estimation of model parameters. Based on the model complexity, computational requirements, and number of parameters, an appropriate sensitivity/uncertainty analysis technique should be selected at this stage (e.g., brute force sampling versus surrogate based analysis). The choice of global versus local sensitivity analysis is problem dependent. The practice of using local analysis as a surrogate for global analysis in drawing general conclusions on model behavior is common. However, as demonstrated by the examples, it is often not applicable because the global sensitivity indices may not be adequately captured by local analysis, especially for a timevarying nonlinear system. Even when the local and global sensitivity indices are constant across all the time values, the relationships may change significantly when some of the underlying model parameters change (e.g., when the range of exposure concentrations is significantly different from those modeled initially), thus the extrapolation of results from sensitivity and uncertainty analyses is not applicable. One typical pitfall of sensitivity and uncertainty analyses is that a significant amount of effort is expended on characterizing uncertainties in a large number of parameters that may turn out to be unimportant, and that a significant number of simulations explore irrelevant or physically unrealistic parts of the parameter hyper space (van der Sluijs et al., 2004). However, this is a trade-off for complex models where it is not easy to characterize a priori the inputs or parameter ranges that are unimportant. The choice of combined uncertainty and variability analysis versus uncertainty or variability analysis alone depends on the decision metric of interest. For example, when population metrics are needed (e.g., 95th percentile exposures in a population) and uncertainties are not significant, variability analysis using Monte Carlo techniques (or surrogate techniques) is sufficient. However, if there are significant uncertainties in the model parameters, a 2-D Monte Carlo approach is recommended for characterizing the population variability and the corresponding uncertainties in population metrics. In cases where point estimates are needed (e.g., risk assessment for a maximally exposed individual), and significant uncertainties are present in estimates of the model structure or parameters, then only uncertainty analysis needs to be performed. Issues in management and communication of uncertainty are beyond the scope of this chapter. However, several reference documents exist in the literature (IPCS, 2006; USNRC, 2007; USEPA, 1997; USEPA, 1999).

Conclusion

20.9

453

Conclusion

Simulation models in quantitative toxicology allow health risks to be estimated for a given scenario involving fate and transport, exposure, and physiological uptake, distribution, and metabolism of chemicals. Individual components of these models as well as the integrated models are often highly complex. Therefore major simplifications of these models can be over-compensated by some model parameters. The model may be applicable for the given conditions but provide erroneous results when it is applied to different conditions. If used incorrectly, these models may provide spuriously accurate predictions and invalid parameter estimations, and fail to emulate the mechanisms involved in the system under study. Therefore, care must be taken to address uncertainties in the formulation and application of these models. In order to address these issues, modern sensitivity and uncertainty analyses methods should be applied routinely as part of model evaluation and application. Currently, gaining insight into a model often involves the adjustment of model parameters and observation of the predicted changes in output. This useful practice can be supplemented by examining the time-dependent global sensitivities of the chosen dose-metric for dominant parameters. The effects of changing parameters or combinations of parameters can often be easily studied in regions where the effects of interactions are small. The examples presented here show the various techniques that can be used for performing sensitivity and uncertainty analysis. A majority of the modern sensitivity and uncertainty analysis methods are independent of assumptions about the model structure. Furthermore, the analysis methods highlighted here can provide information on overall uncertainties and variability in model outcomes as well as contributions of different inputs to the overall uncertainties, including first-order and interaction effects. The example of a 57 parameter PBPK model was used to highlight how a large set of inputs can be screened with respect to a specific dose metric and subsequent analysis performed on relatively important inputs. In this example, the predicted variability across a population was almost entirely determined (>90%) by a small subset (<10) of the parameters. Such a screening approach is applicable once the dose metric has been established, as this greatly reduces the effort required to perform a population simulation and provides estimates of human variability. However, the simplifications should not be extrapolated to other scenarios or dose metrics directly. The second example focuses on characterization of population exposures and doses in the context of an integrated exposure and dose modeling problem using a microenvironmental model coupled with a PBPK model. Uncertainty and variability in the inputs are separately characterized and propagated in order to obtain the uncertainty and variability in the outputs, along with sensitivity indices. The selection of an uncertainty and sensitivity analysis method greatly depends on the types of uncertainties in the inputs and in the model. However, in practice, trade-offs are made based on the computational demands of the model. Direct, straightforward sampling methods are applicable when the model run time is relatively fast (of the order of seconds to minutes per model simulation), whereas approximate surrogate model based techniques are preferred when the models require significantly longer computational time. Finally, it must be emphasized that there is no truly “global” method for characterizing sensitivities and uncertainties. The net impact of a model input on an output metric depends both on sensitivity of output metric with respect to the input as well as uncertainty in the input, as well as on ranges of other parameters. With time, new information may reduce

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(or sometimes increase) uncertainties in the specific input or related inputs, necessitating subsequent iterations of global sensitivity/uncertainty analyses.

Acknowledgements This work was primarily supported by the USEPA-funded Environmental Bioinformatics and Computational Toxicology Center (ebCTC), Grant # GAD R 832721-010. Additional support was provided by the NIEHS sponsored UMDNJ Center for Environmental Exposures and Disease, Grant #: NIEHS P30ES005022.

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21 Evaluation of Quantitative Models in Toxicology: Progress and Challenges Kannan Krishnan1 and Melvin E. Andersen2 1

D´epartement de sant´e environnementale et sant´e au travail, Universit´e de Montr´eal, Canada 2 The Hamner Institutes for Health Sciences, USA

21.1

Introduction

Quantitative models in toxicology facilitate the computation and characterization of the exposure, pharmacokinetics, and tissue interaction or toxicity, based on interrelationships among critical parameters. These models are developed by deriving the structure and its parameters by fitting to experimental data (e.g., quantitative structure-activity relationships (QSARs)), by using a priori equations and parameters to describe the data (e.g., PBPK models), or sometimes by using a combination of both of these approaches (e.g., physiologically based pharmacokinetic-pharmacodynamic (PBPK-PD) models). A quantitative model may not adequately reproduce the system behavior if one or more of the following situations arise (WHO, 2008): 1. Dependency errors: incorrect or lack of consideration of dependence between parameters or processes. 2. Alternative assumptions: lack of consideration of the alternative scientific assumptions regarding structure or parameters. 3. Model detail: the level of detail or complexity included in the model may not be consistent with the end use or the type of data with which the modeling results are compared. 4. Extrapolation uncertainty: the extent to which the new or test situation diverges from the application domain for which a model was parameterized and trained previously. Quantitative Modeling in Toxicology
C 2010 John Wiley & Sons, Ltd

Edited by Kannan Krishnan and Melvin E. Andersen

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For many modelers and end users, demonstrating that a model can predict accurately the outcome of specific future experiments is just as important as establishing a certain level of confidence that the model with its structure and parameters can reasonably predict the system behavior under untested or inaccessible conditions (Kohn, 1995). Testing the outcome of models is not always easy, particularly when there is a lack of methods or tools to access the tissues for measuring the variables predicted by a model. In some cases, only certain aspects or modules of the model can be verified, whereas other aspects of the model structure and parameters cannot be tested confidently against real-life data at all. In such cases, focused sensitivity and uncertainty analyses (Chapter 20) are likely to be of use in assessing the reliability of a model. Obviously, there is not a single method that is applicable to all modeling situations and questions. When it comes to quantitative models, two types of “validation” (i.e., a process by which reliability of a model is established for a defined purpose (OECD, 2007)) are often talked about: internal validation and external validation. Internal validation refers to the process of assessing the goodness-of-fit and robustness of models, and is relevant to regression models in which the model parameters are estimated from a given dataset. On the other hand, external validation, also referred to as “strong validation” (Leijnse and Hassanizadeh, 1994), is applicable in cases where different datasets are used for model calibration and testing the predictive capability of the model. Semi-external validation, even though not often discussed in the literature, might be a case in which some but not all of the model parameters are based on a calibration dataset. As yet, there are no formal guidelines or guidance on validating quantitative models, but the research and regulatory communities continue to investigate the ways of addressing this issue. In this regard, it is increasingly felt that there should be more concern about evaluating a model rather than about validating a model (Barton et al., 2007). The term “evaluation” has broader implications and it would not only invoke comparison of model simulations with experimental data, but also the assessment of the various aspects of the model, including the conduct of sensitivity/uncertainty/variability analyses for assessing the adequacy of the input parameters and structure. Regardless of the terminology (i.e., validation versus evaluation), the intent is essentially the same, that is, to assess whether the key determinants of the system behavior have been adequately captured by the model and whether the model, with its set of input parameters, can reasonably reproduce the system behavior for a defined set of conditions (Krishnan and Andersen, 2007). For facilitating a proper evaluation of models, it is important for developers to document the various aspects related to model development and evaluation in a transparent, reproducible, and comprehensible manner. The World Health Organization (WHO, 2005) published a list of characteristics of exposure models that should be provided by the model developer and considered by the model user (Table 21.1). This template represents a useful starting point for characterizing and documenting other quantitative models as well, even though the specific aspects of model evaluation are likely to differ among the various models. This chapter presents the progress and challenges associated with the evaluation of quantitative models in toxicology. As will become quickly evident, the approaches for evaluating data based models (e.g., QSAR models) are fairly well developed. However, this is not the case with the biologically based models (e.g., PBPK-PD models).

