Mechanical Engineering of the Cytoskeleton in Developmental Biology

MECHANICAL ENGINEERING OF THE CYTOSKELETON I N DEVELOPMENTAL BIOLOGY VOLUME 150

SERIES EDITORS Geoffrey H. Bourne James F. Danielli

1949-1 988 1949-1 984

Kwang W. Jeon

1967-

Department of Zoology The University of Tennessee Knoxville, Tennessee

Martin Friedlander Jonathan Jarvik

1984-1 992 1993-

Department of Biological Sciences Carnegie Mellon University Pittsburgh, Pennsylvania

ADVISORY EDITORS Aimee Bakken Eve Ida Barak Howard A. Bern Robert A. Bloodgood Dean Bok Stanley Cohen Rene Couteaux Marie A. DiBerardino Donald K. Dougall Charles J. Flickinger Nicholas Gillham Elizabeth D. Hay Mark Hogarth M. Melkonian Keith E. Mostov Audrey Muggleton-Harris

Andreas Oksche Muriel J. Ord Vladimir R. Pantic M. V. Parthasarathy Lionel I. Rebhun L. Evans Roth Jozef St. Schell Manfred Schliwa Hiroh Shibaoka Wilfred Stein Ralph M. Steinman M. Tazawa Yoshio Watanabe Robin Wright Alexander L. Yudin

Guest Edited by Richard Gordon Departments of Botany and Radiology University of Manitoba Winnipeg, Manitoba Canada

MECHANICAL ENGINEERING OF THE CYTOSKELETON IN DEVELOPMENTAL BIOLOGY VOLUME 150

ACADEMIC PRESS, INC. A Division of Harcourt Brace & Company San Diego New York Boston London Sydney Tokyo Toronto

This book is printed on acid-free paper. @ Copyright 0 1994 by ACADEMIC PRESS, INC. All Rights Reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher.

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Contributors . . . . . . ... . . . . . .. . . . .. .. . . ... . . . . .. . . . .... . . . ... . . . . .. . . ...... . ... , , , , .. . . . ..... , , ... , , Preface ....... . . . .......... . . ....... .. . . ...... ... . ....... . . . . ........ ............ . . ....... .......

xi xv

Mechanical Stresses in Embryonic Tissues: Patterns, Morphogenetic Role, and Involvement in Regulatory Feedback L. V. Beloussov, S. V. Saveliev, 1. 1. Naumidi, and V. V. Novoselov Introduction . . . . . ... . . . ..... . . .. . . . . ... . . .... . . . .. . . . ..... . . ..... . . ... . . .... . . ... . .. . . ... . . . Determination of Patterns of Mechanical Stresses in Amphibian Embryos ......,. ...... Tentative Estimates of the Range of Absolute Stress Values . . ... . . ..... . ..... . . ..... . . .

I. 11. Ill. IV. Morphogenetic Effects of Reorientation and Relaxation of Tensile Stresses in Amphibian

V. VI. VII. VIII. IX. X.

Surface Tension-lik A Hypothesis of “Hyperrestoration” of Preexisting Stresses .. . ... . . ..... . . ..... . . ... . . . . Some Standard Morphomechanical Situations . . . ...... . ..... . . ... . . ..... . . ... . . . . ... . . .. Qualitative Reconstruction of Morphogenetic Processes during Gastrulation and Neurulation of Amphibian Embryos .. . ..... . . ... . . .. . ... . . ..... . . ... . . .. ... . . ..... . . .... . . Some Views on a Mechanical Approach to Ontogenetic Processes . . . . ... . . . ...... . . ... References . ..... . ..... . . . . . . .. . . . .... . . ..... . . ... . . . . ... . . . ..... . ... . . . . .... . ...... . . .....

8 11 23 24 25 29 31 32

Locomotion of Tissue Culture Cells Considered in Relation to Ameboid Locomotion I. II.

Albert K. Harris Introduction ..... , . .. . . ..... , , .... . . ... , ...... ... . . . . ... . . . ..... . .... , . . .... . ...... , , ..... General Description and Nomenclature of Locomotion in Tissue Culture Cells .... . ..... ,

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CONTENTS

Ill. IV. V. VI.

Exertion of Rearward Traction Forces . .. . . . . . . . . . . . . . . . .. . . . .. , . . . . Retrograde Surface Transport of Attached Markers . . . . . .. . . . . . . _ _..... _ . . . , .... ...... ...... Varieties of Ameboid Locomotion ....., ......... .......................... Conclusions ............................................ References . . . . . . . . .. . . . , , , , , , . . . . . . , . , .. , , , , . . . .

54 61

Role of Mechanical Stimulation in the Establishment and Maintenance of Muscle Cell Differentiation David G. Simpson, Wayne Carver, Thomas K. Borg, and Louis Terracio I. It. 111. IV. V. VI.

VII. VIII. IX. X. XI. XII. XIII. XIV.

xv.

. .. . . . . ............................................. Introduction .. . Cellular Respo ical Lo ........................ ..................... Response of Developing Myocytes to Mechanical Forces . .. , , , . . .. . . . ... . . . . . . . . . . . .. . . Effect of Mechanical Force on Myofibril Formation . . .. ... . .. . . . . . ... . . .... . . . . . . . . . . .. . . . Mechanical Regulation of Adult Cardiac Myocyte Physiology . . . . Mechanical Effects on Skeletal Myocytes . . .. . . Changes in Regulatory Molecules in Response to Load . .. . . . . . . . . . Effects of Decreased Mechanical Load . . . . . . . . . ......................... Effects of Load Changes in Wtfo PathophysiologicalChanges in Lo Receptors of Mechanical Force ...... , , , ............, .. , .. , ......... .. . . . . .......... . . .. . Transduction of Mecha Stretch-Activated Channels . . . .. . . .... . . .. . . . ... .............. Nuclear Matrix . . .... . . . . . . . . ... . . .. . . . . .. . . . .. . . . Conclusion ..........., ................. . .....

69 72 73 75 76 77 78 81 82 82

References .. , . ... . . . ..

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Finite Element Methods for Developmental Biology G. Wayne Brodland .. ,., , , . , , .... , , , .. , , , . .. . . . .. . . . . . .. . , , , , _., . . .. . . . . . . .. . , , . . . .... . ... . . ..... . . . .. , . . . . . .. . . . . . . . ... ... . . .. . . . . . .. . . . . ... . . . , . , , , . . ... . . Ill. Basis of the Finite Element Method . . .. . . . V. Discussion .................................. ......................... ............................................. I. Introduction . . ..

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Substratum Mechanics and Cell Differentiation Michal Opas I. Introduction................................................................................ II. Cytomechanics of Cell-Substratum Interactions ......................................... 111. Regulation of the Choice of Fate of the RPE Cells by Soluble Factors and the Substratum ............................................................................ IV. Cellular Mechanics of Transdifferentiation ................................................ ..... References ....

119 120 125 128 132

Phase Transitions, Interfaces, and Morphogenesis in a Network of Protein Fibers Gabor Forgacs and Stuart A. Newman I. II. Ill. IV.

Introduction................................................................................ Matrix-DrivenTranslocation ............................................................... Physical Mechanisms of MDT ...... .................. ........ Conclusions ...... References

139 141 143

The lnterphase Nucleus as a Dynamic Structure Umberto De Boni Introduction................................................................................ Nuclear Rotation: Chromatin Motion in lnterphase Nuclei in Vim ........... Chromosome Topology in lnterphase Nuclei .............. The FunctionalState of Cells and lnterphase Chromosome Patterns .................... An lntranuclear Motor: Contractile Proteins in lnterphase Nuclei ......................... VI. Conclusions ............................................................................... References ................................................................................ I. II. 111. IV. V.

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Cellular Tensegrity: Exploring How Mechanical Changes in the Cytoskeleton Regulate Cell Growth, Migration, and Tissue Pattern during Morphogenesis Donald E. Ingber, Laura Dike, Linda Hansen, Seth Karp, Helen Liley, Andrew Maniotis, Helen McNamee, David Mooney, George Plopper, John Sims, and Ning Wang I. Introduction................................................................................ II. Mechanical Forces and Establishment of Tissue Pattern ................................

173 175

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Transmembrane Mechanical Coupling within the Extended Cytoskeleton . . . ... . . . . Control of Cell Shape and Function by Alterati Cytoskeletal Response to Mechanical Stress Cytoskeletal Tensegrity . . . . . .. . . . , . , . , , , . . . . . . The Cytoskeleton as a Mechanical Signaling System Conclusions and Implications for Development ....................... . . . . . . .. . . . . . . . . . . ...... . . . ..... . . . .... .. . . . . ..... References .. . . . .... . . .

111. IV. V. VI. VII. VIII.

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Mechanics of the Cytoskeleton and Morphogenesis of Acetabularia B. C. Goodwin and C. Briere I. II. 111. IV. V. VI. VII. VIII.

Growth and Morphoge Cell Wall Dynamics , .. , , , , , . , , . .. . , , , , .. . . . . . . . , _.. . . . . . . . . . .. . . . . . . . . . . . . .. . . .. . . . . . . . . . . Simulations of Acefabdaria Morphogenesis .. . ,..... . . . ...... .. . ..,~.. . . . . ..... . . . . ...... Variations on a Theme .. . . . . . .. . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion , , . , , , , , , . , . . .. , , , , , .. . . , , .. , . . . . . . . . . . Appendix . .. . . ..... . . .. . . . .... . . ... . . . . .. References .. . . . ... . . . .. . . . . . .. . . . .. . . . . .

The Chemical Basis of Diatom Morphogenesis Richard Gordon and Ryan W. Drum Introduction . .. ................................ The Diatom Shell and Observed Stages of Its Morphogenesis . . . . .. . . . ... . . . . . . . . . ... . .

I. II. Ill. Theories and Speculations on Shell Morphogenesis . . ... IV. Instabilities in Diffusion-LimitedAmorphous Precipitationof Silica Generate Space-Filling Branching Patterns ......... ....... V. The Role of Sintering .. .. . . . . . .. . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .. . . . . . VI. Modeling of Sintering , . VII. The Colloidal Nature o f t VIII. Valve Morphogenesis in the Conte IX. Discussion .. ....................... . . .......... ...... Glossary , , .. , , . ..... , , ... . . . . ... . . ... , , , , .. . . . .... . . ... . . . . . .. . . . . . .

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225 225 227 231 232 237 238 239 241

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CONTENTS

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Appendix: Dialogue on Embryonic Induction and Differentiation Waves Richard Gordon. Natalie K. Bjorklund. and Pieter D. Nieuwkoop I. Introduction................................................................................ II. Authors’ Dialogue ......................................................................... References ................................................................................

373 374 414

Addendum to “The Chemical Basis of Diatom Morphogenesis” .................................

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Index ..............................................................................................

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Numbers in parentheses indicate the pages on which the authors' contributions begin.

L. V. Beloussov (1), Department of Embryology, Faculty of Biology, Moscow State University, Moscow 119899, Russia

Natalie K. Bjorklund (373),Departments of Chemistry and Microbiology, University of Manitoba, Winn@eg,Canada R3T 2N2 Thomas K. Borg (69),Department of Developmental Biology and Anatomy, School of Medicine, University of South Carolina, Columbia, South Carolina 29208 C. Briere (225),Laboratoire de Biologie Biotechnologie et Amelioration des Plautes, CNRS ENSA T, Toulouse, France

G. Wayne Brodland (95),Departments of Civil Engineering and Biology, University of Waterloo, Waterloo, Ontario, Canada N2L 3G 1 Wayne Carver (69),Department of Developmental Biology and Anatomy, School of Medicine, University of South Carolina, Columbia, South Carolina 29208 Umberto De Boni (149),Department of Physiology, Faculty of Medicine, University of Toronto, Toronto, Ontario, Canada M5S lA8 Laura Dike (173), Departments of Pathology and Surgery, Children's Hospital and Harvard Medical School, Boston, Massachusetts 021 15 Ryan W. Drum (243),Island Herbs, Waldron Island, Washingon 98297 Gabor Forgacs (139), Department of Physics, Clarkson University, Potsdam, New York 13699 B. C. Goodwin (225),Developmental Dynamics Research Group, Department of Biology, The Open University, Milton Keynes MK7 GAA, United Kingdom xi

xii

CONTRIBUTORS

Richard Gordon (243, 373), Departments of Botany, Radiology, Physics, and Electrical and Computer Engineering, University of Manitoba, Winnbeg, Canada R3T 2N2 Linda Hansen (173),Departments of Pathology and Surgery, Children’s Hospital and Harvard Medical School, Boston, Massachusetts 02115 Albeit K. Harris (35),Department of Biology, University of North Carolina, Chapel Hill, ~ o Carolina ~ h 27599 Donald E. lngber (173), Departments of Pathology and Surgery, Children’s Hospital and Harvard Medical School, Boston, Massachusetts 021 15 Seth Karp (173), Departments of Pathology and Surgery, Children’s Hospital and Harvard Medical School, Boston, Massachusetts 02 I 15 Helen Liley (173), TheJoint Program in Neonatology, Children’s Hospital and Harvard Medical School, Boston, Massachusetts 021 15 Andres Maniotis (173), Departments of Pathology and Surgery, Children’s Hospital and Harvard Medical School, Boston, Massachusetts 02115 Helen McNamee (173), Departments of Pathology and Surgery, Children’s Hospital and Harvard Medical School, Boston, Massachusetts 02 I 15 David Mooney (173), Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02I39 I. I. Naumidi (1), Department of €mbryology, Faculty of Biology, Moscow State University, Moscow 1 19899, Russia Stuart A. Newman (139), Department of Cell Biology and Anatomy, New York Medical College, Valhalla, New York 10595 Pieter D. Nieuwkoop (373),Netherlands Institute for DevelopmentalBiology, Hubrecht iaboratory, 3584 CT Utrechf, The ~ e t ~ e r l a n ~ s V. V. Novoselov (I), Department of €mbryology, Faculty of Biology, Moscow State University, Moscow 1 19899, Russia Michal Opas (119), Department of Anatomy and Cell Biology, University of Toronto, Toronto, Ontario, Canada M5S lA8 George Plopper (173), Departments of Pathology and Surgery, Children’s Hospital and Harvard Medical School, Boston, Massachusetts 02 I 15

S. V. Saveliev (I), lnstitute of Human Morphology, Russian Academy of Medical Sciences, Moscow 1 I74 18, Russia

CONTRIBUTORS

...

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David G. Simpson (69), Department of Developmental Biology and Anatomy, School of Medicine, Universitv of South Carolina, Columbia, South Carolina 29208 John Sims (173), Departments of Pathology and Surgery, Children’s Hospital and Harvard Medical School, Boston, Massachusetts 02 1 15 Louis Terracio (69), Department of Developmental Biology and Anatomy, School of Medicine, University of South Carolina, Columbia, South Carolina 29208

Ning Wang (173), Respiratory Biology Program, Harvard School of Public Health, Boston, Massachusetts 021 15

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PREFACE

A symposium on the Mechanical Engineering of the Cytoskeleton in Developmental Biology, sponsored by the Canadian Society for Theoretical Biology under the aegis of the Canadian Federation of Biological Societies (CFBS) at Queens University in Kingston, Ontario, Canada, was held June 9-10, 1991. Our society is small by CFBS standards. Accordingly, we were allocated a small room adjacent to two huge auditoriums overflowing with molecular biologists and physiologists. To our astonishment, and no small delight, we soon had enough CFBS members playing hooky from their own meetings that we began creating headaches for our hosts. We ran out of standing room and the hall outside our two doorways was packed with additional onlookers blocking traffic. One of the onlookers, a prominent molecular biologist who did not want to be named, was heard to comment on how refreshing it was to look at something other than blots. We certainly were a diverse bunch: plant and animal embryologists and morphogeneticists, civil engineers, cell physiologists, theoretical and mathematical biologists, and statistical mechanics. Our keynote speaker, John P. Trinkaus, highlighted our session with his work on convergent movements of cells in the germ ring of Fundulus during gastrulation. Several of us agreed to put together this volume. [See “ProgramsProceedings of the 34th Annual Meeting of the Canadian Federation of Biological Societies,” pp. 25-26, 33-34, 86, 118-1 19, CFBS, Ottawa (1991) for abstracts.] The participants in this volume have a variety of approaches to the physical mechanics of cell behavior in development that tie directly into modem cellular molecular biology. Our work does not replace the all important “blots,” but rather enhances and complements them. Cells are not just bags of interacting molecules. Their mechanics may be just as important as their “mechanism.” How shall we explain the whole in terms of its parts? The time has come in biology to face this question squarely. The role of mechanics is the central theme of our diverse approaches. Lev Beloussov and colleagues examine the relationships between the mechanical stresses that cells are subjected to during embryogenesis and how they respond at the ultrastructural and cellular levels.

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PREFACE

Albert Harris looks at the relationship between the ameboid locomotion of tissue culture cells (the most observed) and the mechanics of intracellular and membrane force generation. David Simpson, Wayne Carver, Thomas Borg, and Louis Terracio emphasize the relationship between mechanical forces and the molecular and cytoskeletal bases of differentiation of muscle cells. Wayne Brodland takes a look at nonlinear, large deformation finite element methods as a tool for approaching the inverse problem in relating the constitutive (mechanical) properties of cells and their force bearing and generating macromolecules to tissue shaping. Michal Opas concentrates on transdifferentiation of retinal pigment epithelial cells and its relationship to the constitutive properties of the basement membrane. Gabor Forgacs and Stuart Newman look at cell motion driven by the mechanics of gel networks and suggest a mechanism that may be used both intracellularly and in mesenchymal tissues. Umberto De Boni takes us into the universe of the nucleus, where we discover the mechanics of rotation of the karyoplasm and its possible relationship to gene expression. Donald Ingber and colleagues review their concept of cellular tensegrity and how the cytoskeleton may bridge the gap from the nucleus to the plasmalemma. Brian Goodwin and C . Bribre give us a finite element analysis and simulation of that amazing, single-celled alga Acetabularia, well known for classical investigations of the relationship between nucleus and cytoplasm. Richard Gordon and Ryan Drum try to separate the roles of precipitation of silica and the cytoskeleton in the patterning of another algal cell, the diatom. Finally, in an appendix, Richard Gordon, Natalie Bjorklund, and Pieter Nieuwkoop argue over the relationships between the cytoskeleton, waves of contraction and expansion on the surface of amphibian embryos, and differentiation of their cells. Those who attended the meeting will remember a joint presentation of the first mechanical ‘‘differentiation wave” to be discovered (although we now know that David Suzuki, perhaps without being aware of it, found the first such wave in Drosophila). The original presentation was prepared by Wayne Brodland and myself, supplemented by two respective groups of students who were jointly involved in the original discovery. The “dialogue” format of the appendix, much like the heated discussion following our Kingston presentation, represents the latest developments of the rapidly expanding differentiation wave research. Pieter Nieuwkoop’s input provides an essential cautionary note while clarifying our presentation with his unmatched historical and practical knowledge of the problem of embryonic induction. My student, Natalie Bjorklund, the first to see a contraction wave, on axolotl ectoderm explants, keeps us both on our toes. Brian Goodwin also contributed by soliciting most of the reviewers, whose comments have substantially improved our efforts. The assistance of Kwang W. Jeon, Editor of the International Review of Cytology, and the staff of Academic Press in San Diego, especially Charlotte Brabants and Kathryn Spradlin, are gratefully acknowledged.

PREFACE

xvii

We hope you enjoy the multiple levels of mechanical explanation as much as we did during those spring days in Kingston. We are now perhaps ready to continue the efforts of Wilhelm His: Embryology and morphology cannot proceed independently of all reference to the general laws of matter, to the laws of physics and of mechanics. This proposition would, perhaps, seem indisputable to every natural philosopher; but, in morphological schools, there are very few who are disposed to adopt it with all its consequences [His, W. (1888). Proc. R . SOC. Edinburgh 15, 287-298.1

Richard Gordon

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Mechanical Stresses in Embryonic Tissues: Patterns, Morphogenetic Role, and Involvement in Regulatory Feedback L. V. Beloussov,* S. V. Saveliev,t I. I. Naumidi,* and V. V. Novoselov* * Department of Embryology, Faculty of Biology, Moscow State University, Moscow 119899, Russia; and t Institute of Human Morphology, Russian Academy of Medical Sciences, Moscow 117418, Russia

1. Introduction From a mechanical point of view, morphogenesis of living organisms should be viewed as an extremely complicated succession of deformations of viscoelastic bodies. These deformations are created by active (energyrequiring) mechanochemical mechanisms such as contracting actin microfilaments, ionic transport systems (which create and regulate osmotic pressure, both inside cells and in the intercellular spaces), and the insertion-resorption processes of plasma membrane subunits (Burnside, 1971 ; Wessells et al., 1971; Ode11 et al., 1981; Trinkaus, 1984; Stem, 1984; Oster, 1984, 1988; Oster et al., 1985; Radeva et al., 1986; Gordon and Brodland, 1987; Harold, 1990). Each of these events, while being precisely located in space and time in developing embryos, almost inevitably should create mechanical stresses of tension and/or compression in surrounding tissues. While, at first glance, the existence of such stresses may look like a trivial phenomenon, they have recently attracted an increasing amount of interest that is closely associated with the idea that they may have a powerful role in regulating morphogenesis and possibly some other developmental phenomena. The reasoning that supports such an idea is as follows. Morphogenesis, which belongs to a category of distinct self-organizing processes (Goodwin, 1985; Murray, 1989), requires effective nonlinear feedback between its dynamic components. This feedback should, on one hand, rapidly and precisely trace the deformation of embryonic material caused by active lnrernarional Review of Cyrology, Vol. I50

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mechanochemical processes and, on the other hand, affect these very processes. Mechanical stresses look like quite natural tools for this feedback since (1) they are spread quite rapidly (at the rate of elastic deformation waves) throughout embryonic tissues and the turgor-stretched cavities, and in a precisely directed way which uniformly depends upon the geometry of a deformed body (for the biologically oriented examples borrowedfrom elastic shell theory, see Martynov, 1982).(2) Active mechanochemical mechanisms are known to be highly mechanosensitive, both at the cytoskeletal (e.g., Kolega, 1986) and the ionic transport (Christensen, 1987; Morris, 1990) levels. From this point of view, the main regulatory feedback in morphogenesis should occur between the mechanical forces actively generated inside cells (or, in some cases, in the extracellular spaces) and the resulting passive stresses of tension and/or pressure which extend considerable distances along embryonic tissues and through cavities. We call these stress-force feedbacks. In order to transform this general idea into a coherent theory of morphogenesis and other cellular activities, a large body of work needs to be done, including experiments, measurements, and construction of models. This chapter presents some results in this field obtained by several Moscow research groups in the past few decades. More recently, our work has been enriched by collaboration with Professor J. Mittenthal at the University of Illinois, and his ideas are incorporated in this chapter (Mittenthal and Beloussov, 1991). First we discuss how to detect and locate mechanical stresses in developing embryos and present some maps of the stresses based on amphibian embryos. We briefly discuss some attempts to estimate the range of absolute stress values. Then we go on to the morphogenetic effects of artificial stretching and relaxation of stress in embryonic tissues. This brings us to the complicated problem of the role of “surface tension-like’’ and quasi-elastic components in generating and maintaining stresses. Finally, we approach the problem of stress-force feedback and suggest some generalizations in this field which we compare with actual morphogenetic phenomena.

II. Determination of Patterns of Mechanical Stresses in Amphibian Embryos A. Tissue Dissection

One of the simplest and biologically reasonable ways to detect the presence and location of mechanical stresses (Beloussov et al., 1975) is to dissect

MECHANICAL STRESSES AND MORPHOGENESIS

3

or incise embryonic tissues and trace their deformation immediately after dissection under conditions that prevent the tissue from contracting (e.g., moderate cooling, low concentrations of cytoskeletal or metabolic inhibitors). The active contractile responses, which are always expressed by inward rolling of the edges of a dissected piece of tissue after a 1-2 min latent period, can be easily distinguished from passive deformations, which are characterized by insensitivity to temperature and inhibitors, the lack of a latent period, and a marked stage and region specificity. Most of the passive deformations consist of immediate and extensive contraction and/ or bending of the dissected pieces, which could be described as relaxation of preexisting stresses (cf. Jacobson and Gordon, 1976). Rough maps of mechanical stresses can be constructed (Fig. 1) by making a series of precisely located incisions during successive developmental stages of amphibian embryos. The main characteristics of the maps are as follows: (1) Not only the outer embryo surfaces but also certain regularly arranged files of internal cells which cross embryonic tissues (cross-lines) appear to be under considerable tension. (2) These crossline patterns show a remarkable stage and region specificity, remaining topologically unchanged within relatively prolonged developmental periods and then drastically changing. For example, the cross-line pattern remains topologically invariant during the whole gastrulation period (Fig. lB,C), but before the beginning of neurulation the topology is broken by the appearance of the so-called middorsal cross-line bundle (Fig. lD), which increases during the whole neurulation period. (3) After explantation, the tissue regions characterized by the pronounced cross-line system show a remarkable structural stability in the developmental pathways whereas those lacking pronounced cross-lines develop in a quite variable and unstable way (Beloussov, 1979). Beginning from the early neurula stage, both tensile and compressional stresses can be seen in the dorsal embryo wall; these are directed longitudinally and checked by the overlap of dissected tissue edges (Fig. 2B). At the earlier stage, on the other hand, the homologous embryonic region has pronounced tensile stresses (Fig. 2A). It is worth mentioning that no more than 20-30 min are needed for a detailed tensile pattern to appear de nouo in an extirpated fragment of embryonic tissue (Fig. 1J).

13. Measurement of Cell Surface Angles The classical method for evaluating tensile forces by measuring angles formed by cell surfaces at their attachment points (see Thompson, 1942; Steinberg, 1978, his Fig. 4) is based on two general assumptions. (1) All of the mechanical forces that determine the shape of a cell are equilibrated

L. V. BELOUSSOV ET AL.

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H

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\ I

\

'.

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FIG.1 Maps of mechanical stresses for several successive stages ofRuna temporuriu development and for an ectomesodermal explant extirpated from a flank embryo region at the neurula stage. (A) Late blastula, (B) Midgastrula, sagittal section, (C) Same stage, transverse section (along the line indicated in B, (D) Transition from gastrula to neurula, posterior region, (E) Anterior region of early neurula, and (F)Posterior region, same stage. D-F are transverse sections. (G) Early-to-mid neurula, sagittal section, (H) Mid-to-late neurula. frontal section, (I) Similar stage, transverse section. ( J ) Ectomesodermal explant about 20 min after isolation. Heavy contours, distinct stress lines; dotted contours, dispersed stress lines; fine lines, nontensed surfaces; pr, plica rhombo-encephalica; peu, plica encephali ventralis. (Modified from Beloussov et a / . , 1975.)

by tensile forces oriented parallel to cell membranes and located in their immediate vicinity. (2) The network of cell wall tensions in the whole rudiment or in the entire embryo is constantly being mechanically equilibrated. (It is the cell membrane together with a submembraneous (cortical) layer that we call the cell wall.) The latter means that at each cell apex (cell wall intersection points), ZF = 0 where F is a force of tension. The principle of force equilibrium (lack of inertial effects) is widely accepted in biomechanics (Gordon et al., 1972; Ode11 et al., 1981; Goodwin and Trainor, 1985), so we need not discuss it in more detail.

MECHANICAL STRESSES AND MORPHOGENESIS

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FIG. 2 Configurations of the incised parts of Xenopus laeuis embryo dorsal wall immediately after dissection at the early gastrula (A, pointer) and mid neurula (B) stages. Whereas at the early gastrula stage the incised edges move apart, indicating the relaxation of preexisting tensions, at the midneurula stage the incised edges (shown in normal position by dotted contours) markedly overlap each other, indicating the presence of preexisting pressure stresses.

Having obtained a print of a cell network from a histological section, we chose an arbitrary apex point O , , ascribed to the vertical cell wall joining the apex a certain tension force, a (Fig. 3A), and by measuring the angles cy and p, calculated (using the above assumptions) the tension forces b and c in relation to a. Then we went to the next apex, point O,, measured the corresponding y and 6 angles, and expressed the tensile forces e andfin relation to the force d = c (see Beloussov and Lakirev,

B

...........

I..

i"

en

C

nch

D

nI

f

FIG. 3 Construction of maps of tensile stresses by measuring cell surface angles. (A) A scheme of the measurements (for comments, see text). (B) A map of tensile stresses for the suprablastoporal region of R. temporaria early gastrula embryo, sagittal section (cf. Fig. tB). (C) The same map for the left half of a R. temporaria neural plate, transverse section (cf. Fig. 1F). Heavy contours, strongly tensed cell walls; light contours, weakly tensed walls. (D) A markedly bimodal distribution of tensile stresses in cell walls of R. temporaria neural plate (see C). Horizontal axis, relative values of stress forces; vertical axis, number of cell walls measured; am, axial mesoderm; blp, blastopore; dbl, dorsal blastoporal lip; end, endoderm; nch, notochord; ne, neuroectoderm. (Modified from Beloussov and Lakirev, 1988.)

MECHANICAL STRESSES AND MORPHOGENESIS

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1988 for more details). In this way we can go through all of the cell apices in a given area and return to the initial apex from the opposite side, measuring some tensions for the second time. If the repeated measurements of the same wall tensions do not differ greatly from the first ones, we may conclude that the measured domain has been more or less mechanically closed (equilibrated) and our measurements are correct. (If the measurements differ greatly, we have to conclude that some significant tensions are located outside the area studied or the print plane, making our evaluations incorrect.) Measurements performed on a sagittal section of an early gastrula suprablastoporal region and on a transverse section of a neural plate not only satisfied conditions for accuracy but also coincided generally with the maps based on incision experiments (Fig. 3B, cf. 1A and Fig. 3C, cf. l F ) , supporting their validity. We also found a pronounced bimodal distribution of tensile force values in embryonic tissues (Fig. 3D). This confirms the possibility of distinguishing only two classes of tension (strong and weak) in the stress maps and points to the bistability (nonlinearity) of the tensiongenerating mechanisms.

111. Tentative Estimates of the Range of Absolute Stress Values

One approach to this apparently simple but actually complicated task is to use as a starting point the value of the osmotically driven turgor pressure in the blastocoel, which is known to stretch the blastocoel roof (in our observations, the dissected roof immediately contracts by 10 to 50% of its initial length). The osmotic pressure of Danilchek’s solution (Wilson et al., 1989), which is suggested to be roughly isotonic to blastocoel medium, is 325 mosmol = 70 N/cm2. The tangential tensile stress S of a hemispherical shell stretched by this pressure may be calculated by a standard formula, S = rP/(2t), where r is the radius of a hemisphere, P is the pressure,’ and t is the thickness of a shell. Taking, for Xenopus laevis embryos, r = 600 p m and t = 100 pm, we obtain S = 200 N/cm2 = 2 MN/m2 and, taking into account the relative lengths of dissected roof contractions, the Young’s modulus E ranges from about 16 to 80 MN/m2. I Strictly speaking, in this formula P should be equal to the difference between osmotic pressure values of the blastocoel and the external medium, rather than to the osmotic pressure of the blastocoel itself. However, in the first approximation the osmotic pressure of the external medium may be ignored since it is no more than about 25-50 mosmol.

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This shows that in embryonic tissues the values for stress and Young's modulus are in the ranges typical for other biological samples [for example, Young's modulus for the shell membrane of a hen's egg is 8 MN/m2 and that of a human tendon is 24 MN/m2 (Gordon, 1978)l. Note, however, that according to incision experiments, the tension of a blastula surface is relatively small compared, for example, with the tension of an outer layer of lateral ectoderm stretched by neurulation movements. We hope that these rough estimates will stimulate the development of more precise and adequate techniques for measuring stresses in embryonic tissues.

IV. Morphogenetic Effects of Reorientation and Relaxation of Tensile Stresses in Amphibian Embryonic Tissues

A. Tissue Stretching Keller and colleagues (1989) showed that the intercalation movements of cells play a leading role in the morphogenesis of amphibian axial rudiments, as well as in a number of other embryonic processes. In the normal development of amphibian axial organs, the intercalation movements are oriented perpendicularly to the dominating longitudinal stretching of the dorsal embryo wall caused by the involution movements of gastrulation. Is this a coincidence or does it point to a universal relation between the direction of tissue stretching and intercalation movements? To investigate this, the following sets of experiments were made: ( 1 ) rotation of a piece of a late gastrula dorsal wall (neuroectoderm together with the axial mesoderm) 90" around the vertical axis; (2) transplantation of a similar piece into another tensile field created by the neurulation movements of a host embryo (Beloussov, 1980); and (3) explantation of an early gastrula suprablastoporal region onto a piece of adhesive latex film artificially stretched 1.5-2 times perpendicular to the antero-posterior axis of a host embryo (Beloussov et af., 1988). In most of these experiments, the axial rudiments became elongated in the direction of the applied stretching and, hence, perpendicular to their presumptive longitudinal directions. Histological examination showed that this was caused by the reorientation of cell intercalation movements perpendicular to the applied tension. The latex explantation experiments showed that about 30 min of stretching were enough to reorient the intercalation movements and, consequently, the direction in which the rudiment elongated. Thus, tissue stretching may be considered a process that triggers the direction of cell intercalation.

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B. Relaxation of Tensile Stresses

Relaxation of tensile stresses promotes columnarization of cells (mostly in the outer ectodermal layer), lobopodial activity, and loss of cell contacts (mostly in deep ectodermal and mesodermal cells), which may lead to some grave morphological anomalies. In the experiments mentioned earlier (Beloussov et al., 1988), if pieces of suprablastoporal tissue were transplanted onto a nonstretched latex film (or films stretched for no more than 3-5 min), within 1-2 hr the transplants became dissociated into single, actively migrating cells. The structural differences between stretched and nonstretched explant cells were visible several minutes after explantation. Whereas the stretched cells rapidly developed the extended contact zones associated with microfilament bundles (oriented in the direction of stretching), the nonstretched ones reduced the initial (at that stage quite rudimentary) intercellular contacts and produced numerous lobopodia at their basal surfaces. In the next set of experiments (Beloussov et al., 1990), we relaxed the tangential circumferential tensions of the embryonic surface at the early gastrula stage by making incisions in the ventral embryonic regions and inserting a section of homologous tissue in the wound cut. Within a few dozen minutes, the mesodermal and deep ectodermal cells of the relaxed embryos, similar to those placed on unstretched latex films, lost most of their contacts and revealed numerous lobopodia. Later, the external and then the deep ectodermal cells become considerably columnarized, increasing their length/width ratios from about I : 1 to about 1 : 2.5 or 3.0. As a result, the columnarized ectodermal cell areas in the relaxed embryos, which are restricted in the normal embryos by the neural plate regions spread considerably ventralward without becoming sharply delimited from the noncolumnarized ventralmost cells. Another effect of relaxation of tension was the marked inhibition of cell intercalation movements, both in the inner cells of the blastocoel roof at the early gastrula stage and in the axial mesoderm of the late gastrula-early neurula embryos. As a possible consequence of the abnormal enlargement of columnarized cell areas and inhibition of intercalation movements, numerous structural anomalies were found in advanced embryos. These included the abnormal ventral extension, duplicating or even triplications of neural rudiments, duplication of auditory vesicles, fusion of neural and mesodermal rudiments, and inhibition of mesodermal segmentation. One may conclude therefore that the mechanical stresses in embryonic tissues-which regulate the formation of intercellular contacts, the arrangement and dimensions of cell columnarization zones, and the direction of cell intercalation movements-should be considered to be among the most important morphogenetic factors.

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C. Effects of Relaxation of Stress on Neural Tubes

Deformations which immediately followed localized frontal, sagittal, and transverse incisions of neural tubes in the embryos of Hynobius keyserlingii and Pleurodeles waftlii (Saveliev, 1988)showed their outer surfaces are under considerable longitudinal and circumferential tension (Fig. 4A). The tension cannot be associated with hydrostatic pressure in the neurocoel since it is retained in spite of the presence of a neuropore or any artificially created hole. Most likely, it is created partly by the preceding deformation of neural rudiments caused by closure of the neural tube and its subsequent bending, and partly by the dense package of proliferating neuroectodermal cells. Similar tensions have been found in the neural tubes of mouse and rat embryos and in aborted human embryos of 5 weeks.

FIG. 4 Effects of relaxation of tension in the neural tubes of Pleurodeles walrlii embryos. (A) Scheme of incisions along a plane and in b line and their immediate results (a, b). (B) The results of relaxation of stress in a neuroectodermal layer at about 0.5 hr. The grooves only slightly outlined in an intact layer (at left) are extensively reinforced, cells are elongated, and some of them are wedge-shaped (at right). (C,D) Details of cell behavior after relaxation of tension (C) Longitudinal cell reorientation, 10-20 min after relaxation (arrow indicates the dominating direction of cell reorientations). (D) Subsequent loss of cell contacts and cell rounding. (Modified from Saveliev, 1988.)

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The first and universal reaction to relaxation of stress, which took place 1-5 sec after operation, was the extensive elongation of neuroectodermal cells which still retain at that time their ordinary orientation (perpendicular to the tube walls). If the tension was relaxed by inserting an additional piece of homologous tissue in the neural tube (Saveliev and Besova, 1990), such a reaction was more prolonged and led to an elongation that was 1.5-2 times the cell’s length. Another reaction typical for cell areas removed from the incision plane and that took place 0.5-2 hr after relaxation was a pronounced increase in as-yet slightly outlined grooves (Fig. 4B). The next reaction to relaxation caused by extensive incisions was the loss of neuroectodermal cell contact with the outer- and inner-tube surfaces and quite abnormal reorientation of cells in the longitudinal direction of the tube (Fig. 4C) that lasted for about 30 min. Within the next few hours, most of the cells became rounded and lost most of their contacts, leading to complete destruction of the relaxed part of the neuroectodermal layer (Fig. 4D). These experiments demonstrate the high sensitivity of neuroectodermal cells to the tensile regimes in neural tubes. Their reaction to relaxation of tension is generally similar to that reported in the preceding sections for early embryonic tissues. In the normal development of neural rudiments, tension seems to be necessary for maintaining the typical shape and orientation of neuroectodermal cells and the integrity of a neuroectodermal cell layer.

V. Surface Tension-like Components of Stresses in Embryonic Tissues

In physical bodies, tensile stresses may be generated by two basically different mechanisms: surface tension (ST) forces driving the molecules from the surface toward the liquid interior (perpendicular to the tensile force) or quasi-elastic forces associated with the deformation of covalent bonds in the direction of tension, without a molecular outflow. What kind of forces may be responsible for the changes and for maintaining stresses in embryonic tissues? In any case, the existence of quasi-elastic forces exemplified both by active contraction of actin microfilaments and by the tension resistance of (mostly) intermediate filaments cannot be denied. What about ST-like mechanisms? Although living cells cannot be literally identified with liquid drops, some processes that effectively simulate ST phenomena at the subcellular and cellular level are well known and only need to be collected together (as was done, in the framework of another approach more than a decade ago, by Steinberg, 1978).

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To summarize our knowledge to date, at the subcellular level ST-like phenomena may be identified with internalization-resorption (an increase in ST) of cell membrane subunits or the opposite, externalization-insertion (a decrease in ST as far as a negative ST, or surface compression). The first process is usually expressed as endocytosis and the second as exocytosis. Generally (but, as we believe, constructively) speaking, ST-like phenomena may operate at the tissue level as well. In particular, inward cell migration, which decreases the surface-to-volume ratio of a multicellular cluster, should be considered an ST increase whereas cell migration toward the surface as well as cell intercalation (both increase surface-tovolume ratios) considered an ST decrease (down to a negative ST). A. Subcellular Level: Effects of Relaxation of Tension

As was described elsewhere (Beloussov et al., 1990), the tension of the apical ectodermal cell surface drops immediately after tissue incision and recovers again about 4 hr later. What are the relative roles of quasi-elastic (contractile) and ST-like processes in such a restoration, particularly in cell columnarization, which starts quite soon after relaxation? Although the first signs of apical cell membrane resorption (endocytosis) could be seen as soon as 10 min after relaxation (Fig. 5B),within the first hours after relaxation, membrane resorption seems to be slow in relation to the overall transverse contraction of cell bodies, as indicated by the bulging of apical cell surfaces an hour after relaxation (Figs. 5C, C,; 6D). Meanwhile, about 4 hr after relaxation, the apical cell surfaces flatten and become covered by numerous microvilli associated with the subapical microfilament layer and endocytotic vesicles (Fig. 5D,E; 6E,F) indicating the extensive shrinking and resorption of cell membranes. It is worth mentioning that similar structures are quite typical for the bottle-shaped cells from the early gastrula blastoporal area (Figs. 5F, 6C). The rheological conditions in this area are indeed similar to those in the artificially relaxed sheets since the tensile stress in the blastopore vicinity is very low or even negative (compression) because of the vegetalward pushing by intercalated suprablastoporal cells. The predominance of shrinking-resorption processes in apical cell membranes is thus characteristic for low or negative tensile stresses. We may conclude therefore that both quasielastic contraction and ST-like resorption phenomena contribute to restoring tension in relaxed tissues. Meanwhile, there are obviously the resorption processes which provide the stability and irreversibility of restoration of tension. Quite a similar set of events has been observed after surface tension in loach eggs was reduced by sucking out most of the yolk granules (Ivanen-

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FIG. 5 Effects of relaxation by circumferential tensile stresses in the apical regions of the outer ectodermal layer in Xenopus laevis early gastrula embryos by transmission electron microscopy (TEM) and light optical data. (A) Apical surface of intact ectoderm. (B) A fragment of apical ectodermal cell surface, 10 min after relaxation. The pointer indicates the invagination of plasma membrane. Arrows show vesicles forming glycocallix-covered membranes, indicating their recent endocytotic origin. (C, C , ) TEM and light optical picture of an outer ectodermal layer 1 hr after relaxation. At that time, the cell’s length-to-width ratio rises from 1: 1 to 2: 1. The bulging of as-yet rather smooth apical cell surfaces indicates the sphincter-like transverse contraction of cell bodies nonequilibrated with apical membrane (continued)

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FIG. 5 (continued)

resorption. (D) Apical cell area, 4 hr after relaxation. The existence of numerous microvilli underlaid by microfilaments indicates contraction-resorption of the apical cell membrane. (E) A similar area fragment, 4 hr after relaxation. The pointer indicates membrane invagination at the base of a microvillus. (F) A fragment of an apical surface of a blastoporal bottle-shaped cell at the early gastrula stage with numerous microvilli underlaid by microfilaments and endocytotic vesicles. Arrows in B, D-F indicate endocytotic vesicles. Bar = 1 pm.

FIG. 6 Changes in the apical cell surfaces of Xenopus laeuis early gastrula embryos after relaxation of tension: shown by scanning electron microscopy (SEM). (A,B) Apical surfaces of intact lateral ectoderm at the 1 Ith and 13th stages, respectively. The surfaces are almost smooth with only a few microvilli concentrated in the vicinity of the contact zones. (C) Blastoporal area of an early gastrula. The surfaces of invaginating cells (upper part of the frame) are covered by numerous microvilli. (D) The same area and developmental stage as seen in A, 1 hr after relaxation of circumferential tensions. Cell surfaces bulge and are

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still smooth (cf. Fig. 5C). (E) The same area and developmental stage as in B, 4 hr after relaxation. Most of the cells are covered with numerous microvilli (although cell clusters with smooth surfaces can also be seen). (F) A detail of E. A mosaic of still smooth and extensively microvilli-covered cells is seen. Bar = 10 pm. (continued)

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FIG. 6 (continued)

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kov et al., 1990). According to the author’s description, the diminished egg rapidly (within 3-10 min) restored its initial shape (and hence surface tension) by a rapid folding of the cell membrane followed by its internalization (endocytosis). The pronounced endocytosis located only in the folded regions of the yolk syncytium layer has also been observed during Fundulus epiboly (Betchaku and Trinkaus, 1986).