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Table 21.1 Set of characteristics of a model that should be provided by the model developer and considered by the model user (reprinted with permission from the World Health Organisation. Copyright 2005). General model description r Model name r Full model name r Program version, last update, next expected update, expected update features r Responsible institution(s) r Contact person(s) r Contact address(es) r E-mail(s) r Availability 1. General description of the purpose of the model and its components r What is the intended use of the model? r What are the technical and regulatory requirements of the application (e.g., screening-level assessment, regulatory analysis)? r Which exposure routes (dietary and non-dietary ingestion, inhalation, dermal) and pathways are considered? r What is the scope of the basic model structure: single medium or multimedia, single or multiple chemical analysis? r Outline the framework of the model, including key modules and analyses toolboxes. r What are the important assumptions of the model (default values, etc., not covered in subsequent questions)? 2. Individual or population level analysis (level of aggregation) r Is the model developed for individual, cohort, population or population subgroup assessment? r Which sociodemographic definitions are required: age, gender, socioeconomic status, ethnicity, body weight, life expectancy, and so on? r What are the relevant subject/cohort characteristics of the model – urban, rural, residence, workplace, occupation, building type, product use and other personal habits (e.g., smoking, cooking, etc.) – influencing exposures, and so on? r What is the spatial resolution: grid size, local, regional, national? 3. Modeled time resolution r Is the model intended for real-time exposure assessment: minutes to hourly calculations? r Is the model developed for integrated exposure average: daily, seasonal, annual average or lifetime calculations? r Does the model have the capability to model single event, intermittent event and/or continuous exposures? 4. Applicability to diverse exposure scenarios r What is the model’s applicability for different population groups (e.g., workers/laborers, consumers/users, residents/occupants, bystanders, vulnerable groups, etc.)? r What is the model’s applicability for different agents: phase (liquid/solid/gas; in air, gas/vapor/particles), organic/inorganic, reactivity? r What is the model’s applicability for different sources and activities? r What is the model’s applicability for different types of environments (e.g., residential indoor, workplace, recreational, etc.)? (Continued)

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Table 21.1 (Continued) Model inputs 5. Description of data inputs r Which types of data are needed (measurements, physical and chemical characteristics of the agents, estimates from other models, questionnaires, time–activity data, etc.)? r Which are the formats of data inputs (e.g., point estimates, variation, statistical distributions, original survey data)? r Is the model connected to existing databases? If so, what are the database availabilities? r How does the model treat input data limitations (data uncertainty, sparse data, missing data, non-representative, expert judgements, etc.)? Model processes 6. Modeling tool methodology r Is the model deterministic (physical/mechanistic)? r Does it incorporate probabilistic (stochastic) simulation capabilities? r Is it centrally based on statistical (empirical, e.g., regression analysis based) components? r Does the model incorporate other logics, for example, Bayesian? 7. Model code and platform r What is the programming software? r What are the main model algorithms? r What are the model’s system requirements? 8. Model performance and evaluation summaries r Availability of the model’s quality assurance/quality control (QA/QC) documentation r Model evaluation report(s) r Verification and validation study results r Other references (e.g., peer reviewed publications) Model outputs 9. Description of model outputs r What are the model output formats: tables, figures, histograms and pie charts, distributions (e.g., probability/cumulative density functions)? r What are the model output dimensions: media concentrations, intakes, doses? r Does the model output data uncertainties? r What are the post-processing/export capabilities of outputs? 10. Model sensitivity and uncertainty analysis r Does the model provide identification of key inputs and parameters influencing results? r Does the model output display predicted exposure profiles and associated uncertainties (variability and uncertainty analysis)?

21.2 Evaluation of Data Based Models QSAR models are examples of data based models, for which criteria for evaluating the validity and predictive ability have been fairly well developed. The Organisation for Economic Co-operation and Development (OECD), based on an international workshop of experts held in Setubal (Portugal), defined the following principles for the validation and regulatory use of QSAR models (OECD, 2007): (i) a defined endpoint, (ii) an unambiguous algorithm,

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(iii) a defined domain of applicability, (iv) goodness-of-fit (internal performance) as well as predictivity (external validation), and (v) mechanistic interpretation, if possible. The intent and implementation of these principles in model evaluation are discussed below. 21.2.1

A Defined Endpoint

A clear definition of the purpose, in terms of the endpoint (associated with a specific test method or test guideline) being predicted by a given model is essential. The experimental data and predictions of the endpoint should be characterized as to their magnitude and units of measurement. The characteristic experimental conditions that affect the measurement and, therefore, the prediction should be defined upfront. These specifications may include, but are not limited to, the species, strain and sex, temperature and exposure period (OECD, 2007). 21.2.2

An Unambiguous Algorithm

In the context of validation and evaluation of data based models such as QSARs, it is critically important to ensure transparency and reproducibility of algorithms (i.e., set of equations) that generate the output. In this regard, an explicit description of the equations as well as the definition of input parameters should be provided (OECD, 2007). Ambiguity in the underlying equations would only impede their use in regulatory and research applications. 21.2.3

A Defined Domain of Applicability

The applicability of the QSAR model to the set of chemicals is defined by such characteristics as their physiochemical properties, mechanisms of action, structural fragments, and so on. In essence, the application domain should be defined in terms of both descriptor variables (i.e., input parameters) as well as response variables (OECD, 2007). For other kinds of toxicological models, however, consideration of exposure duration, exposure routes and dose ranges may also be relevant in defining the application realm. Basically, in order to avoid misuse of models for predictive or regulatory purposes, it is important to define the domain of valid application as clearly as possible. 21.2.4

Goodness-of-Fit and Predictivity

For data based models, an evaluation of the model fit is the most fundamental aspect of the assessment. The conventional approach in this regard relates to the consideration of R2 , that is, the explained variance (Box 21.1). The value for a given model would be between 0 and 1, where 1 indicates an excellent model, explaining 100% of the response data (Y), contrary to R2 value of 0 indicating that the model has no explanatory power at all. Wold and Eriksson (1995) described that a high R2 value accompanied with a low residual standard deviation alone would not constitute adequate indicators of model validity. Therefore, a number of alternative approaches need to be considered in this regard. These approaches would facilitate either internal validation or external validation. Contrary to biologically based models, the external validation of QSARs is seen as a useful supplement to the internal validation rather than as a requirement to demonstrate the usefulness of the model.

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Box 21.1: Statistical parameters used in assessing model performance (OECD, 2007) Statistics Definition R2

PRESS

Q2

Equation and terms

(SST − SSRe s ) SSRe g SSRe s = =1− SST SST SST
2 SST = i (yi − y¯ ) = total sum of squares
SSRe s = i (yi − yˆ )2 = residual sum of squares SSRe g =
ˆ − y¯ )2 = sum of squares due to the regression i (y yi = observed dependent variable y¯ = mean value of the dependent variable yˆ = calculated dependent variable 2
 Predictive Residual PRESS = i yi − yi/i Sum of Squares yi = observed response for the i-th object

Coefficient of multiple determination (Multiple correlation coefficient)

R2 =

yˆi/i = response for the i-th object estimated by using a model obtained without using the i-th object 2
 ˆi/i PRESS i yi − y 2 Explained variance Q = 1 − =1−
SST ¯ )2 i (yi − y in prediction SST = total sum of squares yi = observed response for the i-th object yˆi/i = response for the i-th object estimated by using a model obtained without using the i-th object y¯ = average response value of the training set

If the model is not robust to small perturbations in the training set, then it is unlikely to be considered as a useful model for predictive purposes (OECD, 2007). In order to assess robustness and internal performance of the QSARs, a number of approaches are used, including: cross validation, bootstrap resampling and Y scrambling (Diaconis and Efron, 1983; Cramer et al., 1988; Wold and Eriksson, 1995). 21.2.4.1

Cross Validation

Here a subset of data is removed once from the original dataset. The remaining, reduced dataset is then used to develop the model, which is then used to predict the deleted datasets (Efron, 1983; Osten, 1988). The squared differences between the true response and the predicted response for each data point or chemical (left out) are added to the predictive residual sum of squares (PRESS). From the final predictive sum of squares, Q2 and other measures such as standard deviation of error of prediction are derived (Box 21.1) (Cruciani et al., 1992; OECD, 2007).

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A common practice is to perform leave-one out cross validation, in which one compound or data point is removed at a time and the model based on remaining data used to predict the deleted data. Along the same lines, “leave many out” cross validation has also been applied. In this case, the entirety of available data is divided into several blocks (called cancellation blocks), and all compounds belonging to a particular cancellation block are left out for assessing the predictive ability of the model (OECD, 2007). 21.2.4.2

Bootstrap Resampling

This method focuses on randomly selecting samples from the original dataset to produce a training set, which can then be used to construct the model and evaluate with the responses predicted for the test set (Efron and Tibshirani, 1993). In this process, while some chemicals or data may be included more than once, others may not be selected during the process. The model based on the training set is then assessed for its ability to predict the test set. The criteria used include PRESS statistic and Q2 (OECD, 2007). 21.2.4.3

Y-Scrambling

Y-scrambling is an effective method for assessing the robustness of the final model and to verify whether the model is based on chance correlation. Accordingly, this method is relevant in case of a need for assessing whether independent variables are randomly related to the response variables (Lindgren et al., 1996). The implementation of this method in QSAR modeling involves assigning each of the response variables randomly to compounds in the test set, and then the calculation of R2 or Q2 to reflect the quality and predictivity of the resulting model (OECD, 2007). 21.2.5

Mechanistic Interpretation

Even though mechanistic interpretations are not routinely possible with data based models, an attempt should be made where possible. Some data based models choose input parameters based on hypothesis and prior knowledge of the mode of action of chemical(s). In such cases, mechanistic relationship between input and output variables would be fairly evident. However, in other cases where the model structure and parameters are derived by fitting to the data, some interpretation of purported mechanistic basis might be possible a posteriori. In the case of data based models, like biologically based models, mechanistic association between the descriptors used in the model and the endpoint predicted would impart greater confidence for use in predictive purposes within the application domain.

21.3

Evaluation of Biologically Based Models

Quantitative biological models are representations of complex reality, and as such can only be validated for some aspects/modules but not for others due to difficulty in obtaining the relevant experimental measures (e.g., the number of initiated cells dividing at a given time, the amount of reactive metabolite produced per gram tissue, concentration of free chemical exiting an internal organ at a given moment). The primary advantage of the

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biologically based models is that they allow us to make predictions of variables that cannot be easily accessed with the available methodologies or that are impossible to measure in an intact biological system using current technologies. Rather than focusing on the extent to which model’s predictions match with some limited data, the objective should be to assess whether the model is fit for the purpose. The model evaluation in this context then focuses on how reliable and credible the model is for the intended purpose, which is broader than how well does it fit to the limited available data. While this aspect has been investigated for PBPK models, it has not yet been systematically applied to other biologically based models. The lessons learned during PBPK model evaluation efforts are, to a large extent, applicable to other biologically based models, including the cell signaling, tissue interaction and response (pharmacodynamic) models. The evaluation of these models should be conducted then along a broad range, such as: (i) model purpose, (ii) model structure, (iii) mathematical representation, (iv) parameter estimation, (v) computer implementation, (v) predictive capacity, and (vi) specialized analyses (i.e., sensitivity, variability and uncertainty analyses) (Andersen, Clewell, and Frederick, 1995; Clark, Setzer, and Barton, 2004; Chiu et al., 2007; Clewell and Clewell, 2008).

21.3.1

Model Purpose

As with the data based models, defining the endpoint as well as the purpose and capability of a biological model is of prime importance. Biologically based models need to specify the intended “Application domain or capability” to ensure a proper evaluation of the model. For example, if the purpose is to aid in inhalation to oral extrapolation of the kinetics of a chemical, then it demands that certain capabilities and parameters be included in the model (e.g., route-specific rates of absorption and clearance). The goal of a modeling effort also dictates the complexity of the resulting model. A model should not be more complex than necessary, given the intended application or end use. Also it is important to realize that a single model will not have all the capabilities to address the requirement of all end users or risk assessments. For example, a model developed for the adult animal may not be able to predict adequately the kinetics or effects of a chemical in the fetus. Similarly, a model developed for investigation of plausible mechanisms and modes of action may not be sufficiently robust to predict population distributions of tissue dose and adverse response associated with a variety of exposure scenarios, exposure routes, and doses.

21.3.2

Model Structure

The conceptual model structure should be consistent not only with the biology of the species but also with the current state of knowledge about the mechanisms of kinetics and dynamics of a chemical. The model structure may not violate the known biological, biochemical or physicochemical theories. The model structure essentially is a statement of the toxicologist as to how the chemical gets into the body, clears out of the body, and interacts with critical tissue components to lead to the onset and progression of disease/toxicity. As such, the model structure should be an appropriate abstraction of the biological system under study, and consistent with the purpose and complexity associated with the biological system itself.

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A model that does not have a defensible or a reasonable biological basis will lack credibility and would not be a good candidate for predictive purposes or reducing uncertainty related to mandated or empirical approaches. 21.3.3

Mathematical Representation

The mathematical representation of specific processes (e.g., enzyme-mediated metabolism, membrane diffusion, etc.) should be consistent with the quantitative methods based on established theories. When there is significant departure in this regard, it is important to document and justify these changes. Further, it is important to verify that the mathematical representation is consistent with the maintenance of mass balance and blood flow balance within the model. The algebraic and differential equations constituting the model should be verified for errors. Fundamentally, the units on both sides of the equation should be identical. (e.g., mg/h on the right-hand side and left-hand side of the equation). 21.3.4

Parameter Estimation

Parameter identifiability and model over-specification are problems inherent to multiparameter models such as PBPK-PD models. So, it is critical to ensure that the input parameters of biological models correspond to physiological, biochemical and/or physicochemical entities. Further, it is important that the parameters be estimated using in vivo data or validated animal-alternative methods (i.e., in vitro, in silico). When the parameters are scaled on the basis of allometric principles or other basis (e.g., difference in tissue surface areas), justification of the method used should be provided. Similarly, when predictive algorithms or QSARs are used for parameter estimation, they should be within the defined domain of application. Overall, a model with biologically and statistically plausible parameters in the plausible range would provide confidence in the use of a model along with its set of parameters for intended purpose. 21.3.5

Computer Implementation

Assessment of the computer implementation is generally accomplished by reviewing the computer code line by line to ensure that it has the proper syntax and mathematical structure and is free of errors (Clark, Setzer, and Barton, 2004). The computer implementation should also be checked for unit accuracy, mass balance, and blood flow balance. Automatic checks for mass balance and blood flow balance can be built directly into the code for most computer applications. When a graphical user interface is used as a front end to develop and parameterize the model, different approaches to evaluating the model code will be necessary (Chiu et al., 2007). Table 21.2 lists the key aspects of QA/QC process for conducting model code checks (USEPA, 2002; NRC, 2007). 21.3.6

Evaluation of Predictive Capacity

The evaluation of the ability of a PBPK model, with its structure and parameters, to adequately simulate the pharmacokinetics and dose metrics for exposure scenarios of

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Table 21.2 QA/QC checks for model codes. Software code development inspections: Software requirements, software design, or code are examined by an independent person or groups other than the author(s) to detect faults, programming errors, violations of development standards, or other problems. All errors found are recorded at the time of inspection, with later verification that all errors found have been successfully corrected. Software code performance testing: Software used to compute model predictions is tested to assess its performance relative to specific response times, computer processing usage, run time, convergence to solutions, stability of the solution algorithms, the absence of terminal failures, and other quantitative aspects of computer operation. Tests for individual model module: Checks ensure that the computer code for each module is computing module outputs accurately and within any specific time constraints. (Modules are different segments or portions of the model linked together to obtain the final model prediction.) Model framework testing: The full model framework is tested as the ultimate level of integration testing to verify that all project-specific requirements have been implemented as intended. Integration tests: The computational and transfer interfaces between modules need to allow an accurate transfer of information from one module to the next, and ensure that uncertainties in one module are not lost or changed when that information is transferred to the next module. These tests detect unanticipated interactions between modules and track down cause(s) of those interactions. (Integration tests should be designed and applied in a hierarchical way by increasing, as testing proceeds, the number of modules tested and the subsystem complexity.) Regression tests: All testing performed on the original version of the module or linked modules is repeated to detect new “bugs” introduced by changes made in the code to correct a model. Stress testing (of complex models): Stress testing ensures that the maximum load (for example, real-time data acquisition and control systems) does not exceed limits. The stress test should attempt to simulate the maximum input, output, and computational. Load expected during peak usage: The load can be defined quantitatively using criteria such as the frequency of inputs and outputs or the number of computations or disk accesses per unit of time. Acceptance testing: Certain contractually required testing may be needed before the new model or model application is accepted by the client. Specific procedures and the criteria for passing the acceptance test are listed before the testing is conducted. A stress test and a thorough evaluation of the user interface is a recommended part of the acceptance test. Beta testing of the pre-release hardware/software: Persons outside the project group use the software as they would in normal operation and record any anomalies encountered or answer questions provided in a testing protocol by the regulatory program. The users report these observations to the regulatory program or specified developers, who address the problems before release of the final version. Reasonableness checks: These checks involve items like order-of-magnitude, unit, and other checks to ensure that the numbers are in the range of what is expected. Source: USEPA (2002), NRC (2007).