B. Subcellular Level: Effects of Stretching One of the universal and nontrivial effects of tissue stretching observed in the earlier-mentioned latex experiments (Beloussov ef at., 1988) was the rapid formation of extensive cell protrusions overlapping the surfaces of adjacent cells only along the stretching direction; sometimes the protrusions were associated with the adhesive intercellular contact zones (Fig. 7C,D, cf. A,B). The same effect can be observed on the apical surfaces of the outer ectodermal cells in the suprablastoporal zone of intact gastrulating embryos (Fig. 7E,F). As shown by incisions, these cells are also extensively stretched by the neighboring and underlying tissues. Since no reserves of a folded membrane could be seen in the control (nonstretched) cells (Fig. 7A,B), the formation of protrusions is most probably associated with the production of new membrane. It is also of interest to trace the rapid shift of the protrusion-generating regime to the shrinking and resorption that passes from the stretched suprablastoporal cells to the contracted cells of the blastopore proper (Fig. 7F). Sometimes both regimes could be seen simultaneously within the same cell (Fig. 7E). Extensive surface membrane production (the analog of a negative ST), as a consequence of stretching, appears to be a widespread phenomenon, particularly in the realm of plant morphogenesis where stretching is initiated by turgor pressure (Harold, 1990). Membrane insertion in the stretched processes and leading edges of moving animal cells is also well known (e.g. Bretcher, 1988). One may speculate that the membrane insertion is mediated by exocytosis, promoted in its turn by a stretch-associated increase in intercellular calcium concentration (Christensen, 1987). C. Cellular and Tissue Level

The most general response of embryonic tissues to relaxation of tension [caused either by incisions (Beloussov et al., 1990), or by a complete extirpation of a tissue fragment (Beloussov and Lutchinskaia, 1983; Beloussov and Petrov, 1983)] consists in the rapid migration of a large number of cells into the tissue depth and thus a decrease in the surface-

flG. 7 Effects of stretching on the protrusive cell activity and production of excessive parts of apical membranes. (A,B) Outer and inner surfaces, respectively, of suprablastoporal explants extirpated from Xenopus laeuis early gastrulae and placed on a nonstretched latex film. Only small intercellular contact zones and no overlapping protrusions can be seen. (C,D) Same surfaces, respectively, of the samples incubated on the 2-fold stretched latex film. Extensive overlapping cell protrusions oriented in the stretching direction and associated with the formation of additional contact zones (D) are seen. For A and C, incubation times are

4 hr; for B and D, 10 min. (E,F) Apical cell surface from suprablastoporal (E) and blastoporal proper (F) zones of intact Xenoppus laevis early gastrulae. The protrusion-generating regime typical for the stretched suprablastoporal cells (arrows) is abruptly shifted to the microvilligenerating regime in the invaginating blastoporal cells (F, pointer). In E, the protrusive regime of a suprablastoporal cell is combined with the production of a few microvilli by the same cell. In B, E, and F, the outer cell membranes are stained with Ruthenium red. Bar = I gm. (B and D are from Beloussov et al., 1988).

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to-volume ratio (Fig. 8E-G). On the other hand, as shown earlier, tissue stretching promotes cell intercalation (Fig. 9) and hence an increase in the surface-to-volume ratio. A similar phenomenon regarding an increase in the surface-to-volume ratio caused by outward cell migration (preceded by quasi-elastic cell stretching) has been reported by Steinberg (1978) in aggregates of chick embryonic heart cells flattened by prolonged centrifugation. One may conclude therefore that at the tissue level, the stretch-dependent ST-like phenomena are effectively simulated by redistribution of cells. As with subcellular phenomena, they may be generally

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FIG. 8 Some characteristic forms of hyperrestoration (HR)of tensile stresses after their

relaxation. (A) An intact epithelial layer moderately stretched by turgor pressure from inside (filled oblique triangle). The tangential stretching stress is proportional to the surface angle values (inset to right), which are relatively high. (B) The same layer immediately after relaxation of tension (caused by incisions, as shown by vertical triangles in (A). The reduction of tangential tensile stresses (E) compared with A is indicated by a decrease in the surface angle values (cf. A, and B,). C-G illustrate the different ways tension is hyper-restored ( C ) Swelling of individual dispersed cells. (D) Columnarization of a coherent cell domain associated with the flattening of adjacent cells: the edges of the layers are assumed to be fixed. (E,F) Sphere formation of explants with the subsequent formation of osmotically swollen cavities. (G) Rolling of explants associated with internal swelling. In the latter case as well as in many normal developmental processes, a series of obliquely stretched cells are formed (“cell fans”), indicating a considerable increase in the resulting tangential tensile stresses ( G , , cf. A, and B,).

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FIG. 9 A diagram for generation of internal pressure stresses (C, double horizontal arrows) as a result of initial stretching (B, horizontal arrows) and stretch-promotedcell intercalation (B, vertical arrows). A shows the suprablastoporal region used for experiments B and C. The double crescent indicates the dorsal hip of the blastopore. For other details, see the text.

characteristic as showing a tendency to increase ST after relaxation and to decrease it after stretching.

VI. Some Concepts Related t o Stress-Force Feedback

A. Models of Cell Columnarization The idea of stress-force feedback as a regulatory function was first suggested by Odell et al. (1981). The authors point out that in a number of morphogenetic processes associated with cell columnarization, the columnarized cells will inevitably stretch tangentially to the apical surfaces of the adjacent cells. It is this stretching which triggers the active tangential contraction of the next cell(s). In such a way, the stretching-contracting wave should spread along embryonic tissue to an indefinite distance. Strangely enough, the best experimental evidence supporting the idea of such a “stretching-contraction response” is related not to the gastrulating multicellular embryo, but to quite another object, namely, the cytoplasmic strands of a slime mold, Physarum (Fleischner and WohlfarthBottermann, 1975). On the other hand, from our observations, the epithelial sheets of metazoan embryos, including sea urchins (Beloussov and Bogdanovsky, 1980) and amphibians (Beloussov et al., 1990), not only tangential stretching, but on the contrary, relaxation of tangential tensions, promotes cell columnarization. The corresponding idea of the inhibition rather than the promotion of cell columnarization by increases in tangential tension, which is opposite to the suggestion by Odell and colleagues, has been developed in the Belintzev et al. (1987) model of epithelial morpho-

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genesis. In contrast to Odell’s model, one can easily interpret the arrest of a cell columnarization wave and hence the stable segregation of a cell sheet under tension to the domains of highly columnarized and tangentially stretched cells, as well as the scale invariance of such a segregation. However, some of the kinds of stress responses described here, including the stretch-dependent cell intercalation, are beyond the scope of the Belintzev et al. model. The stretch-contraction response, even under some more special conditions (see Section WILD) also seems to take place in metazoan embryonic tissues. That makes it desirable to create a more general concept of stress-force relations which could embrace all of the cases mentioned earlier, and which might create a basis for modeling real morphogenetic processes. Such a concept is suggested in the following section.

VII. A Hypothesis of “Hyperrestoration” of Preexisting Stresses

Many, if not all of the cell and tissue responses to stress changes described here may be qualified as the manifestations of a general tendency for restoring and even “hyper”-restoring the initial stress values. On the subcellular level, these are both the membrane resorption processes which follow relaxation (a shift toward tension increase) and the membrane production processes that follow stretching (a shift toward tension decrease). Besides the examples already presented, such an idea may be adequately illustrated by the recently observed stretch and relaxation responses in growing axons (Dennerly et al., 1989). Within a certain stretching range neurites respond to tension as passive viscoelastic bodies, whereas at a stretching threshold of 100 microdynes, an active elongation response, sometimes associated with a marked lowering of tension, was observed; on the other hand, after sudden diminution of tension, neurites contract, sometimes doubling the preexperimental steady-state tension. To summarize the main stress responses exerted at the tissue level, we see that after the initial tangential tension on a cell layer, provided as a rule by turgor pressure (Fig. 8A), is relaxed by incision (Fig. 8B), a piece of tissue, depending on the experimental conditions (generally speaking, on the boundary) reveals different kinds of behavior, all of them nevertheless associated with an increase in tension, either on single cells or on the tissue level. A tissue may dissociate itself into single extensively swollen cells with stretched plasma membranes (Fig. 8C). In an intact layer with its edges fixed, some of the cells become columnar while others are flattened (Fig. 8D). An isolated tissue piece forms a sphere and devel-

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ops an osmotically driven turgor pressure in the newly formed cavity (Fig. 8E,F), which is typical for blastocoel roof tissue (Beloussov and Petrov, 1983). Finally, a piece of tissue (extirpated from more advanced embryos) can also reveal more complicated reactions, including cell columnarization, oblique orientation, inward migration, and increase in turgor pressure (Fig. 8G). According to the “surface angle hypothesis” the formation of obliquely stretched cell groups (“cell fans”) situated in the edge regions of the rolled explants indicates that the initial tangential tension of the intact cell layer is not only restored but even surpassed (Fig. 8G,, cf. A , , B,). The cell intercalation response to external stretching described earlier is interpreted in Fig. 9. After extirpation of a suprablastoporal region (Fig. 9A), a tissue piece is stretched by an external force (Fig. 9B, horizontal arrows). The intercalation response (Fig. 9B, vertical arrows) tends to diminish the apposed stress and in doing so, overshoots zero stress value, developing a negative (pressure) strain (Fig. 9C, double horizontal arrows). We can see again that the initial stress value has been extensively hyperrestored. This permitted us, together with Dr. J. Mittenthal (Mittenthal and Beloussov, 1991), to suggest the following generalization, which may be defined as a hyperrestoration (HR), or HR rule: A cell or a piece of tissue, after being shijited by an external force out of its initial mechanical equilibrium, generates an active mechanical response directed toward restoring the initial stress value, but as a rule overshoots it to the opposite side. The main task which we would ascribe to the HR rule is in promoting the interpretation of the real time spacio-temporal successions of morphogenetic processes. In approaching this task, we should try to outline, first of all, what may be defined as some standard morphomechanical situations, found in various morphogeneses. As will be shown in the next sections, all of these situations can be, on one hand, derived from the HR rule and, on the other hand, be used to reconstruct rather prolonged periods of morphogenesis.

VIII. Some Standard Morphomechanical Situations A. A Unilayered Sheet without Cell intercalation Capacities

In the outer layer of amphibian embryonic ectoderm, the capacities for cell repacking and intercalation are very low, if present at all. Let us consider such a layer with its edges fixed and under moderate elastic

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stretching (Fig. 10, MSl). Suppose that some local influence induces cell 1 to become columnar, that is, to contract its apical surface (ad) and to extend its lateral surface (Isl). If mediated by endo-exocytosis, as discussed before, these processes reinforce each other by the apico-basolatera1 membrane flow (dashed, curved arrows). At the same time, both the lateral and apical surfaces of the adjacent cell 2 (ls2) and (asZ), respectively, are passively stretched by their attach-

n

MS1

a

MS2

r-

I

MS4

FIG. 10 Some standard morphomechanical situations (MS1-4) derived from the HR rule. Dotted curved arrows in MSl indicate the possible Row of membrane particles from the relaxed apical to stretched lateral cell membranes. t ( , Passive (elastical) contraction or compression by outside force; -, passive stretching by outside force; x ,active contraction; e, active stretching. For other designations, see text.

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ment to the corresponding cell 1 walls. Meanwhile, the stretching conditions in Is2 and as2 are different. Whereas in Is2 the contraction response is improbable, being hampered by Is1 stretching, the same response in as2 may be permitted until the common tangential tension of the cells apical surfaces is not too great. Instead, in Is2 membrane insertion is promoted. As a result, cell 2 reproduces the shape of cell 1, that is, becomes columnar. In the same way the next cell, 3, will be involved in columnarization (Fig. 10, MSl ,b) and so on, until the common tension of the apical cell surfaces reaches a certain threshold value, resisting the active contraction of the next cell apical surface. After passing this threshold, the apical surfaces of as-yet noncolumnarized cells should be actively stretched by membrane insertion, rather than becoming columnar. In such a way, a sheet composed initially of similar, roughly isodiametric cells becomes differentiated into the coherent domains of extensively columnarized and stretched cells, which coincides with the conclusions of the Belintzev et al. (1987) model (at the same time it agrees with the idea of Ode11 et al., 1981, of a stretching-contracting wave).

B. A Single Sheet Capable of Cell Intercalation Suppose that a central part of a sheet is stretched by an external force (for example, by turgor pressure in the underlying cavity) while its edges are attached to a nonstretched substrate. According to the HR rule, the strong and stable stretching should promote cell intercalation which will compress or at least relax the attached edge zones (Fig. 10, MS2). That will switch on the membrane resorption processes in the latter (cell columnarization equals apical contraction in the outer parts of edge zones and the loss of cell contacts in internal parts). Now, the apical contraction will reinforce the passive stretching and hence promote further cell intercalation in the central zone. This will relax the edge zones even more, stimulating further cell membrane resorption processes, and so on. Thus, a positive feedback loop will be established between the central and edge zones, continuing to act until the cell’s capacities for intercalation and/ or membrane resorption are exhausted. This situation seems to play a central role in the preinvolution processes of gastrulation, the central zone corresponding to the blastocoel roof, and the edge zones to the marginal ones. Exploiting White’s (1990) ideas on the mechanisms of cytotomy and cell migration, one may suggest that the same dynamic scheme may be applied in these cases as well. For example, during egg cytotomy, the expanding (and membrane insertion) zone corresponds to the polar regions, whereas the contracting (membrane resorption) zone corresponds

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to the furrow region (Fig. 10, MS2’). For a single moving cell, the former corresponds to the leading edge and the latter to the trailing edge. The stress-force feedbacks appear to be astonishingly similar in gastrulation, division of a cell body, and movement of a single cell! C. Two Superimposed and Mechanically Bound Cell Sheets

In the first case (Fig. 10, MS3a), one sheet is capable of cell intercalation (an active sheet, as) whereas the other undergoes passive stretching only (PSI.

Suppose that the cell of an active sheet (marked by a cross in the figure) is intercalated from the deep to the superficial layer of as (solid arrow). To the extent that each cell adjacent to ps is postulated to be mechanically bound to ps, the stretching stress caused by each intercalating cell will spread throughout the entire ps and back to the whole as again, continuing to stimulate cell intercalation in as. In such a situation, as cell intercalation proceeds, the stretching on each as cell (i.e., the length) remains constant. Thus, the positive feedback loop between as and ps remains invariable as long as ps is capable of stretching and as is capable of cell intercalation. This situation is probably similar to that between the outer (ps) and the deep (as) ectodermal layers. In the second case, both superimposed cell sheets are capable of cell intercalation (Fig. 10, MS3b). In this case, a particularly powerful positive feedback loop between the sheets will be created: the active (intercalationmediated) stretching of the top sheet will passively stretch the bottom sheet, promoting cell intercalation in this sheet, which will stretch the top sheet again, stimulating cell intercalation, and so on. This situation seems to come into action during the gastrulation process with the beginning of involution, the pre- and postinvoluted layers being its main components. D. Stretching-Contraction Cell Relay

Consider a dense and viscous two- or three-dimensional tissue in which any cell contraction is rapidly damped in its immediate surrounding rather than elastically transmitted to a large distance (as in MSl; see Fig. 10, MS4). Under these conditions, the next contracting cell will stretch only its immediate neighbors, so that the strains generated by the different cells will not accumulate. Such a situation may take place in the highly viscous multilayered chordomesodermal and neural tissues of amphibian embryos. As shown by modeling (Beloussov and Lakirev, 1988), under these specific circumstances a stretch-contraction response that travels as

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a wave throughout the tissue is plausible (contrary to unilayered epithelia, where such a relay would be effectively hampered by the elastic resistance stresses). The next section describes how these morphomechanical situations can be used to reconstruct the general outlines of amphibian embryo development, from the blastula to the neurula stage.

IX. Qualitative Reconstruction of Morphogenetic Processes during Gastrulation and Neurulation of Amphibian Embryos

We start from the blastula stage with the following initial conditions: (1) the existence of osmotically-driven turgor pressure in the blastocoel cavity which stretches the blastocoel roof; (2) the existence of dorsoventral asymmetry of the embryo, resulting in greater morphogenetic activity on the dorsal side than the ventral. Under these circumstances, at the approximately late blastula stage, the combination of MS3a and MS2 (in Fig. 10) begins to work (Fig. 1IA). As a result, the blastocoel roof is actively stretched and the columnar and contact-free rounded cells are formed on its edges, in the outer and inner layers, respectively. According to the initial condition (2), this process should go on with greater intensity on the dorsal rather than the ventral side (Fig. ZlB). Stretching of the blastocoel roof inevitably makes the preinvoluted part (Fig. IlC, PRI) start covering the postinvoluted one (Fig. 11C, PSI). After firm mechanical contacts between both become established, the MS3b feedback loop switches on and becomes the main driving force for the whole involution process (Fig. 1lC,D). On the edges of both layers, areas of contact-free (mesenchymal) cells are created, accompanied by columnar cells at the outer periphery. In the caudal embryo region, the mesenchymal cells contribute to the future tail bud, whereas in the cranial region of the involuted layer, they contribute to prechordal mesenchyme. All of the previously mentioned processes establish the initial conditions for neurulation. The crucial point here is the anteroposterior elongation of the dorsal embryo surface, which is expressed as passive deformation in the outer ectodermal layer and as active intercalation-mediated stretching in the inner ectodermal layer (hypoectoderm) and chordomesoderm {Fig. 11E,F). In both cases, the longitudinal tissue stretching causes passive transverse compression (Poisson’s mechanical effect). In addition, it leads to passive tissue compression anterior and posterior to the stretching zone. The anterior compression should be greater than the posterior since

zsw

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the latter is continuously relaxed by involution movements. Meanwhile, in both compression zones, owing to the same Poisson’s effect, transverse stretching should take place, which is again greater in the anterior zone. This stress pattern outlines the outer contours of the neural plate (Fig. 1 lF, dotted lines). At the same time, according to MSla, cell columnarization promoted by transverse compression is taking place along a lateral to dorsomedial line (Fig. 11G). Its lateral borders coincide with those of the neural plate. Since the outer surface of the dorsal ectoderm is stretched longitudinally and hence compressed transversely to a greater extent than any other cell layer, the columnarized cells become inclined by their apical edges toward the dorsomedial line (Fig. 11H). Neurulation per se (transformation of a neural plate to a neural groove) may be considered a result of the stretch-contraction wave (according to MS4) that passes along these oblique columnarized cells. This assumption has already been tested by quantitative modeling (Beloussov and Lakirev, 1988).

X. Some Views on a Mechanical Approach t o Ontogenetic Processes Mechanical stresses, in their simplest form being osmotically driven, should be considered as one of the most universal and phylogenetically ancient physical properties of living cells, including the Prokaryota (Harold, 1990). It is not surprising, although it remains of utmost importance, that mechanical stresses not only play a role in regulating morphogenesis proper (the deformations of embryonic material) but also profoundly affect a number of refined intracellular processes, including gene expression (e.g., Allan and Harrison, 1980; Ben Ze’ev, 1985; Braam and Davis, 1990). The idea has also been put forward that mechanically mediated cytoskeleta1 mechanisms may play a crucial role in developmental phenomena related traditionally to chemical inducers (Gordon and Brodland, 1987). Can it be that the involvement of mechanical links may help in interpreting the exciting recent observations on the neuralization of embryonic ectoderm caused by the mere dissociation-reassociation of its cells without any additional chemical inductors (Grunz and Tacke, 1989; Saint-Jeannet et al., 1990)?We cannot exclude such a possibility. At any rate, an “active FIG.ll The morphomechanicalschemes of amphibianembryo development from late blastula to neurula stages. The spacio-temporal time locations of the different morphomechanical situations designated as in Fig. 10 are shown. The heavy arrow-heads point to compressed

cell zones. In C,D, the mechanical bins of post- and preinvoluted cell layers are shown schematically.

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solid body approach” to a developing embryo may become more fruitful than it looks at first glance. References Allan, M., and Hamson, P. (1980). Coexpression of differentiation markers in hybrids between friend cells and lymphoid cells and the influence of cell shape. Cell (Cambridge M U S S . )19, 437-443. Belintzev, B. N., Beloussov, L. V., and Zaraisky, A. G. (1987). Model of pattern formation in epithelial morphogenesis. J . Theor. Biol. 129, 369-394. Beloussov, L. V. (1979). Experiments on changing the tensile fields of amphibian embryos. Ontogenez (Sou. J. Deu. Biol.) 10, 120-129. Beloussov, L. V. (1980). The role of tensile fields and contact cell polarization in the morphogenesis of amphibian axial rudiments. Roux’s Arch. Deu. B i d . 188, 1-7. Beloussov, L. V., and Bogdanovsky, S. B. (1980). Cellular mechanisms of embryonic regulation in sea urchins. Ontogenez (Sou. J . Deu. Biol.)11, 467-476. Beloussov, L. V., and Lakirev, A. V. (1988). Self-organization of biological morphogenesis: General approaches and topo-geometrical models. I n “Thermodynamics and Pattern Formation in Biology” (I. Lamprecht and A. I. Zotin, eds.), pp. 321-336. W. de Gruyter, Berlin, New York. Beloussov, L. V., and Lutchinskaia, N. N. (1983). Study of the relay cell interactions in the explants of amphibian embryonic tissues. Cytologia (Russ.) 25, 939-944. Beloussov, L. V., and Petrov, K. V. (1983). The role of cell interactions in the differentiation of induced tissues of amphibian embryos. Ontogenez (Sou. J . Deu. Biol.)14, 21-29. Beloussov, L. V., Dorfman, J. G., and Cherdantzev, V. G. (1975). Mechanical stresses and morphological patterns in amphibian embryos. J . Embr. Exp. Morph. 34, 559-574. Beloussov, L. V., Lakirev, A. V., and Naumidi, I. 1. (1988). The role of external tensions in differentiation of Xenopus laeuis embryonic tissues. Cell D$f. Deu. 25, 165-176. Beloussov, L. V., Lakirev, A. V., Naumidi, I. I., and Novoselov, V. V. (1990). Effects of relaxation of mechanical tensions upon the early morphogenesis of Xenopus laeuis embryos. I n t . J . Deu. Biol. 34, 409-419. Ben Ze’ev, A. (1985). Cell shape, the complex cellular networks and gene expression. Cell Musc. Motil. 6 , 23-53. Betchaku, T., and Trinkaus, J. P. (1986). Programmed endocytosis during epiboly of Fundulus heteroclitus. Am. Zool. 26, 193-199. Braam, J., and Davis, R. W. (1990). Rain-, wind- and touch-induced expression of calmodulin and calmodulin-related genes in Arabidopsis. Cell 60, 357-364. Bretcher, M. S. (1988). Fibroblasts on the move. J. Cell Biol. 106, 235-237. Burnside, B . (1971). Microtubules and microfilaments in newt neurulation. Deu. Biol. 26, 416-441. Christensen, 0. (1987). Mediation of cell volume regulation by Ca influx through stretchactivated channels. Nature (London) 330, 66-68. Dennerly, T. J., Lamoureux, P., Buxbaum, R. E., and Heidemann, S. R. (1989). The cytomechanics of axonal elongation and retraction. J . Cell B i d . 109, 3073-3083. Fleischner, M., and Wohlfarth-Bottermann, K. E. (1975). Correlation between tension force generation, fibrillogenesis and ultrastructure of cytoplasmic actomyosin during isometric standarts. Cytobiologie 10, 339-365. Goodwin, B. C. (1985). What are the causes of morphogenesis? BioEssays 3, 32-36.

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Goodwin, B. C., and Trainor, L. E. H. (1985). Tip and whorl morphogenesis in Acerabularia by calcium-regulated strain fields. J. Theor. Biol. 117, 79-106. Gordon, J. E. (1978). “Structures, or Why Things Don’t Fall Down.” Penguin Books, Harmondsworth. Gordon, R.,and Brodland, G. W. (1987).The cytoskeletal mechanics of brain morphogenesis: Cell state splitters cause primary neural induction. Cell Biophys. 11, 177-238. Gordon, R., Goel, N. S., Steinberg, M. S., and Wiseman, L. L. (1972). A rheological mechanism sufficient to explain the kinetics of cell sorting. 1. Theor. Biol. 37,43-73. Grunz, H., and Tacke L. (1989). Neural differentiation of Xenopus laeuis ectoderm takes place after disaggregation and delayed reaggregation without inducer. Cell Diff. Deu. 28, 21 1-218. Harold, F. M. (1990). To shape a cell: An inquiry into the causes of morphogenesis of microorganisms. Microbiot. Reu. 545, 381-431. Ivanenkov, V. V., Meshcheryakov, V. N., Martynova, L. E. (1990). Surface polarization in loach eggs and two-cell embryos: Correlation between surface relief, endocytosis and cortex contractility. I n t . J . Deu. Biol. 34, 337-349. Jacobson, A. G., and Gordon, R. C. (1976). Changes in the shape ofthe developing vertebrate nervous system analyzed experimentally, mathematically, and by computer simulation. J . EX^. ZOO^. 197, 191-246. Keller, R., Cooper, M. S., Danilchik, M., Tibbetts, P., and Wilson P. A. (1989). Cell intercalation during notochord development inXenopus laeuis. J . Exp. Zool. 251,134-154. Kolega, J . (1986). Effects of mechanical tension on protrusive activity and microfilament and intermediate filament organization in an epidermal epithelium moving in culture. J . Cell Biol. 102, 1400-1411. Martynov, L. A. (1982). (Russ.) The role of macroscopic processes in morphogenesis. I n “Mathematical Biology of Development” (A. I. Zotin and E. V. Presnov, eds.), pp. 135-154. Nauka, Moscow. Mittenthal, J., and Beloussov, L. V. (1993). A biomechanical model for gastrulation of Xenopus laeuis. I n “Lectures on Theoretical Biology,” (K. Kull and T. Tiivel), Vol. 2, pp. 191-201. Valgus. Tallin (Estonia). Moms, C. E. (1990). Mechanosensitive ion channels. J . Mernbr. Biol. 113.93-107. Murray, J. D. (1989). “Mathematical Biology.” Springer-Verlag, Berlin. Odell, G. M., Oster, G., Alberch, P., and Burnside, B. (1981). The mechanical basis of morphogenesis. I. Epithelial folding and invagination. Deu. Biol. 85, 446-462. Oster, G. F. (1984). On the crawling of cells. J . Ernbr. Exp. Morphol. 83 (Suppl.), 329-364. Oster, G. F. (1988). Biophysics of the leading lamella. Cell Motil. Cyroskel. 10, 164-171. Oster, G. F., Murray, J. D., and Odell, G. M. (1985). The formation of microvilli. In “Molecular Determinants of Animal Form” (UCLA Symp. Mol. Cell Biol. New Ser. Vol. 31). pp. 365-284. Alan R. Liss, New York. Radeva, V., Ichev, K., Uvtscharoff, W., Dolapchieva, S. and Roussev, G. (1986). Some aspects of endocytosis of neuroepithelial cells in early newt’s neurula. Z. Mikrosk.Anat. Forsch. Leipzig, 100, 861-866. Saint-Jeannet, J.-P., Song, Huang, and Duprat, A.-M. (1990). Modulation of neural commitment by changes in target cell contacts in Pleurodeles walrlii. Deu. Biol. 141: 93-103. Saveliev, S. V. (1988). Experimental studies of mechanical tensions in neuroepithelial brain layers. Ontogenez (Sou. J . Deu. Biol.) 19, 165-174. Saveliev, S. V., and Besova, N. V. (1990). Polarization of neuroepithelial cells after introduction of a portion of the neural tube into the neural cavity in amphibian embryos. Ontogenez (Sou. J . Deu. Biol.) 21, 298-302. Steinberg, M. S. (1978). Cell-cell recognition in multicellular assembly: Levels of specificity.

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In “Cell-Cell Recognition” (A. S. G. Curtis, ed.), pp. 25-49. Cambridge Univ. Press, Cambridge. Stem, C. (1984). A simple model for early morphogenesis. J . Theor. Biol. 10, 229-242. Thompson, D’Arcy, W. (1942). “On Growth and Form.” Cambridge Univ. Press, Cambridge. Trinkaus, J. P. (1984). “Cells into Organs: The Forces that Shape the Embryo.” 2nd ed. Prentice-Hall, Englewood Cliffs, NJ. Wessells, N. K., Spooner, B., Ash, J. F., Bradley, M. O., Luduena, M. A., Taylor, E. L., Wrenn, J. T., and Yamada, K. M. (1971). Microfilaments in cellular and developmental processes. Science (Wushingfon,D.C.) 171, 135-143. White J. G. (1990). Laterally mobile, cortical tension elements can self-assemble into a contractile ring. In “Cytokinesis. Mechanisms of Furrow Formation during Cell Division’’ (G. W. Conrad and I. E. Schroeder, eds.), Vol. 582, pp. 50-59. New York Academy of Science, New York. Wilson, P. A., Oster, G., and Keller, R. (1989). Cell rearrangements and segmentation in Xenopus: Direct observations of cultured explants. Development 105, 155-166.

Locomotion of Tissue Culture Cells Considered in Relation t o Ameboid Locomotion Albert K. Harris Department of Biology, University of North Carolina, Chapel Hill, North Carolina 27599

I. Introduction The original purpose for which Ross Harrison invented tissue culture, now more than 80 years ago, was to prove the existence of a particular form of tissue cell locomotion, that of nerve growth cones (Harrison, 1910). He soon found (Harrison, 1914) that nearly all embryonic cell types share similar capacities for active, quasi-amoeboid locomotion of a type which Abercrombie (1980) later aptly termed “crawling locomotion.” Not j ~ sleukocytes, t but also fibroblasts, epithelial cells, pigment cells, muscle cells, even chondrocytes, will crawl about on suitably adhesive, solid substrata. Indeed, the “outgrowth” from explanted tissue fragments actually results from this crawling locomotion of individual cells, rather than from growth per se. Spermatozoa, which move by flagella, and red blood cells, which are purely passive in their displacements, seem to be the only exceptions to the rule that all the component cells of our body can crawl, ilt least during some stage of development. This locomotion is also known to play essential roles in normal embryonic morphogenesis (Trinkaus,

L 984).

Although there are some cases in which one can directly observe the locomotion of cells within living embryos, or even adult tissues (and such observations do generally match what can be seen in culture), it remains true that most of what is known about the crawling locomotion of tissue cells has been learned from studies of cells in tissue culture. This is partly because tissue culture allows optimum visibility, partly also because it permits an almost unlimited degree of experimental manipulation of the chemical and physical environment, and not least because the culture environment tends to stimulate increased cell locomotion. Among other hternalional Review of Cylology. Vol. 150

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Copyright B 1994 by Academic Press, Inc. All rights of reproduction in any form reserved.

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things, these observations have revealed major differences between the locomotion of tissue cells and the locomotion of free-living amebae. It is important to stress these differences, as well as to examine them carefully, because so much of our knowledge of the molecular basis of cell locomotion has been derived from studies of amebae. Indeed, it is also important to realize that there are several distinct kinds of amebae, and that these differ widely in the details of their locomotion (Allen, 1968, 1970). Thus, in order to make optimal use of this molecular knowledge, we need to pay special attention to the differences, as well as to the similarities, between tissue culture cells and these various amebae. Despite these differences (between tissue cells and amebae, as well as between one class of amebae and another), we will find that some common elements seem to be emerging from recent experimental results on the old question of membrane flow; these suggest that the propulsive mechanisms may be fundamentally the same after all. It also needs to be emphasized that the crawling activities of tissue cells have several functions in addition to simply moving cells from one place to another. Cell spreading and elongation are just as important, and are accomplished by the active crawling (in opposite directions) of different parts of the cell’s margin. The characteristic polygonal shapes of fibroblasts result from their cell bodies being stretched tightly between actively crawling cell margins in a continual tug-of-war; the more different regions of force is exertion, the more sides the polygon will have (see Dunn and Brown, 1987). In the case of monopodial fibroblasts, their single actively crawling margin stretches the cell body between itself and immobile cell-substratum adhesions on the opposite cell margin. Likewise, the elongate shapes of muscle cells and myotubes result from the concentration of their locomotory activities in two regions at opposite ends of the cell. In the case of epithelial sheets, flattening onto culture substrata results from active centrifugal locomotion of those cells at the edges of the sheet, which pull and stretch the rest (Vaughan and Trinkaus, 1966). Except in the case of strongly monopodial cells (of which polymorphonuclear leukocytes are the best example), the locomotion of tissue culture cells could fairly be described as competitive spreading, in which whatever net displacement occurs is the result of some parts of the cell margin winning their tug-of-war against the rest. For these reasons, the considerations of propulsive mechanisms that follow will concentrate primarily on the process of active spreading. It is also important to emphasize that, in addition to pulling themselves forward past extracellular materials, tissue cells are also capable of pulling extracellular materials rearward past themselves. In other words, motile cells can sometimes act more like conveyor belts or winches, rather than

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like tractors. This rearward or retrograde transport will be extensively discussed in relation to possible mechanisms of force exertion, but we should also realize that it can itself serve morphogenetic functions. By pulling collagen fibers rearward past their surfaces, fibroblasts can rearrange, align, and adjust the tension in these and other extracellular fibers; this, rather than cell locomotion per se, has been proposed to be a normal mechanism for the embryonic development of ligaments, tendons, muscles, and other connective tissue structures, as well as for their repair during wound healing (Stopak and Harris, 1982). In several respects (such as the excessive strength of the forces they exert) fibroblasts are better adapted for such winching purposes than for moving themselves from place to place. When fibroblasts crawl about in culture, they may actually be trying to compress the substratum. One of Hamson’s first discoveries about the locomotion of tissue culture cells was that they required a solid substratum; tissue cells cannot swim, and will not even flatten without something reasonably solid to attach to (Harrison, 1914). He provided clotted plasma, and later such materials as spiders’ webs, and noticed that the shapes and alignments of these substrata could strongly influence cell morphology; fibroblasts and most other cells will align parallel to fibers and grooves. Just how solid the culture substratum needs to be has turned out to depend on the strength of the contractile forces exerted by cells of a given differentiated type, something that can vary as much a hundredfold (Harris, 1986). The widespread idea that tissue cells merely require an interface (as opposed to a mechanically resisting solid) is a misunderstanding that resulted from the extreme weakness of the pulling forces exerted by a few cell types, such as macrophages and nerve growth cones, which happen to be weak enough to be mechanically supported by films of denatured proteins at air-water interfaces. The locomotion speeds of tissue culture cells are always quite slow-so slow that time-lapse photography or video is the only practical means of studying most of these phenomena. If you simply look at a crawling fibroblast through the microscope, it seems to be standing still. For most cell types (including fibroblasts, epithelial cells, and nerve growth cones), speeds less than a micrometer per minute are the rule; this corresponds to about a millimeter per day. However, there are a few cell types, including polymorphonuclear leukocytes, in which speeds of 20,30, or even 40 pm/ min are observed (which is still slow compared with the free-living amebae and is barely perceptible to the eye). Although a degree of cytoplasmic flow is found in some of the cells with the fastest locomotion (such as polymorphonuclear leukocytes), this flow has been found not to have the fountain-zone type of pattern characteristic of the large amebae (Ramsey, 1972).

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II. General Description and Nomenclature of Locomotion in Tissue Culture Cells

Students of tissue cell locomotion have not always been consistent in their terminology nor can a reviewer dictate a standard usage; however, the following combinations of descriptions and terminology may be of some help. The terms “leading lamella” and “lamellipodia” were introduced by Abercrombie and co-workers (1970a,b) in an attempt to bring more consistency to the field, but they have sometimes been misunderstood. What these authors meant by “leading lamella” was one of the broad, flattened extensions of fibroblasts, or similar cells, generally around a micrometer or so in thickness. Thus, for a monopodial fibroblast there would be one leading lamella, and it would indeed (in the literal sense of the word) lead the rest of the cell; however, tissue cell morphology is often not so simple, and a bipolar cell would have two leading lamellae, a tripolar cell three, etc., while some cells would have one continuous leading lamella extending all the way around their periphery. The point is that there is no real reason to confine this term merely to those flattened protrusions that are actually at the front end (Le., those that are currently leading in a literal sense). To do so would require us to change names every time a cell changed direction. From a more mechanistic point, we can apply the name “leading lamella” to each cellular process which is pulling the cell body in its own direction (whether successfully or not); many cells will thus have a leading lamella at their rear end, as well as one at their front; immobile cells can likewise have leading lamellae. It is also worth noting that when cells are cultured within collagen gels, clotted plasma, or other fibrous materials, then the leading “lamellae” are often conical rather than flattened. However, in all cases, the leading lamellae are the parts of the cell that do the pulling and exert the traction forces against substrata (Fig. 1). The term “lamellipodium” (plural: lamellipodia) was meant by Abercrombie and colleagues to refer to the outer edge or rim of the leading lamella, specifically that part that extends rigidly out over the substratum, which is filled with actin, and which often folds backward to form “ruffles”: in their words: “sheet-like, mobile, commonly transitory, projections’’ (Abercrombie et al., 1970b). The older term “ruffled membrane” was sometimes used in this sense, but sometimes used as an approximate synonym for leading lamella. Whatever initial doubts there may have been about the appropriateness of coining this special name just for the marginal area, subsequent discoveries have confirmed that the lamellipodium is indeed mechanically and functionally special enough to deserve its own

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FIG.1 Diagram of the pattern of forces exerted by a spreading fibroblast or other tissue cell. Traction forces, indicated by arrows, are exerted tangentially through the plasma membrane along the bottom of the cell (as well as along the top, wherever the cell surface adheres to anything) by the leading lamellae. In this case, traction is directed centripetally, from both ends toward the middle, and stretches the cell into an elongated or flattened shape. Net displacement of the cell is the result of a tug-of-war between leading lamellae on opposite sides of the cell.

name. It is distinctly thinner than the leading lamella, only one or two tenths of a micrometer in thickness, and it is densely packed with a meshwork of actin fibers (Small, 1981), with the intensity of actin staining (for example, with phalloidin) usually being distinctly stronger than in the adjacent part of the leading lamella. Furthermore, the disruption of cytoplasmic actin with such things as phorbol ester tumor promoters makes this difference in actin staining even more pronounced, in that the actin fibers in other parts of the cell are disrupted, while the actin in the lamellipodia becomes, if anything, even more densely packed (Danowski and Hams, 1988). Other proteins, talin in particular, are also especially concentrated in lamellipodia (Burridge and Connell, 1983). The term “ruffling” has long been used to refer to the characteristic backfolding movements of the lamellipodia. This term is too aptly descriptive, as well as too familiar to many of us, to be discarded. In time-lapse films of crawling tissue cells, ruffling is perhaps the single most noticeable feature; intuitively, the concentration of ruffling along the cells’ leading margins gives most people the impression of some direct connection between these movements of the cell surface and the exertion of protrusive forces. Whether there is such a mechanistic connection, and what it consists of, has been a central question in the field. As we will see, ruffling is now believed to result from rapid local assembly, not of plasma membrane, but of cytoplasmic actin fibers. Rigid, rod-like protrusions often extend from, or among, lamellipodia; the term “filopodium” (pl: filopodia) should be reserved for these protrusions. They have also been called microspikes and are full of actin. It is important not to confuse them with retraction fibers, which are narrow strands of plasma membrane and cytoplasm which often become pulled out from cell surfaces when cells retract from sites of adhesion-for example, along the trailing margins of fibroblasts or leukocytes, or around the entire cell periphery during mitotic rounding-up-or when cells are detached with EDTA or trypsin (Hams, 1990). In their mechanical proper-

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ties as well as their functional significance, two types of structure could hardly differ more than filopodia differ from retraction fibers: one is rigid and pokes out in front where a cell is spreading and the other is limp and sags behind where a cell is withdrawing. Yet hundreds of scanning electron micrographs have been published showing structures labeled as “filopodia” that (it could hardly be more obvious) are actually retraction fibers (from the bulbous attachments to the substrata at their tips, from their length, sometimes even from sagging shapes). These are imaginatively described as the means by which cells supposedly reach out, grab the substratum, and pull themselves along. Tissue cells often also extend rounded protrusions; it is appropriate to apply the term “lobopodium” (plural: lobopodia) to these. A characteristic type of small, hemispherical protrusion is very commonly seen in tissue culture; these have long been called “blebs,” and the process of their protrusion is called blebbing (Price, 1967). Unfortunately, the term “bleb” is also used for a rather different type of cellular protrusion, in which fragments of certain pathological cells break entirely free from cells. Extensive blebbing (protrusion of numerous lobopodia) occurs when tissue culture cells are sick, as well as following trypsinization, and before and after cytokinesis. It would be a mistake to conclude from this that blebs are artifactual; blebbing can be observed on cells inside living, healthy embryos at least as often as ruffling or the protrusion of filopodia (for example, see the video assembled by Fink, 1991, particularly the sequences of sea urchin gastrulation and the deep cells of Fundulus). Blebbing is a normal part of tissue cell locomotion and raises important questions about the abilities of plasma membrane proteins and lipids to undergo rapid lateral movements relative to one another. Blebs can be protruded from virtually any part of a cell’s surface, but like lamellipodia and filopodia, they strongly tend to undergo their initial protrusion right along the leading margin; they then move gradually rearward from there across the upper surface of the cell (Harris, 1973a). In addition to the rearward movement of these overt protrusions, one also can often observe more shadowy, phase-dense waves moving backward from the advancing margins of crawling fibroblasts. The most distinct of these are called “arcs,” because of their curved shapes, which usually run approximately parallel to the nearest part of the advancing cell margin (Heath, 1983). One fibroblast may have no arcs, while the fibroblast next to it may form one after another; most often, they form immediately following some retraction at the opposite end of the cell. Their structure seems to consist of a slight inpocketing of the plasma membrane, bordered by a transverse strand of cortical cytoplasm. Particles, antibodies, lectins, and other materials that become attached to the outer surfaces of crawling tissue culture cells are actively transported away from ruffling or blebbing

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cell margins; the direction of this transport is the same as that of the movements of arcs, ruffles, etc., which is to say that the direction is rearward relative to the spreading of the cell margin. The term “retrograde surface transport” is being used increasingly to refer to this important phenomenon, which is the subject of Section IV. This transport results in the accumulation of the attached objects into clusters called “caps,” with the accumulation process being called “capping.” The rearward force exerted by crawling tissue cells has come to be known as “traction,” and is a central focus of this chapter.

111. Exertion of Rearward Traction Forces In order to propel itself forward, a cell must somehow exert rearward forces on something in its immediate environment. In the case of tissue culture cells, this traction is exerted through adhesions to such substrata as glass, plastic, plasma clots, collagen fibers, or other materials. Traction can be detected by the distortions that it produces in culture substrata, so long as these are mechanically weak enough to be visibly distorted by traction; substrata that have been used to study traction include plasma clots, collagen gels, silicone rubber membranes, pools of highly viscous silicone fluid, and other inert, insoluble, viscous liquids (Harris, 1973a, 1982; Harris et al., 1980). One can trace lateral displacement of small particles (of carbon black, etc.) incorporated into elastic or liquid substrata; and in the case of the silicone rubber membranes, cell traction produces visible wrinkles. By such means, one can determine where the traction forces are exerted, as well as the directions of these forces and their relative strengths in different cell types and under different experimental conditions. The patterns of wrinkling produced on silicone rubber substrata indicate that fibroblasts exert their traction forces tangentially through their plasma membranes in the areas just behind the leading margins, which is to say in the areas proximal to those where lamellipodia, lobopodia, or filopodia are protruded; indeed, there are noticeable correlations between ruffling activities and the exertion of traction just distal to them. These are the same areas of the lower cell surface where fibroblasts form their focal adhesions to culture substrata, and where the stress fibers terminate in these focal adhesions (Izzard and Lochner, 1976, 1980; Heath and Dunn, 1978). It is noteworthy that the direction of the traction forces is always centripetal, directly away from the part of cell margin undergoing protrusive activity, and generally along the axis of the stress fibers (Harris and Dmytryk, 1988). Obviously, these correlations of location and direction

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strongly indicate that traction forces result from the contraction of the stress fibers, with the contractile forces being conveyed through the plasma membrane by way of the focal adhesions. Several current textbooks describe tissue cells as pulling themselves along by a cyclic alternation of forward protrusion, adhesion of the protrusions to the substratum, followed by contraction of the adherent protrusions, almost like an inch worm. Such descriptions seem to me not so much inaccurate as misleading; although it is true that protrusion, adhesion, and contraction all occur in locomotion, it is not true that they alternate with one another. The inch worm type of explanation would lead one to expect the pulling force to be intermittent, whereas actually it is continuous and steady, growing progressively stronger as cell spreading becomes more complete. It would also lead one to expect that traction could only be exerted right at the leading margins themselves, whereas most of the force is exerted 5-10 pm, or further, behind the leading edge. Conversely, it would not lead one to expect that tissue cells transport attached particles and molecules rearward, often all the way to the nucleus or beyond (as will be discussed in the following section). Finally, such an explanation implicitly suggests that the distance materials could be pulled rearward would be limited to the length of an individual lamellipodium or filopodium. Actually, fibroblasts can continuously “reel in” collagen fibers and other materials, pulling them past their surfaces for distances of many millimeters (Hams et al., 1981). The fundamental question here concerns the relationship between traction (considered as the force that pulls the cell margins forward and outward) and contraction (the force that tends to pull the leading lamellae back). Should we think of them as separate forces, with traction being resisted by the contractility of the cell, or is traction itself an effect of contractility? The essential feature of traction seems to be that the contractility of cytoplasmic actomyosin is somehow concentrated selectively on those parts of the plasma membrane where the adhesions occur. All parts of the plasma membrane cannot be pulled centripetally to the same degree, or there could be neither protrusions nor locomotion; one would not have traction, but simply contraction. The error of the inch worm analogy lies in the implication of some kind of temporal variation in contraction, whereas the real variation is spatial. By pushing outward on some parts of the plasma membrane, while at the same time pulling in on other parts, the cell manages to exert traction; in this way it accomplishes what might have seemed self-contradictory-making itself longer by contraction. Much still needs to be done on the quantitative measurement of traction forces, but several generalizations have emerged. One is that differentiated cell types differ widely in the strength of their traction forces, apparently by as much as two orders of magnitude (Harris, 1986). Somewhat paradoxi-

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cally, there is an inverse correlation between the invasiveness of cell types and the strength of their traction forces; for example, granulocytes are very weak, as are nerve growth cones, with macrophages being only slightly stronger. On the other hand, there is apositive correlation between adhesive strength, including in particular the formation of focal adhesions, and the abilities of different cell types to distort flexible substrata. Likewise there is a strong positive correlation with cytoskeletal organization; cells with well-developed stress fibers can be relied upon to exert strong traction, and drugs which disrupt cytoskeletal organization always weaken this traction. In several cases, it has been shown that conversion of cultured fibroblasts to something resembling a cancerous state weakens the traction forces they exert and disrupts their cytoskeletal organization and their focal adhesions to their substrata (Steinberg et al., 1980; Leader et af., 1983). Depending on other conditions, this combination of changes (disrupted cytoskeleton, disorganization of adhesions to the substratum, and weakened traction) may or may not result in increased cell motility. One condition under which this occurred was when the cell was cultured on (or surrounded by) a relatively nonadhesive substratum. This seems to be because the cell-substratum adhesions had previously been too weak to support the cells’ contractility, so that weakening Contractility increased spreading and locomotion (Danowski and Harris, 1988). Such observations raise the question: To what extent can the invasiveness of malignant cells be explained by an increased ability to crawl across surfaces which are either too weakly adhesive, or mechanically too weak, to support the locomotion of the normal equivalent cells? A related question is whether the loss of anchorage dependence in transformed cells ever results from reductions in contractile strength great enough to permit the cells to use nonadhesive surfaces like agarose as anchorages on which to elongate.