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interest has been conducted using one of the following methods: visual inspection, residual analysis, and statistical tests, as well as discrepancy indices (Chiu et al., 2007). Here the emphasis has been on the “external” validation aspect, even though this is only one of the aspects of model evaluation.

21.3.6.1

Visual Inspection and Residual Analyses

The visual comparison of the simulated data (usually continuous data, represented by solid lines) with experimental values (usually discrete data, represented by symbols) against a common independent variable (e.g., time) is the most frequently used approach to assess the predictive ability of quantitative biological models. The rationale for the use of this rather qualitative approach has been that, the greater the commonality between the simulated and experimental data, the greater the confidence in the model structure and its parameters. The comparison is made not only to infer about the ability of the model to correctly reproduce the whole set of data but also about certain characteristic features of the dataset (peaks, bumps and valleys, saturation of metabolism, etc.). In such cases, the demand on the model is that it be able to adequately reproduce a wide variety of data, rather than provide optimal fit to part of the curve or dataset, using a single set of equations and parameters. Similarly, if the model cannot reproduce the pharmacokinetic profiles with any realistic parameter values, or it can do so only by using values that are inconsistent with other data, then it can reasonably be concluded that the structure is inadequate. Instead of simply visualizing the degree of concordance between experimental data and simulation results, the residuals (i.e., difference between experimental and simulated data) may be examined. The residual analysis can be applied either to the whole model as it is or, in some other cases (as in diagnostic checkup during model building), to some estimated parameters of a tentatively ascertained theoretical model, so as to pinpoint inadequacies (Iyengar and Rao, 1983). The distribution of residuals should be random if the model is adequate. On the other hand, systematic differences between the fitted residuals can often indicate the need for refining the model structure. The visual inspection, supplemented by residual analyses in some cases, has been used frequently for comparing PBPK model simulations with experimental data, pending fuller development of applicable statistical tests and discrepancy indices.

21.3.6.2

Statistical Tests

Statistical tests have not been routinely used for assessing the predictive ability of biologically based models. A wide range of potential statistical tests exists, and the choice of tests depends on the types of data available/generated (Power, 1993). The approaches considered include: correlation/regression, confidence intervals, lack fit F test, t test, and analysis of variance. Correlation coefficients measure the strength of the linear relationship between two variables (i.e., experimental data and model simulations) but its use in model evaluation can be misleading since it indicates only the degree of association. When simple regression of the model simulations and experimental data is computed, the model is considered to be an adequate representation of the real system if the intercept and the slope are close to zero and unity respectively. The regression approach is of limited use for the

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external validation or assessment of the “predictive ability” of biologically based models since values at extremities influence the outcome. The confidence interval approach, on the other hand, involves the comparison of model simulations against experimental data defined with confidence limits or bands. Confidence intervals are constructed for 95% level of probability, for each sampling point. In other words, the simulation value for a given sampling time is compared with the corresponding experimental data with confidence interval estimates. The confidence interval approach may be used in situations where the simulated data can only be compared with a single group of experimental data (e.g., total metabolites excreted at the end of a 24 hour period). Actually, the statistical comparison of the model output with experimental observations is not as easy as it might appear. None of the classical tests (t, Mann–Whitney, two-sample X 2 , two-sample Kolmogrov, etc.) to determine whether the underlying distributions of the two datasets are similar is applicable, since the output processes of almost all real world systems and simulations are non-stationary and autocorrelated (Krishnan and Andersen, 2007). Furthermore, there is a question of whether the use of statistical hypothesis tests is even appropriate. Since the model is only an approximation of the actual system, a null hypothesis that the system and model are the same is clearly false. The more appropriate formulation is: whether or not the differences between the system and the model are significant enough to affect conclusions derived from the model. In this regard, Haddad et al. (1995) indicate that multivariate analysis of variance represents the most appropriate test, with the variance for the simulation data permitting. Alternatively, lack of fit F test represents a useful way of evaluating the adequacy of simulation models because it also permits the consideration of multiple datasets in conducting such an evaluation of model validity. The F statistic in model fitting may be defined as lack of fit: Mean square Pure error mean square

(21.1)

This ratio is compared to the critical value of F at the required degree of confidence and the corresponding degrees of freedom. If the above ratio is greater than F crit , then the model is considered to be inadequate (Iyengar and Rao, 1983).

21.3.6.3

Discrepancy Measures

The discrepancy measures represent an objective manner in which to represent the degree of closeness/discrepancy between model predictions and experimental data. The discrepancy measures are based on a systematic evaluation of the differences between the simulated and experimental data. One approach involves the calculation of the root mean square of the error (representing the difference between the individual simulated and experimental values for each sampling point in a time-course curve), and division by the root mean square of the experimental values (Krishnan, Haddad, and Pelekis, 1995). The resulting numerical values of discrepancy measures for several datasets (each corresponding to an endpoint or study) are then combined on the basis of a weighting proportional to the number of data points contained in the dataset. Such consolidated discrepancy indices

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obtained from several experiments (e.g., exposure scenarios, doses, routes, and species) are then averaged to get an overall index of discrepancy between model predictions and corresponding experimental data (Krishnan, Haddad, and Pelekis, 1995). One caution in using these composite measures with diverse datasets is the requirement to account for the importance of each dataset in providing information about specific model parameters. When there are not adequate data for use in “external” validation, the strategy is to divide the dataset into two parts, one for parameter estimation and the other for model validation, as done in QSAR modeling. Accordingly, leave-one or leave-some out cross validation procedures may be applied, even though there are only limited examples in this regard (Keys et al., 2003; Beliveau et al., 2005).

21.3.7

Assessment of Specialized Analyses

Specialized analyses evaluating the impact of uncertainty, sensitivity and/or variability of model parameters and structure play a more important role in biologically based models than in data based models (Chapter 20). Whereas the uncertainty analysis evaluates the influence of lack of precise knowledge about the numerical value of a parameter or model structure on the model output, variability analysis focuses on changes in model output over the range of parameter values expected for the biological system (Farrar et al., 1989; Portier and Kaplan, 1989; Thomas et al., 1996; Slob, Janssen, and Van Den Hof, 1997). These analyses are conducted in conjunction with sensitivity analysis, that is, evaluation of the effect of a finite change in the value of input parameters on model output (Bois, Zeise, and Tozer, 1990; Clewell, Lee, and Carpenter, 1994). Sensitivity analysis typically aids in the identification of the most critical model parameters, with respect to a given model output (Chapter 20). If the most sensitive parameters of the model are also the most uncertain ones, then focused refinement of parameter estimates should be undertaken. On the contrary, if the most sensitive parameters are least uncertain, then it gives confidence in the use of the model to intended applications.

21.4

Conclusion

The tools and approaches for evaluating the accuracy and reliability of quantitative models are still evolving. The challenges to model evaluation differ somewhat for data based and biologically based models. In the preceding sections, the progress made to-date in evaluating QSARs and PBPK models was summarized. These can serve as a logical starting point for developing strategies of evaluating the confidence and reliability. Whereas model evaluation is more global in sense, validation, as implied commonly, is narrower in its meaning, that is, predictive ability. In order to have confidence in the predictions of a quantitative model, it must (i) reasonably approximate the key processes of the system, without violating scientific theories underlying the processes modeled, (ii) be coded error-free in the form of equations that can be interpreted in terms of system elements, (iii) contain parameter values that are plausible and characteristic for the system, and (iv) reproduce the available empirical data. In this regard, it is important to realize that more than one model may agree with a limited set of data (Oreskes, Shrader-Frechette, and Belitz, 1994). If several models fit the data

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Table 21.3 Elements of external peer review for environmental regulatory models. Model Purpose/Objectives What is the regulatory context in which the model will be used and what broad scientific question is the model intended to answer? What is the model’s application niche? What are the model’s strengths and weaknesses? Major Defining and Limiting Considerations Which processes are characterized by the model? What are the important temporal and spatial scales? What is the level of aggregation? Theoretical Basis for the Model – formulating the basis for problem solution What algorithms are used within the model and how were they derived? What is the method of solution? What are the shortcomings of the modeling approach? Parameter Estimation What methods and data were used for parameter estimation? What methods were used to estimate parameters for which there were no data? What are the boundary conditions and are they appropriate? Data Quality/Quantity Questions related to model design include: What data were used in the design of the model? How can the adequacy of the data be defined taking into account the regulatory objectives of the model? Questions related to model application include: To what extent are these data available and what are the key data gaps? Do additional data need to be collected and for what purpose? Key Assumptions What are the key assumptions? What is the basis for each key assumption and what is the range of possible alternatives? How sensitive is the model toward modifying key assumptions? Model Performance Measures What criteria have been used to assess model performance? Did the databases used in the performance evaluation provide an adequate test of the model? How does the model perform relative to other models in this application niche? Model Documentation and Users Guide Does the documentation cover model applicability and limitations, data input, and interpretation of results? Retrospective Does the model satisfy its intended scientific and regulatory objectives? How robust are the model predictions? How well does the model output quantify the overall uncertainty? Source: USEPA (1994), NRC (2007).

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equally well, then focused experiments may be designed to generate new data that can facilitate the discrimination and identification of the model that most accurately predicts the behavior of the biological system. The biologically based quantitative descriptions, in essence, allow integration of various observations, identification of critical data gaps, and estimation of risk numbers, along with attendant appreciation of areas of significant biological uncertainty. The adequate documentation of the development and evaluation of quantitative models is not only important to impart transparency and credibility but also to facilitate reproducibility such that other modelers can also learn from or review the effort (Clark, Setzer, and Barton, 2004). Useful model documentation would involve the presentation of more than just a diagram of input–output relationships and list of parameters. As indicated in Table 21.1, the list of specifics related to characterization and description of the exposure models identified by WHO (2008) constitutes an excellent template. Accordingly, proper documentation of a quantitative modeling effort should permit an experienced modeler, expert reviewer or an interested end user to reproduce the input–output relationships. In this regard, the datasets and structures that may not have been considered or have been excluded in a modeling effort should be identified along with the rationale. Table 21.3 lists key questions to be considered during peer review of quantitative models (USEPA, 2002, NRC, 2007). A model is only as good as the input parameters. Therefore, accurate parameterization is fundamentally important for constructing useful PBPK, cell signaling, and tissue response models. Effort should be spent to develop parameters that are based on key, sensitive datasets and evaluate whether they are plausible for the biological system investigated. There is increasing concern about the relevance and use of datasets for external validation or assessment of predictive ability of PBPK models. The concern is one of whether we waste some useful data to facilitate their use in testing the predictive ability of the model. In other terms, would it not be more useful to make use of all data to train and parameterize the model and make use of all information contained in available datasets. This debate is particularly relevant when it comes to human data. In this regard, Bayesian analysis using Markov Chain Monte Carlo (MCMC) calculations is increasingly being used to improve the existing parameter estimates based on potentially useful, new information contained in additional datasets (Jonsson and Johanson, 2001, 2002; Bois, 2000a, 2000b). The value and strength of models are not determined by its R2 values but its reliability in retrodiction (i.e., reproducing and explaining what has already been observed), prediction (e.g., forecasting what will happen in a new experiment) and understanding (e.g., how toxicity is manifested in animals or humans) (Rescigno and Beck, 1987). As our ability to quantitatively represent the biological phenomena and key perturbations continues to evolve in conjunction with increased understanding of the biological systems and their components, the future holds great promise for many applications of Quantitative Toxicology. Credible models of dosimetry, tissue interactions, cellular level responses, and tissue response are already on stage. They should gain increasing prominence in toxicology and risk assessment as new approaches are refined and the task of model development joined by a new generation of scientists trained quantitatively in modern biology. These models, especially the PBPK, cell signaling, and tissue response models, are dynamic constructs that reflect the path traveled by the toxicology community, capture the current state of knowledge and facilitate

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more confident predictions of possible future directions in toxicology based on plausible mechanisms and alternative hypotheses.

References Andersen, M.E., Clewell, H.J. III, and Frederick, C.B. (1995) Applying simulation modeling to problems in toxicology and risk assessment – a short perspective. Toxicol. Appl. Pharmacol., 133, 181–187. Barton, H.A., Chiu, W.A., Woodrow, S.R., et al. (2007) Characterizing uncertainty and variability in physiologically based pharmacokinetic models: state of the science and needs for research and implementation. Toxicol. Sci., 99, 395–402. Beliveau, M., Lipscomb, J., Tardif, R., and Krishnan, K. (2005) Quantitative structure–property relationships for interspecies extrapolation of the inhalation pharmacokinetics of organic chemicals. Chem. Res. Toxicol., 18, 475–485. Bois, F.Y. (2000a) Statistical analysis of Clewell et al. PBPK model of trichloroethylene kinetics. Environ. Health Perspect., 108 (Suppl. 2), 307–316. Bois, F.Y. (2000b) Statistical analysis of Fisher et al. PBPK model of trichloroethylene kinetics. Environ. Health Perspect., 108 (Suppl. 2), 275–282. Bois, F.Y., Zeise, L., and Tozer, T.N. (1990) Precision and sensitivity of pharmacokinetic models for cancer risk assessment. Tetrachloroethylene in mice, rats and humans. Toxicol. Appl. Pharmacol., 102, 300–315. Chiu, W.A., Barton, H.A., DeWoskin, R.S., et al. (2007) Evaluation of physiologically based pharmacokinetic models for use in risk assessment. J. Appl. Toxicol., 27, 218–237. Clark, L.H., Setzer, R.W., and Barton, H.A. (2004) Framework for evaluation of physiologically-based pharmacokinetic models for use in safety or risk assessment. Risk Anal., 24, 1697–1717. Clewell, R.A. and Clewell, H.J. III (2008) Development and specification of physiologically based pharmacokinetic models for use in risk assessment. Regul.Toxicol Pharmacol., 50, 129–143. Clewell, H.J. III, Lee, T.S., and Carpenter, R.L. (1994) Sensitivity of physiologically based pharmacokinetic models to variation in model parameters – methylene chloride. Risk Anal., 14, 521–531. Cramer, R.D. III, Bunce, J.D., Patterson, D.E., and Frank, I.E. (1988) Cross Validation, Bootstrapping and Partial Least Squares Compared with Multiple Regression in Conventional QSARs Studies. Quantitative Structure-Activity Relationships, 7, 18–25. Cruciani, G., Baroni, M., Clementi, S. et al. (1992). Predictive ability of regression models. Part I: Standard Deviation of Prediction Errors (SDEP). Journal of Chemometrics, 6, 335–346. Diaconis, P. and Efron, B. (1983) Computer Intensive Methods in Statistics. Scientific American, 248, 96–108. Efron, B. (1983) Estimating the Error Rate of a Prediction Rule: Improvement on Cross-Validation. Journal of American Statistical Association, 78, 316–331. Efron, B. and Tibshirani, R.J. (1993) An Introduction to the Bootstrap, Chapman & Hall, London. Farrar, D., Allen, B., Crump, K., and Shipp, A. (1989) Evaluation of uncertainty in input parameters to pharmacokinetic models and the resulting uncertainty in output. Toxicol. Lett., 49, 371–385. Haddad, S., Gad, S.C., Tardif, R., and Krishnan, K. (1995) Statistical approaches for the validation of physiologically-based pharmacokinetic (PBPK) models. The Toxicologist, 15 (1), 48. Iyengar, S. and Rao, M.S. (1983) Statistical techniques in modeling of complex systems: single versus multiresponse models. IEEE Trans. Syst. Man. Cybernet., 13, 175–189. Jonsson, F. and Johanson, G. (2001) Bayesian estimation of variability in adipose tissue blood flow in man by physiologically based pharmacokinetic modeling of inhalation exposure to toluene. Toxicology, 157, 177–193. Jonsson, F. and Johanson, G. (2002) Physiologically based modeling of the inhalation kinetics of styrene in humans using a bayesian population approach. Toxicol. Appl. Pharmacol., 179, 35–49. Keys, D.A., Bruckner, J.V., Muralidhara, S., and Fisher, J.W. (2003) Tissue dosimetry expansion and cross-validation of rat and mouse physiologically based pharmacokinetic models for trichloroethylene. Toxicol. Sci., 76, 35–50.