IV. Retrograde Surface Transport of Attached Markers A. Description of the Phenomenon

Probably the single most important clue to the mechanism of traction is the phenomenon of retrograde surface transport. Moderately small particles (the ones used have had diameters in the range of 1/5 to 5 pm or larger) that become attached to the outer surfaces of motile tissue culture cells are actively conveyed centripetally, across the outside surface of the plasma membrane, at speeds of from 112 to as much as 5 pm/min, relative to the substratum (Ingram, 1969; Abercrombie er af., 1970c; Har-

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ris, 1973a) (Fig. 2). This is true of epithelial cells, leukocytes, macrophages, and nerve growth cones (Bray, 1970),as well as fibroblasts. Rearward transport occurs over the surface of lamellipodia as well as leading lamellae; it occurs whether or not filopodia are present, but when filopodia are present, then the particles are transported down the sides of any filopodia to which they happen to attach (Isenberg and Small, 1979). Typically the particles are pulled rearward fastest just behind the leading edge, and then slow down progressively (Harris and Dunn, 1972). On the surfaces of fibroblasts and epithelial cells, particles are transported to a ring-shaped area surrounding the nucleus, where they then often undergo phagocytosis. Indeed, the rearward transport phenomenon itself seems frequently to have been mistaken for the results of phagocytosis (Crick and Hughes, 1950), but careful examination, such as by vertical focusing with a microscope objective that has a short working distance, shows that the great majority of particles remain on the outside surface of the plasma membrane during the time that they are being moved rearward; often they even fall off again. In the case of granulocytes, attached particles are transported past the nucleus all the way to the trailing region, called the uropod (Harris, 1973a). A similar phenomenon occurs in the amebae of cellular slime molds, where it was discovered by Shaffer (1962).

FIG. 2 Retrograde surface transport of particles of anion-exchange resin attached to the plasma membrane of a chick heart fibroblast. The fibroblast crawled toward the right, and the positions of its leading margins at 10-min intervals are shown. Particles about a micrometer in diameter were picked up by the advancing cell margin and transported over the outside surface of the plasma membrane toward the center of the cell. The round black dots indicate the positions of these particles at 1-min intervals.

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Both in slime mold amebae and in tissue cells, one can also observe retrograde flow of complex folds and bumps in the plasma membrane itself, even where no visible objects are attached to it; these include arcs, the remnants of blebs, lamellipodia, and filopodia, all of which move rearward at the same speed as any marker particles which are attached to the cell in question. Extremely small particles (“nanoparticles”), with diameters of around 20 nm, can also be transported rearward in a similar fashion across the surfaces of tissue culture cells (De Brabander et al., 1986). In some cases, however, such nanoparticles are found to diffuse more or less freely in the plane of the plasma membrane (De Brabander et al., 1990a,b) although they are attached to it, or to alternate between periods in which they diffuse and periods in which they are transported rearward (Sheetz et al., 1989). The behavior of nanoparticles is discussed more fully in the following section, in relation to the likely mechanism of the phenomenon. Similar patterns of retrograde transport have been observed for various antibodies and lectins bound to the outside surfaces of crawling tissue cells. Although there are exceptions, the general rule is that multivalent antibodies and lectins (in the sense of those with two or more binding sites per molecule) first clump together (this is called “patching”) and are then transported to a single clump; this mass of accumulated marker has been called a “cap” and the process of accumulation has been called “capping”; in the case of leukocytes and lymphocytes, the cap is characteristically located at the end that would be the posterior, if the cell were crawling. Capping of antibodies and lectins has also been observed in fibroblasts (Edidin and Weiss, 1972), and although the capping process is believed to play an important function in the excitation of lymphocytes by attachment of various molecules to their surfaces, it seems likely that the same basic mechanism is used to transport the molecules laterally across the outer surface of the plasma membrane. There are also several reasons to conclude that all these cases of retrograde transport result from the cells’ exertion of traction forces on materials which happen to be more movable than themselves (in other words, that we are dealing with the same basic phenomenon here as we were in the case of the distortions of the rubber substrata). Facts which seem to support this interpretation include the following: (1) The direction of particle transport is always the same as the direction of the traction force (and when a granulocyte reverses the direction of its locomotion, the direction of particle transport is simultaneously reversed: see Hams, 1973a). (2) Particle transport occurs on bottom surfaces of cells (between the surface and the substratum, where traction is exerted) and not just on the top (Harris and Dunn, 1972). (3) Cells can also exert traction on their upper surfaces; this can be detected when they are cultured under a fibrin

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clot or within a collagen gel (Harris, 1973a). (4) The retrograde transport of lectins has been shown to be inhibited behind those parts of cell margins whose locomotion and ruffling activities have undergone contact inhibition (Vasiliev el al., 1976). (5) The strength of the forces pulling particles rearward is quite strong; it is capable of lifting nickel metal particles 5 or 10 pm in diameter against the pull of gravity (Harris, 1990). Even in principle, it doesn't seem possible to draw a line between traction and retrograde transport. Imagine a particle attached to a fibroblast surface, with its retrograde transport being held back by a small spring; now imagine that spring being made progressively stronger, so that retrograde transport gradually verges into traction, not to mention forward locomotion of the cell. 6 . Alternative Hypotheses of Retrograde Surface Transport

The first hypothesis proposed as an explanation for retrograde transport was that the plasma membrane itself flows rearward as a whole, rather like a conveyor belt, carrying the particles along with it (Abercrombie et al., 1970c, 1972;Harris, 1973,1976).For flow to be rearward on both upper and lower surfaces, one had to postulate that membrane was constantly reassembled from cytoplasmic components along the leading margin, and then disassembled somewhere toward the rear. A similar hypothesis had previously been proposed to account for retrograde transport and locomotion in cellular slime mold amebae (Shaffer, 1962). In both cases, the idea was that membrane components would be reused over and over again, recycled rather than resynthesized. Bretscher (1976, 1984, 1990) subsequently proposed a variant hypothesis in which only the lipid flowed rearward, pulling cross-linked proteins along with it. The rates of membrane assembly needed to support the observed speeds of particle transport were calculated and found to be substantial (Harris and Dunn, 1972), although they were no larger than the rates of membrane assembly along the advancing cleavage furrow of a frog egg, 'or in the growth cone of an outgrowing nerve fiber, or even in the normal processes of pinocytosis through coated pits (Bretscher, 1984). Indirect support seemed to come from studies of the appearance of membrane proteins newly synthesized as a result of either virus infection (Marcus, 1962) or cell fusion and nuclear reactivation (H. Harris er al., 1969); in both cases, the newly synthesized membrane components could first be detected right along advancing edges of the lamellipodia, exactly as should have been the case if membrane components were assembled there from cytoplasmic pools. Furthermore, it was demonstrated that the orientation of the Golgi

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apparatus in directionally polarized fibroblasts was exactly as it should have been to provide membrane components to the leading margin (Kupfer et al., 1982) and that viral proteins first reach the infected cells’ surfaces along the leading margins (Bergman et al., 1983). Two other attractions of this theory were that it accounted for the rearward flow of bumps and folds in the membrane (i.e., even where nothing was attached to it) and it made sense of the ability of contact inhibition along advancing cell margins to inhibit locomotory activity (including retrograde transport) in parts of the cell centripetal to the contacts (Vasiliev et al., 1976); apart from membrane flow, it was hard to see why centripetal transport should depend on events along the advancing edge. The main alternative hypothesis was that only small islands of plasma membrane were pulled rearward (DePetris and Raff, 1973; Harris, 1973a), in a sort of countercurrent flow, with each island carrying a particle or substratum adhesion along with it. Such a hypothesis assumes that attachment to an external object or surface induces that particular area of the membrane to become subjected to a rearward force. For example, contact might induce the polymerization of an actomyosin stress fiber from the inner surface of the plasma membrane at the point where the particle, antibody molecule, or lectin had attached to the outer surface. Apparently supporting this kind of induced flow mechanism were observations that antibodies against some membrane proteins remained evenly distributed, while others underwent retrograde transport (Middleton, 1979). In particular, multivalent antibodies and lectins were generally transported rearward, just like particles, whereas equivalent monovalent molecules were apparently not subjected to this transport, in that they remained distributed broadly over the cell surface. Probably the most elegant of all such experiments was that in which Mendoza and Metzgar (1976) used antibodies against fluorescein as a monovalent label for the surfaces of eosinophil granulocytes. The attachments were monovalent because they were not at the usual antibody binding sites, but rather at the opposite “Fc” end of the antibody molecule, which is monovalent, and for which cells of this particular type have many specific receptors; in the experiment, these antibodies remained broadly distributed across the plasma membrane, until addition of their antigen caused them to be cross-linked through their binding sites, at which time they were transported to the uropod region. Other experiments showed that cytoplasmic actin itself accumulates in the cap region (Gabbiani et al., 1977; Toh and Hard, 1977), seeming to indicate some kind of induction of actin contraction, or perhaps some stimulus to the formation of mechanical links between certain special membrane proteins and the cytoskeleton (Bourguignon and Singer, 1977). The whole issue of membrane recycling and flow has been reviewed by Heath and Holifield (1991).

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Still other hypotheses were debated (Berlin and Oliver, 1982),including the idea that the particles might be propelled by something analogous to “surfing,” with rearward moving ruffles serving as the “waves” (Hewitt, 1979). One counterargument is that retrograde particle transport is independent of the cell surface’s orientation with respect to gravity; after all, gravity is what causes a surfboard to slide down the advancing side of an ocean wave, yet fibroblasts can be turned upside down, or stood on end, or on their side, and continue to transport particles just the same. It was then argued that this might be a different kind of “surfing,” in which the role of gravity would be played by the resistance of the particle or its adhesion points to being bent; to avoid bending, they would be pushed ahead of the waves; or that was the idea. However, even this would not explain how particles are transported over smooth areas of cell surfaces, or along the sides of lamellipodia and filopodia, as can be easily observed. C. The Membrane Raking Hypothesis

The true explanation for retrograde surface transport (as well as for its relationship to traction) finally seems to be in the process of being discovered. This new explanation differs from any of the hypotheses discussed earlier, but is closest to the island flow hypothesis. One difference is that the actual “islands” (the parts of the membrane that move rearward) are very much smaller than first proposed (indeed, they are of molecular dimensions), as well as more numerous. Another difference is that the islands’ rearward movement is not necessarily induced by contact with external objects (although this remains uncertain, as will be discussed). The islands may move continually, pulling big objects with them while leaving smaller ones behind. The basic idea has been called “raking” and seems to have been first proposed by Dunn (1980). The best evidence in its support has come from the work of Holifield and others in the laboratory of K . Jacobson (Jacobson et al., 1984; Ishihara et al., 1988; Holifield et al., 1990; Lee et al., 1990; Holifield and Jacobson, 1991). The idea of raking is that a special subset of integral membrane proteins is continually pulled rearward, so that the proteins flow directionally between and among all the other molecules of the plasma membrane. Proteins of this special class are called “tine proteins” because their mechanical function is supposed to be equivalent to that of the tines of a rake (Fig. 3). When attached objects are small enough, or when their attachments are monovalent, then they will slip between the tines, like small objects slipping through a rake. Larger objects, or clusters of cross-linked molecules, are caught, and therefore carried rearward; this is how the hypothesis explains the capping of

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FIG.3 Diagram of the raking mechanism now believed to explain retrograde surface transport. The tines of the rake correspond to a special subset of integral membrane proteins which are mechanically coupled to the cytoskeleton on the inside and to adherent objects on the outside.

multivalent antibodies, but not monovalent ones. Other membrane components could be pulled along with the tine proteins either for steric reasons, simply because of the viscosity of the membrane, or by means of specific bonding to tine molecules (as discussed by Holifield et al., 1990). Current evidence indicates that the tine proteins are mechanically linked to a layer of cortical actin, with this actin layer being continually reassembled along the advancing tip of lamellipodia, “treadmilling” rearward from there, to be disassembled in areas nearer the cell center and recycling back to the leading edge (the evidence for cortical actin treadmilling is the subject of the following section). Note the similarity to the recycling pattern earlier attributed to the plasma membrane itself; which helps to explain two facts that once seemed to make no sense without membrane recycling: (1) Complex surface waves move rearward even in the absence of particles or antibodies, and (2), Retrograde transport can be inhibited behind a given part of a fibroblast’s margin by contact paraIysis (Vasiliev et al., 1976). The evidence for raking remains indirect, consisting largely of differences observed in spatial distributions of monovalent antibodies bound to different cell surface proteins of crawling fibroblasts. Antibodies specific for several of these proteins remain evenly distributed over the cell surface during locomotion, indicating that these proteins are not undergoing directional transport. In contrast to this, antibodies specific for the protein gp80 (the human equivalent of this mouse protein is CD44) become progressively redistributed in a rearward or centripetal pattern, exactly as would be expected if gp-80 were one of the tine proteins. This seems to prove that different membrane proteins undergo active countercurrent flow at the molecular level; it also shows that the directionality of that flow matches that observed for retrograde surface transport (as well as for traction). A crucial question here is the degree to which the putative tine proteins become depleted near the advancing margins of crawling cells, even when not yet bound to any antibodies. To the extent that they do

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(for example, as appears to be true in Fig. 1B of Holifield et al., 1990), then one would not need to postulate that contact with something on the outside induces the tine protein to become coupled with the cytoskeleton in the inside. Future studies should therefore concentrate on this question. If we compare the crawling cell’s surface to a ski lift, then the question becomes whether it is the kind of ski lift where you have to hop on the chairs as they go by, or whether it is the kind where you are clamped onto the moving cable only after you are seated in the chair. The raking hypothesis is also supported by observations (De Brabander et al., 1990a,b) that when submicroscopic gold particles are attached to fibroblast surfaces by low-molecular-weight polylysine, they move randomly, but when identical particles are coupled to polylysine of a higher molecular weight, then the particles undergo active, highly directional retrograde transport. Support also comes from several statistical analyses of the movements of attached particles. Using fibroblasts and macrophages with particles of ground anion-exchange resins bound to their outer surfaces, Dembo and Harris (1981) found that the variations in speed and direction of these particles matched the statistical pattern to be expected of a random walk superimposed on a moving conveyor belt. In other words, each particle’s movement was reducible to the sum of (1) steady movement in the rearward direction, plus (2) random diffusion in the sideto-side direction, plus (3) random diffusion forward and backward (the latter showing up as changes in rearward speed). For each particle, the random fluctuations in speed fit reproducibly under the same frequency distribution as did that particle’s fluctuations in position in the lateral direction. Surprisingly, however, the widths of these frequency distributions differed substantially from one particle to another, and these differences were not correlated with particle size. One possible explanation is that the effective viscosity of the membrane varies from place to place. Another part of this study was the application of Kendall’s statistic for correlations between paired observations to a comparison of sequential particle displacements. This analysis found no correlation, either negative or positive, between changes in the sizes of sequential displacements, either along the axis of net transport or perpendicular to it. This is important because if the particles’ random walks had been constrained by any kind of leash or moving fence around them, this constraint should have revealed itself in the form of a net negative correlation between slow steps and fast steps in sequential time periods. In other words, whenever a given particle moved rearward farther than usual in a given time interval, then during the next time period, its rearward displacement should (on the average) have become a little slower than average, and vice versa, slower movements should have tended to be followed by faster ones. Furthermore. the extent and time dimensions of the inverse correlation

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should have revealed something about the length of the ‘‘leash’’ or the area enclosed by the “fence.” Conversely, the absence of any correlation is what would result if the link between the particle and the actin conveyor belt had been essentially a viscous coupling, for example, if the actin were pulling on the tine proteins, while the particles were attached to some other components of the membrane. An alternative explanation would be that although the particles were attached to tine proteins, these proteins were themselves coupled to the actin only intermittently, with random coupling and uncoupling. Recent statistical analyses by Sheetz et al. (1989) directly support the idea of intermittent, random coupling and uncoupling between particles and the actin conveyor belt, and, in addition, are inconsistent with the idea of rearward flow of the membrane as a whole. Using cultured macrophages, they analyzed movements of very small gold particles (in the ‘same nanometer size range as used by De Brabander’s group), coupled to the cell surface with the lectin concanavalin; they found that these particles spent part of their time diffusing randomly and part of their time being transported rearward; their particles switched randomly back and forth between these two states. When these particles’ root-mean square displacements were calculated and graphed as a function of time, the curve was found to be concave upward (i.e., root-mean square displacement increased more than linearly). The significance of this graph is that random diffusion superimposed on a flowing liquid should have produced a straight line (a linear increase), while random diffusion constrained by some kind of a moving leash or cage should have produced a curve which was convex upward (a less than linear increase). Thus, their results strongly support the idea of random diffusion superimposed on a moving conveyor belt to which the objects are coupled only part of the time.

ID. Treadmilling of Cortical Actin, and Its Relation t o Surface Transport .As to the mechanical force pulling these tine proteins, current evidence indicates that the layer of cortical actin directly underlying the plasma membrane undergoes a continuous retrograde flow (in the identical patterns, and with the same speeds as were previously attributed to the plasma membrane) (Fig. 4). In other words, the actin fibers undergo continuous reassembly along the distal edges of lamellipodia and filopodia, flow centripetally just beneath the membrane, and then disassemble into actin monomers to repeat this treadmilling cycle. Sorrano and Bell (1982), using rectified polarization microscopy, seem to have been the first to observe this phenomenon, but misinterpreted it as a propagation of alternating

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\

C

Retrograde surface transport

4-

FIG. 4 Diagram of the relationship believed to exist between treadmilling of cortical actin and raking of the plasma membrane by tine proteins linked to the rearward-moving actin cortex. Actin fibers assemble continuously just behind the leading margin, move centripetally from there, and undergo continuous disassembly in more central areas of the cell. These actin fibers are believed to pull certain integral membrane proteins (tine proteins) rearward. The raking effect of these moving tine proteins is believed to cause both retrograde surface transport and traction.

compression and rarefaction waves in the cytoskeleton (i.e., with the components oscillating back and forth, rather than undergoing net displacement). The demonstration that actin moves continuously rearward was achieved by Wang (1989, who injected fluorescently labeled actin into cultured fibroblasts and then photobleached small spots in the lamellipodia along their leading margins. These spots moved rearward, as if actin were being continuously assembled just behind the leading edge, and flowing (or treadmilling) rearward from there. Next, Svitkinaand colleagues (1986)used freeze etching to study changes in the cortical cytoskeletons of fibroblasts poisoned with azide, dinitrophenol, and other metabolic poisons. This group had previously discovered that such poisons cause the disruption of cytoplasmic actin fibers (Bershadsky et al., 1980), and now demonstrated that the most labile parts of the actin cortex are those at the advancing cell margin. In addition, this part of the actin cortex was also found to be the first to recover its organization following removal of the metabolic poison. They concluded that actin undergoes continuous assembly along the leading edge, and flows centripetally (rearward) from there. Exactly this pattern of assembly and flow was then demonstrated by Forscher and Smith (1988), using high-resolution video-differentialinterference contrast-microscopy. Their recordings show cytoskeletal structures flowing continuously rearward from the leading edge of a cultured mollusk “bag cell” nerve growth cone. The responses of this flowing sheet to the drug cytochalasin provided the strongest evidence (1) that it is made of actin, and (2) that it was undergoing treadmilling, with assembly right at the cell’s leading margin. Immediately after the culture medium was perfused with cytochalasin, the cytoskeletal sheet pulled away from the cell margin and moved off rearward, reminiscent of the end of a roll

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of paper towels coming off the roller. Soon after the cytochalasin was washed out, a new sheet of cytoskeletal material, presumably actin, formed along the anterior end of the cell and flowed rearward from there. Forscher and Smith (1990) also showed that when marker particles are attached to the outside surfaces of these cells, the particles are carried along with the moving actin cortex, but when the cells are treated with cytochalasin, the particles begin to diffuse randomly. More recently, fluorescence photoactivation of labeled actin has provided further evidence for actin treadmilling in cultured fish keratinocytes (Theriot and Mitchison, 1991) and fibroblasts (Symons and Mitchison, 1991). Photoactivated bands move rearward relative to the advancing cell margins. It is also interesting to note that a very similar pattern of apparent cortical treadmilling has been observed in the ameboid locomotion of nematode sperm cells (Roberts and King, 1991); even though nematode sperm lack actin, they apparently employ the same basic mechanism of propulsion as do fibroblasts and other metazoan cells-except that they use a different protein in place of actin! To summarize the picture which has now emerged from this combination of observations: actin fibers are continually reassembled just inside the leading margin, at the tips of lamellipodia or filopodia. This is where Small and colleagues (1978) had previously demonstrated that cortical actin fibers have their barbed ends (i.e., their ‘‘plus’’ ends, where assembly is most rapid). The assembled actin flows continuously from there in a centripetal, rearward, or retrograde direction (accounting for the moving shadows, protrusions, arcs, etc. seen in ordinary phase-contrast microscopy). This conveyor belt of treadmilling actin is mechanically coupled to a special subset of integral membrane proteins (the tine proteins), with the result that these tine proteins are pulled through the plasma membrane like millions of tiny periscopes sticking up from a fleet of cruising submarines (the submarines being the treadmilling actin); random intermittent uncoupling of these tine proteins permits them to diffuse back toward the leading margin (Fig. 5). By means of its mechanical coupling to these tine

FIG. 5 Schematic diagram of the relationship believed to exist between the actin cortex (represented by submarines) and the tine proteins (represented by periscopes) being pulled reerward through the plasma membrane.

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proteins, the treadmilling actin cortex exerts traction tangentially through the plasma membrane, producing retrograde surface transport and capping as side effects. The least certain aspect of this emerging picture is the extent to which the mechanical coupling of tine proteins to the treadmilling actin either depends on or is favored by their attachment to materials outside the cell.

V. Varieties of Ameboid Locomotion

A. Amoeba proteus Type of Locomotion This familiar type of locomotion is characterized by massive cytoplasmic flow, which is created by interconversions of the cytoplasm between two states of markedly different mechanical stiffness; one seems to be fluid and the other more solid. In the fluid state, cytoplasm flows rapidly forward down the center of a tube composed of cytoplasm that is in a more gellike state. Along the inner surface of the tube, cytoplasm is continually converted from the gelled to the more liquid state, while at the leading end of the cell, the more liquid cytoplasm is converted back into the gelled state in a region called the fountain zone because the pattern of cytoplasmic flow in this area resembles the flow of water in a fountain (squirting outward in the middle, and falling back around the edges). The pattern of flow is much as if one had a pipe made of ice, with water flowing down the center of pipe, and with the ice gradually thawing along the inner surfaces of the pipe and refreezing along its rim at one end, continuously extending the length of the pipe at that end. Not only Amoeba proteus but also the larger multicellular type of ameba variously known as Chaos carolinensis or Pelomyxa carolinense undergoes this type of locomotion, among other species. This has been the most extensively studied of all the different forms of ameboid locomotion to be discussed here (even though it is probably the least commonly encountered in nature). Detailed descriptions, combined with hypothetical mechanistic explanations, were published in a series of classical papers by Mast (1926a,b). More attention has been given to the mechanism of the cytoplasmic flow itself, rather than the relationship between this flow and the forward displacement of the cell as a whole. Beginning with Mast, most workers have assumed that some sort of contraction of the outer “gel” layer serves to squeeze the more fluid central cytoplasm forward, so that the advancing pseudopod would be mechanically equivalent to a sort of herniation, or weak spot. This assumption was courageously challenged by R. D. Allen (1961), who proposed that

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the flowing cytoplasm is instead pulled forward by a shrinkage in volume at the leading end, within the fountain zone, so that the active, forceexerting event would be the eversion and gelation process. Probably the strongest support for this hypothesis was that amebae can continue to flow forward even while a micropipette is being used to suck cytoplasm out of the rear end; if the cytoplasm were simply being squeezed forward, then such suction should prevent the forward protrusion (Allen er al., 1971). Also inconsistent with the idea of simple squeezing from the rear is the ability of isolated cytoplasm to flow in cyclic patterns (Allen et al., 1960); studies of such movements in isolated ameba cytoplasm have played a central role in determining the molecular events that drive cytoplasmic flow; the details of this work have been well reviewed by Taylor and Condeelis (1979). Cytoplasm will also flow in closed circles inside amebae that have been chilled in a refrigerator until they round up, and are then gradually thawed out; this does not seem to be explicable by differences in hydrostatic pressure, since the flow is in closed loops. On the other hand, Allen (1970) thought that rear contraction might really be the true explanation for the locomotion of certain little-studied amebae of the genus Pelomyxa, even if not for Amoeba or Chaos! Except for the presence of the plasma membrane between the cell’s immediate environment and the gelled cortex, the relationship between cytoplasmic flow and cell locomotion would be self-explanatory. In fact, however, the movement of the plasma membrane is quite different from that of the cortical cytoplasm underlying it, raising difficult questions about what sort of forces are transmitted through this membrane. When small marker particles, such as carbon black, are attached to the outer surface of Amoeba profeus, the marker particles flow smoothly forward at the same speed as the leading edge of the ameba, thus remaining a constant distance behind the advancing tip of the pseudopod. Conversely, when a pseudopod is retracted, such marker particles flow back down its sides (Czarska and Grebecki, 1966; Haberey, 1972). Studies with antibodies that bind to cell surface materials likewise indicate that the plasma membrane essentially slides passively across the underlying cortex (Wolpert and O’Neill, 1962). Over longer periods of time (30 min or an hour), such surface markers gradually accumulate at the extreme rear end of the ameba, as if their forward movement were not quite as fast as that of the leading edges. If any parallel can be drawn between this type of ameboid locomotion and the locomotion of tissue cells, it may be that a very few of the molecules of the plasma membrane do move along with the underlying cortex; these would thereby produce a raking effect comparable to that which is believed to explain the backward transport of particles across the surfaces of tissue cells, although it would

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be a much weaker raking effect because a smaller proportion of membrane molecules move along with the underlying cortex. On the other hand, it is important to realize that one of the other respects in which Amoeba, Chaos, etc. differ from fibroblasts, etc. is that these amebae normally contact their substrata at only a few points. Consequently, we also need to consider whether forward translocation may result merely from the dramatic changes in cell shape, as opposed to any contractile forces exerted through the plasma membrane. Answering such questions might require either some method for measuring the relative amounts of force exerted at different parts of their outer surfaces, or perhaps observations of locomotion by amebae that have been confined tightly inside tubes, since this would force large areas of their surfaces into contact with the surrounding substratum while at the same time preventing the amebae from undergoing their usual dramatic changes in shape.

8. Rolling Membrane Type of Ameboid Locomotion A less well-known type of' ameboid locomotion is that employed by the genus Hyalodiscus, among others (see Komnick et al., 1973). These cells apparently move by rolling their plasma membrane around and around like a tractor tread, backward on the bottom and forward on the top (Fig. 6). Thus, marker particles placed on their upper surfaces are carried forward at speeds exactly twice that of the leading edge itself; such particles soon catch up with the leading edge, are swept under the cell, and the cell moves over them (personal observation). The cell takes on a

+>-

:-::,

,,

........................................ c c c c ......._............ ... ..::::::s

FIG. 6 Sketch of the small ameba Hyalodiscus, as seen from above (left), and in cross section (right) The arrows indicate the direction of movement; the double arrow indicates the fact that small particles attached to the upper surface of this type of ameba are carried forward at exactly twice the speed of the ameba's leading margin; this is indicative of the rolling movement of the plasma membrane. When fully spread, these amebae are about 40 p m wide and 25-30 p m from leading edge to trailing margin.

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somewhat crescent-like shape, often with a cluster of attached particles being dragged along by the trailing margin (note that the existence of these clusters indicates that the geometric pattern of membrane flow probably cannot be quite as simple as the movement of a tractor tread). Much more attention needs to be given to the arrangement of cytoplasmic actin and myosin relative to the moving parts of the plasma membrane. To judge from the morphologies of amebae drawn in guides to protozoan identification, this type of locomotion is very widespread among the smaller kinds of ameba.

C. Dictyostelium Type of Locomotion The individual amebae (so-called “myxamoebae”) of this genus are about 10 pm wide and 20 to 30 pm in length when spread on a substratum and undergoing locomotion. They have been meticulously described by Raper (1984). In several respects (direction of transport of attached markers, general morphology, and formation of multicellular aggregates), this seems to be the type of locomotion most closely analogous to that of tissue cells. It is shared by Dictyostelium and the many other cellular slime molds (see Olive, 1975, for extensive descriptions and a taxonomy of these diverse groups), and apparently also by Acanthamoeba (although this question deserves further attention, especially considering the central importance of biochemical studies of Acanthamoeba actins and myosins). Retrograde surface transport of attached markers was discovered in cellular slime mold amebae (Shaffer, 1962) even before it was found in tissue culture cells, and Shaffer’s explanations in terms of plasma membrane recycling and flow likewise foreshadowed the hypotheses made concerning fibroblasts. Presumably the true explanation will also turn out to be the same combination of membrane raking and cytoskeletal treadmilling as seems to be the true explanation in tissue cells. If so, then the genetic advantages of Dictyostelium would become a great help in analyzing the system of tine proteins as well as their molecular connections to the actomyosin cytoskeleton. Another point of similarity with tissue cell locomotion is that cellular slime mold amebae form multicellular aggregates. Furthermore, the slug or grex crawls along as a mass, raising the question of whether the mechanism propelling this mass of many thousands of cells is the same as that which propels the individual cells from which it is made, as was advocated by Shaffer (1962), and which also seems to be the case for sponges (Bond and Harris, 1988).

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D. Locomotion of the Shelled Amebae

Members of several genera of amebae form shells, from which they protrude pseudopodia, and which they drag about more or less in the fashion of a snail with its shell. In the genus Arcella the shell is secreted, while in Difjugiu it is made mostly of small sand grains gathered by the ameba and glued together with secretions. Members of both these genera protrude many long, narrow, cylindrical, rather straight pseudopodia, within which a fountain zone pattern of cytoplasmic flow can be observed. These pseudopodia are adhesive, and also respond to contact (and adhesion) with external objects by contracting (Mast, 1931; Wohlman and Allen, 1968) When one of these pseudopodia contacts a solid substratum (i.e., something less movable than the ameba itself), then its adhesion and contraction have the effect of pulling the cell forward; and when the contacted object is small and movable (e.g., a small grain of sand, or something edible), then the contraction of the pseudopod will pull this object toward the ameba’s cell body (Fig. 7). The process by which pseudopodia respond to contact by contraction was studied by Eckert and McGee-Russell (1973); they showed that contact induces an increased birefringence along the length of the pseudopod that is indicative of the organization of a contractile strand of actomyosin. They also used transmission electron microscopy to demonstrate the formation of these contractile strands. The responses of these pseudopodia to small particles are also interesting. When Difjugiu are brought into contact with particles of carbon black, the results differ, depending on the size of the attached particles (A. K. Hams, unpublished observations). Large particles (many times the diameter of a pseudopod) caused the pseudopod to contract as a whole, pulling the particle back toward the cell body. In contrast, very small particles (smaller in diameter than the pseudopodia themselves) did not

FIG. 7 Sketch of the shelled ameba DifPugia. Their long, thin pseudopodia react differently to particles of different sizes: very small particles are pulled rearward along the side of the pseudopod (lower); large particles cause the whole pseudopod to contract and pull the particle along with it (middle); and particles of intermediate sizes stimulate the pseudopod to bend sharply toward the point of contact, and to move this bend back toward the cell center (personal observations, see text). Their shells are approximately 100 jm in diameter, with individual pseudopods having widths of about 5 pm.

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cause any retraction but were transported smoothly up the side of the pseudopod, as if by some kind of shearing force, reminiscent of what happens on the surfaces of crawling fibroblasts. Particles of intermediate size (i.e., those of approximately the same diameter as the pseudopodia) produced yet another response: the pseudopodia responded to these by bending toward the particle so as to form a sharp kink, within the angle of which the particle was gripped (much as person might hold an orange squeezed in the angle of a flexed elbow). Such bends are then propagated down the length of the pseudopod, carrying the particles with them toward the cell body. These descriptions are based on unpublished personal observations; they are included to illustrate the similarities and differences among the different kinds of ameboid locomotion with respect to surface transport. The ability to transport attached particles centripetally without net retraction of the pseudopod should be examined more carefully; not only is it analogous to what happens to tissue cells, but in relation to the observations of Eckert and McGee-Russell (1973), may indicate that contact with smaller objects induces the polymerization of cytoplasmic strands which are proportionally smaller as well.

E.

Locomotion of tabyrinthula

Of the types of ameboid organism discussed here, Labyrinthula is probably the least widely known, as well as the one which differs most widely from our usual expectations about what cells can do. On the other hand, it is also the one which is most prevalent in nature, as well as the one with the greatest economic and ecological impact. Species of Labyrinthula infect marine plants, especially the sea grasses Zostera and Thalassia, and are suspected of being the pathogen responsible for decimating the Atlantic eel grass beds in the 1930s, producing drastic ecological changes (see Olive, 1975). If you plate out a few small pieces of seaweed onto nutrient agar, colonies of Labyrinthula will grow and can be easily isolated. There are also freshwater species of related genera. These organisms form multicellular colonies interconnected by a network of tracks called “slimeways,” within which the individual cells move to and fro (Watson, 1957). It was long debated whether Labyrinthula was essentially syncytial, with the slimeways being cytoplasmic connections, or whether the slimeways were extracellular secretions separate from the cells. What made this question so confusing was the ability of the slimeway material to undergo active locomotion on its own, beyond where the cells had yet moved, combined with the ability of the cells to survive physical separation from the the slimeways. In other words, the organism behaved in some respects as though syncytial, but in other respects as though

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cellular. This puzzle was finally resolved by Hohl(l966) and Porter (1969, 1972), using combinations of transmission electron microscopy and timelapse photography, and the true answer turned to be very surprising indeed (see also Pokorny, 1967). Although the slimeways are indeed secretions, they consist of tubes of plasma membrane enclosing extracellular actin and myosin (Bell et al., 1978; Nakatsuji and Bell, 1980), together with the cell bodies (Fig. 8). In other words, the individual cell bodies are completely enclosed in their own plasma membranes; but outside of this, they secrete additional sheets of a material which apparently also has all the properties of a plasma membrane; and between these inner and outer membranes, they secrete proteins equivalent to actin and myosin. The extracellular membranes undergo active locomotion, presumably by means of the extracellular actin and myosin they enclose; membranous sheets extend forward many tens of micrometers beyond the cell bodies. Their protrusion resembles that of the leading edges of crawling fibroblasts; not only are they flattened in the same way, but they sometimes undergo ruffling movements. The individual cell bodies are elongated, with tapered, conical ends (proportioned much like an American football) with one nucleus per cell. These cell bodies glide smoothly through the slimeways, without either internal cytoplasmic flows or changes in shape to indicate the source of their propulsive force. Often, the cell bodies move as chains, either one after the other, or as streams that are many cell bodies in width; large numbers of cells often move in the same direction simultaneously, as if linked together in some way. On the other hand, we

FIG. 8 Sketch of the colonial marine slime mold Labyrinthula. Five cell bodies are shown inside a short length of one of these organisms’ characteristic slimeways; the slimeways consist of tubes of secreted extracellular plasmalemma membrane enclosing extracellular actin and myosin. The cell bodies secrete both the extracellular membrane and the extracellular actin and myosin. The individual cells move slowly through the slimeways, probably pulled by the actin and myosin, while the slimeways can crawl actively outward well beyond the farthest point yet reached by cell bodies. The forward extension of slimeways closely resembles the extension of leading lamellae from fibroblasts; here the slimeway materials are shown extending toward the upper right (based on time-lapse films and personal observations).

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can apparently dismiss the idea of some kind of hydraulic propulsion, in the sense of simple pressure differences from one part of the slimeway system to another, because it is not unusual to see ring-like groups of cell bodies moving round and round in small circles. Another possibility is that the cell bodies slide or are pulled along strands of actin and/or myosin, perhaps somewhat in the fashion of a ski lift. Many interesting questions about mechanical interactions between actin, myosin, and plasma membranes seem ripe for solution in these least-studied of the ameboid organisms. They seem to provide an excellent model system for studying the interactions of actin and myosin with plasma membranes, as discussed in the following section.

VI. Conclusions A. Common Elements in the Locomotion of Amebae and Tissue Cells

The concepts of membrane raking and cortical actin treadmilling, although developed to explain the locomotion of tissue cells, also provide a unifying perspective from which to relate the different types of ameboid locomotion to one another (some of the possible relationships between different kinds of ameboid locomotion have also been recently reviewed by Condeelis, 1992). Because the Dicfyostelium type of locomotion is most similar to that of tissue culture cells (note some of the parallels pointed out by Vasiliev, 1991), the retrograde surface transport observed in these amebae should be reexamined for evidence of both actin treadmilling and membrane raking. In the case of Amoeba proteus, the peculiarities of its locomotion, in particular the failure of marker particles to be transported rearward, may be explained by a much weaker mechanical coupling between cortical actin flow and proteins within the plasma membrane proteins. In other words, if raking tine proteins were much less numerous in Amoeba than in tissue cells, this would account for the observed differences in surface transport, and the sliding of the gelled cortex relative to the overlying plasma membrane. Furthermore, there is the similarity between cytoskeletal treadmilling in tissue cells and the classical sol-gel conversion in the fountain zone of Amoeba, with actin polymerization playing the role of gelation; perhaps similarities can also be found at the molecular level. In the case of the Hyafodiscus type of ameboid movement, the peculiar pattern of transport of attached markers (forward across the top, backward across the bottom) may be explained by the rearward pull of the actin

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cortex on plasma membrane tine proteins somehow being confined to the part of the plasma membrane that makes up the cell’s lower surface (in contact with the substratum) at any given time. This part of the membrane would thus be pulled rearward, leaving the rest of the plasma membrane (specifically those parts making up the cell’s upper surfaces) free to flow passively forward. As a possible explanation for why only the lower surface membrane should be pulled rearward by the cortex, a likely possibility would be that contact with exterior objects (in this case, the substratum) promotes the formation of links between the actin cortex and plasma membrane proteins. Such an induction of links in response to contact would also explain the confusing pattern of marker particle transport observed in DiffEugiaand other shelled amebae. It would explain not only the total contraction of pseudopodia that contact large objects, but would also account for the transport of smaller particles along the sides of pseudopodia. The question here is similar to that discussed earlier in regard to tissue cells-whether the coupling of tine proteins to the cytoskeleton is induced or otherwise favored by the attachment of these proteins to things outside the cell. Labyrinthula seems to be the most different, not only from tissue cells but from other amebae. Nevertheless, its locomotion does seem to depend on mechanical connections between actomyosin and plasma membranes, in this case both their outer (extracellular) plasma membranes and the plasma membranes surrounding the individual cells. Indeed, the membranous fans which these creatures protrude can so closely resemble lamellipodia as to suggest that both cortical treadmilling and membrane raking should be looked for in Labyrinthula. Should either or both be found, then the peculiar extracellular membrane and cytoskeleton of this neglected organism would offer special experimental opportunities for studying raking and treadmilling in partial isolation from cytoplasm. 6 . Prospects for Future Research on Tissue Cell Locomotion

The first priority for research in this area now seems to be critical testing and proof of the related hypotheses of membrane raking and cortical actin treadmilling, as well as of the idea that treadmilling provides the motive force for raking. The second priority would then be to reexamine guidance phenomena such as contact inhibition and chemotaxis in terms of membrane raking and actin treadmilling. Indeed, studies of such control mechanisms may well provide the kind of decisive proofs (or conceivably disproofs) of raking and treadmilling that are needed. The results so far look encouraging. For example, in the well-studied phenomenon of polymorpho-

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nuclear leukocyte chemotaxis, it has been well established that the chemical attractants cause actin polymerization, and do so selectively on the side of the cell where the attractants are most concentrated (Fechheimer and Zigmond,l983; Cassimeris et al., 1990). In the case of membrane raking, one priority should be a more complete census of the tine proteins, as well as a determination of what molecular properties govern whether a given integral membrane protein will or will not be dragged along rearward between its neighboring molecules by the pull of the treadmilling actin cortex directly beneath it. Presumably, this must be a matter of whether mechanical links are formed between the cytoskeleton and a given membrane protein; thus, it is a good question whether the same intermediary proteins (talin, vinculin, and a-actinin) that have been identified as mechanical links in connecting stress fibers to adhesion plaques (Burridge, 1986) will also turn out to participate in membrane raking. Are the integrins themselves tine proteins, or are they swept along by other membrane molecules? In either case, a further question is whether the accumulation of integrins and other adhesion molecules into plaques is accomplished by a smaller scale version of capping, with the site of the focal adhesion being a focus toward which cortical actin flows. Recent findings indicate that the cytoplasmic domain of these molecules is sufficient to cause accumulation at the focal adhesion sites (LaFlamme et al., 1992), and it will be particularly important to determine the extent to which the coupling of tine proteins to the cytoskeleton is promoted by the binding of materials to the extracellular ends of these proteins. These questions, in turn, raise the issue of the relationship between cortical actin and stress fibers. Does part of the cortical actin become reorganized into stress fibers (and thus associated with myosin and tropomyosin) as it moves centripetally? Or are the stress fibers formed separately; in which case how much of the traction force is due to the treadmilling of the cortical actin and how much of it is due to the sliding-filament contraction of the actin and myosin making up the stress fibers? Other questions arise concerning whether interactions with myosin contribute to the centripetal movement of treadmilling actin, how the roles of type I and type I1 myosins in locomotion differ from one another, and how much (if any) of the centripetal force applied to the plasma membrane is due to its attachment to type I myosin. As the tine proteins become better characterized, it will be interesting to determine the consequences €or cell behavior of either increasing or depleting the proportion of these proteins making up the plasma membrane, or the effects of altering their affinities for bonding to the cytoskeleton. For example, the rounding-up of fibroblasts during mitosis, despite the retention of their adhesions to the culture substratum (Harris, 1973b), may be explained by a generalized

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breakage of the mechanical links between the cytoskeleton and tine proteins, which allows strands of plasma membrane to be pulled away from the cell body. Although membrane raking can explain nearly all the phenomena once attributed to membrane recycling, there is still the troubling fact that newly synthesized membrane proteins really do first appear on the surface along the leading margin (Marcus, 1962; Harris et al., 1969; Bergman el al. 1983). This suggests a continuing need for open minds on the issue of localized membrane reassembly and rearward flow; perhaps some really does occur, even if it is only superimposed on raking (see the interchange between Jacobson et al. and Bretscher, 1990). Important questions also remain concerning the pushing force that extends lamellipodia outward. To what extent is this osmotic, or caused by the swelling of the actin gel, as opposed to resulting directly from the addition of actin monomer to the tips of cortical actin fibers? These issues have been carefully analyzed by Oster (1984) and by Oster and Perelson (1987). The concept that ruffling represents rapid local assembly of cytoplasmic actin has very important implications for the phenomenon of contact inhibition of cell locomotion (Abercrombie, 1970); specifically, it implies that the paralysis of ruffling that occurs along the contacted cell margins genuinely does amount to some kind of localized “turning off” of the propulsive machinery. Time-lapse films of contact paralysis have always given this intuitive impression, of course, and there was also the demonstration by Vasiliev et al. (1976) that retrograde surface transport ceases behind contacted margins, but we have not understood the nature of the molecular process being turned off (Fig. 9). Apparently it is a combination of cortical actin assembly and membrane raking. If that is the correct interpretation, then we need to ask how contact between two cells inhibits further actin assembly in the part of the cortex directly underlying the contacted area, and to what extent the invasiveness of noncontactinhibited cells is attributable to continued actin assembly and lamellipodium formation, even adjacent to intercellular contacts. We must never forget that the uncontrolled locomotion of cancerous cells is one of the most important reasons for research on this subject, and it may not be too much to hope that those same abnormalities that release cells from contact inhibition may somehow be made the basis of treatments selectively toxic to cells whose locomotion is uncontrolled. Today’s chemotherapy is based almost entirely on the defective control of growth that characterizes cancerous cells; perhaps the defects in their control of locomotion can eventually be made the basis of entirely new types of selective toxicity. Based on the findings reviewed above, what seems to be needed is some way to make it fatal for cells to continue

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FIG. 9 Diagram of contact paralysis of retrograde surface transport. Cultured cells in a small cluster have been coated with lectins or other markers but undergo retrograde surface transport primarily (or only) from the free margins. Thus, little or no capping occurs on the central cell because it is contacted on all sides. Likewise, the contacted sides of the other cells remain uncleared. This indicates that the raking process, and probably also actin treadmilling, is inhibited along parts of the cell margin which come into contact with other cells (see Vasiliev et a / . , 1976).

actin treadmilling and membrane raking where and when these processes should have been inhibited by intercellular contact.