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Kohn, M.C. (1995) Achieving credibility in risk assessment models. Toxicol. Lett., 79, 107–114. Krishnan, K. and Andersen, M.E. (2007) Physiologically-based pharmacokinetic and toxicokinetic modeling, in Principles and Methods of Toxicology (ed. A. Wallace Hayes), Taylor and Francis, New York, pp. 232–291. Krishnan, K., Haddad, S., and Pelekis, M. (1995) A simple index for representing the discrepancy between simulations of physiological pharmacokinetic models and experimental data. Toxicol. Ind. Health, 11, 413–422. Leijnse, A. and Hassanizadeh, S.M. (1994) Short communication on model definition and model validation. Adv. Water Resour., 17, 180–184. Lindgren, F., Hansen, B., Karcher, W., et al. (1996). Model validation by permutation tests: Applications to variable selection. Journal of Chemometrics, 10, 421–532. NRC (National Research Council of the National Academies) (2007) Models in Environmental Regulatory Decision Making, The National Academies Press, Washington, DC. OECD (Organisation for Economic Co-operation and Development) (2007) Guidance Document on the Validation of (Quantitative) Structure Activity Relationship [(Q)SAR] Models. OECD Series on Testing & Assessment No 69. ENV/JM/MONO(2007)2. Oreskes, N., Shrader-Frechette, K., and Belitz, K. (1994) Verification, Validation, and Confirmation of Numerical Models in the Earth Sciences. Science, 263, 641–646. Osten, D.W. (1988) Selection of optimal regression models via cross-validation. Journal of Chemometrics, 2, 39–48. Portier, C.J. and Kaplan, N.L. (1989) Variability of safe estimated when using complicated models of carcinogenic processes. A dose study: methylene chloride. Fundam. Appl. Toxicol., 13, 533–544. Power, M. (1993) The predictive validation of ecological and environmental models. Ecol. Model., 68, 33–50. Rescigno, A. and Beck, J.S. (1987) The use and abuse of models. J. Pharmacokinet. Biopharm., 15, 327–344. Slob, W., Janssen, P.H.M. and Van Den Hof, J.M. (1997) Sturctural identifiability of PBPK models: practical consequences for modeling strategies and study designs. Crit. Rev. Toxicol., 27 (2), 261–272. Thomas, R.S., Bigelow, P.L., Keefe, T.J., and Yang, R.S.H. (1996) Variability in biological exposure indices using physiologically based pharmacokinetic modeling and Monte Carlo simulation. Am. Ind. Hyg. Ass. J., 57, 23–32. USEPA (US Environmental Protection Agency) (1994) Guidance for Conducting External Peer Review of Environmental Regulatory Models. EPA 100-B-94-001, US Environmental Protection Agency, Washington, DC. USEPA (US Environmental Protection Agency) (2002) Guideline for quality assurance project plans for modeling. EPA/240R-02-007. Office of Environmental Information, US Environmental Protection Agency, Washington, DC. Available at http://www.epa.gov/QUALITY/qs-docs/g6m-final.pdf (accessed 20 November 2009). WHO (World Health Organization) (2005) Principles of characterizing and applying human exposure models. (IPCS harmonization project document; no. 3), WHO, Geneva, 76 pp. WHO (World Health Organization) (2008) Guidance document on characterizing and communicating uncertainty in exposure assessment. http://www.who.int/ipcs/methods/harmonization/areas/ exposure assessment/en/index.htmlS (accessed 20 November 2009). Wold, S. and Eriksson, L. (1995) Statistical validation of QSAR results, in Chemometric Methods in Molecular Design (ed. H.V.D. Waterbeemd), Wiley-VCH Verlag GmbH, Weinheim, pp. 309–318.

Index

References to figures are given in italic type. References to tables are given in bold type. absorption 25 acceptable daily intake (ADI) 4–5 acceptable level of exposure 372–373 acceptance testing 468 accumulation 62–63 see also tissue concentration acetylcholinesterase (AChE) 137–139 AChE see acetylcholinesterase ACSLXtreme software 97–98 acute toxicity 299–300, 401 compound category formations 300–303 expert systems and 308–311 mammals 300–308 additivity 285–286 adduct formation, DNA 277 age 108 liver weight and 116–119 physiological data availability and 111–116 air quality modeling 449–451 Akaike information criterion (AIC) 386 alcohols 305–306 alkanes 304 anilines 306 APEX model 324–325 area under concentration-time profile (AUC) 401, 403 aryl hydrocarbon receptor (ACR) 167–168, 187 atmospheric flux 333 attractor states 182, 194 AUC (area under concentration-time profile) 401, 403 automatic differentiation 440 autoregulation motifs 188–194 B-esterase 151, 152–157, 154, 161 background level estimation 326 Bayesian analysis 345, 362–365

Quantitative Modeling in Toxicology
C 2010 John Wiley & Sons, Ltd

benchmark dose modeling (BMD) 374–375 benchmark response 380–382 confidence limits 384 continuous data 376, 381, 381–382 data format 377–379 data requirements 376 dichotomous data 381, 386–388 epidemiological data 389 example model output 392–398 genomics data 390 model parameter selection 380–382 model parameters 383–384 model selection 379–380, 385–386 procedures 376–380 results evaluation 384–385 software 376-377, 390 benchmark response 380–382 benzene 337 atmospheric flux 331–334 groundwater contamination 334–336 Bernebaum additivity 286 beta-testing 468 biologically based dose-response (BBDR) models 7, 10 hypothalamus-pituitary-thyroid axis 255–257, 263 mixtures 289–290 biologically equivalent dose (BED) 10 biologically-based dose-response models, see also benchmark dose modeling biomarkers 339–344 biomonitoring 354–355 data interpretation 356–359, 358 limitations 355 Bischoff, Kenneth 8 bistable systems 185–188, 189–194 transcriptional switches 224–227

Edited by Kannan Krishnan and Melvin E. Andersen

478

Index

blood concentrations 32–33 human physiological data availability 114–116 PBPK model 28–32 samples 355 tissue flow data 122–123 body weight 110, 116, 118 tissue clearance rate and 406 bootstrap resampling 465 brain blood flow 122–123 manganese uptake 62–63 weight 118–120 BTEX 97–100 1,3-butadiene 389 Calendex 361 cancer 5 DNA adduct formation 277 modes of action 272–273, 279 multiple modes of action 272–279, 279 risk assessment 219–220, 247 tumor promotion 274–275 two-stage clonal growth model 270–272 vinyl chloride case study 412–422 see also carcinogenesis carbamate insecticides 137, 138 carbon disulfide 389 carbon tetrachloride 235–238, 236, 290 carcinogens see cancer cardiac output 125 cardiopulmonary parameters 123–125 category formation 300–303 cell death 239 cell differentiation 185 cell replication 274–275 cell-response modeling 13–15 cellular fates 182, 183, 183, 194–196 cellular response motifs 12–13, 14–15 feed-forward motifs 227–228 organisation into transcriptional networks 228–231 ultrasensitive 201–202 cerebral blood flow 122–123 chloral hydrate 291 chloroethylene oxide 413–414 chloroform 235, 237–238, 365, 450 cell death 239–240 metabolism 239 PBPK model 247–249 regenerative proliferation 240–241 risk assessment 246–247 chloroprene 302 β-chloroprene model 37–47 chlorpyriphos 139–140, 140, 145

metabolism 139 physiological parameters 144 chlorpyriphos model pharmacodynamics 152–157 pharmacokinetics 149–152 cholinesterase inhibition 139–140, 144–148 model simulations 157–162 see also chlorpyriphos model clonal growth model, cancer 270–271 compartments 8–9, 22, 38, 40 metabolic rates 24–30 competitive metabolic inhibition 88 Completed Exposure Pathway 318 completeness uncertainty 433 confidence limits 384 confidence weighting 433 Consolidated Human Activity Database (CHAD) 329, 361, 437 continuous data 376, 381–382, 385, 388, 392–396 copper 60 cross-route extrapolation 407 cross-species extrapolation 76–77, 158, 404–407, 419 Cumulative and Aggregate Risk Evaluation System (CARES) 361 cusp catastrophe surface 225, 226 CYP enzymes 52, 417–419 cytochrome P450 142, 187, 413, 417 cytotoxicity 235–238, 239–240 carbon tetrachloride 236 model parameter estimation 242–245 Bayesian 243–245 PBPD model 239–242 data formats 376, 377–379 data uncertainty 434 databases 108–109, 310 data availability 110, 111–116 Dedrick, Robert 8 dermal absorption 25 determinism 3–4 development (of a model) 430–431 dibromochloromethane 365–366 dichotomous data 376, 386–388, 392–394 diet effect on manganese tracer kinetics 72–75 manganese uptake 63–66 diffusion limited tissue distribution 25, 170 dimethyl- p-nitrophenylphosphorothionates 306 discrepancy measures 470–471 discrete models 3–4 distribution (of toxic moiety within tissues) 25 DNA, adduct formation 277 dose 5

Index dose extrapolation 5, 407 dose metrics 400–402, 408 calculation 409–410 dose-dependent hepatic sequestration 170–173 dose-response assessment 6, 9–10, 354–355, 356–357, 372–373, 410 effective dose see ED50 elimination 63–66, 64, 74 energy intake 117 Environmental Protection Agency (EPA) 108–109, 329, 374, 376, 381, 401 enzymes induction 89 metabolic inhibition 85–88 quantitation studies 52–54 epidemiological data 389 vinyl chloride 423–424 epigenetic landscape 182, 183 error 459–460 see also uncertainty; variability Escherichia coli 182 estrogen 221–222, 221 ethanol 291 ethers 304 ethylene oxide, PBPK model structure 23 Euler integration 28, 29, 30 evaluation 460 biologically based models 465–471 data-based model 462–465 predictive capacity 467–471 excretion 25, 257 expert systems 308–311, 309–310 exposure assessment 6, 318, 331–334, 371, 372, 411–412 atmospheric flux 331–334 averages over time 321 background levels 326 benzene 331–336 biomarkers 339–344 biomonitoring 354–355 current developments 322–324 exposure estimation 319 groundwater contamination 334–336 information loss 321 inhalation and ingestion 66–68, 330–331 manganese 66–68 microenvironments 320 numerical inversion 344–345 PBPK modeling 38–40 person-oriented 324–331, 325 population exposure 336–339 reverse see exposure reconstruction stochastic inversion 345

479

types 319–322, 323 uncertainty 437–438 exposure conversion factor 364–365 Exposure Factors Handbook 360–361 exposure reconstruction 339–344, 356–359, 359, 360–361, 411–412 Bayesian analysis 362–365 exposure conversion factor approach 364–365 numerical inversion methods 344–345 optimization 346–347 quantitative structure-property relationship approach 365–366 stochastic inversion 345 exposure routes 317–319 external validation 460 extrapolation 419 cross-species 158, 404–408 metabolic rate 53–54 Michaelis constant 54–55 time 68 factorial model design 288 Fast Equivalent Operating Models (FEOM) 346–347 feed-forward loops 227–228 feedback loops 181–182, 210–212 iodide regulation 259–260 negative 224–227 feedback processes 12, 13 Fick’s laws 24 fixed-ratio ray designs 288 forward dosimetry 356 fuzzy theory 434 Gamma models 383, 383, 386–387 gasoline 93 GATA-1 transcription factor 188 gene autoregulation motifs 188–194 bistability 192–194 governing equations 189 phase plane description 194 protein governing rates 192 genomics 10–11, 294–295 benchmark dose modeling 390 see also gene autoregulation motifs global sensitivity analysis (GSA) 441–444, 448–449, 452 high dimensional model representation 445 results application 445–446 stochastic response surface method 444–445 surrogate-based modeling 444–445 globus pallidus 59 glomerular filtration rate 124–125

480

Index

goodness-of-fit 463–469 groundwater contamination 334–336 Haber’s law 401 HAPEM model 324–325 hazard identification 5–6, 371 heart 123–125 hepatic function see liver 2,4-hexadienal 302 high dimensional model representation (HDMR) 445 Hill equation 173–175, 201–202 Hill models 388, 389 homo-multimerization 204–205 HPT axis, physiological parameters 262–263 human equivalent dose (HED) 404 humans blood flow 122–123 brain weight 118–120 chloroform cytotoxicity 245 energy intake 117 extension of animal models to 78–79, 158 heart weight 120 kidney weight 120, 121 liver weight 116–118 physiological parameter databases 108–109 vital capacity 124–125 see also cross-species extrapolation hypothalamic-pituitary-thyroid (HPT) axis 253–254 model development 260–261 model governing equations 257–260 modeling approaches 255 published datasets 262–263 hypoxia 205–207 hypoxia inducible factor-1 (HIF-1) 206 hysteresis 185 in silico modeling 48–49 in vitro systems enzyme quantitation 52–55 for PBPK parameter determination 50– 51 metabolic rate constants 51 system choice 51 ingestion 330, 331 inhalation 331 inhalation studies 404 cross-species equivalence metrics 405 manganese 66–68 insecticides see organophosphates insecticides, organophosphate see organophosphate insecticides intake, iodide 257

integration algorithms 30–33 interactions 284–288 biologically-based dose-response models 289–290 physicochemical 85–89 physiological 84 internal validation 460 interval analysis 434 iodide 253–254 intake 257 Kepone 290 ketones 305 kidney blood flow 123 chloroform cytotoxicity 246–247 weight 120, 121 labeling index (LI) data 238–239 Latin hypercube sampling 436–437 LD50 test 6, 299–300 narcotics 304–305 read-across 302 LeadScope Toxicity Database 310, 311 lethal dose see LD50 test LI data 241–242 LifeLine 361 linearized multistage (LMS) models 5 liver 65 blood flow 122 chloroform cytotoxicity 238–245, 246–247 clearance 33–34 sequestration 170–173 TCDD distribution 168–173 TCDD induction 175–177 tissue weights 116–118 LMS see linearized multistage model local sensitivity analysis 439–441 log-logistic models 387 logistic models 387 lowest observed adverse effect level (LOAEL) 373 lumping of mixtures 93 M-nullcline 194 Madonna 170 gene autoregulation model 189–194 mammals acute toxicity 300–308 see also humans; mice; primates; rats manganese deficiency 59 manganese model 61 asymmetrical diffusion 75 bilial elimination 63–66 dietary uptake 63–66

Index elimination raters 64 extension to primates and humans 77–78 inhalation exposure calibration 66–68 neurotoxicity 59–60 parameter sensitivity adjustments 68 results 68–75 risk assessment 79–80 structure 61 tissue binding 61–63 tissue uptake 62–63 manganism 60 margin of exposure (MOE) 404 Markov Chain Monte Carlo modeling 345–347 MATLAB 238 maximum likelihood estimate (MLE) 374 MC4PC 309 mechanistic models 4 MEGen software 35–37 animal selection 40–43 β-chloroprene model 37–47 compartment selection 40, 41 exposure route settings 38–40, 39 Functions page 40 membrane permeability 24–26 MENTOR model 323–324, 328, 324–325 mercury 356 metabolic equivalent of tasks (MET) 330 metabolism 25 chloroform 239 inhibition 85–89 mathematical representation 25 organophosphates 139–140 physiologically based pharmacokinetic models (PBPK) 33–34 rate 53–54, 85–89 rate constants 52 vinyl chloride 414–417 metals 294 methylene chloride 293, 404 mice 108, 243–245 Michaelis constant 54–55 microarray data 390 microenvironments 320, 335 basic equations 335 Microsoft Excel 377 microsomal protein (MSP) 52 mitogen-activated protein kinase (MAPK) 14, 205–206 response motif cascade 212–214 mixtures 83–84, 366 additivity 285–286 biologically based models 289–290 BTEX model 97–100 component identification 294 experiment design 288

481

fixed-ratio ray models 288 heavy metals 294 interaction thresholds 290–293 lumping 93 methods for analysis 284–288 number of components 99–100 organophosphates 159–162 PBPK modeling 90–91 response surface equation 287 toluene-xylene 95–100, 98, 99 model definition 3–4 desirable characteristics 461–462 development 431 evaluation see evaluation physiologically based pharmacokinetic see physiologically based phamacokinetic model uncertainty 433 validation see validation Monte Carlo methods 436–437 exposure reconstruction 345–347, 362 sensitivity analysis 441 uncertainty analysis 450–451 see also Bayesian analysis Morris’s test 442–443, 446 multimedia level estimation 329–330 multimerization 204 multistage models 387 NANOG gene 211 narcotics, acute toxicity 303–306 National Center for Environmental Assessment 108 National Exposure Model (NEM) 322 neurotoxicity, manganese 59–60 nitroaromatic compounds 306–307 no observed adverse effect level (NOAEL) 375 dose metric choice 410 no observed effect level (NOEL) 4, 372, 373 non-polar narcosis 304 nonlinear response modeling 14, 173–175 see also feedback loops; ultrasensitivity nullclines 194 numerical inversion 344–345 OCT4 gene 211 oral absorption 25 Organization for Economic Cooperation and Development (OECD) 462–465 organochlorine pesticides 283–284 organophosphate insecticides 137, 138, 140–142 metabolism 139–140 pharmacodynamics 143–148