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Sheetz, M. P., Turney, S., Quian, H., and Elson, E. L. (1989). Nature (London) 340, 284-288. Small, J. V. (1981). J. Cell B i d . 91, 695-705. Small, J. V., Isenberg, G., and Celis, J. F. (1978). Exp. Cell Res. 127, 421-429. Sorrano, T., and Bell, E. (1982). J. Cell Biol. 95, 127-136. Steinberg, B. M., Smith, K., Collazo, M.,and Pollack, R. (1980). J. CellBiol. 87(3) 304-308. Stopak, D., and Harris, A. K. (1982). Deu. Biol. 90, 385-398. Svitkina, T. M., Neyfakh, A. A,, and Bershadsky, A. D. (1986). J. Cell Sci. 82, 235-248. Syrnons, M., and Mitchison, T. (1991). J. Cell Biol. 114, 503-513. Taylor, D. L., and Condeelis, J. S. (1979). In!. Reu. Cytol. 56, 57-144. Theriot, J. A., and Mitchison, T . J . (1991). Nature (London) 352, 126-131 Toh, B.H., and Hard, G. C. (1977). Nature (London) 269, 695-697. Trinkaus, J. P. (1984). “Cells into Organs.” Prentice Hall, Englewood Cliffs, NJ. Vasiliev, J. M. (1991). J. Cell Sci. 98, 1-4. Vasiliev, J. M., Gelfand, 1. M., Domivina, L. V., Dorfman, N. A,, and Pletyushkina, 0. Y. (1976). Proc. Natl. Acad. Sci. U.S.A. 73, 4085-4089. Vaughan, R. B., and Trinkaus, J. P. (1966). J . Cell Sci. 1,407-413. Wang, Y . - L .(1985). J. Cell Biol. 101, 597-607. Watson, S. W. (1957). Ph.D. Thesis, Univ Wisconsin, Madison, WI. Wohlman, A., and Allen, R. D. (1968). J. Cell Sci. 3, 105-114 Wolpert, L., and O’Neill, C. H. (1962). Nature (London) 1%, 1261.

Role of Mechanical Stimulation in the Establishment and Maintenance of Muscle Cell Differentiation David G. Simpson, Wayne Carver, Thomas K. Borg, and Louis Terracio Department of Developmental Biology and Anatomy, School of Medicine, University of South Carolina, Columbia, South Carolina 29208

1. Introduction

During the formation and development of striated muscle, the cells are constantly receiving mechanical and chemical signals. The interpretation of these signals is critical for the developmental process as well as for maintaining the adult form. While the separation of these signals is not completely possible, the principal focus of this chapter will be on the mechanical factors and their relationship to the development of striated muscle and the maintenance of differentiated structure and function. The structural organization of the cell and its interaction with the surrounding extracellular matrix (ECM) is critical to the development of the muscle cell. Muscle cells consist of several structural compartments that are all interrelated and involved in the perception of mechanical signals. These interfacing units are three-dimensional networks whose organization is tissue specific and reflects the unique functions of each tissue. In striated muscle cells these compartments are (1) extracellular, (2) cytoplasmic, and (3) nuclear (Fig. 1). Each compartment transmits information across at least one membrane interface that sets the boundary of the particular compartment. The nucleus, surrounded by the nuclear membrane complex, contains the genetic material necessary for cellular functions. The three-dimensional arrangement of the DNA is a major part of a nuclear matrix that is interconnected with the chromosomes and the nuclear envelope (Getzenberg et al., 1991). The spatial and positional organization of the DNA is believed to play a significant role in gene regulation by controlling the interaction of various transcription factors with the DNA (Getzenberg er al., 1991). The connecInternational Review of Cytology. Vol. 150

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Copyright 0 1994 by Academic Press, Inc. All nghts of reproduction in any form reserved.

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FIG. 1 A schematic diagram of the three major compartments that play a role in the transmission of mechanical forces. The extracellular matrix transmits forces from adjacent cells and tissues to the sarcolemma, where it is attached to the cell by integral membrane protein receptors known as integrins. Integrins appear to be pivotal molecules for transmitting force since they span the sarcolemma and are attached to the cytoskeleton. The cytoskeleton in turn attaches to the contractile apparatus and to the nucleus, thus serving to organize the complex cytoplasm and to transmit force to the nucleus. The nucleus in turn is composed of a system of filaments known as the nuclear matrix which organizes the chromatin and nucleolus into specific functional domains. Thus, the same basic organizational pattern exists to integrate forces from outside the cell, move them across the cell membrane, through the cytoplasm to the nucleus, and affect gene expression.

tion of the DNA to the nuclear envelope as well as its organization into a supercoiled structure has invited speculation that mechanical alteration of the nuclear envelope would in turn cause an alteration (either exposure or masking) of the DNA, thus functioning as an important component of gene regulation. The cytoplasmic compartment of striated muscle cells is specialized for the generation and transmission of contractile force. The well-documented organization of the contractile apparatus will not be analyzed because its structure has been recently reviewed (Epstein and Fischman, 1991).

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However, the interaction of the contractile apparatus with the other cytoskeletal elements also plays an important role in the generation of force and transmission of mechanical tension (Price, 1991). Cytoskeletal components, such as vinculin, talin, nonsarcomeric actin, titin, a-actinin, desmin, and others, are arranged in a three-dimensional network that provides positional information to the contractile fibers. This arrangement serves to interconnect the adjacent myofibrils as well as to position the myofibrils in relation to the sarcolemma (Forbes and Sperelakis, 1983; Borg et a!., 1990; Borg and Terracio, 1990). Through this arrangement the position of the contractile apparatus is maintained in a specific relationship to the sarcolemma during the contraction-relaxation cycle. This relationship is important for Ca2+ exchange and thus controlled contraction and force generation (Terracio and Borg, 1988). In addition to the lateral anchoring of the cytoskeleton, there are also the termination sites at the intercalated disc. This insertion site is obviously important in the transmission of force from cell to cell. The cytoplasmic compartment is also connected to the nuclear compartment by the cytoskeleton (Bissell et al., 1982). This interconnection is important in determining the positioning of the nucleus within the cell. While little is known concerning nuclear positioning in striated muscle, it is thought to be very important in other systems. Nuclear positioning as established by the cytoskeleton may be important in establishing the regional domains of protein synthesis that may be essential for myofibrillogenesis and the turnover of myofibrillar components (Blau, 1989; Pavlath et al., 1989; Samarel, 1989; Robinson and Samarel, 1990; Russell and Dix, 1992).The role of the cytoskeleton in binding mRNA has been documented in other cellular systems but has received scant attention in striated muscle, where it could have a significant functional role due to the complex organization of the cytoplasm. The three-dimensional organization of the ECM has been well described in striated muscle where it forms a stress-tolerant network (Borg and Caulfield, 1979; Borg and Terracio, 1990; Robinson et al., 1983, 1987). The arrangement of the ECM has been shown to play an important role in the development of striated muscle by providing positional information as well as being involved in the transmission of mechanical forces (Sanes et al., 1986; Ocalan et al., 1988; Goodman et al., 1989). The ECM consists primarily of (1) collagen, (2) noncollagenous glycoproteins, and (3) proteoglycans. The major collagen types are the interstitial collagen types I and 111, and basement membrane collagen type IV. The amount and type of the interstitial collagens has been shown to influence the mechanical properties of striated muscle by altering its compliance (Borg and Terracio, 1990; Weber et al., 1987). Noncollagenous glycoproteins, such as laminin, fibronectin, and others, are associated with cell function; however, only

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the basement membrane component laminin has been shown to influence the differentiation process of muscle cells (Ocalan et al., 1988; Goodman et al., 1989; Sanes et al., 1986). Little is known concerning the function of proteoglycans in muscle development. Potentially, they may play an important role in binding growth factors such as fibroblast growth factor (FGF) and transforming growth factor-beta (TGF-P). The interaction of the ECM network with the muscle cell is modulated by its attachment to the sarcolemma at specific sites near the Z-bands (Terracio et al., 1990). This interaction appears to be mediated in part by specific receptors termed integrins (Hynes, 1987; Borg and Terracio, 1990; Ruoslahti, 1991; Terracio et al., 1991). These receptors link the externally located ECM components with the elements of the cytoskeleton and are important in the transmission of mechanical information (Ingber et al., 1990; Terracio et al., 1989, 1991; Borg and Terracio, 1990; Vandenburg, 1992). However, the precise mechanism(s) of the transmission of mechanical stimulation is not understood. The integration of mechanical stimulation within and between these three arbitrary compartments has been initially described as a system of dynamic reciprocity (Bissel et al., 1982). The proposed pathway begins with mechanical signals from the ECM being transmitted across the sarcolemma through integrins to the cytoskeleton. In turn these forces are transmitted to the nuclear matrix, where they may alter gene expression. The transmission of mechanical stimulation in muscle cells must occur in both directions, with the binding site at the Z-band on the sarcolemma having a pivotal position, The dynamics of this interaction would change with development as well as in the adult phenotype upon stimulation. In this chapter we review the evidence for this hypothesis with emphasis on the heart, but with supporting evidence from skeletal muscle and other systems where it is germane. Although this is not an exhaustive literature review, we have tried to reference some of the older literature to give credit to those investigators who postulated a role for mechanical stimulation well before it was popular.

II. Cellular Responses t o Mechanical Loading

The striated tissues of the myocardium and axial skeleton are exquisitely sensitive to changes in mechanical load. In the heart, an acute increase in preload can act to augment cardiac output on a beat-to-beat time scale (Braunwald, 1965). In skeletal muscle, it serves to accelerate shortening

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velocity and increase contractile force (Edman et af., 1978; Walker, 1976; Abbott and Aubert, 1952). A sustained elevation in either preload or afterload provokes a hypertrophic response in both types of muscle (Karsner et al., 1925; Thomsen and Luco 1944; Gutmann et af., 1971; Vandenburgh er af., 1989). A chronic reduction in these mechanical parameters leads to the loss of muscle mass and a decrease in overall performance (Sulzer, 1897; Lippman and Selig, 1928; Solandt and Magladery, 1942; Hellerstein and Santiago-Stevenson, 1950; Samarel et af., 1987). A fundamental concern has been to define the underlying mechanisms by which these tissues modulate their structure in response to physical perturbations. Significant efforts have also been made to determine if there is a single, unique, mechanical parameter which is common to preload and afterload that is ultimately responsible for regulating the physiology of these muscles in the steady state (Morgan et al., 1987).

111. Response of Developing Myocytes t o Mechanical Forces

During early embryonic life, the developing cardiac myocyte displays a rounded, ovoid shape (Witte, 1919; Muir, 1957). Myofibrils are disseminated throughout the sarcoplasm and intercellular junctions are distributed at irregular intervals along the periphery of the cells. With continued development, the myocytes grow severalfold in size and begin to gradually elongate to assume a rod-like shape. The myofibrils proliferate and become realigned in parallel with the long axis of the cell. In conjunction with these events, the fascia adherens, gap, and desmosomal junctions congregate at the distal ends of the cells to form the intercalated disc (Chacko, 1976). The heart cell appears to have the intrinsic capacity to undergo these cytoarchitectural changes, but physical forces which originate outside the myocyte proper are believed to have a profound impact on the extent to which this morphogenetic program is expressed. The essential role which mechanical forces play in directing cardiac morphogenesis is readily apparent when an intact, developing heart is partially unloaded. Bishop et af. (1990) have attempted to achieve this by transplanting an intact and functional 12-day-old neonatal rat heart into the anterior eye chamber of an adult host rat. In principle, such an expldnt is isolated from the forces normally associated with hemodynamic perfusion and cardiac afterload. The myocytes of these unloaded hearts undergo the transition between hyperplastic and hypertrophic growth that is characteristic of the neonatal heart. However, in the absence of a sufficient

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external load, they fail to elongate fully and their myofibrils remain haphazardly distributed in the sarcoplasm. In the converse experiment, how does an increased load affect the developing heart? When the conotruncal loop of a stage 21 chicken heart is banded, the animal experiences an average increase in blood pressure of over 46%. This results in a 34% increase in ventricular weight, and has been attributed to myocyte hyperplasia (Clark et a!., 1989). A sustained elevation in load provokes a similar response in mammalian systems. If the pulmonary artery of a developing rat heart is banded, the myocytes of the right ventricle increase in number, undergo a substantial increase in cross-sectional area, and assemble additional myofibrils (Olivetti et al., 1988). These data suggest that mechanical loading may serve to regulate the transition between hypotrophic and hypertrophic growth in the developing heart. Some yet-undefined load threshold is also apparently necessary to direct the developing rnyocyte to assume its fusiform shape and initiate the alignment of the myofibrils in parallel with its long axis. If this hypothesized threshold is not exceeded, the differentiation process appears to be arrested at an early stage and the cardiac myofibrillar apparatus fails to mature fully. Marino et al. (1987) have examined the load-dependent nature of myofibrillar differentiation by culturing beating and nonbeating heart cells in suspension or attached to a substratum. These experiments assumed that beating, attached myocytes would be subject to the most external load as a result of the forces generated by their isometric contraction against the substratum. Quiescent, attached cells should experience an intermediate degree of load from forces associated with substrate adhesion and cell spreading. Beating myocytes in suspension culture should be loaded only by the elastic forces which reside within the myofibrillar apparatus, cytoskeleton, and sarcolemma. Finally, nonbeating, unattached myocytes should experience only the elastic forces which cause the cells to round up in suspension culture. Nonbeating myocytes in both groups, and unattached beating myocytes (underloaded ?) all displayed similar rates of protein synthesis and generated a rudimentary, poorly organized myofibrillar apparatus. Myocytes which beat isometrically against the substratum displayed elevated rates of protein synthesis and expressed a more elaborate myofibrillar apparatus. Additional experiments demonstrate that isometeric contraction specifically accelerates myosin heavy chain synthesis and promotes its accumulation in cultured neonatal cardiac myocytes (McDermott et al., 1985; Samarel and Engelman, 1991). Once the presumptive myocyte has undergone commitment, it appears to be inherently capable of assembling the rudiments of a myofibrillar apparatus, even when it is only passively loaded by its own internal elastic

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forces. Extrinsic forces have been directly implicated in promoting the maturation of these myofibrils and promoting their realignment during development (Terracio et af., 1988a,b, 1990a,c). In primary culture, the beating neonatal heart cell typically displays a nonpolar, stellate shape (Atherton el af.,1986; Atherton and Behnke, 1989; Hilenski et al., 1991). Myofibrils radiate throughout the sarcoplasm and terminate in peripheral areas in a succession of focal adhesions. When cyclic episodes of a 10% linear stretch are applied to such cells, a marked morphological transformation occurs. Within 24 hr the cells assume a more elongated shape and redistribute the bulk of their myofibrils along a unique axis perpendicular to the direction of stretch (Terracio et al., 1988a,b). A single, continuous episode of static stretch is sufficient to promote the accumulation of askeletal actin messenger RNA (mRNA), a substantial increase in total protein synthetic rates (Komuro et al., 1990a-c, 1991),and a considerable degree of cytoskeletal remodeling in cultured neonatal heart cells (Terracio et al., 1988a,b; Sharp, personal communication). An external load also appears to play a crucial role in modulating protein metabolism in cultured skeletal muscle myotubes. Cyclic episodes of stretch accelerate protein synthesis and stimulate cell growth in these preparations (Vandenburgh et al., 1989, 1990). During development the intact heart must be subjected to a complex set of mechanical forces as it contracts and undergoes hemodynamic perfusion. The rod-like shape of the adult myocyte and the uniform alignment of these cells within a given layer of the heart may be established during development as a result of the vectorial summation of these forces. Presumably, these tensile and compressive forces are distributed throughout the heart by the elaborate extracellular matrix in which the cells are enmeshed (Borg and Caulfield, 1981). The orientation of skeletal muscle fibers may also be established by external forces during development (Vandenburgh, 1988). When proliferating skeletal myotubes are grown in uitro on a substratum that is under constant tension, they become oriented along a common axis in parallel with the direction of stretch. Similar conditions may be imposed on the developing myotube in uiuo as a result of the elongation and growth of the underlying bone.

IV. Effect of Mechanical Force on Myofibril Formation Externally derived forces may also serve as an early signal that acts to direct the nucleation of myofibrils in the developing heart (Hilenski er al., 1991). Tokuyasu (1989) has indirectly addressed this issue by sequentially examining myofibrillar structure at different time points during chick em-

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bryogenesis. He found that putative myofibrils (i.e., actin- and titinpositive filaments) appear to be assembled from a nearly continuous band of zonula adherens-like intercellular junctions and a discrete series of vinculin-positive foci. Such vinculin-positive foci have also been reported to exist in cultured muscle cells and are believed to represent nascent costameres and/or Z-discs (Sanger et at., 1984, 1986). In the chick heart these ectopic structures appearjust about the time that discernible contractile activity begins. This phase of development is marked by the morphogenetic movements of heart tube formation and looping (Nakamura et al., 1980; Manasek el al., 1984). Since the primitive myofibrils of the heart appear to be attached to the sarcolemma through nascent costameres (Sanger et a / . , 1984, 1986; Terracio et al., 1990b) and fascia adherens junctions (Tokyasu et al., 1981; Tokyasu, 1989), they appear to be subject to the extrinsic tensile forces that must accompany these morphogenetic events (Nakamura et a / . , 1980; Manasek er al., 1984). These forces would inevitably stretch the myocyte and may signal the cell to initiate the nucleation and proliferation of primitive myofilaments. The redistribution of myofibrils that occurs in uitro when neonatal heart cells are stretched could be a reflection of such a phenomenon (Terracio et a / . , 1988a,b,c, 1990~).Thus, the cardiac phenotype appears to result from a combination of factors; notably, the intrinsic genetic makeup of the heart cell dictates the potential structure that it can achieve, but external mechanical load modulates the extent to which this genetic program is expressed (Cooper, 1987).

V. Mechanical Regulation of Adult Cardiac Myocyte Physiology The mechanical regulation of adult cardiac myocyte physiology is most easily observed during nonsteady-state conditions. One of the most conspicuous responses of the adult heart to a sustained elevation in load is a transient increase in protein synthesis (Morkin et a / . , 1972; Everett et al., 1977; Sanford et a/., 1978; Morgan et a&., 1987; Peterson e t a / . , 1989). Studies of isolated, perfused hearts provide convincing evidence that ventricular wall stretch represents the mechanical factor most closely associated with this response (Morgan et a/.,1987).Retrogradely perfused hearts which beat and develop intraventricular pressure (isovolumetric contraction), beating hearts which do not develop intraventricular pressure, and tetrodotoxin (TTX)-arrested hearts (nonbeating) all synthesize total cellular proteins at nearly identical rates (Morgan et a/., 1980; Gordon et al., 1987). If an artificial hemodynamic afterload is applied to an isolated,

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beating heart, it causes a suppression in protein degradation and a substantial elevation in its baseline protein synthetic rate (Morgan et al., 1980, 1986). Passively stretching the ventricular walls has an almost identical effect on protein synthesis. Isolated hearts can be globally stretched by regulating the pressure at which they are perfused (Vogel et al., 1982; Gordon et al., 1986) or by controlling the volume of perfusate that is within the lumen of their ventricles (Poche et al., 1971). If perfusion pressures are elevated from 60 mm Hg to 120 mm Hg, protein synthetic rates are markedly increased (Xenophontos et al., 1986). Elevating the intraventricular pressure from 0 mm Hg to 25 mm Hg has a comparable effect. Isolated papillary muscles behave in a similar manner. Electrically stimulated, unloaded muscles and flaccid, unstimulated controls incorporate radiolabeled amino acids at similar rates (Peterson and Lesch, 1972). Passively stretching the muscle along its long axis promotes a considerable increase in protein synthesis. These classic studies provide convincing evidence that contractile activity itself does not have a significant role in controlling cardiac metabolism. One serious limitation of these experiments is that they all assume that any mechanical parameter which acutely accelerates protein synthesis in uitro must, by extension, also be responsible for modulating cardiac metabolism in viuo during the steady state and periods of growth. The validity of this assumption is difficult to assess since only the initial phases of relatively short-term phenomena can be investigated in perfused hearts and isolated papillary muscles. An issue that has not been adequately addressed in any model of cardiac physiology concerns the effects of mechanical perturbations on the rate at which proteins are degraded. A comprehensive examination of these processes is absolutely necessary in order to understand how physical forces act to modulate striated muscle mass. During cardiac and skeletal muscle hypertrophy, the rates of protein synthesis and degradation both appear to be increased, but protein synthesis is elevated to a greater degree. Therefore, net growth occurs (Sanford et al., 1978; Laurent et af., 1978; Zak and Rabinowitz, 1979; Laurent and Millward, 1980).

VI. Mechanical Effects on Skeletal Myocytes Tensile forces also have a profound impact on the biology of adult skeletal muscle. The skeletal muscles in the extremities of quadrupeds have been extensively used to study the mechanical regulation of striated tissue. It is possible to surgically manipulate these muscles in viuo and separate the mechanical aspects of contractile function from the electrochemical

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events of excitation-contraction coupling. Skeletal muscle hypertrophy can be elicited by chronically elevating the preload or afterload which the muscle experiences (Thomsen and Luco, 1944; Gutmann et al., 1971; Holloszy, 1977). Immobilizing a limb in a cast or surgically fixing it in place with pins causes the intrinsic muscles of that extremity to atrophy (Lippman and Selig, 1928; Solandt et al., 1943; Thomsen and Luco, 1944). Surgically unloading a skeletal muscle by severing one of its tendonous insertions also initiates atrophy (Solandt et al., 1943; Gutmann et al., 1971). Unlike the heart, skeletal muscle mass is subject to a considerable degree of regulation from the central nervous system and as a result denervation compromises its structure (Lippman and Selig, 1928; Solandt and Magladery, 1942). In part, this response appears to develop because such an injury can act to reduce the resting tension that exists within the affected muscle. The effects of denervation may be partially overcome by experimentally increasing the preload of the denervated muscle. Thomsen and Luco (1944) studied this phenomenon by surgically altering the attachment site of the soleus muscle in adult cats. They fixed the muscle in a state of hyperextension, hypoflexion, or at an intermediate length that approximated its normal position. The hind limb was then immobilized. In selected animals the nerves to the soleus were also ablated. These experiments demonstrated that stretch alone was sufficient to initiate hypertrophy, and that by increasing the preload of the muscle, the effects of denervation could be substantially overcome (Thomsen and Luco, 1944; Gutmann et al., 1971).

VII. Changes in Regulatory Molecules in Response t o Load

Perturbations in cellular loading that increase protein synthetic rates in the heart appear to exert their effects primarily by modulating the absolute capacity of the myocyte to produce protein (McDermott and Morgan, 1989). Ribosomal RNA (rRNA) and messenger RNA are synthesized and accumulated at accelerated rates during normal postnatal myocardial growth (Peterson et al., 1989; Camacho et al., 1990) and during the early stages of cardiac hypertrophy in the adult (Siehl et al., 1985; Coleman et al., 1989). Mechanically accelerated protein synthetic rates in isolated hearts and cultured myocytes are also preceded by an expansion in the pools of mRNA and rRNA available for translation (McDermott et al., 1985, 1987; Chua et al., 1987; McDermott and Morgan, 1989; Komuro et al., 1991). There is only limited evidence to suggest that protein synthetic

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rates are modulated to any great extent by a change in the efficiency at which existing ribosomes are translated (Xenophontos ef al., 1986). The specific identity of cardiac genomic sequences that are responsive to changes in load is just now beginning to be characterized. A welldocumented, immediate early response found in a variety of preparations is the induction of proto-oncogenes and the accumulation of their protein products (Mulvagh et al., 1987; Izumo et af., 1988; Long et al., 1990; Komuro et al., 1990a, 1991). Despite exhaustive study, the function of these small nuclear proteins remains highly speculative. The early expression of these proteins during hypertrophy suggests that they could represent components of a secondary signal transduction system. Such a system could serve to amplify primary signals received from the cytoplasm and/ or convey information throughout the nucleus (Sambucetti and Curran, 1986; Distel et al., 1987). Trans-acting signals appear to be a necessary part of any cascade that serves to upregulate the transcriptional activity in a wide variety of genes (Iwaki et al., 1990). The expression of proto-oncogenes during the early stages of cardiac hypertrophy is somewhat puzzling. In cardiac tissue they appear to be consistently expressed in response to an increased load (Mulvagh et al., 1987; Izumo et al., 1988; Dunnmon et al., 1990; Long et al., 1990; Komuro e f al., 1990a,b, 1991). Conflicting reports in the skeletal muscle literature have indirectly attributed very different effects to the expression of the proto-oncogene family. Many of these sequences are believed to be regulated by a protein kinase C-dependent mechanism (Komuro et al., 1990a,b, 1991). Under some circumstances, phorbol esters which activate this enzymatic pathway, and presumably the expression of these genes, appear to cause a depression in contractile protein synthesis and promote the dissolution of the myofibrils in cultured skeletal muscle myotubes (Lin et al., 1987, 1989; Choi et af., 1991). In contrast, phorbol esters that reportedly activate protein kinase C activity in cardiac myocytes induce the expression of the proto-oncogenes c-fos, c-jun, and egr-1 ; the accumulation of contractile proteins; and the assembly of myofibrils (Dunnmon et al., 1990). It is possible that these discrepancies represent a species, cell type, or culture-specific phenomenon. The net effect of proto-oncogene expression in any cell type undoubtedly depends upon the specific subtypes which are active at a given time as well as their relative concentration. Heat shock proteins are also induced during the immediate early stages of load-induced cardiac hypertrophy (Delcayre et al., 1988; Izumo et al., 1988; Moalic et af., 1989), yet the function of these proteins also remains unclear. The heat shock family exhibits thermoprotective properties in many cell types, and their expression is believed to confer a survival advantage during different forms of environmental stress (Linquist and

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Craig, 1988). Representative heat shock proteins also appear to act as molecular chaperones (Ellis, 1987, 1990, 1991). In this capacity they may act to ensure that proteins assume their proper tertiary structure, selfassemble into functional polymeric units, and cross lipid bilayers (Ellis, 1987; Sheffield et al., 1990; Singh, 1990; Hartl, 1991). Many of these functions may be needed to support the assembly of cytoskeletal structures and proliferation of the mitochondria during myocyte growth. Many questions remain to be answered concerning the functional significance of proto-oncogene products and heat shock proteins during loadinduced changes in protein synthesis. A more complete inventory of the circumstances under which they are expressed must be made. It is not known if their transient expression is necessary or sufficient to promote cardiac growth. A detailed examination of how these proteins interact with the second tier of load-sensitive genetic sequences and their protein products is also needed. Unfortunately, their role in these processes remains largely speculative. Their expression may represent a specific or incidental response to mechanical perturbations. The function of these proteins during the steady state also awaits further study. The identification of a putative heat shock protein in heart cells that transiently causes the disassembly of the myofilament-like stress fibers of fibroblasts further complicates these issues (Miron et al., 1991). During immediate late phases of a load-induced acceleration in protein synthesis, gene sequences that encode structural and channel proteins are expressed at elevated rates (Lee et al., 1987,1988; Simpson et al., 1989; Nagai et al., 1989; Mercadier et al., 1990). The increased transcription of many of these messages is correlated with the increased synthesis of the corresponding protein product (Lee et al., 1988). This is consistent with the notion that protein synthesis rates appear to be controlled in the heart primarily by modulating the capacity of the cell to produce protein (McDermott et al., 1985,1987; Chua et al., 1987; Komuro et al., 1991).Not surprisingly, the expression of a small percentage of genes also appears to be suppressed during the intermediate phases of adaption to an increased load (Komuro et al., 1990~). Perturbations in load can also selectively alter the composition of the heart cell by initiating the expression of alternative isoforms of some protein species. The transition of myosin heavy chain isoenzymes, which occurs in some mammals during cardiac development and hypertrophy, has long been recognized and studied (Everett et al., 1977; Chizzonite et al., 1982; W. A. Clark et al., 1982, 1984; Gustafson etal., 1986; Imuramura et al., 1990). As a more complete catalog of the specific load-sensitive gene sequences is accumulated, the mechanisms by which they are controlled may be delineated. Of particular interest is the determination of how these genes might be induced by immediate early gene products.

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The mechanisms by which the cell establishes an equilibrium with the prevailing workload and controls its message levels, myofibrillar content, and overall mass remain to be elucidated.

VIII. Effects of Decreased Mechanical Load

The mechanisms which mediate cardiac atrophy are not as well documented, in part because this process is so difficult to model. Adult hearts have been partially unloaded from hemodynamic afterload by transplanting them into the abdominal cavity of a homotypic recipient (On0 and Lindsey, 1969; Dittmer and Goss, 1973). The auxiliary heart is grafted to the aorta of the host and is then perfused in a retrograde fashion. Within 7 days, these auxiliary hearts display an apparent decrease in total RNA, a depression in total protein synthesis, and a loss in total protein content (Klein, 1986; Klein et al., 1991). This is consistent with the reports (Samarel et al., 1987) that protein synthetic rates are also depressed during starvation-induced cardiac atrophy in adult rabbits. To study the mechanical regulation of cardiac mass and myofibrillar organization, Cooper and his colleagues developed a model based on the surgically unloaded papillary muscle (Tomanek and Cooper, 1981 ;Cooper and Tomanek, 1982; Thompson et al., 1984; Kent et al., 1985; Cooper et al., 1986).Their experiments demonstrate that cardiac muscle is extremely sensitive to localized changes in load. In adult cats, hypertrophy of the free wall of the right ventricle and its papillary muscles can be initiated by partially occluding the pulmonary artery (Cooper et al., 1985). This hypertrophic response will develop even if the heart is surgically denervated or if the animals are chronically infused with a- (terazosin) and p- (propanolol) adrenergic blockers. Unloading a single small papillary muscle in the right ventricle will in no way modify the progression of hypertrophy in this chamber, regardless of when this procedure is conducted in relation to the pulmonary occlusion. However, within 3-7 days of surgery, the unloaded papillary muscle displays a conspicuous reduction in overall size and a focal loss of electron-dense Z-line material (Kent et al., 1985). As time progresses, these relatively localized Z-line abnormalities become increasingly more widespread. Myofibrillar polarity and alignment are lost and the relative concentration of contractile proteins is reduced. Performance aberrations develop in parallel with these structural changes, including a decrease in shortening velocity, a depression in active force generation, and an overall reduction in all length-tension values (Tomanek and Cooper, 1981; Cooper and Tomanek, 1982; Kent et al., 1985). When these unloaded papillary muscles are subsequently reattached and re-

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loaded by surgical intervention, the Z-line abnormalities are reversed, normal myofibrillar alignment is rapidly reestablished, and the mechanical indicators of performance return to control values (Thompson et af., 1984).

IX. Effects of Load Changes in Vitro

In uiuo as well as in uitro the adult myocyte, like the developing heart cell, appears to have a load threshold which must be exceeded in order for it to maintain the structure of its fully differentiated rnyofibrillar apparatus. In serum-supplemented culture medium, the nonbeating adult cardiac myocyte attaches and spreads out over the substratum (Simpson et al., 1993). After 14 days of culture it displays a spread and flattened shape that resembles the conformation of the fully spread neonatal heart cell. As these fully differentiated cells spread in culture, they gradually develop focal loss of Z-line material, express poorly defined sarcomeres, and lose their myofibrils (Simpson et al., 1988; Decker et al., 1990, 1991; Clark et af.,1991). Aberrant thick and thin filament organization evolves, t-tubules lose their association with the Z-discs, and the sarcoplasmic reticulum undergoes an extensive reorganization. Many of these degenerative changes occur in culture entirely independent of any change in cell shape (Decker et al., 1991). The acquisition of rhythmic beating activity in uitro by fully spread, disorganized myocytes is associated with an increase in cell size, the accumulation of protein, and the incorporation of myosin into elaborate myofibrillar arrays (Clark et af., 1991). These myofibrils display welldefined sarcomeres with Z-discs that are in intimate contact with t-tubules (Decker et al., 1990, 1991).

X. Pathophysiological Changes in Load

The sensitivity which striated tissue displays to perturbations in load suggests that potentially serious consequences may result when pathophysiological conditions alter the mechanical properties of the surrounding environment. For example, although a prolonged episode of ischemia can impair blood and nutrient delivery to a relatively small, confined region of the heart, this condition may affect the structure and overall performance of a substantially larger region of the muscle. In the affected region, ischemia can compromise cardiac performance and impair the ability of

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the myocytes to perform useful work. At the same time, adjacent regions of muscle may experience an increase in load as they work to compensate for the impaired performance of the ischemic tissue. These circumstances may establish a spiraling cycle of degeneration (Sole and Liew, 1988), atrophy, and cytoskeletal damage in the ischemic region, and induce a hypertrophic response in the surrounding muscle. This chapter has already discussed how such perturbations might affect the rate at which various myofibrillar proteins are expressed as well as how a sustained change in load can alter the isoform composition of the contractile machinery. Another variable which must be considered is the response of the interstitial cells of the heart to localized deviations in load. Carver et al. (1991) have demonstrated that cyclic episodes of stretch will alter the expression of collagen isoforms in cultured cardiac fibroblasts. Repetitive cycles of stretch promote the preferential accumulation of collagen type 111 mRNA and its protein product. To a lesser extent even a sustained static stretch has a similar effect. In the intact heart, such an isoform shift may further modify the mechanical properties of the alreadytaxed ventricle. Even short periods of ischemia can alter normal myofibrillar-cytoskeletal-sarcolemmal interactions (Ganote and Vander Heide, 1987). Ganote and Vander Heide (1987) and Steenbergen et al. (1987) report that global episodes of ischemia in isolated hearts provoke the depletion of vinculin and a-actinin from the Z-discs and costameres. The redistribution of these structural proteins and the loss of costameric integrity must have a profound impact on the ability of the damaged myocytes to function. Such acute changes in cytoskeletal order suggest that it may be desirable to design therapeutic interventions that inhibit the formation of such cytoskeletal lesions. Physical forces, which originate outside the cell proper, appear to play a unique and pervasive role in controlling the differentiated state of the striated muscle cell. These extrinsic forces are implicated in directing essential aspects of cardiac morphogenesis (Nakamura et al., 1980; Manasek el al., 1984; Terracio et al., 1988a,b; Bishop et al., 1990) and appear to represent a potent determinant of striated muscle function (Starling, 1918, 1920; Braunwald, 1965), metabolism (Peterson and Lesch, 1972; Kira et al., 1984; Gordon et al., 1986; Morgan et al., 1987) and structure (‘Cooperand Tomanek, 1982; Cooper et al., 1985; Cooper 1987) throughout life. The mechanical regulation of striated tissue appears to represent a mechanism which ensures that myofibrillar mass and contractile performance are balanced to meet the prevailing workload. A number of second messenger pathways have been implicated as possible conduits by which information concerning a perturbation in load is communicated to the intracellular environment.

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XI. Receptors of Mechanical Force

Of obvious importance in this process are cell surface components through which physical stimulation may be transmitted to the interior of the cell. It is probable that many effects of mechanical stimulation are transduced through the interactions of the cell with the surrounding extracellular matrix. The ECM is known to influence various aspects of cell behavior, including migration, morphology, differentiation, and proliferation (Borg et al., 1990: Borg and Terracio, 1990). Cell surface components, including integrins, have been shown to interact with the extracellular matrix (Buck and Horwitz, 1987; Hynes, 1987: Ruoslahti, 1991). Several lines of evidence suggest that specialized regions of the cell membrane exist where the ECM is linked to the cytoskeleton via integrins (Burridge et al., 1988; Borg and Terracio, 1990). A high concentration of integrins has been noted in focal adhesions, sites of cell-substratum contact in uitro. In addition, a variety of cytoskeletal molecules have been localized to the focal adhesion, including vinculin, talin, paxillin, and a-actinin. It is currently not clear what the specific role of each of these components is in linking the transmembrane integrin to the actin cytoskeleton. However, it is thought that the interactions between the actin filaments, focal adhesion proteins, including integrins, and possibly intermediate filaments act to modify the relative positions of the cell membrane, nuclei, and other cellular components in response to mechanical force (Terracio and Borg, 1988~). This does not appear to be exclusive to cells grown in culture because similar distributions of these proteins have been found in dense plaques of smooth muscle cells and myotendinous junctions of skeletal muscle in uiuo (Geiger et af., 1980; Shear and Bloch, 1985: Tidball et al., 1986). It has been postulated that the interaction of the actin cytoskeleton with integrins at these sites may function to transmit force generated during muscle contraction across the cell membrane (Burridge et al., 1988). The cytoskeleton may also play an important role in regulating gene expression through interactions with specific mRNAs (Jeffrey, 1989; Biegel and Pachter, 1992). Thus, mechanical force could influence gene expression through altered integrin-cytoskeletal interactions.

XII. Transduction of Mechanical Force by lntegrins

Recent experiments suggest that integrins transduce signals from the surrounding microenvironment that are involved in the regulation of a variety of cellular processes, including changes in cytoplasmic pH, calcium ion

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transients, and alterations in gene expression (Werb et al., 1989; Ingber et al., 1990; Ng-Sikorski et al., 1991). As mentioned above, integrins may transmit signals from the surrounding environment via their role as bridges from the ECM to the cytoskeleton. Recent evidence also suggests that integrins may be involved in the transmission of biochemical signals that can affect cellular processes (Kornberg and Juliano, 1992). The identification of potential regulatory proteins, including tyrosine kinases, within focal adhesions suggests that these specialized cell sites may be involved in transmembrane signaling. Studies using antibodies to cluster integrins on the surface of carcinoma cells demonstrated enhanced tyrosine phosphorylation of a complex of 120-130 kDa proteins (Kornberg et al., 1991). This suggests that clustering of integrins at specific sites on the cell surface, such as at focal adhesions, may play an important role in the transmission of biochemical signals within cells. It is easy to envision that high densities of integrin receptors at specialized sites, such as at the costameres of heart myocytes (Terracio et al., 1989; Hilenski et al., 1991), may play a significant role in signal transduction in response to mechanical stimulation. Interactions have also been noted between integrins and ion channels. 'The integrin IIb/IIIa has been shown to affect calcium homeostasis (Burridge et al., 1988). That is, in cells which lack the IIb/IIIa complex, calcium ion influx is reduced by 50%. It is suggested that binding of the integrin to its ECM ligand may induce conformational changes in the integrin that subsequently alter the function of adjacent or interconnected ion channels (Burridge et al., 1988). The localization of abundant integrins at sites such as focal adhesions or costameres may have significant impact on ion channels at these locations. Calcium ion fluxes at these sites may influence calcium-dependent enzymes, including proteases, which act on cytoskeletal components. For instance, calcium-dependent calpain I1 has been localized to the focal adhesion and acts on cytoskeletal components, including talin (Beckerle et al., 1986, 1987). It is possible then, that alterations in the expression or distribution of integrins in response to mechanical stimulation may transmit signals to the interior of the cell through subsequent rearrangements in the cytoskeleton or through a biochemical signaling pathway involving ion channels or tyrosine kinases. As mentioned, integrins are transmembrane heterodimers of a and p chains that link the ECM outside of the cell to the cytoskeleton inside the cell. Recent evidence has begun to show that the short cytoplasmic domain may play a key role in the cell by altering the structure or organization of the cytoskeleton following binding of ligands to the integrin. Experiments interchanging the p l and p3 cytoplasmic domains have illustrated that interactions with a chains are not dependent on the transmembrane or cytoplasmic region of the p chain (Solowska et al., 1991).Recent studies

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interchanging a-chain cytoplasmic regions have illustrated that these portions of the integrin are important in postligand binding events (Chan et al., 1992). For instance, placing either the a-2 or a-5 cytoplasmic region on the VLA-2 integrin chain confered the ability to contract collagen gels on fibroblasts in uitro whereas the a-4 cytoplasmic region did not. On the other hand, the a-4 cytoplasmic domain resulted in a migratory phenotype in transfected cells. These results illustrate that the integrin cytoplasmic domain may be essential in translation of specific information from ligand binding to the cell, potentially through interactions with the cytoskeleton. The a-chain cytoplasmic domains have very little homology except in the GFFKR sequencejust inside the transmembrane region (Hynes, 1992). In addition, several of the integrin (Y chains, including a-6,are alternatively spliced within the cytoplasmic region. Also, the p4 integrin chain has an unusually long cytoplasmic region and is found concentrated at the hemidesmosomes of epithelial cells (Sonnenberg et al., 1991). In these cells, the p4 integrin is found associated with intermediate filaments instead of the actin cytoskeleton. The cytoplasmic regions then may interact with different cytoskeletal or other intracellular proteins to mediate distinct cellular events in response to ligand binding.

XIII. Stretch-Activated Channels

Most cell membranes contain stretch-activated (SA) ion channels that are regulated by mechanical stimulation or membrane tension (Sachs, 1988; Morris, 1990). Stretch-activated channels have been identified in a wide range of animal cells and all are permeable to cations. Two general groups have been characterized: nonselective cation channels, which are essentially equally permeable to various cations; and selective channels, which are much more permeable to potassium ions than sodium ions (Yang and Sachs, 1990). The opening of a channel in response to mechanical stimulation appears to be derived from a strain within the cell membrane (Sachs, 1988). The flux of ions through the channel and membrane voltage appears to be, at least in part, necessary for the channel to remain gated. It has been suggested that the gating of calcium-permeable channels by mechanical or electrical stimulation may play a significant role in the entry of calcium ions into developing myocytes (Entwistle et al., 1988). The number of stretch-sensitive channels on the surface of myocytes is related to the developmental and differentiative state of the muscle cells (Franc0 and Lansman, 1990). Stretch-sensitive channels are present at high densities in skeletal myoblasts; however, there is a significant reduction in their activity that is concurrent with the differentiation of skeletal myoblasts

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into multinucleated myotubes. This suggests that the influx of calcium ions into myoblasts and myotubes may be by different mechanisms and that this may influence the function of the particular cell type. It is currently not entirely clear what the role of the cytoskeleton or other cell surface molecules is in the activation of stretch-sensitive channels. Pretreatment of cells with colchicine or vinblastine, which interfere with microtubules, followed by examination of SA channels, indicated no effect on the sensitivity of these channels (Sachs, 1988). Contrary to this, cytochalasins, which interfere with actin-containing microfilaments, increased sensitivity of the cells to mechanical stimulation. Also, the pretreatment of cells with phalloidin, which stabilizes F actin, had no effect on SA channels. Further evidence that implies a role for the cytoskeleton in SA channel activation is that in cell membrane areas where the underlying cytoskeleton is disrupted, SA channel activity is absent. It has been suggested that the viscoelastic properties of the actin network and the arrangement of the constituent actin filaments may play a role in the response of SA channels to mechanical stimulation (Sato et al., 1987; Sachs, 1988). It is currently unclear how SA channels may be associated with the actin cytoskeleton; however, the size and localization of spectrin has led several investigators to view this protein as a link between the actin network and SA channels (Guharay and Sachs, 1984). Also, the developmental accumulation of spectrin coincides with the appearance of SA channel activity in some cells (Nelson and Lazarides, 1985; Sachs, 1988). Although there is strong correlative evidence pointing to an important role for the cytoskeleton in activating SA channels by mechanical stimulation, direct demonstrations of this is lacking. As described above, mechanical stimulation may be transduced to cells in two general mechanisms; through the ECM-integrin-cytoskeletal network, or through ion channels and associated second messenger systems. However, it is still not clear how second messenger systems are stimulated in cells by mechanical forces. An early report suggested that the transduction of mechanical stimulation requires growth factors in some instances (Vandenburgh, 1983). That is, mechanical stimulation had an effect only when growth factors were present. It has been suggested that mechanical stimulation may cause an alteration in growth factor receptors which, in turn, amplifies the growth factor binding reponse (Vandenburgh, 1992). However, many second messengers have been shown to be induced by mechanical stimulation in the absence of exogenous growth factors in the medium. It is not clear if these responses occur independently of growth factors or if the growth factors are produced by the cells being stimulated and subsequently act on surrounding cells or themselves to induce second messenger systems.