482

Index

organophosphate insecticides (Cont.) pharmacokinetics 142–143 see also chlorpyriphos organophosphate insecticides phamarcokinetics 149–152 OxyR transcription factor 204 p value 384–385 P-nullcline 194 parametric uncertainty 434 perchlorate 293 perfusion limited tissue distribution 25, 170 person-oriented exposure assessment 323, 326–331, 327 background levels 326 microenvironment concept 335 multimedia levels 329–330 pesticides see organochlorine pesticides; organophosphate insecticides pharmacodynamics 6 cytotoxicity 239–242 neonatal rat 158–159 organophosphates 143–148 pharmacokinetics 7 cross-route extrapolation 407 dose extrapolation 407 impact on risk assessment 403–404 interactions in mixtures 84–89 organophosphates 149–152 systems approaches 8–9 time extrapolation 407–408 phase space 194 Philadelphia, Pennsylvania 338–339, 340, 341 phosphorothionates 139–140 phosphorylation 207–208 physicochemical interactions 85–89 physiological parameters 415 age-based differences 108 β-chloroprene model 38 chloroform cytotoxicity 242 chlorpyriphos metabolism 144 cross-species variation 77 data availability 110, 111–116, 117–118 data gaps 125–126 databases 108, 108–109 distribution characterization 435–436 estimation 447–449 evaluation 467 HPT axis 262–263 interactions and 84 uncertainty 434 unimportant 447–448, 452 variation across life stages 76–77

physiologically based pharmacokinetic models (PBPK) 7, 21–22, 399–400 structure and purpose 22–24, 23 see also evaluation ADME processes 25 β-chloroprene 37–47 blood concentrations 32–33 chemicals modeled 47–48 chloroform cytotoxicity 238–239 compartment change rates 24–32 compartments 8–9, 22, 38, 40 computer implementation 35–37 enzyme induction 89 evaluation 465–471 extrapolation 76–77 across life stages 76–77 cross-species see cross-species extrapolation global sensitivity analysis 442–443 hypothalamus-pituitary-thyroid axis 255 in vitro derived parameters 50–54 linking to BBDR models 263–265 manganese see manganese model metabolic rate 33–34, 52, 85–89 metabolism 33–34 mixtures 90–91, 289–290, 290–291 higher-order mixtures 95–100 ‘lumping’ models 93–95 model reduction 446–449 organophosphates 140–142 pharmacokinetics 142–143 physiological parameters see physiological parameters risk assessment and 79–80 software 35–37, 95–96 TCDD 168 tissue binding 61–62 tissue concentrations 32 tissue uptake 92–93 uncertainty/variability analysis 430–431, 433, 449–451 vinyl chloride 412–422 volatile organic compounds 358–359 platelet-derived growth factor (PDGF) 13 pNEM model 324–325 point of departure (POD) 373 polynomial models 388, 389 population exposure modeling 336–339, 438–439 positive cooperative binding 202–204 power models 389 predicted residual sum of squares (PRESS) 464 primates 77–78 probit models 387 proliferation 240–241

Index carcinogenic 275 simulation 241–242 prolyl hydroxylase (PHD) 206 proteins binding interactions 25, 85 induction 175–177 networks 12 phosphorylation 207–208 see also gene autoregulation motif PU.1 transcription factor 188 pulmonary absorption/excretion 25 purpose (of model) 23–24, 466 (Q)SAR Application Toolbox 301, 310, 311 quality assessment 468 see also evaluation quantal-linear models 387 quantitative structure-activity relationships (QSAR) acute toxicity 307 narcotics 303–306 non-narcotics 306–307 other compounds 307–308 evaluation 462–465 PBPK modeling 48–50 quantitative structure-property relationships (QSPR) 365–366 randomness 432–433 ratios in risk assessment 402–403 rats extension of adult model to other life stages 76–77 extension of models to humans and primates 77–78 manganese absorption model 67–77 neonatal cholinesterase inhibition model 158–159 organophosphate model 158–159 physiological parameter databases 108, 108–109 REACH legislation 300–303 read-across 301–303 Red Book 5 reference concentration (RfC) 375 reference doses (RfD) 375 regenerative proliferation, simulation 241–242 regression testing 468 renal function see kidney reptiles 187 residual analysis 469 response pathways all-or-none 222 combinations 212–214 ultrasensitive 205–207

483

feedback 210–212 reverse dosimetry 357 Bayesian statistics 362–365 exposure reconstruction 360–361 Monte Carlo methods 362 risk assessment 371–373 process overview 5–6 benchmark dose model 374–375 cancer 399 carcinogens 219–220, 247 chloroform cytotoxicity 246–247 cross-route extrapolation 407 dose metric calculation 409–410 dose metric selection 400–402 exposure level assessment 411–412 genomics data 390 guidance documents 5–6 history 4–5 integrated exposure 320–321 interactions in mixtures 292–293 manganese 79–80 pharmacokinetic model selection 409 pharmacokinetics, study selection 408–439 ratio concept 402–403 time extrapolation 407–408 uncertainty factors 410–411 risk characterization 6 Runge-Kutta integration 29, 30–31, 32 Sarin 137, 138 sensitivity analysis 439–441 global 441–446 guidelines 451–452 local 439–441 manganese model 68, 70 see also ultrasensitivity sequence generators 436–437 SHEDS model 324–325 signaling motifs 182 sodium-iodide symporter (NIS) 258 software acute toxicity prediction 308–311 benchmark dose modeling 376–377, 390 code evaluation 467–469, 468 cytotoxicity modeling 238 PBPK modeling 35–37 mixtures 95–96 quality assurance checks 468 SOX2 gene 211 spatio-temporal random field (STRF) theory 338 species, extrapolation between see cross-species extrapolation spleen 120–121, 121 spreadsheet programs 95–96

484

Index

statistical tests 469–470 stochastic human exposure and dose simulation (SHEDS) model 361 stochastic inversion 345 stochastic response surface method (SRSM) 444–445, 450–451 stress pathways 12, 211 stress testing 468 striatum 59–60, 62–63, 65 styrene 23 substrate competition 209–210 sulfonamides 85 surrogate-based global sensitivity modeling 444–445 switching 181–182 systems approaches 8–9, 10–12 Taylor series 286 TCDD see 2,3,7,8-tetrachlorodibenzo- p-dioxin TCP (trichloropyridinol) 142, 151–152 temperature-dependent sex determination (TSD) 187 2,3,7,8-tetrachlorobenzo- p-dioxin (TCDD), PBPK model structure 23 2,3,7,8-tetrachlorodibenzo- p-dioxin (TCDD) 167–169, 187, 255 diffusion-limited tissue uptake 170 TetraQSAR system 310 thyroid human 265 see also hypothalamic-thyroid-pituitary thyroid-stimulating hormone (TSH) 257–260 tiered uncertainty analysis 432 time extrapolation 407–408 tissue dose 322 tissues binding, manganese 61–62 concentration 401 uptake 75 weights brain 118–120 heart 120 kidney 120 liver 116–118 spleen 120–121 TN see transcriptional networks tolbutamide 85 toluene, PBPK model structure 23 TOPKAT 309, 309 total-order indexing 440, 443–444, 444 Tox Filter 310 ToxBoxes 310, 311 Toxicity Testing in the 21st Century: A Vision and A Strategy 232

toxicogenomics 294–295 transcription networks (TN) 187–188, 220– 222 switches 222–227 transcriptional networks (TN) 228–231 transcriptional switches 222–227 transcriptome 182 trichloroethylene 293, 359, 404, 405– 406 trichloropyridinol (TCP) 139, 142, 151–152 trihalomethanes 365 2,6,7-trioxabicyclo[2.2.2]-octanes 306 TSD (temperature-dependent sex determination) 187 tumor promotion 274–275 two-stage clonal growth model 270–272 ultrasensitivity 193–194 combinations of motifs 212–214 Hill function 201–202 positive feedback loops 210–211 substrate competition 208–210 zero-order 207–208 see also sensitivity uncertainty 403, 406, 429–430, 449–451 analysis guidelines 452 analytic tiers 432 benchmark dose modeling 375 characterization of parameter distributions 435–436 distinguished from variability 437– 438 due to model 433 integrated models 431–432 interval analysis 434 natural 432–433 propagation 436–437, 452 representation 434–435 risk assessment 410–411 sensitivity and 441–442 use of results 445–446 urinary excretion 25 urine sampling 355 USEPA see Environmental Protection Agency validation 460, 464–465 variability 429–430 distinguished from uncertainty 437–438 natural 432–433 vinyl chloride 404, 407–408, 412–422 epidemiological analysis 423–424 metabolism 414–417 virtual individuals 329, 437–438, 438

Index volatile organic compounds (VOC) 91, 93–95, 94, 95–97, 293, 366 exposure reconstruction 358–359 Waddington, C.H. 182 water disinfection byproducts 449– 451 Weibull models 387 weights brain 118–120 heart 120 kidney 120

liver 116–118 spleen 120–121, 121 Xenopus laevis 186–187, 209 xylene 446–448 Y-scrambling 465 zero-order ultrasensitivity 207–208 zinc 60

485