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XIV. Nuclear Matrix

In addition to the potential second messengers described above, direct transmission of mechanical forces could play an important role in the regulation of cellular functions. As indicated earlier, the cytoplasmic compartment has been shown to be linked to the nuclear matrix (Berezny, 1991), allowing mechanical force to be transmitted to the nucleus. The structure and function of the nuclear matrix have been reviewed by Getzenberg et al. (1991). It has been determined that the arrangement of chromatin loops has a profound effect on the regulation of gene expression. Nuclear functions are not randomly dispersed throughout the nucleus but are localized to discrete regions and occur in association with the nuclear matrix (Pinkel et al., 1989). The demonstration that matrix-associated regions (MARs) may be a new form of cis-acting sequence elements that require precise positioning to be functional (Van Driel, 1991; Berezny, 1991; McKeon, 1991) strongly supports a role for mechanical transmission of information in regulating gene expression. Recent studies have also indicated that the nucleolus and distribution of ribosomal genes follow these same patterns of nuclear order and organization (HernandezVerdun, 1991). This fibrillar and granular organelle, which is essential for ribosome biogenesis, possesses a critical polarity and organization that reflect activation or inactivation of the ribosomal genes (Haaf et al., 1990). The fundamental elements of the model of dynamic reciprocity proposed by Bissel (1982) can now be framed in an experimental paradigm that can be tested. As the binding proteins associated with MARs and other components of the nuclear matrix become characterized, regulation and expression in response to mechanical transmission of forces can be studied. Although most of this work comes from other systems, it is highly likely that muscle, a tissue exquisitely sensitive to load and other mechanical stimuli, will respond in a similar fashion.

XV. Conclusion

In this chapter we have attempted to present support for the hypothesis that mechanical stimulation plays an essential role in development of muscle cells and maintenance of function. Although we feel the evidence to support such a hypothesis is strong and have made it the focus of this chapter, it should be pointed out that mechanical stimulation is not the only morphogen at work. Mechanical stimuli function in conjunction with growth factors and other morphoregulatory molecules to achieve the final

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form and function of muscle. Future experimentation, both in uiuo and in v i m , needs to be focused on the interaction of both mechanical and chemical stimulation. The development of molecular probes as well as sophisticated measurements of force will be essential to our understanding of the role of mechanical stimulation of muscle cells in development, growth, and disease.

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Finite Element Methods for Developmental Biology G. Wayne Brodland Departments of Civil Engineering and Biology, University of Waterloo, Waterloo, Ontario, Canada N2L 3Gl

I. Introduction The finite element method is a modeling tool that has much potential in the analysis, study, and simulation of biological systems. This is especially true in developmental biology, where highly nonlinear behavior often occurs, and alternative, effective methods of analysis do not currently exist. The method is highly general, and can be used to study a wide range of developmentally important phenomena, including morphogenetic changes in shape, pattern formation, heat flow, and thermodynamically defined phenomena (Abel et al., 1981; Brodland and Clausi, 1993). If the interactions that govern a process can be described mathematically, the process can be modeled using the finite element method. A detailed discussion of those aspects of the finite element method that are relevant to developmental biology would require many volumes. The purpose of this chapter is to outline the physical basis, formulation, and principal features of the method, and to present solutions to technical difficulties that arise when the method is applied to developmental biology. We begin by briefly investigating the role of modeling and the features one might expect of a well-conceived model.

II. Modeling in Developmental Biology

A. Role of Modeling

Modeling serves several important functions. First, the formulation of a mathematical model requires knowledge of the detailed relationships

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between all relevant, governing quantities. Even though much may be known about the behavior of certain systems, key relationships may be unknown or may be known only qualitatively. These limitations in understanding can often be identified through the exercise of formulating the problem mathematically. A well-conceived model allows the relationships between the behavior of the subcomponents of a system and the behavior of the system as a whole to be investigated. Such models can take several forms. In biological systems, the kinematic relationship between local epithelial shapes and the global shape of the structures they produce has been treated by Jacobson and Gordon (1976), Hilfer and Hilfer (1983) and Brodland (1990). Most of these works make extensive use of computer simulations. Other studies have made it possible to relate forces to the changes in shape they produce (Ode11 et al., 1981; Weliky and Oster, 1990; Clausi, 1991; Dunnett et al., 1991; Brodland and Clausi, 1993). Models also provide a powerful scheme for testing hypotheses. Once a model of a system has been constructed, it can be used to see whether the observed phenomena are produced, qualitatively and quantitatively, by the model. If they are not, it indicates that the model may be in error. Jacobson (1980), discussing neurulation, a mechanical process in which a sheet of cells undergoes in-plane motion and rolls up to form a sealed tube, indicates the importance of computer simulation in ascertaining which forces are sufficient to cause the shape changes observed. Recent three-dimensional finite element-based simulations of neurulation (Brodland and Clausi, 1993; Clausi and Brodland, 1993) have made it possible to test various hypotheses about the forces that drive this process. If an accurate model of a biological system can be constructed, it can be used to investigate the consequences of subtle changes in the system (Dunnett et al., 1991). This feature is particularly useful since is not possible, in general, to perform such “sensitivity analyses” by other means. In some cases, much can also be learned by considering what is called the inverse problem. Rather than determining the changes in shape that are produced by particular forces, one might formulate the problem to determine the forces required to produce an observed change (Brodland and Shu, 1993). Certain mathematical criteria must be satisfied, however, in order for this kind of problem to be solved (Beck, 1977). If a model is to be accurate, it may have to satisfy, in addition, certain phenomenon-related requirements. One such set of requirements for the analysis of morphogenetic movements is discussed by Brodland and Clausi (1993).

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B. Some Difficulties Specific t o Developmental Biology The modeling and analysis of processes of interest in developmental biology pose a number of special challenges, as noted by Gordon (1985). One of the most serious of these is the significant changes in shape that embryonic tissues undergo during development. In the language of mechanics, such structures are said to undergo large deflections. Engineering structures are, in general, designed specifically so that they do not change shape perceptibly. Thus, traditional engineering analysis methods, which focus on structures undergoing infinitesimal deflections, must be modified for studying significant shape changes in biological systems. Analytical methods have been devised to study simple geometries that undergo large deflections and thus can change shape significantly (Green and Adkins, 1970). More recently, numerical implementations of these approaches have made it possible to analyze gross shape changes in more general structures (Brodland and Cohen, 1987). Particular care must be taken to distinguish between Eulerian and Lagrangian formulations (Malvern, 1969) when analyzing such structures. Another property of biological systems is that, in numerous cases, they undergo significant local shape changes. In terms of mechanics, they undergo large strains. This gives rise to a variety of modeling complications, especially in formulating constitutive equations, such as those that relate stress and strain (Malvern, 1969). A third characteristic of biological systems is that their components typically have mechanical properties that are substantially different from typical engineering materials (Gordon and Brodland, 1987). Typical engineering materials do not, for example, undergo stretch-induced contractions as microfilaments do. Furthermore, in biological systems, only limited success has been realized in measuring in situ mechanical properties and in quantifying their suspected spatial and temporal variations. The above three difficulties are significant and have, no doubt, considerably impeded the application of finite element methods and other forms of analysis to the study of morphogenesis. However, recent advancements in numerical methods and in computers now make such analyses feasible. Finite element models, in particular, are ideal for these analyses since they satisfy all of the criteria given in the previous section for a wellconceived model. In addition, they allow phenomena of various scales to be modeled. For example, finite element formulations might be used to model whole embryos, tissue layers, patches of cells, individual cells or arbitrarily small components of cells, such as individual actin filaments. In addition, temporal changes in properties can be modeled. Finally, as discussed in the next section, current finite element formulations are highly

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general and allow the effects and interactions of a wide variety of phenomena to be studied. A strict finite element formulation, in contrast to many other discrete modeling approaches, has the advantage of ensuring self-consistency and accuracy even when a wide range of different physical phenomena, including those which are mechanical, thermodynamic, and biochemical, act simultaneously. Some finite element software packages for performing nonlinear analyses are available commercially. In general, these cannot adequately model the degree of nonlinearity encountered in developmental biology problems. In addition, such packages are unable to properly model the unusual physical properties of real biological systems. Instead, custom software, like that developed by Cheng (1987a,b) or Brodland and Clausi (1993) must be used.

111. Basis of the Finite Element Method A. Approach

If a system is complex, it might not be possible to directly develop equations that describe the behavior of the system. However, it might be possible to write equations that describe the behavior of its subcomponents (e.g., cells). If the behavior of these subcomponents is also complex, further subdivision (e.g., in terms of cytoskeletal components) might produce discrete, finite-sized regions for which suitable equations could be written. The finite element method provides a systematic means for using this geometric and behavioral information to construct systems of equations that can be solved on a computer. It can be shown that such solutions can accurately predict both local interactions and the behavior of the system as a whole provided that the rather modest conditions outlined below are met. Figure 1 shows in a simplified way how finite element modeling works. A two-dimensional framework of a building is a relatively complex mechanical system (Fig. la). It is natural to view the frame as an interconnected assemblage of beams and columns. This suggests subdividing the building into beam and column elements (discrete units) for analysis purposes (Fig. lb). This is a valid discretization because each element is finite in size and mathematical descriptions of the mechanical behavior of each element are available. Element numbers are shown in outline in Fig. lb. Elements interact with each other at points called “nodes,” indicated with bold numbers. A finite element analysis was performed to

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b

a

Beam Element

Column

\

Column Element

Fixed Supports

Vertical Loading

FIG. 1 Finite element analysis of a building framework. (a) The initial state of the framework. (b) One possible subdivision of finite elements in the structure. Elements are numbered in outline. Nodes are numbered in boldface. (c) Deflection of the structure due to the action of the indicated loads. Displacements are exaggerated for illustrative purposes.

determine the deflection of the structure that would result from the loads in Fig. lc (the deflections in the figure are exaggerated). As a result of the analysis, details of member-member interactions and the behavior of the structure as a whole are available. Note that the mechanical behavior of the system as a whole is influenced by each of its components, and that the actual behavior of any one component is affected by the system of which it forms a part.

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B. Biological Application

Neural tube morphogenesis is a mechanical process that has received much attention. A precise description of this process requires a mathematical approach. However, to mathematically describe the process in terms of equations which can be solved directly would be difficult, if not impossible. Mathematical descriptions of the behaviours of the components of the system might, however, be possible. In the case of a neural plate, the morphologies and individual mechanical behavior of the microfilaments, microtubules, cell membrane, and cytoplasm might be known. The finite element method can thus be used to produce systems of equations that can be solved using a computer, and that accurately model both local mechanical interactions and the mechanical behavior of the neural plate as a whole. Figure 2 shows how the finite element method can be used to model part of a sheet of epithelial cells. Assume that the cell cytoplasm is viscous, that paraxial microtubules are present, and that microfilaments span the apical end of each cell (Fig. 2a; for illustrative purposes, only two cells are shown). Individual microtubules might then be represented as rodlike finite elements and the viscous cytoplasm as a quadrilateral element (Fig. 2b). Figure 2c shows one possible deformed shape produced by the mechanical interaction of these components. The deflections shown here have not been exaggerated. Again, the mechanical behavior of the system is influenced by each of its components, and the actual behavior of each component is affected by the system as a whole. The essential idea, then, behind the finite element method is that an object, or system, of interest is divided geometrically into a collection of elements. Each element is finite in size and and is chosen so that its behavior can be described mathematically. Elements interact with each other at points called nodes. The method provides a formal and welldefined way to produce systems of simultaneous equations that model a real system and that can be solved. The method is powerful because it makes it possible to accurately model complex interactions between large numbers of components provided that a straightforward mathematical description of the physical behavior of each component is available. C. Historical Developments

Although much of the mathematical foundation of finite element methods was laid during the 1940s and 1950s, not until the 1960s did the method begin to establish itself as one of the standard tools for modeling and analysis of physical systems. Much of its development was driven by the

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a Apical Surface

Microfilament Bundle 3

Microtubule cytoplasm

-

A

Cell Sheet

1 Basal Surface

b

FIG. 2 Finite element analysis of a cross-section of a patch of epithelial cells. For illustrative purposes, only two cells are shown. (a) The initial state of cells which form the sheet. (b) Subdivision of the cells into finite elements. There are separate finite elements for microfilament bundles, microtubules, and the cell cytoplasm. (c) Shape changes in the sheet caused by microfilament shortening and microtubule lengthening. In this example, the shape changes are not exaggerated.

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need for high strength-to-weight, load-carrying aerospace components and structures. Designs often called for complex shapes, making it impractical to use traditional stress analysis methods to evaluate the efficacy of proposed designs. Detailed stress analyses were, nonetheless, required. The development and accessibility of powerful mainframe computers during the 1960s made it feasible to develop computer-based methods to perform these analyses. In time, a method which became known as the finite element method emerged. Since then, the method has been generalized and used extensively to study systems involving deformation of materials, fluid flow, heat transfer, contaminant transport, molecular diffusion, and a host of other phenomena (Abel et al., 1981). The finite element method has become mature in the sense that modern rigorous mathematical formulations of the method have been reconciled with its more pragmatic earlier formulations. In addition, the power, flexibility, and accuracy of this general-purpose analysis tool have been established through its extensive use in engineering and various branches of science and mathematics. The finite element method has only recently been applied to problems in developmental biology (Clausi and Brodland, 1993; Brodland and Clausi, 1993). This may seem surprising since the method has been used extensively in orthopedic implant design and other areas of medicine for some time (Schreiber and Jacob, 1984). The reason for this is that many of the processes of interest in developmental biology are highly nonlinear, and finite element methods capable of properly dealing with such substantial nonlinearities have only become available recently (Brodland and Cohen, 1987). Finite element analyses typically produce large systems of simultaneous equations which must be solved. Recent developments in numerical methods have made it possible for personal computers and computer workstations to perform significant finite element analyses, including analyses of morphogenetic changes in shape. Space does not permit a detailed treatment of the finite element method. Instead, this chapter attempts to elucidate the basic nature of the finite element method and to indicate its potential as a tool for studies in developmental biology. Wherever possible, intuitive arguments are used. Rigorous mathematical justifications for these arguments are found elsewhere.

IV. Formulation of the Finite Element Method As noted earlier, the finite element method involves breaking a system or region of interest into finite-sized elements. Equations describing the

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physical behavior of each element are then written. Finally, systems of equations which describe the behavior of the system are constructed and solved to determine the behavior of the system. The advantage of this apparently circuitous procedure is that it allows the behavior of the system to be determined, provided that the behavior of its subcomponents is known. This feature is especially useful in the analysis of complex structures, such as sheets of cells or whole embryos.

A. Quantities of I n t e r e s t The first step in a finite element analysis is to identify the quantities of interest. If we are studying the mechanical changes of shape in a sheet of epithelial cells, the quantities of interest might include the spatial positions of each of the nodes with time, the forces or stresses within each cell and between cells, adenosine triphosphate (ATP) concentrations, and descriptors of gel-sol behavior. In a biochemically based problem of pattern formation, we would want to know the local concentrations of each of the morphogens and their by-products (Harrison, 1987). In an analysis of a building structure, quantities of interest include displacements of the nodes of the structure, as well as stresses and strains in each of the members. Next, it is necessary to choose a set of independent quantities (primary quantities) in which all other relevant quantities can be written. These quantities must be sufficient to completely describe the system. In the finite element method, these primary quantities determine the state space available at each node. All subsequent steps in the method are formulated in terms of these nodal values. Sometimes the choice of primary quantities is difficult. Usually they are a subset of the quantities of interest. In the case of a building analysis, the primary set might consist only of the nodal deflections, since member stresses and strains, called secondary quantities, can be determined from the primary quantities. Table I lists possible primary and secondary quantities of interest for several classes of problems. B. Element Geometries

In dividing the system of interest into discrete elements, the next step of the analysis, two properties of the elements available must be determined: their geometries and their shape functions. For any given problem, the elements must have suitable geometries so that when they are assembled, they can both span and completely fill the system.

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TABLE I Generalized Forces, Displacements, and Stiff n e w s for a Variety of Problem Typesa Generalized displacements Primary quantities

Secondary quantities

Generalized stiffnesses

Mechanical forces

Physical displacement

Mechanical stiffness of members

Change in cell Mechanical shape forces

Physical displacement

Member stresses and strains Component stresses and strains Thermal strains

Thermal resistivity

Morphogen gradients Field gradients

Absorptivity of medium Permittivity

Problem type

Generalized forces

Building framework

Thermal analysis Pattern formation Electric fields

Heat sources Temperatures Morphogen generators Electric potential

Morphogen concentrations Current sources

Mechanical stiffness of components

Secondary quantities can be determined from primary quantities and are not included explicitly in the formulation.

A wide variety of finite element shapes exist. These make it possible to efficiently represent almost any imaginable region of interest. A small library of elements which can be used to subdivide a region of interest is shown in Fig. 3. One-, two-, and three-dimensional elements are available to satisfy the dimensionality of any given problem and to represent the geometries of its component parts. It is sometimes appropriate to mix elements of different dimensions. For example, a mechanical analysis of a single cell might use volume elements to represent the cytoplasm, planar elements to represent the cell membrane, and rod elements to represent microtubules.

C. Shape Functions One of the most important steps in the formulation of a finite element problem is the choice of shape functions. These functions define quantities within a given element in terms of its nodal values. The importance of these functions is often overlooked. When the choice of shape functions is not appropriate, a wide range of serious errors or spurious behaviors can result (Irons and Ahmad, 1986). These errors and their causes can be difficult to identify.

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FINITE ELEMENT METHODS FOR DEVELOPMENTAL BIOLOGY

b

FIG. 3 Some possible element geometries. (a) A rod element. It might be used to represent a microtubule or a segment of a microfilament bundle. (b) A quadrilateral element. It might be used to represent a cell membrane. (c) An 8-noded volume element, sometimes called a brick element. It is useful for representing cytoplasm and other space-filling components. (d) A 4-noded shell element. It might be used to represent a curved section of a tissue layer consisting of several hundred cells in a finite element analysis of a whole embryo.

The importance of choosing appropriate shape functions can be demonstrated by comparing two analyses of a flexible microfilament. In Fig. 4a, the microtubule is represented by an element that has linear shape functions. The transverse displacement, u(x) of the microtubule is given in terms of its end displacements, ui,by u(x) = (1

1

I:{

- x/L,x/L)

2

1

2

FIG. 4 The effect of different shape function choices on element behavior. (a) When a rod element is defined by linear shape functions [Eq. (l)], only deformations in which the rod remains straight are allowed. The element is said to have two translational degrees of freedom, namely, the transverse displacements of its two ends. (b) When cubic shape functions are used [Eq. (2)], the rod can flex. This element has four degrees of freedom-independent translation and rotation of each of its ends.

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The quantities 1 - x / L and x / L are the shape functions, Nj; they define the displacements inside the element in terms of its node displacements. In Fig. 4b, the microtubule is represented by an element that has cubic shape functions. This is the lowest order shape function that is consistent with arbitrary transverse end displacements and rotations (Brodland and Cohen, 1987). The transverse displacement, u(x) of the microtubule is then given in terms of its end displacements, u l , and u2 and rotations el and 8, by

u(x) = (253 -

3p+

1, - 253

+ 352, 5 3 - 252 + t, 5 3 - 5 2 )

where the shape functions are given by the cubic functions, 2 t 3 - 3t2 + 1, - 2 t 3 + 3t29 t3- 25, + 5, and t3 - 5,. Suppose that a mechanical process which involves microtubules is studied and that the elements shown in Fig. 4 are used to represent single microtubules. The element shown in Fig. 4a has linear shape functions and must, therefore, remain straight. If microtubule bending is known a priori not to be important, that element would adequately represent the behavior of individual microtubules. If, on the other hand, microtubule bending is important, the element in Fig. 4b would have to be used since it uses cubic shape functions and, therefore, accommodates microtubule flexure. Alternatively, consider what would happen if linear (nonbending) elements were used to analyze the building framework shown in Fig. 1. In that case, an erroneous prediction of zero displacements everywhere would result (assuming the members are axially incompressible). In order for an element to successfully represent the behavior of its subject, its shape functions must have certain mathematical properties. Some of these properties are fundamental to all finite element formulations. Others are highly dependent on the behavior of the subject and its component parts. A discussion of the mathematical properties of shape functions is beyond the scope of this work. Here we note that the shape functions must satisfy completeness criteria for the specific problem being studied (Norrie and devries, 1978), and that elements in which they are used must satisfy the “patch test” (Irons and Ahmad, 1986). The reader is encouraged to consult some of the finite element textbooks cited here for details. We again emphasize that the proper choice of shape functions is of utmost importance to the success of the analysis.

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D. Discretization The next step in the analysis is to divide the area of interest into discrete elements. This process is called discretization. The accuracy of an analysis is highly dependent on this step. The appropriate subdivision of a subject will depend on its underlying structure, the kinds of behavior anticipated, and the shape functions used in its elements. Discretization and element choice are often suggested by the geometry of the system being studied. Whether a particular breakdown is appropriate will depend on the quantities of interest. A subdivision for a mechanical analysis may be quite different from one for a thermal analysis or an analysis of morphogendriven pattern formation. As noted earlier, elements of appropriate geometry must be available to completely span and fill the region of interest. They must also model the essential behaviors of the system’s component parts. As also noted earlier, elements of different kinds and different dimensions can be mixed together. However, an essential condition is that all nodes of adjoining elements be connected. For the planar region shown in Fig. 5a, the subdivision shown in Fig. 5b is allowable, while that shown in Fig. 5c is not. The same principles apply to the construction of three-dimensional meshes. Three main interacting factors determine the accuracy of a finite element analysis: element geometry, shape functions, and the way a system is divided into elements. In general, if higher-order shape functions are used, fewer elements are required. However, even large numbers of elements will not overcome the inadequacies of elements which contain faulty or incomplete shape functions. One of the challenges of finite element analysis is to find an efJicient combination of these for any particular analysis. Finding effective combinations requires experience. Smaller elements are required in regions where spatial gradients of the quantities of interest are high. When the shape functions in any two directions are the same, the dimensions of the element should be made the same as nearly as possible. In general, an aspect ratio of 2 : 1 on any element is considered a limit for a good mesh design. The mesh refinement process is nearly always iterative, requiring adjustment of the mesh based on preliminary analyses. During the 1970s and 1980s, numerous new elements were developed. Some of these have considerable advantages over others in specific situations (Zienkiewicz and Taylor, 1989, 1991). However, in the analysis of large-strain and large-deflection problems, elements which have triangular or quadrilateral faces and which use linear shape functions tend to be the most efficient and stable (Brodland and Clausi, 1993).

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f2

FIG. 6 Nodal forces and displacements on a quadrilateral element. Note that the indices on corresponding forces and displacements are the same. Each force or displacement corresponds to a degree of freedom.

E. Physical Properties Generalized displacements, uifor a quadrilateral element will be related to its generalized forces,fi (Fig. 6 and Table I). The details of this relationship will depend on the shape functions of the element as well as its current geometry and physical properties. In general, the relationship between nodal forces and displacements for a particular element can be written as a matrix equation IJ =

B(f)

where u and f a r e vectors of the form u = (uI, u2, u3, . is a matrix function. The inverse relationship, f = @(u)

(3)

. . , u , ) and ~ 6 (4)

is used more frequently for finite element analyses. In a typical finite element formulation, equations relating f and u for each element are combined to produce a single system of simultaneous equations. In many problems, the resulting equations are linear, that is, f = k u

(5)

where k, the generalized stiffness matrix, is an n by n array of numbers.

FIG. 5

A plane figure and two possible ways to break it into smaller units. (a) The plane region. (b) This breakdown is valid, because it satisfies all of the rules given in the text. (c) This breakdown is not valid. As shown by the enlargement of “A,” in Fig. 5(c), nodes on the two smaller elements are not connected to a node on the larger element which they border. In addition, a region at B is not spanned by the mesh. Finally, several elements, marked with the letter “C,” have excessive aspect ratios.

G. WAYNE

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BRODLAND

Even if this system consists of several thousand equations, standard methods exist for solving it. The procedure for determining k will depend on the nature of the problem. Typical approaches include energy methods and variational formulations (Zienkiewicz and Taylor, 1989, 1991). When the mechanics of a continuum are being modeled, for example, the stiffness matrix k can be derived using energy considerations, and is given by k = JVB%BdV

(6)

where the matrix B typically depends on specific spatial derivatives of the shape functions. The matrix D is called the constitutive matrix and describes the physical properties of the material. In some cases, it is possible to mathematically carry out the matrix multiplication and integration indicated in Eq. (6). In such cases, closedform expressions for the components of the stiffness matrix can be obtained. The calculation of such expressions is, at best, a tedious process. An alternative approach is to evaluate Eq. (6) by numerical integration. Gauss quadrature is the most common approach (Irons and Ahmad, 1986). In this method, the value of the matrix product, BTDB, is evaluated at specified points over the element and a particular weighted sum of the resulting products is taken as an estimate of the integral. In the analysis of biological cells and other essentially incompressible bodies, two serious problems arise with this approach. In order to obtain a sound stiffness matrix, particular patterns of integration points must be used (Logan, 1986). When such points are used, the resulting stiffness matrix contains elements which approach infinity. This causes insurmountable numerical problems when an attempt is later made to solve the assembled set of simultaneous equations. These values give rise to what is called “locking” (Belytschko and Ong, 1984). In a mechanics problem, this manifests itself in the resistance to certain modes of deformation erroneously becoming infinite. If the number of integration points is reduced sufficiently to overcome locking (Fig. 7a), a new problem, called “hourglassing,” occurs. In physical terms, this manifests itself as a complete lack of resistance to certain kinds of deformation which should be resisted. Spurious deformations like that shown in Fig. 7b can result. Other modes of deformation are unaffected (Fig. 7c). So-called “anti-hourglassing” techniques exist to restore resistance to these spurious modes (Belytschko and Ong, 1984). When elements change shape significantly during an analysis, it is important to distinguish whether the material properties are based on the initial or the deformed configuration (Malvern, 1969). For example, heat flux would presumably depend on current area, while material stiffness might be defined per unit of undeformed area. Furthermore, stretching along a direction which might be oblique to the orientation of the element

111

b

0

0

0

0

+

FIG. 7 Hourglassing. When insufficient points are used to perform a Gauss quadrature, elements lack resistance to certain modes of deformation. (a) The stiffness of each element is evaluated using a single Gauss point. (b) This mode of deformation is not appropriately resisted. (c) This mode is unaffected.

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might cause complex, coupled anisotropic behavior in a material which exhibits isotropic behavior when strains are small. Even greater care is required when there are significant element rotations. Principal value techniques then provide the optimum approach to relating generalized stresses and strains (Metzger and Dubey, 1987). When large strain or rotations occur or if the basic material response is nonlinear, then Eq. (5)does not provide a good estimate of the behavior of the element. This is a significant problem in analyzing developing embryos since significant shape changes are frequently the topic of study. That problem can be circumvented in the direct stiffness version of the finite element method by linearizing Eq. (4)to produce a sequence of incrementally linear equations of the form Af

=

k*Au

(7)

where k* is a tangential stiffness matrix. A small increment of load, Af is applied or a small time step taken, and incremental displacements Au calculated. An incremental approach is also required when properties or driving forces vary with time. Also, in the case of time-dependent behavior, an effective tangential stiffness matrix can be constructed which, in the case of viscoelastic materials, accounts for both the elastic and viscous components of its behavior (Zienkiewicz and Taylor, 1991).

F. External Driving Forces

When external forces are applied, or generalized body forces are acting (see Table I), their effect on the nodes must be determined. Equivalent of the element (Fig. nodal loads, fi, depend on the shape functions, Ni, 8). In solid mechanics problems, such formulas for equivalent nodal loads can be derived using the concept of virtual work. In other fields, where a variational formulation is employed, equations to provide equivalent nodal forces can be derived from the functional. These equations typically take the form

.L =

SB Ni(UJTOd<

(8)

G. Assembly

The elements in a structure interact with each other in such a fashion that the generalized nodal displacements of corresponding nodes of adjoining elements are the same. Thus, in addition to satisfying a relationship of the form of Eq. ( 5 ) or (7) for each element, it is also necessary to enforce

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External

ment boundary. B

FIG. 8 Equivalent nodal forces.

compatibility of nodal displacements. In practice, these objectives are satisfied simultaneously by establishing a global node numbering system and assembling the elemental Eqs. (5) or (7) into a global system of equations. To illustrate the assembly process, consider two bar elements in series which carry a tensile axial load (Fig. 9). Each element is governed by an equation of the form

Now, the total force at each node will be equal to the sum of the forces at that node from each of the elements. Thus, we have

G. WAYNE BRODLAND

114 1

3

2

I

Global Node Numbers:

2

Local Node Numbers:

? \

-

2

A

1

Element

a

Node

FIG. 9 A two-element subdivision.

or

F=K*U where F is matrix of total nodal forces in terms of the global numbering scheme, U is the corresponding global displacement matrix, and K* is the global stiffness matrix relating F and U. Equation assembly is not difficult. However, for large or complex problems, careful bookkeeping is required. When a nonparametric formulation is employed or if there are significant rotations of elements, it becomes necessary to use rotation matrices to convert the effects of local forces and displacements to global effects (Weaver and Gere, 1980). H. Solution Techniques

A host of techniques exist to solve the global system of simultaneous linear equations [Eq. (1 I)]. The most popular are Gaussian solvers and LU decomposition solvers such as the Cholesky solver. For more detail, see Dhatt and Touzot (1984). For a nonlinear analysis, the parts of the problem which change from step to step must be recalculated with each time or load step. This may include the material properties and the element geometries. In the case of problems where the topology of the mesh changes, even the mesh may have to be recalculated (Brodland ef al., 1991). It is advisable to incorporate an automatic mesh generator in such cases. Time-dependent problems give rise to other solution difficulties, some of which are discussed in the next section.

V. Discussion A. Analysis of Time-Dependent Phenomena

In general, formulations for time-dependent processes can be cast in the form of Eq. (7). Consider, for example, a time-dependent problem for

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115

which the governing equations can be written in the form

F

=

KU

+ CUAt

where U = mJ/dt. In general, this equation is solved by evaluating it at each step of a sequence of discrete time steps (Zienkiewicz and Taylor, 1991). The loads, tangential stiffnesses, and displacements associated with each time step are denoted with subscripts, the most recently calculated values being denoted by subscript n. It can be shown that the iterative solution steps to Eq. (12) can be written in the form U,+I =

(C

+ PAtK)-’{[C

-

At(1 - P)K]un - f*}

(13)

where p is a parameter, and In general, this is known as an implicit formulation of the problem. Implicit solutions of the form given in Eq. (13) are computationally expensive to perform, but are generally stable. When P = 0 and C is diagonal so that its inversion is trivial, the formulation is called “explicit. ” Computationally, an explicit formulation is highly efficient. However, it can become unstable if At is not sufficiently small (Dhatt and Touzot, 1984). Should that happen, the calculated values may have no meaningful relationship to the system being modeled. In the case of time-dependent problems or static problems solved by dynamic relaxation (Chu and Wu, 1986), both implicit and explicit methods can be used.

B. Verification of Results It is important to verify the accuracy of a completed analysis. Inaccuracies may result from errors in the problem statement, unsuitable shape functions, formulation or programming errors, or poor spatial or temporal subdivisions. Many formulation and programming errors and some shape function inadequacies can be identified using the patch test and analyses of problems for which comparative numerical, theoretical, or experimental solutions exist. When a subdivision is not sufficiently fine in scale, errors and artifacts associated with the particular spatial and temporal breakdown result. These can often be identified by refining the breakdown in a uniform way. If the formulation is valid, the solution will be independent of the subdivision used, for a certain range of scales. Limitations on computer memory and speed, and rounding-off errors restrict the fineness of subdivision. Errors which result from the use of unsuitable shape functions are more insidious and are often difficult to identify.

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C. Practical Considerations

A wide range of practical considerations affect the accuracy and speed of a finite element solution. As with all mathematical analyses, advantage should be taken of known symmetries in the problem and of any dimensional reductions which might be possible. Stiffness-based finite element formulations produce large systems of linear equations which must be solved. It is therefore desirable to make the system of equations as small as practical, and to minimize its bandwidth (Dhatt and Touzot, 1984) through node renumbering. In many cases, the stiffness matrix is symmetrical and only one symmetrical half of it need be stored. Preprocessing software to help construct and verify the suitability of a finite element mesh and to optimize its bandwidth is often advantageous. A postprocessor to graphically display the results of an analysis and facilitate its interpretation is almost essential. D. Recent Advances

As noted above, a number of technical challenges arise when the finite element method is applied to problems in which large shape changes occur. Brodland and Clausi (1993) have recently surmounted these challenges using the approach outlined above, and have produced a custom finite element code for analyzing developmental phenomena that is valid even when substantial shape changes occur. They have used this finite element code to investigate the mechanics of invagination, wave propagation, and pattern formation (Brodland and Clausi, 1993). The approach they used makes it possible to identify the fundamental physical bases of these phenomena and to investigate the geometric and mechanical factors which influence them. Neurulation, an important developmental process, produces a complex sequence of in-plane and out-of-plane shape changes in the sheet of tissue which begins this process as the neural plate. A number of theories exist to explain how these shape changes are driven. The finite element code noted above has made it possible to test these hypotheses (Clausi and Brodland, 1993). Among other things, this analysis demonstrates that some mechanisms, which intuitive reasoning and analogies with other systems suggest could drive neurulation, cannot. The finite element method has much potential as a tool for studying problems in developmental biology. It is hoped that this outline of the method, its technical challenges, and some recent results obtained will help to motivate its further application in developmental biology.

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Acknowledgments This research was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC). Critical reading of the manuscript by D. A. Clausi is gratefully acknowledged.

References Abel, J. F., Kawai, T., and Shen, S.-F. (eds.) (1981). “Interdisciplinary Finite Element Analysis.” Cornell Univ. Press, Ithaca, NY. Beck, J. V. (1977). “Parameter Estimation in Engineering and Science.” Wiley, New York. Belytscho, T., and Ong, W. E . (1984). Comput. Meth. Appl. Mech. Eng. 43, 251-276. Brodland, G. W. (1990). in “Biomechanics of Active Movement and Deformation of Cells” (N. Akkas, ed.), pp. 505-510. Springer-Verlag, Berlin. Brodland, G. W., and Clausi, D. A. (1992). “Embryonic tissue morphogenesis modelled by FEM.” ASME J . Biochem. Eng. (in press). Brodland, G. W., and Cohen, H. (1987). i n t . J. Solids Struct. 23, 1340-1356. Brodland, G. W., and Shu, D.-W. (1993). In “Dynamical Phenomena at Interfaces, Surfaces and Membranes” (G. Forgacs and D. Beysens, eds.), pp. 237-245. Nova Science Publishers, New York. Brodland, G. W., Dell, M. J., Burnett, E. F. P., and Gailey, C. (1991). International Symposium on Roofing Technology. Natl. Roofing Contractors Assoc., Rosemont, IL. Cheng, L. Y. (1987a). J. Biomech. Eng. 109, 10-17. Cheng, L. Y. (1987b). J. Biomech. Eng. 109, 18-24. Chu, P. C., and Wu, L. (1986). Znt. J. Mech. Sci. 28, 231-250. Clausi, D. A. (1991). “Finite Element Simulation of Early Embryonic Development.” M.Sc. Thesis, University of Waterloo, Ontario. Clausi, D. A., and Brodland, G. W. (1993). “Mechanical Evaluation of Current Theories of Neurulation Using Simulations.” (in preparation). Dhatt, G., and Touzot, G. (1984). “The Finite Element Method Displayed.” WileyInterscience, New York. Dunnett, D., Goodbody, A., and Stanisstreet, M. (1991). Acfa Biotheoret. 39, 63-79. Gordon, R. (1985). J. Embryol. Exp. Morph. 89, Suppl., 229-255. Gordon, R., and Brodland, G. W. (1987). Cell Biophysics 11, 177-238. Green, A. E., and Adkins, J. E. (1970). “Large Elastic Deformation.” 2nd ed., Clarendon Press, Oxford. Harrison, L. G. (1987). J. Theor. Biol. U5,369-384. Hilfer, S. R., and Hilfer, E. S. (1983). Deu. B i d . 97,444-453. Irons, B., and Ahmad, S. (1986). “Techniques of Finite Elements.” Ellis Honvood, Chichester. Jacobson, A. G. (1980). Am. Zoo/. 20,669-677. Jacobson, A. G., and Gordon, R. (1976). J. Exp. Zool. 197, 191-246. Logan, D. L. (1986). “A First Course in the Finite Element Method.” PWS, Boston. Malvern, L . E. (1969). “Introduction to the Mechanics of a Continuous Medium.” PrenticeHall, Englewood Cliffs, NJ. Metzger, D. R., and Dubey, R. N. (1987). i n t . J. Plast. 4, 341-368. Norrie, D. H., and deVries, G. (1978). “An Introduction to Finite Element Analysis.” Academic Press, New York.

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Odell, G. M., Oster, G., Alberch P., and Burnside, B. (1981). Deu. Biol. 85, 446-462. Schreiber, A and Jacob, H. A. C. (1984). Acra Orthopaed. Scand. Suppl. 207, 1-34. Weaver, W., and Gere, J. M. (1980). “Matrix Analysis of Framed Structures.” Van Nostrand Reinhold, New York. Weliky, M., and Oster, G. (1990). Deuelopmenr 109, 373-386. Zienkiewicz, 0. C., and Taylor, R. L. (1989). “The Finite Element Method,” Vol. 1. McGraw-Hill, Maidenhead. Zienkiewicz, 0. C., and Taylor, R. L. (1991). “The Finite Element Method,” Vol. 2. McGraw-Hill, Maidenhead.

Substratum Mechanics and Cell Differentiation Michal Opas Department of Anatomy and Cell Biology, University of Toronto, Toronto, Ontario, Canada M5S 1A8

1. Introduction

In most normal tissues the cytoarchitectural organization of cells is thought to be in mechanical equilibrium with the substratum. The development and differentiation of tissues, however, depend on the ability of cells to move and control their shape. In cell movements a force-generated by the contractile cytoplasmic machinery, which includes the cytoskeletal microfilaments-is translated into traction through cell-substratum adhesion. Thus, the cell-substratum interface is the site of developmentally significant adhesive interactions. In this chapter I concentrate on the cytomechanics of the regulation of expression of the differentiated phenotype in retinal pigmented epithelial (RPE) cells and, subsequently, on the cytomechanics of the process by which RPE cells alter their identity to become other distinct cell types, also known as “cell type conversion” or “cellular metaplasia” (Okada, 1986). Throughout, the term “transdifferentiation” is used to describe a wide range of phenomena that lead to alterations in cell phenotypic expression. Transdifferentiation is thought to be closely related to tissue regeneration and occurs in several systems (Moscona and Linser, 1983; Lopashov and Zviadadze, 1984; Eguchi, 1986; Schmid and Alder, 1986; Okada, 1986; McDevitt, 1989; Beresford, 1990; Chandebois, 1981; Watt, 1991). The ability of one cell type to convert to another is clearly exemplified in the transdifferentiation of ocular tissues (Okada et al., 1979; Okada, 1980). The embryonic retina provides an excellent in uitro system for transdifferentiation studies because neural retina (understood here as flat Muller glial cells) converts into melanin-producing RPE, which in turn converts into crystallin-producing lens epithelium and forms lentoid bodies (Okada, International Reuiew of Cytology, Vol. I50

119

Copyright 0 1994 by Academic Press, Inc. All rights of reproduction in any form reserved.

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1980). More often, however, and especially when presented with insulin, the neural retina skips the conversion to RPE and transdifferentiates directly into lens epithelium (de Pomerai and Clayton, 1980). Whereas primary cultures of RPE are phenotypically stable and rarely transdifferentiate (Eguchi and Okada, 1973), tertiary RPE cultures (Itoh and Eguchi, 1986a) destabilize and routinely transdifferentiate into lens epithelium, but never into neural retina. Transdifferentiation of chick RPE into neural retina, however, was achieved by continuous delivery of basic fibroblast growth factor (bFGF) (Park and Hollenberg, 1989, 1991; Pittack et al., 1991; Guillemot and Cepko, 1992). It has been widely accepted that both the biochemical and mechanical properties of the growth substratum have a profound influence on the expression of the differentiated cell phenotype (Ben-Ze’ev, 1986, 1989, 1991; Watt, 1986; Ben-Ze’ev et al., 1988; Farmer and Dike, 1989; Ingber and Foikman, 1989a,b; Opas, 1989; Ingber, 1990, 1991a). For some time, we have been studying the role played by substratum biochemistry and mechanics in the maintenance of the differentiated RPE phenotype in uitro (Opas, 1989; Opas and Dziak, 1988, 1990, 1991). We have subsequently started to examine the roles played by substratum mechanics and biochemistry in the transdifferentiation of retinal tissues, RPE in particular (Opas and Dziak, 1993). However, before discussing those, it is necessary to briefly review the general aspects of interactions of cells with their substrata.

II. Cytomechanics of Cell-Substratum Interactions

In uitro studies of cell interactions with glass substrata clearly demonstrated that the most adhesive organelle is the focal contact (Burridge et al., 1988). Focal contacts are specialized, highly adhesive membrane-cytoskeleton complexes associated with the ends of microfilament bundles and a set of focal contact-specific proteins such as vinculin, talin, tensin, paxillin, and several others (Burridge and Feramisco, 1980; Geiger et al., 1980; Burridge and Connell, 1983; Wilkins et af., 1986; Burridge et af., 1988; Burridge and Fath, 1989; Pavalko et al., 1989; Turner et al., 1990). These proteins are instrumental in anchoring microfilament bundles to the plasma membrane in the contact region. It has been known for some time that cells adhere to substrata via a variety of proteins of the extracellular matrix (ECM), which forms substrata in uiuo and covers inert substrata in uitro (Grinnell, 1978). It has also been clearly demonstrated that strong cell adhesions are realized through intimate linkages of the cytoskeleton, namely, actin-containing microfilaments and their associated proteins, and

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proteins of the ECM (Singer, 1979; Singer et al., 1984; Hynes et al., 1982; Burridge and Fath, 1989). Transmembrane linkage of the cytoskeleton to the ECM can be realized by many proteins; recently, however, the integrin superfamily of cell surface receptors has been the most studied (Hynes, 1987, 1992; Albelda and Buck, 1990;Reichardt and Tomaselli, 1991 ;Ruoslahti, 1991). Integrins play a pivotal role in linking the cytoskeletal complex to the proteins of the ECM in the focal contact (Burridge et al., 1988). While the prominent microfilament bundles (stress fibers) are contractile (Kreis and Birchmeier, 1980; Burridge, 1981), it has been shown that myosin and tropomyosin may be excluded from the termini of stress fibers (Geiger et al., 1984; Opas and Kalnins, 1986). This suggests that while the more proximal parts of stress fibers are contractile (Kreis and Birchmeier, 1980), their termini may be specialized for attachment. It has also been hypothesized (Volk and Geiger, 1984) that focal contacts, together with their associated proteins, act as organizing centers for the surrounding cytoplasm. In this scheme, contact is made initially by the receptors, then vinculin is recruited into the focal area, and finally F-actin is accumulated to form a microfilament bundle. This hypothesis has been challenged by DePasquale and Izzard (1987; 1991), who postulate that the local accumulation of talk and F-actin precedes the formation of a focal contact and the recruitment of vinculin. It is not clear how focal contact-associated stress fibers form in spreading cells. A spreading cell generates centripetal tension (Oster and Perelson, 1987) that is transmitted to the substratum by peripheral adhesions, which are often arranged in a fairly regular distribution (Segel et al., 1983). Development of an isometric contraction promotes the formation of microfilament bundles (Fleischer and Wohlfarth-Bottermann, 1975; Korohoda and Kajstura, 1982; Tucker et al., 1985; Kolodney and Wysolmerski, 1992), which in turn are contractile (Kreis and Birchmeier, 1980). The contractile microfilament bundles break down the circumferential arrangement of adhesions and the initially round, spread cell becomes irregularly stretched between the few strongest points of attachment to the substratum. In this simplified, mechanistic model, the arrangement of stress fibers in a fully spread cell has been proposed to partly reflect the lines of a tension field generated by cellular contractile activity and spatially restricted by adhesions to the substratum (Greenspan and Folkman, 1977). It is essential to the present considerations that the focal contacts be the major cellular organelles through which traction is exerted (Chen er al., 1985b; Opas, 1987; Aubin and Opas, 1988; Ingber et a)., 1993). In fact, it has been shown that they are the structures that transmit the forces generated in the cytoplasm to the substratum and are perfectly capable of remodeling the ECM in what appears to be a purely mechanical activity

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in many cases (Avnur and Geiger, 1981; Singer et al., 1984; Haston er al., 1983; Opas and Dziak, 1991). The properties of the substratum affect cell morphology through adhesion. Reciprocally, adherent cells modify the substratum chemically by depositing proteins of the ECM (Grinnell, 1978; Singer, 1979) and degrading them by secretion of proteases (Chen er al., 1984, 1985a; Chen, 1990; Pollanen er al., 1988), and mechanically by exerting traction (Harris et al., 1980, 1981; Harris, 1984b; Aubin and Opas, 1988). To remodel the ECM substrata, cells require both a functional contractile apparatus and a set of integrins appropriate for a given set of ECM proteins (Ehrlich et al., 1986; Kelley et al., 1987; Welch ef al., 1990; Klein et al., 1991; Olson et al., 1991; Schiro et al., 1991; Tomasek et al., 1992). In a spread cell, tension is transmitted to the substratum. When the substratum is elastic enough, it becomes deformed, reflecting the forces exerted on it by the adherent cell (Harris er al., 1980, 1981). From the pattern of substratum deformation, it is possible to infer the magnitude and directions of the forces operating in the cell-created tension field (Harris, 1984a,b). Thus, the degree and pattern of substratum deformation will correlate with the adhesion pattern and organization of the contractile cytoskeleton of the cell performing the work. Conversely, a change in the adhesion pattern and stress fiber distribution will be evoked in a cell or group of cells subjected to external tension (Fleischer and Wohlfarth-Bottermann, 1975; Kolega, 1986). The RPE and the neural retina derive from the same neuroepithelial tissue, the optic vesicle. Following invagination of the optic vesicle into the optic cup, the fates of the neuroepithelial cells become established: the inner layer of the cup is destined to give rise to the neural retina while the outer layer will become the RPE. However, it has been known for some time that cell fates in the developing retina are not fixed at early stages of histodifferentiation (Okada et al., 1979; Okada, 1980; de Pomerai et af., 1982; Moscona and Linser, 1983; Moscona, 1986). The RPE maintains a high degree of plasticity in that it can transdifferentiate into either lens epithelium (Eguchi, 1986) or neural retina (Coulombre and Coulombre, 1965). The molecular basis for the control of cell fate in the developing retina, is not clear at present. When grown in v i m , RPE cells form colonies in which cells in the central part of the colony are differentiated, that is, they are cuboidal, pigmented, and tightly packed. The differentiated RPE traits are gradually lost by those cells occupying the area toward the edge of the colony where the cells become progressively less pigmented. Finally, the RPE cells at the very periphery of the colony display features typical of undifferentiated cells in that they are depigmented, well spread and flat, and fairly motile (Crawford, 1979; Turksen et al., 1983).

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This gradient in cell morphology is paralleled by a redistribution of actincontaining microfilament bundles from a linear arrangement of prominent microfilament bundles and stress fibers in the edge cells to an arrangement of compact rings of microfilaments circumscribing the cell apices in the differentiated cells in the colony center (Owaribe et al., 1981; Owaribe and Masuda, 1982; Turksen et af., 1983; Opas and Kalnins, 1985; Opas et al., 1985; Sandig and Kalnins, 1988; Owaribe, 1990). The proteins of the circumferential rings of microfilaments in the differentiated cells are spatially segregated across the width of the ring, with vinculin concentrated on its outer, membrane-facing side, and myosin and tropomyosin predominating on its cytoplasmic side (Opas and Kalnins, 1985).This suggests that the outside of the ring is specialized for membrane attachment and the inside for contraction, implying a certain homology of protein distribution with the stress fibers. Also, while peripheral RPE cells display predominantly cell-substratum adhesiveness, cells toward the colony center shift progressively to predominantly cell-cell adhesiveness (Turksen et al., 1983; Opas, 1985; Opas et af., 1985). The gradient in cell-substratum adhesiveness coincides with the progressive accumulation of ECM toward the colony center (Turksen et al., 1984; Crawford and Vielkind, 1985) in such a manner that cells at the periphery of the colony are exposed to nearly bare glass while the cells in the colony center rest on a thick pad of gel-like ECM. To account for these observations, I have proposed (Opas, 1987) that the organization of the cytoskeleton in RPE cells in uitro is a function of cell adhesiveness and substratum deformability, where both linear and circumferential arrangements of microfilaments reflect the lines of a tension field generated by the cell’s contractile activity and spatially restricted by adhesions. Both the stress fibers and the circumferential rings of microfilaments are contracting isometrically (Kreis and Birchmeier, 1980; Owaribe et af., 1981). The obvious difference in the arrangement of stress fibers and the circumferential microfilament bundles is brought about by the radically different spatial distribution of predominant sites of adhesion, which influence the distribution of stress in the cell-generated tension field. While in the spread cells the predominant sites of adhesion are the focal contacts in a planar arrangement, in packed cells the predominant adhesion form is the belt of zonulae adhaerentes circumscribing the apices of the cells. The RPE in uiuo is a two-dimensional association of tightly adherent cells which actively contract (Crawford, 1979; Owaribe et af., 1981),forming a tensile sheet which rests on an elastic support, that is, a basement membrane (Honda, 1983). What, then, is the relationship between the aforementioned observations of cells in uitro to the in uiuo situation? Although it is widely believed that differentiated epithelial cells seldom

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develop stress fibers and focal contacts, and that the most prominent microfilamentous structure of epithelia in uivo is the apical ring of microfilaments, it is also generally accepted that microfilaments are responsible for epithelial motility both in vitro and in uiuo (Kolega, 1986). Also, cell sheets subjected to mechanical stress, such as endothelia (Wong et al., 1983; Byers et al., 1984; Fujiwara et al., 1986; Drenckhahn and Wagner, 1986; Kim et al., 1989) and mesothelia (Sugimoto et al., 1989, 19911, develop stress fibers. Using RPE cells grown on their native basement membrane, Bruch’s membrane, I have shown that these cells attach to the basement membrane and given sufficient space, will spread on it and develop stress fibers and focal contacts. The composition and general arrangement of these is indistinguishable from that of the stress fibers and focal contacts of the cells grown on glass or plastic (Opas, 1989). Similar results were obtained using the RPE cells covering an artificial wound inflicted on a cell sheet grown on the native basement membrane (Hergott et al., 1989). It is thus obvious that the basement membrane is sufficiently rigid to provide at least some support for spreading of cells, formation of contractile stress fibers, and development of cell traction. Cell behavior on the basement membrane contrasts with that on the malleable gels of basement membrane proteins, such as the commonly used Matrigel (Kleinman et al., 1986). When RPE cells are plated onto the protein gel, they do not spread on the bulk of the gel, which becomes contracted into compact aggregates after a few days of culture (Opas, 1989).The basement membrane protein gel has very low structural rigidity, and hence does not allow an equilibrium to be established between the forces generated by the cell’s contractile apparatus and the elastic forces of the substratum, which would result in the formation of stress fibers. This is in agreement with data collected for the cytoskeletal organization of mesenchymal cells in collagen gels of varying mechanical properties (Farsi and Aubin, 1984; Tucker et af.,1985; Mochitate et af., 1991; Tomasek et al., 1992). The cells on the basement membrane protein gel exert traction, which, not being counterbalanced by substratum elastic forces, initially contracts, and eventually tears, the gel. It is interesting that it has been shown that the RPE cells, after pharmacological transformation with a phorbol ester, 12-0-tetradecanoylphorbol13- acetate (TPA) are able to spread on the hydrated basement membrane protein gel (Opas and Dziak, 1990). This phorbol ester promotes the transformed phenotype and, more specifically, a severe alteration of cell shape and/or the degree of cell rounding, the loss of stress fibers, and the loss of focal contacts without affecting the deposition of ECM components by epithelial cells (Rifkin et al., 1979; Schliwa et al., 1984; Kellie et al., 1985; Ljubimov et al., 1985; Dugina et al., 1987). The transformed phenotype

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is associated with diminished cell traction and diminished ability of cells to deform substrata (Steinberg et al., 1980; Danowski and Harris, 1988). The effects of TPA may be explained by the reorganization of microfilaments. It has been shown (Kellie et al., 1985; Lassing and Lindberg, 1988) that although there is a redistribution and loss of stress fibers in TPA-treated epithelial cells, the polymerized pool of F-actin does not change, which suggests that TPA shifts the actin pool from prominent microfilament bundles to an F-actin meshwork. It is the F-actin meshwork which, in the absence of focal contacts, is responsible for a net centrifugal flow of cytoplasm and the increase in radial area in a spreading cell (Vasiliev, 1982). This nonvectorial spreading is soon restricted and then polarized by the development of stress fibers and focal contacts (Vasiliev, 1991) which are extremely well developed in the RPE cells (Opas, 1985). Therefore, the reduction of cell traction through disruption of prominent stress fibers with TPA treatment, with the F-actin meshwork left functional, allows RPE cells to spread on malleable substrata. Collectively, these data give strong support to the assumption that both in v i m and in viuo, cells are indeed in mechanical equilibrium with their substrata.

111. Regulation of the Choice of Fate of the RPE Cells by Soluble Factors and the Substratum

As I have indicated in the preceding section, the neural retina in primary culture is pluripotential (Okada et al., 1979). The neural retina, when cultured with care, converts into RPE, which in turn converts into lens epithelium and forms lentoid bodies (Okada, 1980; Moscona and Degenstein, 1981, 1982; Moscona et al., 1983; Moscona, 1986). Under the influence of soluble factors such as insulin, the neural retina may skip the conversion to RPE and transdifferentiate directly into the lens epithelium (de Pomerai and Clayton, 1980). In contrast to primary cultures of the neural retina, primary cultures of the RPE are phenotypically stable, rarely transdifferentiating (Eguchi and Okada, 1973). However, tertiary RPE cultures destabilize and routinely transdifferentiate into lens epithelium but never into neural retina (Itoh and Eguchi, 1986a). Possible pathways of transdifferentiation in retinal tissues are shown in Fig. 1. Our approach has been to first answer why destabilized RPE converts into lens but not into neural retina in vitro, and conversely, why the neural retina readily converts into lens but seldom into RPE. To do this, we used cultures of neural retina and phenotypically destabilized RPE cells (Itoh and Eguchi, 1986a,b) to investigate the effect of changes in substratum biochemistry, spatial complexity, and/or mechanics on RPE phenotypic

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\

\

\

Rigid BM

Bruch's membrane

Soft BM gels

Pseudostratified

FIG. 1 Possible pathways of differentiation and transdifferentiation of retinal tissues. The jagged outlines indicate proliferative phenotypes, while the smooth outlines indicate nonproliferative phenotypes. The continuous lines denote established pathways: thick lines indicate normal differentiation pathways, while the thin lines indicate pathways resulting in either differentiation or transdifferentiation in uitro. The dashed lines indicate pathways which can be induced experimentally. The pointing fingers show pathways which are affected by those factors denoted by italics. RPE, retinal pigmented epithelium; NR, neural retina; NE, neuroepitheliurn; BM, basement membrane; FGF, fibroblast growth factor. Full details are given in the text.

expression. Our results point to a major role for past proliferative behavior in transdifferentiation of the neural retina, and to the current mechanical properties of the substratum for transdifferentiation of RPE. Thus, aggressive proliferation stimulates the neural retina cells to express the lens phenotype without expressing the RPE phenotype. In contrast, the RPE cultures occasionally transdifferentiate into lens epithelium on substrata which restrain their ability to spread, such as the basement membrane protein gels, but reexpress the differentiated RPE phenotype on more solid substrata which promote cell spreading, such as carpets of immobilized proteins of the basement membrane. In spite of its very occasional occurrence, the expression of lens phenotype by RPE cells on basement membrane protein gels has been unexpected because it is well established that growing cells on or in basement membrane gels promotes the expression in vitro of the differentiated epi-

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thelial phenotype in general (Hadley et al., 1985, 1990; Ben-Ze’ev and Amsterdam, 1986;Li et al., 1987; Kubotaet al., 1988;Ingberand Folkman, 1989b; Aggeler et al., 1991; Streuli et al., 1991) and in RPE in particular (Opas, 1989; Opas and Dziak, 1991; Rizzolo, 1991). Because it has been shown that FGFs invariably direct the choice of fate of presumptive RPE toward neural retina (Park and Hoilenberg, 1989, 1991; Pittack ef al., 1991; Guillemot and Cepko, 1992), we used bFGFtreated cultures of presumptive RPE as a model transdifferentiating system. To examine the effect of the mechanical properties of the substratum on the choice of fate by the presumptive RPE, we exploited a system of biochemically related substrata with vastly different mechanical properties (Opas and Dziak, 1991), that is, hydrated basement membrane gels and carpets of immobilized basement membrane proteins. We examined the effects of bFGF on growth and on expression of differentiated traits by presumptive RPE grown on Bruch’s membrane in retinectomized eye cup explants, and compared them with the effects of bFGF on RPE cells grown on either basement membrane protein gels or basement membrane protein carpets (Opas and Dziak, 1994). When present in the culture medium, bFGF redirects the choice of fate of presumptive RPE from the RPE fate into the neural fate. However, the mechanical properties of the substratum determine the extent to which a neural phenotype is expressed by the transdifferentiating cells (Opas and Dziak, 1994). The RPE transdifferentiates into a pleomorphic neuroepithelium on rigid, two-dimensional basement membrane protein carpets, into a pseudostratified neuroepithelium on highly malleable basement membrane protein gels, and into a stratified, neural retina-like neuroepithelium on its native basement membrane, which is of an intermediate rigidity (Fig. 1). The stratified neuroepithelium newly formed in the eye cup explants, except for the inverted polarity, has morphology corresponding to that appropriate for an equivalent stage of retinal histodifferentiation in an embryo, and expresses neuronal markers in a distribution appropriate for its developmental age. Using 1 , 1 ’-dioctadecyl-3,3,3’,3’-tetramethylindocarbocyanineperchlorate (DiI), we have determined which cell type shows responsiveness to the mitogenic action of bFGF. In agreement with the results of Guillemot and Cepko (1992), we have shown that bFGF is not a mitogen for the presumptive RPE cells, while it is a potent one for the presumptive neural retina. Therefore, in the eye cup explants, there is a subpopulation of bipotential presumptive RPE cells which are responsive to bFGF, most likely by virtue of being at least partly spread (extended). The effect of bFGF on these bipotential cells is to redirect the choice of their fate from RPE toward the neural retina. Once committed to the retinal fate, these cells are stimulated to divide by bFGF. This suggests that the transdifferen-

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tiation of presumptive RPE into presumptive neural retina occurs after cells withdraw from the cell cycle, lending support to a “direct transdifferentiation” hypothesis (Beresford, 1990). It should be stressed, however, that we have observed, on both the basement membrane protein gels and the eye cup explants, a substantial number of cells that express both RPE and neuronal markers. Similar coexpression of RPE and neuronal traits (pigmentation and the presence of neurofilaments) has been observed in transdifferentiating RPE by Guillemot and Cepko (1992).

IV. Cellular Mechanics of Transdifferentiation

When plated onto Bruch’s membrane, the RPE cells spread on the membrane (Nicolaissen er al., 1989; Opas, 1989) and attempt to contract it, at which they succeed if the Bruch’s membrane explant is not fixed to a solid support. Thus, a period of contractile activity resulting in at least some degree of cell spreading occurs on those substrata which are mechanically rigid enough to support it-basement membrane protein carpets and the Bruch’s membrane of the eye cup explants. This is in contrast to basement membrane protein gels, which do not offer enough support to allow for any spreading of RPE cells (Opas, 1989; Opas and Dziak, 1990). It has been shown that although cell attachment to a substratum is a stimulus sufficient to initiate protein synthesis, in order to initiate DNA synthesis, a cell has to be attached and spread to some degree (Folkman and Moscona, 1978; Ben-Ze’ev et al., 1980; Benecke e f al., 1980; Ingber et al., 1987; Ingber, 1990). This is likely to be a reason why we observe aggressive cell proliferation on basement membrane protein carpets, a considerable degree of cell proliferation in the eye cup explants, and almost no cell proliferation on basement membrane protein gels. When grown on planar, rigid, basement membrane protein carpets, RPE cells are stimulated to spread and divide. In the absence of bFGF, the presumptive RPE cells acquire and maintain RPE markers with time in culture. In the presence of bFGF, the presumptive RPE loses the RPE markers, transdifferentiates into a pleomorphic neuroepithelium, and acquires a general neural marker such as the neural cell adhesion molecule. However, because the bFGF-treated cells on the basement membrane protein carpets never progress far along the neural retina histodifferentiation pathway, the mitogenic stimulus provided by spreading on rigid basement membrane protein carpets is strong enough to override the bFGF-derived stimulus to transdifferentiate into neural retina-like neuroepithelium and to prevent further histodifferentiation. This is in contrast to the situation on the malleable basement membrane protein gels, where

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the presumptive RPE cells transdifferentiate into a pseudostratified neuroepithelium but do not progress further along the neural retina differentiation pathway for lack of a sufficient degree of cell proliferation. Notwithstanding the differences in the nature of the transdifferentiating tissues, the cytomechanical requirements for the transdifferentiation of presumptive RPE into presumptive neural retina resemble those for the transdifferentiation of the presumptive neural retina into lens epithelium, where a brief period of cell spreading was shown to be a necessary prerequisite for the process to occur (Okada et al., 1982, 1983). It appears therefore, that while bFGF provides a permissive signal for the conversion of the cell population from the RPE to the neural retina fate, the mechanical properties of the growth substratum control how far the committed cells will progress in their differentiation along the neural pathway. The presumptive RPE in uiuo is a tightly packed, polarized cell layer resting on Bruch’s membrane, which contains laminin, fibronectin, collagen type IV, and heparan sulfate proteoglycan (Turksen et al., 1985). RPE cells in uitro synthesize and deposit all of these components of the ECM irrespective of the nature of their growth substratum (Turksen et al., 1984; Opas, 1989). Cells interact with their substrata through a variety of proteins that comprise the ECM, and it is the nature of the ECM which to a large extent determines cell shape (Watt, 1986; Stoker et al., 1990) and regulates phenotypic expression (Hadley et al., 1985, 1990; Ben-Ze’ev and Amsterdam, 1986; Li et al., 1987; Kubota et af . , 1988; Ingber and Folkman, 1989b; Opas, 1989; Aggeler et al., 1991; Ben-Ze’ev, 1991; Streuli et al., 1991). Specific proteins of the ECM play a role in the control of cell phenotypic expression. For example, in muscle, the interplay between two proteins, laminin and fibronectin, seems to control a switch between proliferation and differentiation pathways in uitro (Hedin ef al., 1988, 1989; Von der Mark and Ocalan, 1989). In the control of cell phenotypic expression by the mechanics of the substrata, cells require a functional contractile machinery (Olson er al., 1991; Tomasek et al., 1992). Cells recognize proteins of the ECM through cell surface receptors, which are members of the integrin superfamily (Hynes, 1987; Albelda and Buck, 1990; Reichardt and Tomaselli, 1991). However, the occupancy of cell surface receptors by ECM proteins is not itself sufficient for a cell to respond; the response of cells to a variety of stimuli depends also on the mechanical properties of the ECM and, consequently, on cell shape (Nakagawa et al., 1989; Ingber, 1991a; Schwartz et al., 1991; Sutton et al., 1991). The relationship between the mechanical properties of the substratum and the cellular response to stimuli is best exemplified by the importance of cell shape, as controlled by the mechanics of the substrata, in soluble factor signaling. It has been shown that both contact with the substratum and the degree of cell spread-

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ing modulate cell responsiveness to soluble factors (Ingber and Folkman, 1989b; Schubert and Kimura, 1991; Sutton et al., 1991). Accordingly, it has been demonstrated in a variety of different cell-substratum systems that cells which are spread either do not enter or withdraw from the differentiation pathway (Folkman and Moscona, 1978; Ingber et al., 1987; 1990; Ingber, 1990; Opas and Dziak, 1990, 1991; Mooney et al., 1992). While the role and pathways of soluble factors in cell signaling are being unraveled (Westmark and Heldin, 1989; Ullrich and Schlessinger, 1990), the mechanisms of signaling by attachment factors, for example, by proteins of the ECM, remain relatively obscure. The soluble factor bFGF provides the necessary signal for bipotential RPE cells to commit to the neuronal fate. After the decision to convert from RPE to the neuronal fate has been made, attachment factors may play a major role in its realization. It is now well established that attachment factors regulate the overall cytoskeletal organization and thus modulate the cell’s ability to adhere, spread, and exert traction (Bereiter-Hahn, 1987; Opas, 1987; Hay and Svoboda, 1989; Oster, 1989). A change in cell shape, strength of traction, or any other mechanical property is likely to affect second messenger pathways via stretchactivated ion channels or the activation of enzymes such as kinases (Sachs, 1989; Ingber, 1991a; Watson, 1991; Ingber et al., 1992). Substratum mechanics, through reduced traction and cell rounding, may evoke the same cellular response as soluble factors; it has been shown that intracellular pH increases as cells spread on immobilized fibronectin and/or are stimulated by bFGF (Ingber et al., 1990; Schwartz et al., 1991). Spread cells have a higher intracellular pH than round ones (Schwartz et al., 1989; 1991) and activation of the Na+/H+ antiporter (cytoplasmic alkalinization) is a common and immediate response to most growth (soluble) factors (Moolenaar, 1986; Grinstein et al., 1989). Clustering of integrins evokes generation of cytosolic Ca2+transients (Jaconi et al., 1991) which, again, parallels those evoked by soluble factors (Watt e f al., 1991; Kuriyama er al., 1991, 1992). It appears that the mechanical immobilization of integrins is crucial for signaling by an attachment factor (Schwartz et al., 1991) to occur, possibly via tyrosine kinase activation (Kornberg et al., 1991; Kornberg and Juliano, 1992). Although soluble factors (e.g., bFGF) and attachment factors (e.g., fibronectin) may activate the same intracellular effector mechanisms (e.g., the Na+/H+ antiporter), it has been shown that they do so by separate pathways (Ingber er al., 1990). Even in the case in which signaling by both soluble factors and integrin clustering has been shown to occur through protein tyrosine phosphorylation, the time course of the soluble factor signaling is different from that of the integrin-mediated signaling (Kornberg et al., 1991). Clustering and immobilization of integrins influ-

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ences gene expression (Werb et al., 1989). It has been recently postulated that this influence would also involve homeobox genes (Edelman, 1992). The integrin-mediated signaling via tyrosine kinase and the second messenger pathway has just started to be examined. However, it is also conceivable that there is a direct, structural connection between the cell surface and the nucleus. Structural elements of the cytoplasm and the nucleus appear to be interconnected and linked to the cell surface (Penman et al., 1982; Geiger, 1983; Fey et al., 1984). This structural linkage is most likely responsible for a functional one; for example, it has been observed that the degree of cell spreading is closely followed by the degree of nuclear flattening (Ingber et al., 1987). Using tensegrity modeling, in which elements of cellular structure are considered to be a three-dimensional array of discrete compressionbearing elements (e.g., microtubules) interconnected by arrays of tensiongenerating elements (e.g., microfilaments), Ingber and his collaborators (Ingber and Jamieson, 1985; Ingber and Folkman, 1989a; Ingber, 1991b, 1993; Ingber er al., 1993) have shown that mechanical events occurring at the cell surface may directly affect nuclear architecture (Hansen and Ingber, 1992). Thus, along with the mechanical signaling by the ECMintegrin complexes through established second messenger pathways (Ingber, 1991b; Kornberg and Juliano, 1992), gene expression may be mechanically regulated by physical stresses exerted on the structurally integrated cell-ECM complex (Bissell et al., 1982; Bissell and BarcellosHoff, 1987; Hansen and Ingber, 1992). Mechanically, Bruch’s membrane is a substratum of a rigidity intermediate between the rigidities of basement membrane protein gels (low rigidity) and basement membrane protein carpets (high rigidity). What controls, then, the choice between RPE and neural retina fate in the presumptive RPE? The obvious question also arises as to why the RPE cell response to the mechanical properties of the substratum is not linear: those cells which became committed to the neural fate show the greatest progression along the neural retina pathway on a substratum of intermediate rigidity. It is quite possible that neither the extreme cell extension on the basement membrane protein carpets nor the lack thereof on the basement membrane protein gels provides the right combination of inputs from the ECM, or clustering and immobilization of integrins, or signaling via the cytoskeleton to the nucleus (Ingber, 1991b). This, by analogy to other cell systems (Folkman and Greenspan, 1975; Schubert and Kimura, 1991; Sutton et al., 1991), would affect RPE cell responsiveness to bFGF. Strong support for this assumption comes from the experiments of Ingber and Folkman (1989b), who showed that endothelial cell differentiation and angiogenesis in uirra is stimulated by bFGF only on fibronectin carpets of intermediate malleability but on neither rigid nor highly malleable fibronectin carpets.

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Thus, it is clear that cytomechanics play a very important role in cell signaling and gene expression. At the supracellular scale, it has been demonstrated that mechanical forces play a crucial role in the morphogenesis of an embryo (Kucera and Monnet-Tschudi, 1987; Beloussov et al., 1988). How the global mechanics of an embryo translate into the control of cell behavior and gene expression remains to be investigated; however, it is more than likely that cytomechanics of the kind sketched in this chapter play an important role in the development of an organism. Acknowledgments I thank Miss Suzanne Tharin for critically reading the manuscript and Dr. Donald E. Ingber for providing manuscripts prior to publication. Support by a grant from the RP Research Foundation and by Grant MA-9713 from the Medical Research Council of Canada is gratefully acknowledged.

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Phase Transitions, Interfaces, and Morphogenesis in a Network of Protein Fibers Gabor Forgacs* and Stuart A. Newmant *Department of Physics, Clarkson University, Potsdam, New York 13699; and ?Department of Cell Biology and Anatomy, New York Medical College, Valhalla. New York 10595

I. Introduction The cytoskeleton, the scaffold of an individual cell, determines its ability to adopt different shapes and carry out complex types of motion. The state of the cytoskeleton can also influence gene expression (Cervera et al., 1981). These functions of the cytoskeleton are achieved by means of an intricate network of fibers in the form of microfilaments, microtubules, and intermediate filaments, which crisscross the entire cell (Alberts et al., 1989). Some of the most striking properties of this network are the following: The assembly has the physical properties of a gel, but a dynamic one, constantly being formed and disassembled. The fibers are anchored to proteins in the plasma membrane and to pinning sites on a substratum. Other molecules and macromolecular structures are attached to the network and may act as cross-linkers. The basic elements have well-defined functions (actin microfilaments play an essential role in motion, intermediate filaments prevent the excessive stretching of the cell, etc.), but the cytoskeleton’s most important characteristics derive from the fact that it is a collective system. Although the motion of the cell, for instance, is initiated by local signals such as binding of ligands to specific receptors on the external surface of the cell, these signals affect the entire network, which then changes its shape in a specific manner, depending on the type of motion (Hall et al., 1989). A basic question in connection with such a network is at what point in the course of its organization it acquires gel-like properties. From a purely physical point of view, there clearly should exist a critical value either in International Review of Cytology, Vol. 150

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the concentration of the assembling filaments, in the value of the strength of their interaction, or in the number of cross-linkers, at which the distinct properties of the gel state emerge. In this chapter we present results obtained in a model tissue system, where the above question can be studied in detail. The system consists of liquid drops containing assembling fibers of type I collagen, which under appropriate conditions exhibit the phenomenon of matrix-driven translocation (MDT), described in detail in Section 11. This system is based, in part, on materials from the extracellular matrix of mesenchymal tissues and may provide a model for shape change in such tissues. Although tissues are organized on a larger scale than single cells, we believe our results also provide some insight into the network-based properties of the cytoskeleton. A gel is the result of a geometrical phase transition in the course of which the internal connectivity of the system changes markedly. Such phase transitions can be studied by means of percolation theory, which is an analytical tool to describe clustering and network formation (Stauffer, 1985). It is widely used to study systems in which connectivity plays an essential role. In addition to gel formation in solutions of polymers (Gibbs et al., 1973; de Gennes, 1976a; Bouchaud et al., 1986), examples of which are the cytoskeleton or the extracellular matrix, percolation theory is used to model diverse phenomena such as continent formation (de Gennes, 1976b),galaxy formation (Schulman, 1986),a number of important properties of water (Stanley et af., 1981),the spread of infectious diseases (Bailey, 1975), forest fires (MacKay and Jan, 1984), dielectric breakdown in conductive networks (Essam, 1980; Stauffer, 1979),disruptive bond formation at interfaces (Forgacs et al., 1986,1988), macroscopic elasticity of random elastic networks (Thorpe, 1986), and the conductive properties of random resistor networks (Clerc et al. 1990). The common ingredient in these systems is that at a given value of certain characteristic parameters, a macroscopic, connected cluster forms in the system (e.g., a cluster of connected polymer molecules in gel formation; a connected cluster of burning trees in a forest fire, etc.) When such a macroscopic connected cluster is formed, the physical properties of the system can change drastically. In the case of solid gel formation, the polymer solution has liquid properties before the gel forms, that is, a well-defined value of the viscosity, whereas in the gel phase the viscosity is practically infinite and the system has well-defined elastic properties. The value of the characteristic parameter at which the macroscopic cluster appears is called the “percolation threshold.” This parameter for gel formation may be the concentration of the polymers in solution. In the case of continent formation, it might be the sea level, for forest fires, the density of trees, etc. The properties of the system which change at

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the percolation threshold are in some cases readily observable k e . , a continent forms), but in other cases must be probed for (i.e., elastic properties of gels, conductive properties of resistor networks). In the case of the cytoskeleton or the extracellular matrix, percolation theory can provide quantitative conditions for the sol-gel transitions. In Section I1 we describe our model tissue system, and the observed phenomenon of MDT. In Section 111, on the basis of experimental and theoretical considerations, we argue that MDT is a consequence of network formation. Section IV contains a discussion of the possible relevance of network formation in cell and tissue biology.

II. Matrix-Driven Translocation The objective of the studies to be described was to isolate and characterize a subset of morphogenetic phenomena (Newman ef af., 1985, 1987). In the MDT assay, cells or polystyrene latex particles were suspended in a solution of the extracellular matrix protein type I collagen. This was referred to as the primary fluid. Another solution was prepared without cells or latex particles (the “secondary fluid”). Droplets of the two fluids were injected into opposite ends of a parallel plate arrangement as shown in Fig. 1. Under specific conditions a sharp interface formed between the two droplets, which is evident from the uniform spreading or translocation of the primary fluid along the interfaces between the secondary fluid and the bounding subtrata. The two droplets thus behaved as immiscible fluids. The motion was always unidirectional, proceeding with a velocity on the order of 1 mm/min, which excludes diffusion as a possible mechanism. Translocation was observed for 5-10 min (Newman el al., 1985). The following conditions must hold for the phenomenon to take place: 1. The concentration of collagen, pc in the primary and secondary fluids must be above p* = 1.5 mg/cm3. If pc < p*, no interface is formed and the two droplets coalesce after a transient period. 2. The number density of cells, or latex beads, ng,in the primary fluid must be greater than n* = 2 x lo6 per cm3. If n, < n*, no interface

FIG. 1 Matrix-driven translocation experiment performed between two plates, viewed from the side. In this figure “gel” refers to a liquid containing connected protein fibers.

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forms and the boundary between the primary fluid and the secondary fluid becomes diffuse. 3. If the experiment is carried out with beads, translocation is observed with beads 6 pm in diameter, but not with 0.2 pm-beads. 4. Translocation is observed only when strong intermixing is used at each stage of the preparation of the assay. An additional set of phenomena, which occurred at a slightly higher collagen concentration, in which MDT became dependent on the presence of the matrix protein fibronectin in the secondary fluid (Newman et al., 1985; Forgacs et al., 1989) is not discussed here. MDT resembles morphogenetic processes, for example, the sorting out of different cell types from a heterogeneous mixture, and the engulfment of one tissue fragment by another (Steinberg, 1975). Steinberg and coworkers (Steinberg, 1962, 1978; Steinberg and Poole, 1982) have considered the morphogenetic behavior of tissues in terms of their resemblance to liquids. Tissue fragments can flow in response to external forces, round up when suspended in a fluid medium, and coalesce with other such fragments, much like liquid droplets. Mixtures of cells from different types of tissue will sort out into homotypic islands, and will eventually separate out completely, like a suspension of oil in water (Steinberg and Poole, 1982). After sorting out has occurred, the relative configurations of the tissues are what would be predicted if tissues, like simple liquids, exhibited interfacial tensions with respect to their surroundings. In the case of tissues, these surroundings could be other tissues, culture media, or artificial substrata. In order to explain the observed behavior of tissue fragments in contact, Steinberg formulated the “differential adhesion hypothesis” (DAH) (Steinberg, 1978; Armstrong, 1989) according to which cell populations in the process of rearrangement mimic the behavior of ordinary immiscible liquids. The quantitative analysis of the differential adhesion principle was carried out in terms of the surface tension of the individual tissue fragments (Steinberg, 1978). Steinberg and co-workers showed that the spreading of certain tissues on others, or the engulfment of some tissues by others, is strongly correlated with their cohesive and adhesive properties, which eventually determine their surface tensions. Living tissues seem to form a hierarchy according to the magnitude of their surface tension. A number of processes in the developing embryo are compatible with the assumption that they are driven by interfacial or surface tension forces. Some examples are gastrulation (Holtfreter, 1944; Phillips and Davis, 1978), wound healing (Lash, 1955) the spreading of chick blastoderm on the inner surface of the vitelline membrane (Downie, 1976), the spreading of the chick embryonic epicardium over the myocardium (Ho and Shimada, 1978), the elongation of the salamander pronephric duct

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over the lateral mesoderm (Poole and Steinberg, 1981),or the condensation of precartilage mesenchymal cells (Frenz et al., 1989). If tissues in some cases indeed behave similarly to liquids, then many of their properties can be studied by analogy, using the numerous methods and techniques worked out for liquids. This should have important consequences for the understanding of certain types of morphogenetic movements, especially in the early embryo, where the liquid properties of tissues are the most pronounced. On the basis of its similarity to tissue engulfment, we were led to analyze MDT in terms of fluid interfacial phenomena. Whereas DAH relies heavily on the importance of direct cell-to-cell adhesion to explain the generation of tissue interfaces and surface tensions, there are no direct cell-to-cell or particle-to-particle interactions in the MDT assay, or for that matter, in the mesenchymal tissues for which they provide a model. We have, therefore, been led to consider other types of mechanisms for MDT.

111. Physical Mechanisms of MDT Two distinct fluids confronting each other at a vertical interface, as shown in Fig.1, can undergo changes in relative position as a result of adhesive interactions that occur at this interface and at their interfaces with other bounding substrata. A general class of such phenomena is known as “wetting” (for a review, see Forgacs et al., 1991a).

A. Wetting Wetting is an interfacial phenomenon that takes place when one of two (or more) thermodynamic phases in coexistence is preferentially attracted by a “spectator phase,” typically the wall of a container (see Fig. 2). A liquid in coexistence with another fluid forms a contact angle with the substratum, which in this case is represented by the wall of the capillary. It follows from the requirement of mechanical stability that at equilibrium, the surface or interfacial tensions yas (between the substratum and the fluid denoted by a), yps (p fluid-substratum), and yab (a fluid-p fluid) satisfy Young’s equation (Young, 1805) (1) 0 = YPS - Yas Here 0 is the contact angle. For 0 > 0, none of the fluids is preferentially attracted to the wall of the capillary (see Fig. 2), whereas at 0 = 0, the Yap cos

a fluid spreads along the substratum and is said to completely wet the

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FIG. 2' Schematic representation of wetting in a geometry relevant to MDT. The a fluid partially wets the p fluid-capillary wall interface if 0 > 0 in equilibrium. If 0 = 0, wetting is complete and the a fluid extends indefinitely to the left.

substratum. When 0 > 0, wetting is partial or incomplete. The transition from 0 > 0 to 0 = 0 is the wetting transition. This transition may be first order (in which case 0jumps abruptly from some finite value to zero) or second order (in which case 0 decreases continuously to zero). The change of the contact angle and, consequently the wetting transition, can be induced by varying some external parameter (temperature, concentration, etc.). Wetting is thus the result of a delicate interplay between adhesive interactions (between fluids and their substrata) and cohesive forces (within the fluids). The similarity between the configurations in Fig. 2 and Fig. 1 is evident. The following identification seems plausible: yas,yps and yap,respectively, are the interfacial tensions between the primary fluid and the plates, between the secondary fluid and the plates, and between the primary and secondary fluids. We assume that the driving force behind the spreading of the primary fluid is the wetting mechanism. When p c < p * and nB < n,* the balance of adhesive and cohesive forces is such that each of the two droplets retains equal contact with the bounding plates. However, when pc > p* and nB > n*, the balance of forces is shifted. This leads to the primary fluid wetting the interface between the secondary fluid and the bounding plates. For this spreading motion to take place [and consequently for cos 0 in Eq. (1) to be larger than zero], we must have yps > yms.We have not yet been able to measure these interfacial tensions when S represents the plastic or glass plates used in the MDT assay. However, our preliminary results for the case when S represents air (which served as the upper substratum in the original MDT experiments (Newman et al., 1985) unambigously indicate that indeed yps > yas. It is not possible at this point to determine whether this wetting is complete (0= 0),or incomplete (0 > 0 ) ,because the gelation of collagen takes place simultaneously with MDT. Thus the final configuration with 0 < 0 in Fig. 1, may be due to freezing as a result of gelation, rather then

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the manifestation of a partially wet equilibrium state. In order for this mechanism to provide a satisfactory account of MDT, it is necessary to identify the basis of the changes in the balance of adhesive and cohesive forces that occur during the experiment. B. Percolation

The experimental results indicate that at pc = p* and nB = n*, a phase transition takes place in the primary fluid. We suggest that at pc > p* and nB > n*, a change occurs in the connectivity properties of the primary fluid (Forgacs et al., 1991b). Collagen is a rod-like protein molecule which undergoes an assembly process to form macromolecular fibrils and, ultimately, macroscopic fibers. In a molecular state the rod has a length ( L )of 300 nm and a diameter ( d ) of 1.4 nm (Giraud-Guille, 1989). This corresponds to an aspect ratio of x = L / d = 214. It is well known that a solution of rigid rods of such dimensions undergoes a first-order thermodynamic phase transition from an isotropic liquid state to an anisotropic liquid crystal (Onsager, 1949; Flory, 1956) provided that for the rod volume fraction, u, one has u

2

(2)

l/x

A number of experimental studies indicate that collagen indeed may form a liquid crystal (Giraud-Guille, 1989; Murthy, 1984; Bouligand and GiraudGuille, 1984). It has also been shown theoretically (Bug et al., 1985) that a system of rigid rods undergoes a percolation transition at pc

2

1/Vexc = l/xV

(3)

Here Vex, = L2d and V = Ld2 are the excluded volume and the true volume of a single rod, respectively. Both conditions (2) and (3) are valid in the limit of large x. Since u = Vpc, expressions (2) and (3) are equivalent. In order to decide whether it is the percolation or the liquid crystal transition that takes place, detailed experimental study of the system in question is needed. We can ask, however, whether the phase separation observed in the MDT experiment can be attributed to either of these effects. The specific volume of collagen is 0.66 cm3/g (Brokaw et al., 1985), pc = 1.5 mg/cm3*and the aspect ratio of collagen fibers used in the MDT experiment (which were not in molecular form, but rather in the form of assembling fibers, with d = 1.4 pm and L 50-100 pm), is x- 35-70. With these values, the inequality in Eq. (3) is not satisfied. However, the relationships in Eqs. (2) and (3) have been derived under the assumption that the solution of rods is homogeneous. This may easily be achieved with rods of molecular size, but not with rods of macroscopic

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size. In the latter case, Brownian motion cannot randomize any heterogeneities that may arise from gravitational effects or nonlinearities in the fiber assembly process. If we consider only gravitational effects, it can lo-* g) is homobe calculated that a suspension of collagen fibers (mass geneous only on a length scale of 10 nm = m; thus it is inhomogeneous on any realistic, experimental length scale (Obukhov, 1988; Forgacs et al., 1991b). A homogeneous solution can be produced only by strong intermixing, which may explain why MDT is observed only under this condition. In the presence of such intermixing, expression (3) is modified and the condition for percolation becomes (Obukhov, 1988)

-

ux2 2 1

(4)

Putting into this expression the experimental values ( p c = 1.5 mg/cm3, 35-70), we obtain ux2 2 1.2, which compares very well with the theoretical value in Eq. (4). These considerations are therefore consistent with the assumption that at p = pc, n = nB a percolating cluster of connected rods appears in the pure collagen solution. If a percolating cluster existed in both the particle-containing and the particle-free regions, no interface would form, since the matrix regions would not constitute distinct thermodynamic phases. If, however, one or more of the parameters defining the percolating cluster were near their critical values, the cluster would readily be disrupted by a critical number of cells or beads. We suggest that such disruption is the basis of the formation of a distinct phase in the particle-containing matrix region. On the assumption that the particles prevent fiber-fiber interactions either by steric effects or by direct binding, quantitative estimates can be made of the number of particles that would be necessary to prevent a percolating cluster from forming (Forgacs et al., 1991b). We have esimated that a value on the order of lo6particles/cm3 would be disruptive if the diameter of the particles were comparable to the diameter of a collagen fiber (1.4 pm) (Brokaw et al., 1985). These predictions are in accord with the experimental observations listed in points 2 and 3 of Section 11.

x

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IV. Conclusions

The establishment of boundaries of immiscibility between adjacent blocks of tissue is the basis of developmental compartmentalization in insects (Crick and Lawrence, 1975), and plays an important role in segmental organization in a wide variety of species (Newman, 1993). Boundaries of immiscibility also provide an opportunity for morphogenetic rearrangements based on interfacial forces. For tissues in which cells are

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in direct contact with one another, the DAH (Steinberg, 1978; Steinberg and Poole, 1982;Armstrong, 1989)provides a reasonable physical account of such boundary formation. Indeed, recent studies in which mouse L cells were transfected with plasmids that caused them to express different levels of the same cadherin molecule (Friedlander et af.,1989) have confirmed the DAH. In mesenchymal tissues, however, cells are not in direct contact with one another, but instead are surrounded by relatively large amounts of extracellular matrix. The establishment of boundaries of immiscibility and related morphogenetic changes in such tissues are not straightforward consequences of differential adhesion. In Section 111, we provided an analysis-based on global connectivity changes, or percolation, in a network of collagen fibers-that accounts for phase separation and morphogenesis in a model tissue system. It seems likely that developing tissues, and tissues of healing wounds and invading tumors, could utilize this class of physical effects, which are indeed generic (Newman and Comper, 1990) to virtually all semisolid materials, living and nonliving, which are made up of fibrous components. The cytoskeleton is a member of this category of materials. Given that its various fibrous Components are subject to assembly and disassembly in response to internal and external physiological effectors, it would be surprising if changes in network properties of the sort discussed here in relation to collagen matrices did not play a part in the cytoskeletal transduction of physical forces and molecular signals during cell locomotion and regulation of gene activity.

References Alberts, B., Bray, D., Lewis, J., RafF, M., Roberts, K., and Watson, J. D. (1989). “Molecular Biology of the Cell,” 2nd ed. Garland, New York. Armstrong, P. B. (1989). Crit. Rev. Biochem. Mol. Biol. 29, 119. Bailey, N. (1975). “The Mathematical Theory of Infectious Diseases.” Hafner, New York. Bouchaud, E., Delsanti, M., Adam, M., Daoud, M., and Durand, D. (1986). J . Physique (Paris) 47, 1273. Bouligand, Y., and Giraud-Guille, M. M. (1984). In “Biology of Invertebrate and Lower Vertebrate Collagen” (A. Basirati and A. Garrone, eds.), p. 115. Plenum Publishing, New York. Brokaw, J. L., Doillon, C. J., Hahn, R. A., Birk, D. E., Berg, R. A., and Silver, F. H. (1985). Int. J . Biol. Macromol. 7, 135. Bug, A. L. R., Safran, S. A,, and Webman, I. (1985). Phys. Reu. Lett. 54, 1412. Cervera, M., Dreyfuss, G., and Penman, S. (1981). Cell (Cambridge, Mass.) 23, 113. Clerc, J. P., Giraud, G., Laugier, J. M., and Luck, J. M. (1990). Adu. Phys. 39, 191. Crick, F. H. C., and Lawrence, P. A. (1975). Science (Washington, D.C.) 189, 340. de Gennes, P. G. (1976a). J . Physique (Paris) 37, L1.

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de Gennes, P. G. (1976b). La Recherche 7, 921. Downie, J. R. (1976). J . Embryol. Exp. Morph. 35, 59. Essam, J. W. (1980). Rep. Prog. Phys. 43, 233. Flory, P. J. (1956). Proc. R . Soc. London Au4, 73. Forgacs, G., Luck, J. M., Nieuwenhuizen, Th. M. , and Orland, H. (1986). Phys. Rev. Lett. 57, 2178. Forgacs, G.,Luck, J. M., Nieuwenhuizen, Th. M. , and Orland, H. (1988). J. Stat. Phys. 51, 29. Forgacs, G . , Jaikaria, N. S. , Frisch, H. L., and Newman, S. A. (1989). J . Theor. Biol. 140, 417. Forgacs, G., Lipowsky, R., and Nieuwenhuizen, Th. M. (1991a) I n “Phase Transitions and Critical Phenomena” (C. Domb and J. L . Lebowitz, eds.), Vol. 14, pp. 136-363. Academic Press, London. Forgacs, G., Newman, S . A , , Obukhov, S. P., and Birk, D. E. (1991b). Phys. Reu. L e f t . 67, 2399. Friedlander, D. R., Mege, R. M., Cunningham, B. A., and Edelman, G. M. (1989). Proc. Natl. Acad. Sci. U . S . A . 86, 7043. Frenz, D. A., Jaikaria, N . S., and Newman, S. A. (1989). Deu. Biol. 136,97. Gibbs, J. H., Cohen, C., Fleming, P. D., and Porosoff, H. (1973). J. Solution Chem. 2,277. Giraud-Guille, M. M. (1989). Biol. Cell. 67, 97. Hall, A. L., Warren, V., and Condeelis, J. (1989). Dev.Biol. 136,517. Ho,E.,and Shimada, Y. (1978). Dev.Biol. 66, 579. Holtfreter, J. (1944). J. Exp. 2001.95, 171. Lash, J. W. (1955). J . Exp. 2001.128, 13. MacKay, G., and Jan, N. (1984). J. Phys. A: Math. Gen. 17, L757. Murthy, N, S. (1984). Biopolymers 23, 1261. Newman, S . A . (1993). BioEssays 15, 277. Newman, S.A , , and Comper, W. D. (1990). Development 110, 1 . Newman, S. A , , Frenz, D. A., Tomasek, J. J., and Rabuzi, D. D. (1985). Science (Washington, D . C . ) 228, 885. Newman, S. A., Frenz, D. A., Hasegawa, E., and Akiyama, S. K. (1987). Proc. Natl. Acad. Sci. U . S . A . 84,4791. Obukhov, S. P. (1988). J. Phys. A: Mafh. Gen. 21, 3975. Onsager, L. (1949). Ann. N . Y . Acad. Sci. 51, 627. Phillips, H.M., and Davis, G. S. (1978). Am. Zool. 18, 81. Poole, T. J., and Steinberg, M. S. (1981). J. Embryol. Exp. Morph. 63, 1. Schulman, L.S. (1986). Science (Washington, D . C . ) 233, 425. Stanley, H. E., Texeirea, J., Geiger, A., and Blumberg, R. L. (1981). Physica 106A, 260. Stauffer, D.(1979). Phys. Rep. 54, 3. Stauffer, D. (1985). “Introduction to Percolation Theory.” Taylor & Francis, London. Steinberg, M. S. (1962). Proc. Natl. Acad. Sci. U . S . A . 48, 1769. Steinberg, M. S. (1975). J . Theor. B i d . 55, 431. Steinberg, M.S. (1978). In “Specificity of Embryological Interactions” (D. R. Garrod, ed.), pp. 583-607. Chapman and Hall, London. Steinberg, M. S., and Poole, T. J. (1982). I n “Cell Behavior” (R. Bellairs and A. S. G . Curtis, eds.), pp. 583-607. Cambridge Univ. Press, Cambridge. Thorpe, M. F. (1986). Ann. N . Y. Acad. Sci. 484, 206. Young, T. (1805). Philos. Trans. R . Soc. London 95, 65.

The lnterphase Nucleus as a Dynamic Structure Umberto De Boni Department of Physiology, Faculty of Medicine, University of Toronto, Toronto. Ontario Canada M5S lA8

1. Introduction

The spatial organization of the contents of interphase nuclei is of increasing interest, largely because of an increasing body of evidence which shows that interphase nuclei in different tissues in general and in cells of the central nervous system (CNS) in particular exhibit distinct patterns of chromatin organization. The interphase nuclei of different CNS cells display distinct and nonrandom arrangements of specific DNA sequences (Manuelidis, 1984a,b; Manuelidis and Borden, 1988; Billia and De Boni, 1991; Holowacz and De Boni, 1991). This has been postulated to indicate that transcription may be, in part, controlled and regulated by nuclear compartmentalization (Manuelidis, 1985a,b). This concept is supported by the argument that the primary DNA sequence alone, which is common to the cells of a given organism, cannot fully account for the different tissue- or cell type-specific gene expressions which occur within interphase nuclei (Pienta et al., 1991). Further support comes from observations of an association between changes in chromatin organization and altered functional states in cells. In fact, as early as 1949 it was recognized that electrical stimulation of hypoglossal neurons in situ resulted in a significant repositioning of nucleolar satellite DNA, concurrent with intense RNA synthesis (Barr and Bertram, 1949, 1951). More recently, specific chromatin domains have also been shown to reorganize and move significantly during neuronal differentiation (Manuelidis, 1985) as well as in neurons that exhibit altered functional states such as those which occur within epileptic foci in the human cerebral cortex (Borden and Manuelidis, 1988). In addition, observations of cells in vitro have shown that chromatin moves in a quantifiable manner within the spatial confines of interphase nuclei, a motion traditionally Internarional Reuien of Cyrolog)~,Vol. I S 0

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termed nuclear rotation (Pomerat, 1953; Pomerat et al., 1967; De Boni and Mintz, 1986). The rate of such motion in neurons in uitro is altered by nerve growth factor or neurotransmitters (Fung and De Boni, 1988), agents which also alter neuronal gene expression (Greenberg et al., 1985, 1986). Together, these observations correlate changes in dynamic positions of gene sequences within the three-dimensional (3-D) space of neuronal interphase nuclei with changes in gene expression, and suggest causal links. The existence of such links is further supported by the emerging concept that the 3-D organization of the genome may play an important role in the control of gene expression (Pienta et al., 1991). The work presented here is intended to summarize some of the evidence describing the 3-D organization of interphase nuclei and to correlate this evidence with results that show that the organization of interphase nuclei is dynamic and under the control of physiological stimuli.

II. Nuclear Rotation: Chromatin Motion in lnterphase Nuclei in Vitro

Motion of chromatin domains within interphase nuclei has been described for several cell types maintained in v i m . It is particularly pronounced in neurons, a cell type which is permanently arrested in interphase. When assayed by quantification of nucleolar displacement over time, this motion is termed “nuclear rotation.” In much of the work described here the quantification of nuclear rotation was derived from time-lapse photomicrographs and was expressed as the planar angle, subtended at the center of nuclei of circular geometry, through which nucleoli move over time. The term “nuclear rotation” itself is derived from the seminal work carried out by Pornerat (1953) and by Paddock and Albrecht-Buehler ( 1986a,b) and is based on the observation that intranuclear motion is most readily discernible and quantifiable in cells in which nucleoli are located near the nuclear periphery. As indicated later, the motion of chromatin structures is not restricted to circular trajectories, but occurs in three dimensions within the spatial confines of the nucleus. Therefore, it might be considered prudent to replace the traditional term “nuclear rotation” with the term “chromatin motion.” For this reason “nuclear rotation” will be retained where appropriate for the citations employed but will be replaced by the term “chromatin motion” where this latter terminology more appropriately describes the results.

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The first observations of nuclear rotation, which was seen as the motion of nucleoli in neuronal nuclei, were made by Murnaghan (1941) and by Nakai (1956) and were quantitatively analyzed by Pomerat and colleagues (1967) and Lodin and colleagues (1970). Nuclear rotation in non-neuronal cells was shown to occur in epithelial cell types (Pomerat, 1953; Leone et a!., 1955; Hinschke, 1956; Capers, 1960; Bourgeois et al., 1981). In some of these cell types, nuclear rotation during interphase is frequently either very slow or absent altogether, unless these cells are treated with agents which alter membrane permeability, such as monensin or phytohemagglutinin. In contrast, several neuronal types in uitro, at least while actively differentiating, invariably exhibit nuclear rotation. This observation speaks against the argument that nuclear rotation is related to events initiating mitosis (Bard et al., 1985), events which do not occur in differentiated neurons. Nuclei of many cell types and especially those of neurons maintained in uitro have a spherical geometry. It is unlikely, then, that the motion of nucleoli in these cells would be restricted to a particular nuclear plane; rather, it is likely that nucleolar motion extends throughout the karyoplasm. Indeed, dot-product vector analyses of consecutive XYZ positions of chromatin domains showed that nuclear rotation represents the motion of chromatin domains along curvilinear trajectories, occurring in three dimensions throughout the karyoplasm (De Boni and Mintz, 1986). Using living neurons in uitro whose nuclei were labeled with the DNA-specific dye 4,6-diarnidino-Zphenylindole (DAPI), this work also showed that displacement of chromatin domains is not restricted to motion of nucleoli but that it includes additional chromatin domains. Nuclear rotation occurs independently of the concurrent motion of juxtanuclear, cytoplasmic structures (Albrecht-Buehler, 1984; De Boni and Mintz, 1986; Hay and De Boni, 1991); this observation supports the hypothesis that the motion described as nuclear rotation is driven from within the nucleus (see the following discussion). We had proposed that nuclear rotation may function in the transposition of specific chromatin domains to transcriptionally active compartments (De Boni and Mintz, 1986; De Boni, 1988a; Fung and De Boni, 1988). Nuclear rotation would thus be expected to be intermittent rather than continuous since changes in gene expression are clearly synchronized in time with induced altered neuronal activity (Greenberg et al., 1986; Cole ef al., 1989). Subsequent work clearly showed that nuclear rotation is indeed saltatory and includes reversal in direction in all three spatial dimensions (De Boni and Mintz, 1986; Hay and De Boni, 1991). These saltatory aspects of motion are obscured when quantifying mean rates of nuclear rotation

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as the cumulative distance traversed by chromatin domains, such as phase dark nucleoli and major domains stained supravitally with DNA-specific, fluorescent dyes (Pomerat et af., 1967; De Boni and Mintz, 1986; Fung and De Boni, 1988; De Boni, 1988a; Schiffmann and De Boni, 1991). This paradigm provides information on mean rates of chromatin motion. However, it smoothes the actually saltatory nature of nuclear rotation, which is clearly evident in plots of the instantaneous position of chromatin domains versus time (Figs. 1,2a,b). The saltatory behavior of nuclear rotation is also evident in frequency power spectra (Fig. 2c) derived from fast fourier transform analyses of chromatin motion over time (Park and De Boni, 1991). This latter work with dorsal root ganglion neurons and additional work with PC12 cells in uitro (Figs. 1,2) clearly established nuclear rotation as a periodic motion of chromatin domains, within spatially restricted nuclear compartments (see the following discussion). In dorsal root neurons, such domains move at mean rates of 2.2 f 0.04 deg/min, with dominant power bands at frequencies ranging from 0.47 c/hr to 2.91 c/hr. Resonance in these power spectra, indicated by observations of significant power fractions at frequencies corresponding to multiples of the fundamental wavelength, suggests that nuclear rotation consists of forced harmonic motion, a motion under multiple levels of control. While such mechanisms of control remain enigmatic, it has been demonstrated that changes in intracellular calcium concentrations alter nuclear rotation rates (Fung and De Boni, 1988). It may thus be speculated that one level of control may be related to the cycling, free calcium levels reported to occur in nuclei of excitable cells (Przywara et af., 1991). Given that a large amount of the nuclear content of neurons in uitro exhibits saltatory motion, it is important to predict the location of the interface between moving karyoplasm and the relatively stationary cytoplasm. The presence of an extranuclear, cytoplasmic motor would result in motion of the nucleus in toto, including its envelope, as previously proposed. It has been argued (Albrecht-Buehler, 1984) that an interface for nuclear rotation between the outer nuclear membrane and the cytoplasm is most likely, because the evidence for stable connections between the endoplasmic reticulum and the outer nuclear membrane is uncertain. Rates of nuclear rotation increase in the presence of Monensin, whose action on the Golgi apparatus seems consistent with the production of breaks between the nuclear envelope and endoplasmic reticulum. This led to the conclusion that the ties between the nucleus and cytoplasm are dynamic (Albrecht-Buehler, 1984). Such a dynamic association between the nuclear envelope and the cytoskeleton is, however, not supported by results which show that the

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FIG. 1 A representative series of time-lapse, phase-contrast photomicrographs (10-min intervals between frames) of the nucleus of a PC12 cell in uitro, showing the phenomenon of nuclear rotation (chromatin motion). Note the pronounced changes in the intranuclear, spatial position of the nucleoli and the reversal of direction (g,h). Also note the changes in rate of motion per interval, indicating the saltatory nature of motion. The black dot marks a juxtanuclear, cytoplasmic structure, which remains relatively stationary while the nuclear content shows significant displacement. Magnification: 3000 X .

outer membrane of the nuclear envelope is intimately linked with intermediate filaments of the cytoskeleton (Georgatos and Blobel, 1987) and that the pattern of the juxtanuclear cytoskeleton is not dramatically different in cells with stationary nuclei and those that have rotating nuclei (Paddock and Albrecht-Buehler, 1986a,b).

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It is conceptually difficult to place the locus of the sliding interface for nuclear rotation between the outer nuclear membrane and the cytoplasm unless the filamentous structures between the nuclear envelope and cytoplasm are totally dynamic. Time-lapse video records show that nuclear rotation in dorsal root neurons in vitro and in PC12 cells (Fig. 1) does not include the motion of cytoplasmic organelles, such as cysternae of endoplasmic reticulum, mitochondria, and Nissl clusters in the juxtanuclear zone (Pomerat, 1953; Albrecht-Buehler, 1984; De Boni and Mintz, 1986). Moreover, juxtanuclear cytoplasmic structures located within fractions of a micrometer of the outer nuclear membrane remain stationary when chromatin is clearly seen moving past such structures, even when the intermediate filament network is disrupted by acrylamide (Hay and De Boni, 1991). This is not surprising in view of ultrastructral evidence which shows that the outer nuclear membrane of dorsal root sensory neurons is extensively continuous with membranes of the endoplasmic reticulum (De Boni, 1988a,b). The absence of resolvable changes in the morphology of the immediate juxtanuclear area during periods of significant motion of nucleoli supports the hypothesis that an interface between the outer nuclear membrane and the cytoplasm is unlikely. A relative motion between the membranes forming the nuclear envelope is also unlikely, as previously pointed out (Albrecht-Buehler, 1984; Paddock and Albrecht-Buehler, 1986a,b; De Boni, 1988a). A large number of nuclear pores connect inner and outer nuclear membranes, at densities of up to 18 pores per square micrometer of membrane in cerebral cortex cells (Lodin et al., 1978). There exists no evidence that pore complexes, organelles with an estimated, aggregate molecular weight of 10 x lo7 daltons (Davis and Blobel, 1986), undergo rapidly reversing cycles of disassembly and assembly, at rates compatible with observed chromatin motion. Additional constraints on motion between inner and outer nuclear membranes may be associated with their fusion to the spokes of nuclear pore complexes (Maul, 1977; Unwin and Milligan, 1982; Burke, 1990).

FIG. 2 The dynamics of motion of two nucleoli (solid and dashed lines, respectively) in two representative, binucleolate PC12 cells in uitro, (A) in the absence of nerve growth factor and (B) following differentiation by nerve growth factor (7 days, 100 ngfml). The angle between vectors is derived from dot-product vector analyses of the spatial positions of nucleoli within spherical nuclei (see the text and Park and De Boni, 1991). Saltatory motion is evident as changes in the rates of angular displacement over time (A,B). In the absence of nerve growth factor, the motion of both nucleoli is synchronous. This synchrony is also reflected in the similarity of frequency power spectra of motion (C) of the two nucleoli (solid and hatched bars, respectively) shown in A. In cells differentiated with nerve growth factor (B), such synchrony of motion between nucleoli is lost and the mean rate of motion is significantly decreased (note the different scale of the y-axis).

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An interface for motion between the lamina and the inner nuclear membrane is similarly unlikely, given the presence of specific, integral membrane proteins (Gerace er al., 1974, 1978) and lamin B, which anchor the lamina-pore complex to the inner nuclear membrane by a specific glycoprotein (Lebel and Raymond, 1984). Relative motion of the lamina along the inner nuclear membrane would require connections between these elements to be dynamic. Given the dimensions of nuclei of dorsal root neurons, together with measured rates of chromatin motion of 0.3 pm/min and more at the nuclear periphery, lamina sliding along the inner membrane would have to move through at least 3 pore diameters per minute. Ultrastructural evidence shows that the lamina is invariably interrupted in the regions underlying nuclear pores. Motion of the lamina relative to the inner nuclear membrane would therefore result in the presence of lamina underlying nuclear pores; this is never observed. As indicated above, disruption of the intermediate filament network by acrylamide results in a 4-fold increase in the mean rate of chromatin motion, within an apparently stationary envelope. This increase in the rate of chromatin motion occurs concurrently with significant changes in thickness of the nuclear lamina, as shown by ultrastructural examination of neurons exposed to acrylamide. Lamina thickness decreases significantly ( P < 0.0001) from 20.86 5.10 nm (n = 159) in controls to 16.05 2 4.37 nm ( n = 103) in nuclei of neurons treated with 4 mM acrylamide (Hay and De Boni, 1991). While acrylamide has actions on cell function other than disruption of intermediate filament bundles, including changes in phosphorylation of neurofilament protein (Howland and Alli, 1986), intermediate filaments and nuclear lamins share extensive alpha-core epitopes with intermediate filaments (McKeon er al., 1986). The reduced lamina thickness after acrylamide exposure indicates that such lamina epitopes may also be disrupted by acrylamide and that the associated increase in rates of nuclear rotation may be the result of removal of a damping constraint on chromatin motion, which is normally provided by an intact lamina. Together, the above arguments support the hypothesis that nuclear rotation represents the motion of chromatin domains within nuclei and not a motion of the nucleus in rum, including its envelope. In view of the controversy regarding the subcellular site of the interface of the observed motion, work was undertaken to determine whether nuclear rotation is associated with the motion of chromatin domains relative to each other (Park and De Boni, 1991).This work, using direct, quantitative analyses of the dynamics of nucleolar fusion during redifferentiation of living neurons in uitru, clearly showed that intranuclear domains may indeed move independently and relative to each other, although within spatially restricted nuclear territories. Moreover, the results showed that nucleolar fusion is invariably preceded by a significant burst in the rate of nuclear rotation.

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This work also provided additional evidence which shows that nuclear rotation is not restricted to motion of nucleoli. As nucleoli undergo fusion as a function of in uitro age and their number per nucleus decreases, the number of kinetochore signals, detected by immunocytochemistry , also decreases (De Boni et al. 1992; Park and De Boni, 1992). This decrease in the number of kinetochore signals is associated with a concomitant increase in the volume of the remaining signals detected. This observation is indicative of additional clustering and thus of motion of chromatin domains relative to each other. Together, the results indicate a clear correlation between the periodic and pulsatile nature of nuclear rotation and nucleolar fusion in neurons in uitro; they indicate that nucleolar fusion, clustering of specific chromatin domains, nuclear rotation, and differentiation are linked (Park and De Boni, 1991,1992). Moreover, the results support the hypothesis that nuclear rotation may be driven by an intranuclear motor, a hypothesis supported by additional evidence discussed later. We conclude, therefore, that the interface of chromatin motion must lie between the inner nuclear membrane on the outside and a component of chromatin on the karyoplasmic side. We have proposed that nuclear rotation may function in the transposition to transcriptionally competent compartments of those chromatin domains actively transcribed. This hypothesis is supported by the association of actively transcribed genes with specific intranuclear loci that are associated with “nuclear channels” (Hutchison and Weintraub, 1985), and by theoretical considerations of a phenotypically defined, albeit dynamic, three-dimensional structure of the cellular genome (Blobel, 1985). Observations of nuclear rotation in general, and of the pronounced motion of supravitally stained large chromatin masses which move in tandem with nucleoli (De Boni and Mintz, 1986) in particular, have been restricted to cells in uitro. Under these conditions nuclear rotation is especially pronounced during early stages of redifferentiation and may slow down or cease altogether in mature, fully differentiated neurons (Pomerat et al., 1967; Park and De Boni, 1991). It is not known whether pronounced motion of the nuclear contents occurs in neurons in situ, although an increasing body of indirect evidence indicates that such motion occurs in viuo during differentiation and adaptation to altered functional states, as decribed later.

111. Chromosome Topology in lnterphase Nuclei

During interphase, most of the chromatin within a nucleus is less condensed than it is during stages of the cell cycle associated with mitosis.

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As a result, individual chromosomes or components thereof, with the exception of nucleoli, cannot readily be discerned. Early work by Rabl (1885) indicated, however, that such interphase chromatin may retain a telophase-like arrangement of chromosomes, with centromeres and telomeres remaining associated with opposite poles of the nucleus. Evidence for this was confirmed in the specialized, polytene nuclei in salivary gland cells of Drosophila larvae (Agard and Sedat, 1983; Hochstrasser er al., 1986; Hochstrasser and Sedat, 1987a,b).In contrast, mammalian cell types frequently display a non-‘‘Rabl-type” chromosome topography (Moroi et al., 1981; Brinkley el al., 1986; Manuelidis, 1984b, 1985a; Haaf and Schmid, 1989, 1991; Haaf et al., 1990). With the advent of in situ hybridization, it has become possible to show, however, that different DNA sequences are not randomly positioned within interphase nuclei, but rather, that they are organized into a 3-D pattern which is cell type specific (Manuelidis, 1984a,b, 1985a,b; Manuelidis and Borden, 1988; Arnoldus et al., 1989; Billia and De Boni, 1991). Highly repetitive, nontranscribed chromosome domains such as centromeric satellite DNA (sDNA) (Jones, 1970; Pardue and Gall, 1970; Rae and Franke, 1972; Manuelidis, 1982, 1984b, 1985a,b; Joseph et al., 1989; Masumoto et al., 1989a,b) and telomeric DNA sequences (Mathog et al., 1984; Hochstrasser et al., 1986; Katsumoto and Lo, 1988; Rawlins and Shaw, 1990a,b; Billia and De Boni, 1991) become nonrandomly and reproducibly fixed to cell type-specific, intranuclear sites (Fig. 3). This rearrangement of patterns probably occurs during postmitotic, final differentiation (Manuelidis, 1984b). Similar results were obtained by immunocytochemistry used to detect kinetochore proteins associated with sDNA (Moroi et al., 1981; Earnshaw et al., 1984; Hadlaczky et al., 1986; Chaly and Brown, 1988; Holowacz and De Boni, 1991). These observations, together with the fact that such reproducible patterns are not observed in tumors of neurectodermal origin (Manuelidis, 1984a; Cremer et af., 1982) indicate that the observed patterns are related to the functional state of cells and possibly to cell type-specific gene expression. In fact, domains remote from centromeres, such as locus 1~36.3,for instance, may be dynamically and reversibly positioned into transcriptionally active regions in the nuclear interior without cytotypic orientation (Manuelidis and Borden, 1988). In this manner, the relatively fixed, repetitive centromeric and telomeric regions are envisioned to act as general organizing centers, still permitting other chromosome domains to occupy dynamic loci under control of transcriptional demands and possibly permitting efficient processing of both housekeeping and cell specific transcripts. The intranuclear position of those chromatin domains which are apparently fixed, as indicated by their cell type-specific, spatial position can,

a”’

b”’

FIG. 3 Localization by in situ hybridization of satellite DNA in a neuron in the hippocampal CA3 region and in a neuron of cerebral cortical layer 111. (See the text and Billia et al., 1992). A,B. Phase-contrast micrographs of sections showing respective position (arrows) of the neuronal nuclei shown in a’ and b’. Two consecutive, optical sections (2-pm steps) show differences in the cell type-specific number and spatial positions of satellite DNA detected by irnmunofluorescence (a’””, CA3 neuron; b’,b”, cortical neuron). This is also evident in corresponding, computer-assisted 3-D reconstructions (a’ ”, b’ ”, sDNA is stippled, nucleoli are black) of the nuclei shown in a’ and b’. Magnification: A,B; bar= 100 wm. a”,a” ,b’ ,b” ; bar = 5 b m .

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however, be altered to some extent. Neurons within epileptic foci in human cerebral cortex show changes in the intranuclear, spatial positions of specific gene sequences, changes not detected in the same neuronal type in adjacent tissue, outside the epileptic focus (Borden and Manuelidis, 1988). This important finding provides a potential link between positioning of specific gene sequences and neuronal function. The nuclear content thus has been postulated to represent a dynamic system controlled physiological stimuli. A unifying theory for the function of differential chromosome patterns in different cell types has yet to be proposed. Moreover, it remains unclear whether the changes observed in the spatial distribution patterns of specific chromatin domains in interphase nuclei of cells which exhibit altered function are causal in altered function or are merely associative. Nevertheless, the emerging recognition that those physiological stimuli which result in activation of second messenger systems are also associated with rapid changes in gene expression may well provide a functional link between stimuli, altered gene expression, and the associated changes in the intranuclear, spatial position of specific DNA sequences.

IV. The Functional State of Cells and lnterphase Chromosome Patterns

As outlined earlier, a considerable body of evidence indicates that specific chromatin domains in interphase nuclei of cells in uitro may move within the global confines of interphase nuclei. In addition, chromosome patterns in cells in viuo are dynamic, either during differentiation when cells exhibit stage-specific, characteristic patterns of centromeric satellite DNA (Manuelidis, 1985a) or under conditions of altered functional states (Borden and Manuelidis, 1988). Together, these results indicate that rearrangement of the spatial positions of specific chromatin domains may depend upon transcriptional demands of the cell and may be taken to indicate the presence of a potential link between the positioning of specific gene sequences and cell function. Difficulties in interpretation arise when the rate of motion observed as nuclear rotation, which exceeds 0.4 pm/min under certain experimental conditions (Pomerat, 1953; De Boni and Mintz, 1986; Fung and De Boni, 1988; Hay and De Boni, 1991), is contrasted with the reproducible spatial positions of satellite and telomeric DNA sequences in neurons (Manuelidis, 1984a,b; Manuelidis and Borden, 1988; Billia and De Boni, 1991). The possibility must thus be considered that the pronounced saltatory motion of nuclear contents measured as nuclear rotation in cells in uitro

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in general and in neurons in uitro in particular may correlate with the redifferentiation of these cells which occurs following their transfer to in uitro conditions. In contrast, the more selective repositioning of chromatin domains in neurons in situ (Borden and Manuelidis, 1988) may reflect comparatively minor changes in chromatin organization, possibly associated with altered demands in gene expression. These considerations led to the hypothesis that changes in altered cell function in general and in gene expression in particular should be associated with changes in rates of chromatin motion, which is in turn associated with altered interphase chromatin patterns. The available evidence clearly shows that activation of membrane receptors, by neurotransmitters or their agonists, results in changes in gene expression within minutes, both in cells in uitro (Greenberg et al., 1986) and in functional, organotypic cell assemblies where neurotransmitters alter expression of specific neuronal “competence” genes of the proto-oncogene family (Douglas et al., 1988; Cole et al., 1989; Herrera and Robertson, 1990). Associations between activation of receptors by neurotransmitters and altered chromatin patterns have indeed been demonstrated. In dorsal root ganglion neurons in uitro, agents which alter neuronal gene expression, including neurotransmitters, also alter rates of chromatin motion. In these cells, chromatin motion is altered in a dose-dependent, reproducible manner by a-amino butyric acid (GABA), a neurotransmitter to which dorsal root ganglion neurons express receptors (Holz et al., 1986), and by nerve growth factor, with the changes in rates of motion occurring at the same time as the changes in gene expression (Fung and De Boni, 1988; De Boni, 1988a). While it has not been established which mechanism mediates the induced changes in chromatin motion, GABA can activate at least two receptor subtypes on dorsal root ganglion neurons. Of these, receptors of the GABA-A type directly control a chloride channel (Robertson, 1989) while GABA-B responses are mediated by a linking G-protein (Holz et al., 1986; Goh and Pennefather, 1989). It is thus possible that receptor activation and chromatin patterns are linked through a second messenger system-a hypothesis supported by results presented later. Analyses of the three-dimensional distribution of kinetochores by immunocytochemistry, and of centromeric satellite DNA sequences by in situ hybridization in nuclei of murine dorsal root ganglion neurons, showed that the changes in rates of chromatin motion observed in response to receptor activation by neurotrophic ligands were indeed associated with rearrangements of specific chromosome domains (Holowacz and De Boni, 1991). Moreover, in situ hybridization using a biotinylated mouse satellite DNA probe added further evidence for distinct, nonrandom patterns of interphase chromosomes in dorsal root sensory neurons.

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In these cells, kinetochores (Holowacz and De Boni, 1991) as well as satellite DNA sequences (Billia and De Boni, 1991) occur in clusters associated with nucleoli and throughout the nucleoplasm, with kinetochores colocalizing with the corresponding satellite DNA in a distinct orientation with respect to the loci of the satellite DNA. Specifically, nucleolus-associated kinetochores appose the corresponding satellite DNA at the interface between the satellite DNA and the nucleolar border. Nucleoplasmic kinetochores consistently occupied a 5-pm distance from the nuclear center which represented 70% of the spherical nuclear radius. The corresponding satellite DNA loci was frequently associated with the nuclear membrane, with kinetochores located on the surface of the satellite DNA that faced the nuclear interior. Such specific kinetochore-satellite DNA associations suggest a role for kinetochores in satellite DNA organization within the interphase nucleus. However, GABA induced a significant reorganization in the spatial distribution of kinetochores. Following exposure to GABA, the total number of kinetochore signals decreased, compared with controls. This significant change was associated with a decrease in the number of nucleoplasmic signals, that is, a decrease of those signals situated in the spatial domain between the nucleolus and the nuclear membrane. The effect occurred in a dose dependent manner, upon a 1-hr exposure to 0 . 5 , 5 , or 10 mM GABA, and was interpreted to indicate that GABA either induces additional clustering of kinetochores within the nucleoplasmic compartment or, alternatively, that some kinetochores within the nucleoplasmic compartment are relocated to those clusters already associated with the nucleolar periphery. Such a reorganization has been previously described as occurring in mouse Sertoli cells after nucleolar activation (Haaf el al., 1990), and in human lymphocytes where exposure to phytohemagglutinin results in the recruitment of ribosomal DNA sequences into actively transcribing nucleolar organizer regions (Wachtler e l al., 1986). Together the results indicate that reorganization of chromatin at the supramolecular level may occur in response to changes in the physiological state of cells. Alternatively, such reorganization may occur in association with changes in the state of cellular differentiation which are needed to accommodate a new transcriptional state. A body of evidence thus indicates that rearrangement of chromosome patterns may occur in cells in uitro as well as in cells in uivo under pathological conditions (Borden and Manuelidis, 1988). To ultimately assign a functional role to these phenomena, however, it would be necessary to show in intact cell assemblies that changes in the organization of chromatin domains within neuronal interphase nuclei may occur in response to physiological stimuli.

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The hippocampal slice preparation is considered an excellent model for studying of cellular interactions at levels which range from electrophysiology to detailed studies of molecular aspects associated with intercellular signaling. In this preparation, brief electrical stimulation of the perforant path with high-frequency pulses produces a long-lasting increase in the amplitude of the population spike, a phenomenon referred to as long-term potentiation (LTP) (Bliss and Lomo, 1973; Bliss and Gardner-Medvin, 1973). The long duration of LTP, together with the proposed role of the hippocampus in memory (Lynch and Baudry, 1984; Thompson, 1985; Teyler and DiScenna, 1985,1987), has led to the use of LTP as a model in studying the cellular changes associated with learning and memory. Some of these changes include the expression of “immediately early” genes (Cole et al., 1989; Dragunow et al., 1989a,b), RNA synthesis (Goelet et af., 1986), and de n o w protein synthesis (Abraham and Otani, 1989; Frey et af., 1988; Krug et al., 1984; Montarolo et al., 1985, 1986). In fact, LTP is most sensitive to inhibition of protein synthesis during or immediately following stimulation (Stanton and Sarvey , 1984). Inhibition of protein synthesis also prevents LTP-associated changes in synaptic morphology (Petit, 1988), a finding which supports a role for de nouo protein synthesis in LTP. In a test of the hypothesis that a change in compartmentalization of specific chromatin domains is associated with an altered functional state and is not restricted to isolated neurons in v i m , the topology of sDNA sequences was examined by in siru hybridization in conjunction with three-dimensional reconstruction in nuclei of hippocampal CA1 pyramidal neurons exhibiting LTP, and in neurons exposed to bath-applied N-methylD-aspartate (NMDA). This work showed that LTP is associated with a rearrangment of interphase chromatin, indicated by enhanced clustering of satellite DNA sequences (Billia er al., 1992), a clustering similar to that induced in dorsal root ganglion neurons exposed to GABA in uitro (Holowacz and De Boni, 1991). Such clustering was clearly restricted to that neuronal population which exhibited LTP and was absent in dentate neurons within the same slice-neurons which did not exhibit LTP with the experimental paradigm used. Clustering of sDNA sequences occurred regardless of whether LTP was induced by electrical stimulation or hippocampal CAI neurons were activated by NMDA. Moreover, the observation that the effect of NMDA was clearly abolished when the protein kinase inhibitor H-7 was coapplied with NMDA (Billia et al., 1992) suggests a link, through a second messenger system, between agonist-mediated receptor activation and chromatin pat terns.

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The cellular response to extracellular stimulation requires signal transduction to the nucleus via second and third messenger systems, and a recognition mechanism by which a subset of genes can be activated or repressed. Evidence exists which shows that calcium may be part of such a system. Changes in intracellular calcium concentrations alter rates of chromatin motion (Fung and De Boni, 1988) and it has been reported that a stimulated rise in intracellular calcium is greater in the nucleus than in the cytoplasm (Przywa e? al., 1991). These results add to a body of evidence which shows that the activation of the NMDA receptor leads to an increase in intracellular calcium (Kuba and Kumamoto, 1990; Lynch e? at., 1983; MacDermott e? at., 1986). This increase triggers events which lead to consolidation of LTP through protein kinase C, which in turn activates phosphorylation of nuclear transcription factors (Schonthal, 1990). Together, these observations of selective chromatin rearrangments in cells within complex neural networks, such as the hippocampal slice preparation, suggest that chromatin motion is not an event restricted to isolated cells in vitro. They also show that changes in interphase chromosome patterns are induced by physiological stimuli and are possibly mediated by second messenger systems, as postulated earlier.

V. An lntranuclear Motor: Contractile Proteins in lnterphase Nuclei

The mechanisms for generating the motive force involved in chromatin motion and rearrangement are unknown. It had previously been suggested that chromatin motion in cells may be driven by an extranuclear, cytoplasmic, actin-based motor (Leone et al., 1955; Paddock and AlbrechtBuehler, 1986a). This was based upon the demonstration that cytoplasmic actin filaments in 3T3 cells undergo reorganization at the same time as changes in the rates of chromatin motion. This hypothesis is, however, contradicted by the repeatedly reported observation that chromatin motion may occur independently of concurrent motion of juxtanuclear, cytoplasmic structures (Albrecht-Buehler, 1984; De Boni and Mintz, 1986; Hay and De Boni, 1991) and the demonstration that specific chromatin domains such as nucleoli may move relative to each other (see earlier discussion and Park and De Boni, 1991). Moreover, dorsal root sensory neurons in uitro, which exhibit significant chromatin motion, have no, or only trace amounts of, filamentous actin within the somata (Hay and De Boni, 1991). While antiactin antibody detected actin

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throughout somata and neuronal processes, fluorescein-labeled phalloidin, which is selective for f-actin (Estes et al., 1981), failed to decorate actin within somata. It did, however, react with f-actin in neuronal processes and in the cytoplasm of underlying non-neuronal cells in the same cultures (Hay and De Boni, 1991). The absence of f-actin within neuronal somata thus makes it unlikely that cytoplasmic actin acts on chromatin motion. This leads to the conclusion that there is adistinct possibility that the motor postulated to drive chromatin motion may be located in the subcellular compartment enclosed by the inner nuclear membrane-the karyoplasm. Biochemical analyses clearly show that actin and myosin are constituents of the nonhistone protein fraction of interphase nuclei and of isolated nuclear matrices (Ohnishi et al., 1963; 1964; Jockusch et al., 1974; Hauser et al., 1975; LeStourgeon et al., 1975; Clark and Merriam, 1977; Fukui, 1978; Bremer et al., 1981; Capco et al., 1982; Nakayasu and Ueda, 1983, 1984, 1985, 1986; Brasch, 1990), including a chemically distinct ic.,o form of actin found in isolated nuclei (Bremer et al., 1981; Kumar et al., 1984). A significant fraction of actin in interphase chromatin has been shown to exist in the f-actin form (Clark and Rosenbaum, 1979). This is supported by ultrastructural studies employing phalloidin-gold complexes, which have shown that the nucleoplasm of Physarum polycephalum cells is the most heavily labeled of all cellular compartments (Lachapelle and Aldrich, 1988). Both actin and myosin have been shown to be a constituent of the nuclear matrix (Douvas et al., 1975; Wunderlich and Herlan, 1977; LeStourgeon, 1978; Fukui, 1978). Actin has been shown to be associated with the nucleolus (Hauser et al., 1975), and a specific association of myosin I has been demonstrated with the inner nuclear membrane (Rimm and Pollard, 1989). While the function of these proteins is open to speculation, it was suggested that they might function in changes of nuclear shape (Horowitz et al., 1986), in chromatin condensation (Rungger et al., 1979), in nucleocytoplasmic transport (Schindler and Jiang, 1986; Ueyama et al., 1987), in gene expression (LeStourgeon et al., 1975), and as a transcription initiation factor (Egly et al., 1984; Scheer et al., 1984; Ankenbauer et al., 1989). Criticisms that nuclear actin is in equilibrium with cytoplasmic actin and that it is without function (Goldstein et al., 1977) were challenged by the finding of a form of actin specific to nuclei (Bremer et al., 1981; Kumar et al., 1984). In this work, analyses of actin derived from nuclear fractions indicated that nuclear actin, while similar to cytoplasmic actin, is chemically distinct. These same authors also found that nuclear and skeletal muscle actins are similar and have suggested that nuclear actin has the

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capacity to interact with myosin and thus has a potential function in force generation. Evidence for a second contractile protein within nuclei, myosin, which is associated with the nuclear envelope (Berrios and Fisher, 1986), was confirmed by the purification and characterization of a nuclear actinbinding protein in Acanthamoeba (Rimm and Pollard, 1989). This nuclear actin-binding protein is antigenically related to myosin I, although it does not exhibit most of the characteristics that define myosins, such as actinactivated ATPase and ATP-sensitive actin binding. Nuclear actin-binding protein does, however, exhibit binding to DNA, while actin, myosin I, and alpha-actinin do not. This nuclear actin-binding protein represents the first actin-binding protein to be localized exclusively to the nucleus, although its function is not yet known. Rimm and Pollard (1989) propose that this protein may attach DNA to the actin-containing nuclear matrix, as previously postulated (Armbruster et al., 1983; Nakayasu and Ueda, 1983,1985,1986;Crowley and Brasch, 1987). Despite this accumulated body of biochemical evidence which localized actin to interphase nuclei at relatively high concentrations, its precise intranuclear localization remained obscure. Recent and continuing work using laser confocal immunocytochemistry and immunogold techniques at the ultrastructural level, has shown, however, that actin and myosin occur as aggregates in nuclei of intact neurons (Milankov el al., 1991; Milankov and De Boni, 1993). Specifically, actin-like and myosin-like antigens were demonstrated to be present as aggregates in nuclei of fixed but intact neurons maintained in v i m , as well as in nuclei of neurons within intact sensory ganglia. Threedimensional reconstruction from confocal images as well as ultrastrucural localization place some of these aggregates at the nucleolar periphery, from where actin also extends into the nucleoplasm along chromatin fibers. Labeling with fluorescent-palloidin shows that only those actin aggregates associated with the nucleolar periphery contain sufficient f-actin to be detectable by phalloidin. It is of interest to note that use of antibodies against subclasses of alphaactin isoforms indicated that nuclear actin is more closely related to an alpha-sarcomeric isoform than to smooth muscle actin. This was indicated by decoration of nuclear actin aggregates by an antibody to alphasarcomeric actin, including a highly specific monoclonal antibody, but not by a highly specific antibody against a synthetic decapeptide unique to smooth-muscle actin. In contrast, actin in neuronal cytoplasm was labeled with antibody to smooth-muscle actin. Given the evidence for the occurrence of actin as well as myosin aggregates within interphase nuclei, it remained to be demonstrated that the

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intranuclear f-actin present has the capability to functionally interact with myosin. The existence of such an interaction is indicated by the ultrastructural localization of arrowhead patterns in nuclei of mildly fixed and perme1991), abilized neurons labeled with heavy meromyosin (Milankov et d., or by heavy meromyosin conjugated to colloidal gold (Amankwah and De Boni, 1994). Such labeling resulted in the decoration of putative intranuclear microfilaments typical of actin decorated by heavy meromyosin (Tshikawa et al., 1969; Schloss et al., 1977). In summary, the demonstrated presence of actin and myosin aggregates in interphase nuclei, together with the observation that nuclear actin may interact in a typical manner with a fragment of myosin, supports the hypothesis that these macromolecules may be the motor responsible for chromatin motion and the formation of chromatin patterns.

VI. Conclusions

The combined results of the work decribed in this chapter show that interphase nuclei exhibit cell type-specific, reproducible compartmentalization of specific DNA sequences such as sDNA, transfer DNA, and others, as well as compartmentalization of nucleoli and kinetochores. The results also indicate that such compartmentalization is dynamic, both during differentiation and during changes in functional state induced by physiological stimuli. The hypothesis that the spatial, intranuclear sites of pre-mRNA processing and transcription may differ between cell types and that the functions of small nuclear ribonucleoproteins (snRNPs) and actin within interphase nuclei may be related is supported by recent work by Sahlas and co-workers. In fact, rat pheochromocytoma cells, when differentiated into neuron-like cells with nerve growth factor, exhibit a snRNP topology which is clearly distinct from that which is observed in the same cell type before exposure to nerve growth factor. Moreover, based on quantitative evidence of changes in the extent of the association between snRNP and actin aggregates, it may be concluded that the functions of snRNPs and intranuclear actin may indeed be dynamically related (Sahlas et al., 1993). While the nature of the intranuclear motor which translocates specific chromatin domains during interphase remains enigmatic, the presence of intranuclear aggregates of actin and myosin, together with the demonstration that nuclear actin may functionally interact with myosin, suggests that actomyosin complexes may provide the motive force required for chromatin motion and thus patterning of chromatin in interphase nuclei. The demonstration of multiple intranuclear aggregates of such actomyosin

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complexes could also account for the forced harmonic motion described earlier, which is associated with the postulated multiple levels of control (see Section 11). The mechanisms that control chromatin motion remain enigmatic. Changes in intracellular calcium concentrations do, however, alter rates of nuclear rotation (Fung and De Boni, 1988). It may thus be speculated that one level of control may be related to the cycling, free calcium levels reported to occur in nuclei of excitable cells (Przywara et al., 1991). A vast amount of DNA within a nucleus must be dynamically organized and requires a structural system to coordinate the expression of genes which make life possible (Pienta et al., 1991). The definition of exact functional associations between the supramolecular organization of chromatin and cell function in general and gene expression in particular requires much additional effort but may ultimately lead to a critical test of the hypothesis that there is a causal link between chromatin motion and its organization into a pattern which permits gene expression.

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Cellular Tensegrity: Exploring How Mechanical Changes in the Cytoskeleton Regulate Cell Growth, Migration, and Tissue Pattern during Morphogenesis Donald E. Ingber, Laura Dike, Linda Hansen, Seth Karp, Helen Liley,* Andrew Maniotis, Helen McNamee, David Mooney,t George Plopper, John Sims, and Ning Wang** Departments of Pathology, Surgery, and the *Joint Program in Neonatology, Children’s Hospital and Harvard Medical School, Boston, Massachusetts 021 15; +Departmentof Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139; and **Respiratory Biology Program, Harvard School of Public Health, Boston, Massachusetts 021 15

1. Introduction How do cells regulate their growth and form? What are the basic principles of tissue construction? How is biological pattern generated? Is there any unifying theory of organic design? These are the fundamental questions that led to the emergence of the modern field of biology almost two centuries ago (Lenoir, 1982). Developmental morphologists initially thought that the forces that guide pattern formation resulted from physical interactions between different biological materials (Needham, 1968; Thompson, 1977; Lenoir, 1982). In essence, these early biologists viewed the problem of biological organization as a question of mechanics. However, as the dominance of mechanics in physics waned, the mechanical approach in biology also lost favor. Soon greater emphasis was placed on chemical analysis, characterization of molecular determinants, and, more recently, on the sequencing of specific genes. This reductionist approach resulted in identification of thousands of molecules that appear to be involved in morphogenetic regulation, including the three major classes of biopolymers that comprise the intracellular cytoskeleton (CSK): microfilaments (MFs), microtubules (MTs), and intermediate filaments (IFs). Major advances also have been made in terms of characterizing chemical mechanisms that are used to regulate the polymerization of these individual polymers (Stossel, 1989; Mitchison, 1992). Yet, we still do International Review of Cytology,Vol. I50

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not understand how these different CSK filament systems interact and assemble in three dimensions so as to create cells that change shape, divide, polarize, and move. In other words, the basic laws of cell and tissue architecture remain to be defined. It is becoming increasingly clear that what caught the attention of early developmental morphologists is essentially true. While chemicals mediate morphogenesis, mechanical forces also play a major regulatory role. Generation of tissue pattern in the embryo requires that local differentials in cell shape and mechanical stresses be established so that tissue bending and expansion can proceed (Beloussov et al., 1975; Thomspon, 1977). These transformations are driven by tensile forces that are generated within the CSK. Exogenous mechanical loads also are important determinants of tissue pattern (Ingber, 1991a). For example, in bone, the extracelMar matrix (ECM) that surrounds cells is deposited along lines of tension and compression that are characteristic for any structure of that shape and size with similar load-bearing properties (Koch, 1917). Mechanical forces due to blood pressure and flow similarly mold the cardiovascular system (Russell, 1982) and intrathoracic forces are critical for normal lung development and function (Rannels, 1989; Stamenovic, 1990). We now know that tissues are dynamic structures and that remodeling is regulated by their consituent cells. Thus, somehow individual cells must be able to recognize and respond to mechanical stress by remodeling their ECM and changing their own shape and orientation, until the preexisting force balance is regained. These structural changes result from coordinated alterations in the “extended CSK,” that is, the continuous molecular support scaffolding that stretches from nucleus to CSK to nucleus, across the ECM and intercellular junctions, and physically integrates all cells and nuclei within complex tissues (Fig. 1). Thus, an explanation of morphogenetic regulation will require an understanding of how forces are transmitted through this extended CSK as well as how this complex lattice responds to mechanical stress. This chapter focuses on the role of the CSK in cell shape determination and tissue morphogenesis. We first briefly review what is known about the role of mechanical changes in the CSK during embryological development. We then concentrate on the mechanism by which mechanical forces are transmitted across the cell surface and through the CSK, as well as how they regulate cell shape. An analysis of the biomechanical basis of cell shape control leads us directly to two central questions: (1) How do changes in mechanical forces alter CSK organization? (2) How do changes in CSK structure regulate cell growth and function? To answer these questions, we review results from recent studies which show that the CSK can respond directly to mechanical stress. We show that the particular type of mechanical response that living cells exhibit is consistent with a theory of CSK architecture that is based on tensional integrity and is known as

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FIG. 1 The extended cytoskeleton. The intracellular CSKs of neighboring epithelial and mesenchymal cells physically connect through cell-cell junctions and adhesive contacts to a common basement membrane scaffold. This structural continuum must be continuously remodeled in order for morphogenesis to proceed. This hand-drawn depiction shows the appearance of the extended CSK after all membranes and soluble proteins are removed. (Based on work from many laboratories, including Wolosewick and Porter, 1979; Fey er al., 1984; Green et a / . , 1986; Bershadsky et al., 1987.)

“tensegrity.” Inherent to the tensegrity model is an efficient mechanism for integrating changes in structure and function at the tissue, cell, nuclear, and molecular levels. We explore the possibility that CSK tensegrity may also provide a mechanical basis for cell locomotion as well as a structural mechanism for coupling mechanical and chemical signaling pathways inside the cell. In this manner, we hope to begin to define basic principles of cell and tissue architecture and, in the process, formulate testable hypotheses relating to morphogenetic regulation that may be addressed experimentally in the future.

II. Mechanical F o r c e s and Establishment of Tissue P a t t e r n Much recent work on control of embryological development has focused on the role of genetic and chemical regulators (e.g., homeobox genes, soluble growth factors). However, the developing embryo also exhibits

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dramatic changes in tissue structure and pattern that result from the action of mechanical forces (Beloussov et al., 1975). Mechanical tension is generated within the CSK of individual cells and transmitted throughout developing tissues, initially through cell-cell contacts and later via cell-ECM adhesions as well (Takeichi, 1991; Edelman, 1992; also see the following discussion for more details). In this chapter,we explore the mechanism by which these changes in mechanical stresses regulate histogenesis. However, first we need to briefly review how tissue pattern first becomes established in the early embryo. The first time in development that mechanical interactions become visible is in the eight-cell stage when compaction occurs; the previously loose cluster of spherical cells becomes contracted within a tight ball. At this point in development, all of the cells are interconnected through homotypic interactions among transmembrane cadherin receptors that mediate cell-cell contact formation (Winkel et al., 1990). However, when the inner cells exert tension to produce compaction, they “feel” the mechanical resistance of neighboring cells on all sides, whereas when the outer cells pull, they are resisted only along their inner and lateral borders. At the same time, the axis of cell polarity is first established. It is interesting that the primordial cell orientation occurs only in cells at the periphery of the cell cluster; no polarity develops in the central cells (Johnson and Ziomek, 1981). Whether a mechanical change per se is responsible for this polarization remains to be determined experimentally. However, internal mechanical transformations clearly play a major role during subsequent remodeling of the embyro. For example, during gastrulation, changes in mechanical stresses cause entire cell layers to bend inward and invaginate while others fold outward (Beloussov et al., 1975). The cell shape changes that drive this remodeling result directly from mechanical interactions within the CSK of the cells that comprise these tissues (Granholm and Baker, 1970; Beloussov et al., 1975; Keller, 1981). Gastrulation can also be redirected by applying external mechanical force (Beloussov et al., 1988) or by genetically disrupting IFs which normally support mechanical loads that are generated by cells and transmitted throughout the growing embryo (Torpey et al., 1992). Cytoskeleton-based cell shape transformations also drive bending of epithelial tissues and pattern remodeling during neurulation (Burnside, 1971 ;Gordon and Brodland, 1987). Mechanical tension is generated within contractile MFs in each cell apex and resisted both by intracellular axial MTs and by extracellular junctional contacts that connect the apical borders of neighboring cells. A purse string-like contraction within the apex of each cell becomes amplified throughout the interconnected cell layer so that changes in cell shape (from columnar to fan-shaped) and subsequent outward bending of the entire neural epithelium result. Neural crest cell

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migration is also mediated by cell-ECM interactions (Duband et ai., 1986) which likely involve transmission of mechanical force (Harris et al., 1980). In other tissues (e.g., salivary gland), the stability of tissue morphology has been shown to require both CSK tension (Spooner and Wessells, 1972; Ash et al., 1973) and the continued presence of an ECM resisting scaffolding (Banejee ef al., 1977). Establishment of a stable force balance between cells and their ECM is also critical for maintenance of specialized tissue architecture in the adult (reviewed in Ingber, 1991a).For this reason, cells lose their specialized forms and round when removed from their ECM attachments (e.g., during dissociation of whole tissues using proteolytic enzymes). It is interesting, that when embryonic epithelia and mesenchyme are isolated from different tissues and then recombined, it is the mesenchyme that dictates tissue pattern (Sakakura et al., 1976). For example, mixing mammary epithelium with kidney mesenchyme results in development of tubular structures which are lined by cells that secrete milk proteins. The opposite tissue mix produces acini-containing cells that transport sodium and water. It is important to note that variations in the pattern-directing behavior of different mesenchymes correlate with their ability to generate mechanical tension (Nogawa and Nakanishi, 1987). The mechanical resistance of the ECM and its ability to modulate epithelial cell shape may therefore be fine tuned by additional mechanical stresses that are transmitted to the ECM from surrounding mesenchyme (Ingber and Jamieson, 1985). In fact, during morphogenesis of glandular organs (e.g. , pancreas), the adjacent mesenchyme condenses (contracts) at the same time that the nearby epithelium buds outward from the primitive gut. It is possible that mechanical forces that are generated within the mesenchymal cell CSK could be responsible for both morphogenetic events, that is, physical compaction of the mesenchyme and outward pulling on the epithelial ECM (i.e. ,basement membrane). The importance of cell-generated tractional forces in the development of mesenchymal tissue patterns is already well established (Harris et al., 1980, 1981; Stopak and Hams, 1982; Stopak et al., 1985; Nogawa and Naganishi, 1987: Ettinger and Doljanski, 1992). One example of how mechanical changes in the CSK can influence mammalian development comes from examining patients with Kartagener’s syndrome who exhibit a mutation in the gene that codes for dynein. Dynein is an MT-associated motor protein that is involved in generation of the mechanical force that drives MT bending in specialized CSK structures, such as flagella. In these patients, sperm are not motile, mucus clearing is defective because of dysfunctional respiratory cilia, and most impressively, the organs of the thorax are completely reversed (i.e., the heart is on the right instead of the left). This real-life example clearly

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shows how a molecular alteration that influences the mechanical properties of a single structural element within the CSK can be amplified to alter the development of tissue and organ patterns. Finally, a discussion of the importance of physical forces in pattern formation could not end without mention of plant morphogenesis. The long-recognized “gravitropic” behavior of plants clearly demonstrates the critical role that mechanical forces can play in the establishment of three-dimensional tissue form. This appears to be the result of a direct effect at the cell level since application of mechanical loads also induces reorientation of the axis of cell division in cultured plant explants (Lintilhac and Vesecky, 1984). These changes in growth pattern may be transduced through the CSK since the nuclear division axis in plants is normally determined by the location of a series of CSK filaments that stretch from the nucleus to the cell periphery (Flanders et al., 1990).

111. Transmembrane Mechanical Coupling within the Extended Cytoskeleton

To understand how individual cells sense and transmit physical forces that regulate morphogenesis, we must first identify the molecular path by which these forces are transferred across the cell surface. As in any architectural structure, mechanical loads are transmitted throughout tissues across structural elements that are physically interconnected. Thus, one would expect mechanical forces that are applied to whole tissues (e.g., blood pressure in vessels) to be transferred to individual cells through their interconnections with their surrounding ECM, which forms the support scaffolding that holds all tissues together. Cells attach to ECM by binding to specific transmembrane ECM receptors, such as integrins. Integrins are members of a superfamily of cell surface receptors that were first identified by their ability to bind to a specific three-amino-acid sequence (RGD) that is found within many ECM proteins (Hynes, 1987; Ruoslahti and Pierschbacher, 1987; Albelda and Buck, 1990). Each integrin receptor contains one a and one /3 subunit; the combination of different subunit types provides molecular specificity (e.g., aspl recognizes fibronectin, a$, recognizes collagen). The intracellular portion of certain /3 integrin subunits (e.g., p,) binds to actinassociated proteins (e.g., talin, vinculin, paxillin, a-actinin) and thereby physically interconnects ECM with the CSK (Burridge el af.,1988; Turner and Burridge, 1991). Any molecular link that physically interconnects transmembrane receptors with CSK elements could provide a potential path for transmitting

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mechanical force across the cell surface. Integrins are one example, but there are others. For example, another cell surface ECM receptor, the heparan sulfate proteoglycan, syndecan, also appears to interconnect with the actin CSK (Bernfield et al., 1992). In addition to ECM contacts, MF and I F networks of adjacent epithelial cells also structurally interconnect (Fig. 1) by binding to common junctional structures (adherens zonules and desmosomes, respectively) along the lateral cell borders (Fey et al., 1984). Cadherins, cell adhesion molecules (CAMS), and other cell-cell adhesion molecules (Albelda and Buck, 1990; Takeichi, 1991 ; Edelman, 1992), most likely mediate the transfer of force in these regions. However, before addressing the question of how cells sense external forces, it is important to emphasize that activation of a cellular response does not result from transmission of mechanical loads to a cell which previously experienced none. All cells are prestressed structures in that they generate mechanical force within their CSK and exert tension on their ECM adhesions. For this reason, cultured cells physically contract malleable ECM gels (Emerman and Pitelka, 1977; Ingber and Jamieson, 1985; Li et al., 1987; Mochitate et al., 1991) and pull flexible silicone rubber substrata up into “compression folds” (Harris et al., 1980; Harris, 1982). Calculations of the force exerted on individual cells by what we normally consider large-scale forces, such as gravity, reveal that it can be many times less than that which is generated within the CSK and resisted by the ECM (James and Taylor, 1969; Albrecht-Buehler, 1990). The critical point here is that CSK tension is the major force acting on adherent cells and thus, all external mechanical loads are imposed on a preexisting force balance. If this were not true, then many physiological stresses (e.g., shear in blood vessels) would cause cell detachment and death.

IV. Control of Cell Shape and Function by Alterations in the Cytoskeletal Force Balance

What happens when the cellular force balance is altered? One way to accomplish this is by physically stretching or compressing cells and tissues. Past studies clearly show that these types of mechanical perturbations have dramatic effects on cell form, growth, gene expression, and production of specialized cell products (reviewed in Ingber, 1991a). However, these complex systems are very difficult to analyze, especially at the molecular level. Cells also spontaneously change both their force balance and function when they are cultured on ECM substrata that differ in mechanical integ-

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rity (Fig. 2). In general, cells express tissue-specific functions and fail to proliferate when attached to malleable ECM gels, yet the opposite result is obtained (low differentiation and high growth) when the same ECM molecule is coated on a rigid plastic dish (Michalopoulos and Pitot, 1975; Bissell et al., 1987; Li et al., 1987; Ben Ze’ev et af., 1988; Opas, 1989; Vernon et al., 1992). The major difference between malleable ECM gels and rigid ECM-coated dishes is their ability to resist cell tractional forces and thus, support tension-dependent changes of cell shape (Ingber and Jamieson, 1985; Li et al., 1987; Vernon et al., 1992). Cells extend and flatten on rigid surfaces that can resist CSK tension but remain round on flexible substrata. However, the effect of cell spreading on function is not “all or none.” For instance, cell growth increases in a dose-dependent manner when cell extension is progressively promoted by raising ECM coating densities (Ingber, 1990). Thus, the term “cell shape” as used in this chapter does not refer to a specific form (e.g., round versus bipolar or polygonal); rather, it relates to changes in the actual degree of cell extension. This parameter can be easily quantitated by measuring changes in projected cell areas. Direct evidence for the importance of the cellular force balance in determination of cell shape comes from a recent study using membranepermeabilized cells (Sims et al., 1992). Cells that adhered to ECM-coated dishes underwent dramatic changes in shape after they were permeabilized with saponin when a CSK-stabilization buffer that maintains the contractile function of MFs was used. When calcium and adenosine triphosphate (ATP) were added, the cell, CSK, and nucleus all retracted in acoordinated manner even though there was no membrane integrity and thus, no osmotic pressure difference across the cell surface (Fig. 3). Retraction of these ATP-stimulated cells could also be enhanced by dislodging integrin receptors from outside the cell using soluble GRGDSP peptide. This treatment increased both the rate and extent of cell and nuclear retraction. However, Growth

Differentiation

Malleable

t

t

Rigid

t

t

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ECM Gel

FIG. 2 Control of cell growth and differentiation by altering ECM mechanics. In general, cells remain quiescent and differentiate when they are cultured on malleable ECM gels that permit cell retraction and rounding. In contrast, the same cells spread, grow, and lose specialized functions when cultured on rigid ECM substrata. (Based on work from many laboratories, including Emerman and Pitelka, 1977; Li et a / . , 1987; Opas, 1989; Mochitate et al., 1991; Vernon et al., 1992.)

FIG. 3 Integrated changes in cell, CSK, and nuclear shape in living and membrane-permeabilized cells. Time-lapse video micrographs which show the process of cell and nuclear rounding in (a-d) a living cell following trypsinization and (e-h) a cell made permeable with saponin that was exposed to medium containing calcium and ATP. Note that the cell and nucleus retract in a coordinated manner under both conditions. (See the text and Sims et al., 1992 for more details.)

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soluble GRGDSP had little effect in the absence of ATP, that is, when the cells had no internal tension. Furthermore, cell and nuclear retraction were prevented by a synthetic myosin peptide (IRICRKG) that interferes with actomyosin binding and prevents rigor complex formation. Thus, these results confirm that the structural stability of the cell depends on a dynamic balance of mechanical forces. Mechanical tension is generated within contractile MFs through actomyosin interactions, transmitted across transmembrane integrin receptors, and resisted by fixed ECM anchoring points. When this CSK force balance is altered, integrated changes in cell, CSK, and nuclear shape result. This study (Sims et al., 1992) provides perhaps the best evidence to show that changes in nuclear shape also result directly from the action of mechanical tension that is generated by actomyosin interactions. Nevertheless, arguments have been raised to suggest that mechanical changes that are associated with cell shape changes do not control switching between growth and differentiation but instead, that they are just parallel events. For example, contraction of malleable ECM gels also promotes formation of cell-cell contacts (Bissell et al., 1987; Ben Ze’ev et al., 1988), which are thought to be important for tissue function (Mesnil et al., 1987; Goulet et al., 1988). Other culture conditions which increase cell-cell contact formation, such as the use of high cell plating densities (Ben-Ze’ev et al., 1988) or poorly adhesive substrata (Landry et al., 1985; Koide et al., 1990; Tong et al., 1990), also stimulate differentiation and suppress growth in certain cell types. On the other hand, all of these culture conditions also permit cell rounding and thus allow mechanical stress to be dissipated. Similar arguments relating to causality were raised following the initial demonstration by Folkman and Moscona (1978) and others (Maroudas, 1973; Ben Ze’ev et al., 1980) that growth is tightly coupled to cell shape. One reason for concern was that poorly defined substrata (e.g., tissue culture dishes, complex ECMs) and serum-containing medium were used in these early experiments. Thus, it was not possible to determine whether cell spreading (i.e., a mechanical change) directly promoted growth, whether cells became sensitive to different classes of growth factors when substratum adhesivity was altered, or whether cell growth was regulated indirectly through de nouo deposition of ECM molecules beneath the cells. To approach this question directly, we developed a more defined method to alter the cellular mechanical force balance and control cell shape. The approach we chose was to vary the density of the cell’s ECM attachment points and thus the number of sites that can physically resist cell tractional forces (Fig. 4). To accomplish this, cells were cultured on bacteriological plastic dishes that were precoated with varying densities of a single type of purified ECM molecule (e.g., fibronectin, laminin, or differ-

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can be switched between growth and differentiation by increasing the density of a single type of purified ECM ligand that is coated on an otherwise nonadhesive bacteriological plastic dish. In general, growth increases and differentiation-specific functions (e.g., gene expression) decrease in direct proportion as the ECM coating density is raised and cell spreading is promoted. (Based on work in Ingber and Folkman, 1989a; Ingber, 1990; Mooney e l al., 1992a,b.)

ent collagen types). Serum was specifically excluded from these studies because it contains numerous growth factors as well as two highly adhesive ECM proteins, fibronectin and vitronectin. Instead, a chemically defined medium containing a constant and saturating concentration of soluble mitogen was used (Ingber and Folkman, 1989a; Ingber, 1990; Mooney et al., 1992a,b). These studies revealed that a variety of different purified ECM rnolecules, derived from both basement membrane (laminin, type IV collagen, fibronectin) and interstitial matrix (type I collagen, gelatin, fibronectin), share a common mechanism for switching cells between growth and differentiation that is based on their ability to modulate cell shape (Fig. 4). On low ECM densities that prevented cells from spreading, capillary cells formed tubes (Ingber and Folkman, 1989a) and hepatocytes expressed high levels of albumin mRNA as well as increased secretion of multiple liver-specific proteins (Mooney et al., 1992a). In contrast, loss of differentiated functions and concomitant upregulation of growth were observed on high ECM densities that supported extensive cell spreading whether endothelial cells or hepatocytes were used (Ingber, 1990; Mooney et al., 1992a). More recently, a similar correlation between cell shape and growth was obtained using pulmonary vascular smooth muscle cells. The importance of this fundamental regulatory coupling between cell shape and growth becomes most clear when it is lost. For example, uncoupling between cell shape and proliferation forms the basis for anchorageindependent growth (Wittelsberger et al., 1981), which is the hallmark of neoplastic transformation (Shin et al., 1975). Thus, while soluble growth factors stimulate cell proliferation, rnechanical changes may control cell shape and growth responsiveness locally and thereby establish the local growth differentials that are responsible for the development of tissue patterns (Ingber and Jamieson, 1985; Ingber

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and Folkman, 1989a,b). In fact, tight coupling between changes in cell shape and alterations in growth is observed during angiogenesis in uiuo (Folkman, 1982; Ingber, 1991b) as well as in uitro (Ingber and Folkman, 1989a).However, large-scale changes in cell shape are not always apparent during growth and expansion of other tissues, at least when viewed using histological sections. It is important to note that cells may change their force balance and even physically enlarge or shrink without changing their shape. For example, a large round cell can become a small round cell if the surrounding ECM is flexible. Alternatively, a cell that is confined within a relatively rigid ECM (e.g., cartilage, bone) may vary the level of isometric tension within its CSK without any obvious expansion of cell volume or change in cell borders. Increasing tension to high levels within the CSK while maintaining fixed ECM adhesions could cause outward pulling on the central nucleus and result in nuclear extension. This possibility is important because nuclear enlargement appears to be a prerequisite for entry into S phase (Yen and Pardee, 1979; Nicolini et al., 1986; Ingber et al., 1987) and histological sections reveal that proliferative cells exhibit larger nuclei in uiuo (Jacobi et al., 1982) as they do in uitro (Ingber et al., 1987). Finally, the degree to which a normal cell must spread in order to grow and thus, its sensitivity to mechanical forces, also may vary greatly. Hepatocytes are completely growth inhibited when they are round whereas lymphocytes retain the ability to proliferate when they are spherical and in suspension. However, even suspended lymphocytes may need to pull on a resisting substratum, in this case the cell membrane of another cell (e.g., macrophage), in order to respond to soluble stimuli and proliferate. Chondrocytes similarly retain the ability to proliferate when they are round and pulling on their own hydrated proteoglycan-rich ECM gel, yet these cells grow more rapidly when they are physically extended on a rigid substrate (Glowacki et al., 1983). In the absence of any anchorage to ECM, normally adherent cells lose viability, undergo apoptosis, and die (Meredith et al., 1993). This “selective suicide” mechanism actually may be used when dissolution of the basement membrane is induced during physiological involution of certain tissues (Wicha el al., 1980; Ikawa et al., 1984; Ingber et al., 1986; Talhouk et al., 1992). In summary, the large-scale alterations in shape that are commonly observed in cultured cells are essentially a visual manifestation of underlying changes in the CSK force balance. A rigid substratum that is highly adhesive can effectively resist CSK tension and promote cell, CSK, and nuclear extension, whereas malleable substrata cannot. This is an important difference because most cultured cells must spread in order to grow. In living tissues, cells are sometimes surrounded by a relatively rigid ECM. Under these conditions, changes in the CSK force balance

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may alter subcellular structure and thereby influence cell function without a global change in cell shape. In other words, regulatory information may be provided to the cell as a direct result of changing the CSK force balance, rather than being due to a specific alteration in cell size or form. However, this has been a difficult hypothesis to prove since cell shape and CSK tension are tightly coupled in uitro and are very difficult to separate experimentally.

V. Cytoskeletal Response t o Mechanical Stress We recently set out to address the question of whether the cellular response to force is elicited by a specific change in cell shape or if the CSK can sense direct transfer of mechanical loads (Wang et al., 1993). First, a new method had to be devised in which defined mechanical stresses could be applied directly to transmembrane ECM receptors without producing large-scale changes in cell shape. This was accomplished in collaboration with Jim Butler (Harvard School of Public Health) by adapting a magnetic twisting device that was previously developed by Peter Varberg to measure viscoelasticity within the cytoplasm of living cells. In our modification of this technique, adherent endothelial cells were allowed to bind to spherical ferromagnetic microbeads (5.5 pm diameter) that were precoated with specific cell-surface receptor ligands. After 1015 min (while the beads were still on the cell surface), the magnetic moments of the beads were aligned by applying a brief but strong external magnetic field (1000 gauss for 10 psec). The weak magnetic field produced by the beads themselves (remanent field) was measured in the same direction of magnetization using a sensitive in-line magnetometer. A weaker, but sustained, twisting field was then applied at a 90"orientation to apply mechanical torque (shear stress) to the aligned beads. In the absence of resistance, the beads would rotate completely (90") and thus, the remanent field vector measured in the original direction would rapidly drop to zero. In this manner, resistance to rotation exerted by associated CSK elements could be quantitated by measuring changes in the rate and degree of bead reorientation in the new direction. When cells were allowed to bind beads coated with a synthetic RGD peptide that is a ligand for many integrin receptors, greater resistance to mechanical deformation was observed as the level of force applied across integrins was increased. In other words, the CSK became much stiffer at high levels of applied stress (Fig. 5 ) . We also could show that beads coated with antibodies directed against a single type of transmembrane ECM receptor, integrin PI, exhibited similar stiffening behavior. The specificity

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STRESS (dynes/cm*) FIG. 5 CSK stiffening in response to mechanical stress applied using the magnetic twisting device. Note the linear relationship between stiffness (the ratio of stress to strain) and the stress applied to integrin receptors using beads coated with RGD peptide. In contrast, no stiffening was observed with beads coated with acetylated low-density lipoprotein (AcLDLbead) that bind to cell surface scavenger receptors. Cyt, cytochalasin D (0.1 pg/ml); Noc, nocodazole (10 pg/ml); Acr, acrylamide (4 m M ) . At these doses, each CSK modulating drug only altered the morphology of its respective target filament system when analyzed by immunfluorescence microscopy (not shown). (This figure is based on work described in N. Wang et al., 1993.)

of force transmission was confirmed by the finding that beads coated with nonspecific ligands, such as acetylated low-density lipoproteins (AcLDL) or bovine serum albumin, bound cell surface receptors; however, they did not support a significant stiffening response (Fig. 5 ) . Beads coated with integrin ligands also induced formation of focal adhesions containing talin, vinculin, and a-actinin along the surface of the beads, whereas beads coated with nonspecific ligands did not. As described earlier, these actinassociated proteins form the molecular bridge that physically links integrins with actin MFs. Finally we could confirm that the stiffening response resulted from transfer of force to the actin CSK since cytochalasin D (cyto D), a drug which disrupts MF lattice integrity, greatly suppressed the stiffening response (Fig. 5). Taken together, these results suggest that at least one type of transmembrane ECM receptor, /3l integrin, can act as a cell surface mechanoreceptor in that it can transfer mechanical forces across the cell surface and to

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the CSK through a specific molecular pathway. This finding is consistent with the observation that ECM is the site of mechanical force transfer in many specialized cellular force receptors (e.g., hair cells in the inner ear, stretch receptors in muscle; Ingber, 1991a). Recent studies suggest that homologs of ECM molecules and their integrin receptors may mediate transfer of transmembrane forces and regulate pattern formation in plants as well (Wagner et al., 1992; Wayne et al., 1992). Analysis of the results obtained with the magnetic twisting device suggested that CSK filament systems other than MFs may also contribute to the cellular response to force. For example, treatment with cyto D reduced the CSK stiffening response only by approximately 65% (Fig. 5). In fact, the importance of IFs and MTs was confirmed by disrupting them using acrylamide and nocodozoale, respectively. The stiffening response was inhibited by approximately 25% when either drug was given alone (Fig. 5). Furthermore, combining cyto D with nocodozoale resulted in complete suppression (Wang et al., 1993). Thus, while integrins may initially transmit force to MFs in focal adhesions, higher order structural interactions between all three CSK filament systems appear to be responsible for efficient transduction of a mechanical stimulus into a cellular response. In answer to our initial question, these experiments also show that a purely mechanical signal can elicit a global CSK response, even in the absence of a large-scale change in cell shape.

VI. Cytoskeletal Tensegrity

A. A Mechanical Explanation for the Cytoskeletal Response t o Stress How could altering the CSK force balance convey regulatory information to a cell? One clue to this mechanism came from our studies with the magnetic twisting device, which revealed that CSK stiffness increased in direct proportion as the stress applied to integrins was raised (Fig. 5). It is important to note that this particular type of mechanical behavior, this linear relationship, is not normally observed in man-made materials. However, it is commonly observed in studies with biological tissues (Fung, 1967; Pinto and Fung, 1973; McMahon, 1984). While this novel type of mechanical behavior is thought to be a characteristic of a continuous prestressed lattice (Stamenovic, 1990), no current mechanical or mathematical theory can explain this type of linear relationship. We thought that if we could explain this behavior, we would be in a better position to understand how the CSK responds to mechanical signals during developmen t .

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We have previously proposed that cells and tissues are constructed according to the rules of an architectural system that depends on tensional integrity, rather than compressional continuity, for its stability (Ingber et al., 1981; Ingber and Jamieson, 1985; Ingber and Folkman, 1989~;Ingber, 1993a). This building system, which is known as “tensegrity,” was first described by the architecthnventor, Buckminster Fuller (Fuller, 1961). Tensegrity models are typically constructed using a series of isolated rigid (compression-resistant) struts that are physically pulled up and open through interconnection with a continuous series of tension elements (Fig. 6). Tensegrity structures are, by definition, prestressed in that they require continuous transmission of internal tension to maintain their stability. In contrast, most man-made structures are compression-dependent and gain their stability from the placement of one structural component on top of another. The human body may be viewed as a tensegrity structure composed of a series of rigid bones that are held up by a continuous series of muscles and tendons. We have previously demonstrated that cell models built using tensegrity architecture mimic many complex cell behaviors (Ingber and Jamieson, 1985; Ingber and Folkman, 1989~;Ingber, 1993a). For example, these models predict that cells will spread on rigid substrata and round on malleable foundations; that cell, CSK, and nuclear shape will change in a coordinated manner in spreading cells; and that the nucleus will polarize and move basally when cells attach to a substratum. All of these predictions have been confirmed in studies with living cells (Emerman and Pitelka, 1977; Ingber and Jamieson, 1985; Ingber et al., 1986a; Ingber et al., 1987; Ingber, 1990). As an initial attempt to determine whether cells use a tensegrity mechanism to respond to mechanical stress, we measured the stress-strain relation of a stick and string tensegrity model by loading it with metal weights (Fig. 6) and measuring the linear deformation (strain) of the entire structure. A linear relationship between stiffness and applied stress was obtained (Wang ef al., 1993) that precisely mimicked the behavior we measured in the CSK of living cells using the magnetic twisting device (Fig. 5). In contrast, nonprestressed tensile filaments taken from the same structure did not exhibit this linear behavior and the compression-resistant struts were essentially infinitely stiff over the range of forces applied. The important point here is that the CSK response to applied stress appears to be a property of the integrated molecular network and not a characteristic of any one of its individual parts. When the applied force was increased, the mechanically interdependent structural elements spontaneously rearranged without disruption of the network or loss of tensional integrity (Fig. 6). Purified F-actin gels that lack structural continuity and prestress (internal tension) either do not exhibit force-induced stiffening or, if they do, the response is nonlinear (Zaner and Valberg, 1989;Janmey

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FIG. 6 Tensegrity models constructed from wooden applicator sticks and elastic string, and loaded with metal weights of increasing mass (from left to right). Note that the structure exhibits a global response to applied stress in that all of its mechanically interdependent elements rearrange rather than deform locally.

et al., 1991).Thus, our dataare consistent with the possibility that the CSK responds to mechanical stress as a tensegrity network: its mechanically interdependent structural elements rearrange globally rather than deform locally in response to stress. Tensegrity arrangements may be used at higher levels in the organic system’s hierarchy, as previously suggested (Ingber and Jamieson, 1985; Ryan, 1989; Pienta and Coffey, 1991), given that intact tissues exhibit a similar linear stiffening response.

B. Tensegrity Models Mimic the Actin Cytoskeleton

Do living cells use tensegrity architecture to organize their CSK? As described earlier, cells do generate force within their contractile MFs and transfer tension throughout the CSK. Furthermore, both external ECM adhesions and intracellular MTs act as compression-resistant elements which oppose MF-based tension (Harris et al., 1980; Joshi et al., 1985; Danowski, 1989; Lamoureux et a f . , 1990; Sims et al., 1992), as would be expected of a tensegrity network (see the following material for more discussion). However, past studies have shown that cells can spread and flatten without intact MTs (Domnina et at., 1985;Vasiliev, 1987; Middleton et al., 1988) and that MT disruption results in IF retraction (Blose et al., 1984; Hollenbeck et al., 1989). Thus, if cells use tensegrity, then the actin lattice itself must exhibit the properties of tensional integrity.

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The only requirement of a tensegrity network is that tension be continuous and compression local. One way to approach this question is to assume that the actin CSK is a continuous tensegrity network composed of MFs that both generate tension and vary locally in terms of their relative flexibility (i.e., their ability to withstand compression). In living cells, MFs generate tension through actomyosin filament sliding (Sims et af., 1992), much as they do in muscle cells (Korn, 1978; Hynes et af.,1987). Changes in filament rigidity are caused by differences in the density of crossbridge formation by different actin-associated proteins, such as myosin, tropomyosin, and a-actinin (Weeds, 1982). By building three-dimensional models that incorporate these characteristics, we were able to test whether the tensegrity hypothesis predicts the specific changes in CSK structure that are observed in living cells (Ingber, 1993a). Our model of the actin M F lattice was constructed using tubular soda straws as struts that were pulled open by a continuous elastic tension element that ran through the central space in all of the tubes (Fig. 7). As shown by Buckminster Fuller many years ago, tensionally stabilized structures spontaneously triangulate their internal support elements as a result of balancing force vectors in the pattern in which they are distributed in space (Fuller, 1965; Edmondson, 1987). In most man-made structures, diagonal supports must be placed in the corners of rectangular wall frames to stabilize their form. In contrast, tensegrity structures stabilize themselves against both internal forces and externally applied mechanical loads.

FIG. 7. A tensionally integrated model of the actin cytoskeleton constructed from plastic soda straws interconnected by a central filament of black elastic thread. (A) A loose, triangulated, isotropic lattice. This highly unstable structure is held open by additional black elastic filaments which are not visible against the black background. (B) The loose isotropic lattice (shown in A) transforms into a highly packed tetrahedron containing multiple struts along each edge using the geometric conversion scheme laid out in Fig. 9.

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FIG.8 An overhead view of an extended lattice containing many tetrahedra oriented vertex to vertex. This structural array is known as an “isotropic vector matrix” or an “octet truss.’’ Note the hexagonal pattern which dominates the lattice. (B) A hand-drawn depiction of a region from a published immunofluorescence micrograph (Fig. 13 in Lazarides, 1976) which shows the pattern exhibited by an actin geodome in a living cell. Note the correspondence between the hexagonal arrays. (Taken fron Ingber, 1993a).

For this reason, tensionally integrated lattices (e.g., Fig. 8A) are often used in the design of “space platforms” for work in microgravity environments. The soda straw model we constructed was capable of exhibiting multiple isotropic (nonpolarized) forms that differed in size, degree of compaction, and stability (Fig. 7). The large, loosely packed structure (Fig. 7A) was inherently unstable and had to be held open by interconnections with external rigid supports (external threads were used for this linkage). Thus, it did not exhibit the self-supporting properties of tensegrity . However, this unstable lattice converted into a self-supporting, tightly packed tetrahedron (Fig. 7B), simply through the action of inward pulling and twisting. This geometric transformation occurred without breaking struts or altering local spatial relationships on each triangular face and thus, without losing tensional integrity (Fig. 9). Although these models were constructed with

FIG.9 The loose unstable lattice at the left (see also Fig. 7A) transforms into a highly packed, stable tetrahedron containing multiple struts along each edge (shown at the right) as a result of progressive compacting, equatorial twisting, and folding. This geometric interconversion does not require disruption of structural integrity or loss of tensional continuity; Fuller called this interconversion “the jitterbug.” (Taken from Ingber, 1993a; it is based on figures in Fuller, 1979 and Edmondson, 1987.)

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soda straws and internal threads, it should be noted that similar structures can be built using the classic tensegrity building approach in which the compression struts are completely isolated from one another (Fig. 10). Both types of structures exhibit similar geometric conversions because they both depend on tensional integrity and not on compressional continuity for their stability. It is interesting that the loose soda straw structure (Fig. 7A) spontaneously remodeled into a linear bundle arrangement rather than a tetrahedron when external resistance sites were employed and tension was applied along a single axis (Fig. 11A-C). Because this is a prestressed structure with internal tension, a single severing event at one of the vertices caused the remaining triangular struts to unfold and align, thereby increasing bundle thickness and length (Fig. 1 lC,D). Similar rearrangements within a larger lattice containing multiple interconnected modular units of this type would result in formation of a single large filamentous bundle stretching between the two external adhesion sites. Essentially, this geometric transformation describes exactly what is likely to occur during stress fiber formation within the basal actin CSK. When a round cell attaches and exerts tension on its ECM resistance sites, the previously loose and isotropic actin lattice (analogous to Fig. 7A) would be expected to flatten (Fig. 11A) as the cell pulls itself downward toward the substratum. Continued transmission of tension throughout the interconnected lattice would promote structural remodeling and concomitant formation of linear MF bundles (stress fibers) that stretch from one focal adhesion site to another (Isenberg et af., 1976; Isenberg and Wohlfarth-Botterman, 1976). As in the soda straw models, once remodeling is complete (Isenberg et al., 1976; Kreis and Birchmeier, 1980), tension within stress fibers becomes isometric as a result of fixed compression-resistant ECM contacts. The finding that mechanical manipulation of cells increases formation of stress fibers in uitro (Franke et al., 1984; Kolega, 1986) and in uiuo (Wong ef al., 1983) strongly supports the hypothesis that formation of actin bundles is driven by tension molding of the continuous actin lattice, rather than a simple series of chemical changes. However, chemical modifications clearly mediate and facilitate this process (Stossel, 1989). While stress fibers are easily visualized along the ventral surface of the cell, they are not representative of the entire actin CSK. Actually, the majority of MFs form a continuous loosely packed network that stretches from the cell periphery to the nuclear border and interlinks with basal stress fibers (Ben Ze’ev er al., 1979; Heuser and Kirschner, 1980; Schliwa and Van Blerkom, 1981). Even portions of the MF network that are distal from the cell base undergo extensive remodeling when cells attach and pull on their ECM anchors. For example, many investigators have reported

FIG. 10 A cytoskeletal tensegrity model that is constructed using rigid struts that d o not

touch one another undergoes the same geometric conversions as did the soda straw model. Use of this model clearly demonstrates the importance of tensional integrity for the stability of this type of triangulated structure. (Built using a Tensegritoy building kit, Tensegrity Building Systems Inc., Barrytown, NY.)

FIG. 11 The tensionally integrated model of the actin cytoskeleton shown in Fig. 7A mimicking stress fiber formation. (A) Increased basal tension causes the unstable isotropic lattice to flatten. (B) Application of tension along the horizontal axis (through black tensile threads) results in progressive alignment of struts along the lines of force. (C) Sustained application of tension results in the formation of bundles of parallel filaments that contain multiple struts oriented in tandem. Triangulated side struts at the top of the bundle interconnect it with the remaining CSK lattice above (not shown). (D) Because the triangulated side struts are prestressed, severing a single vertex causes them to spontaneously straighten, thereby promoting bundle elongation and thickening. Similar tension molding of neighboring lattice modules on either side (not shown) would result in further bundle elongation and formation of stress fibers along tension field lines. Note the repetitive sarcomere-like banding pattern within the elongated bundle. (Taken from Ingber, 1993a.)

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that the apical actin network reorganizes into polygonal nets and highly triangulated, dome-like structures during cell spreading; these have been referred to as “geodesic domes” or “actin geodomes” (Lazarides, 1976; Rathke et at., 1979; Heuser and Kirschner, 1980). It is interesting that these geodesic structures can also be explained by purely mechanical considerations using the tensegrity paradigm (Ingber, 1993a). For example, let the loose anisotropic lattice shown in Fig. 7A represent a basic structural module within the apical actin lattice. In contrast to the cell base, there would be no local adhesion sites to resist CSK tension. Thus, sliding of actomyosin filaments would proceed in three dimensions until the MFs could shorten no further. Because they are fully contracted and resisted by opposing filaments, these MFs would essentially act as semirigid struts under global tension. If the loosely packed unstable MF lattice were to compact in response to this increased inward pull in the manner shown in Fig. 9, then we would expect to see compact tetrahedra form within the CSK lattice. Furthermore, each tetrahedron would have multiple struts oriented in parallel along each of its edges (Figs. 7B and 10). Additional expansion of this contraction wave through the interconnected lattice would result in the formation of extensive triangulated structures composed of multiple tetrahedra (Fig. 8A). The formation of a dome would result from the bending of this planar triangulated lattice as it is pulled downward over the spherical nucleus by cell flattening. The development of extensive actin geodomes will of course depend on many factors, including the level of CSK tension, the mechanical integrity of the lattice, the shape of the cell, and the size of the nucleus. These triangulated nets and domes may therefore be less well developed and much more difficult to visualize in certain cells. As we have recently demonstrated (Ingber, 1993a), these complex, triangulated, soda straw structures which contain multiple tetrahedra packed edge to edge exhibit repeating hexagonal patterns that are extremely similar to those observed by immunofluorescence microscopy within apical actin geodomes in living cells (Lazarides, 1976) (Fig. 8B). High-power transmission electron micrographs of these actin domes (Rathke et al., 1979) also reveal arrangements of MFs that are nearly identical to those seen in the soda straw models (Ingber, 1993a). Furthermore, these micrographs show that each edge in the dome contains multiple M F struts oriented in parallel, just as predicted by the model (Figs. 7B and 10). It is interesting that the vertices of the actin geodomes of living cells are the only regions which do not contain tropomyosin or myosin; thus these regions are thought to be more flexible than the intervening struts (Lazarides, 1976). Furthermore, the length of the struts (4pm) that form the edges of the triangulated actin dome in living cells corresponds exactly to the spacing that is responsible for the sarcomere-

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like pattern of stress fibers (Lazarides, 1976; Rathke et al., 1979), again as the tensegrity models predict (Figs. 7 and 11). Taken together, these findings strongly suggest that many of the patterns exhibited by the actin CSK may result from dynamic tension-molding of a continuous tensegrity network. However, the MF-based actin CSK must be viewed as an energy-dependent tensegrity structure in that dynamic changes in structure between stable and unstable forms (e.g., Fig. 9) require active generation of tension and hence the presence of ATP (Bereiter-Hahn et al., 1990). In the absence of ATP, the cells may more closely resemble geodesic structures that are constructed entirely from nonextensible materials (i.e., rigor mortis). C. Cell Spreading and Motility via Tension Molding of the Actin Cytoskeleton

A variety of models have been proposed to explain how cells change shape and move (reviewed in Ingber, 1993a). However, none of these models fully explains how a cell that exerts inwardly-directed tension can extend processes outward and move forward. Analysis of the process of cell attachment and spreading has revealed some common features (Vasiliev, 1987; Lotz et af.,1989; our unpublished observations). Cells first attach to immobilized ligands (e.g., RGD sequences within ECM molecules) through binding interactions with transmembrane ECM receptors, such as integrins. These adhesions then become concentrated within small focal contacts that are oriented in arcs or rings along the cell periphery. Focal adhesion complexes form as actinassociated proteins and MFs are recruited to the site of contact. Formation of focal adhesions is accompanied by a strengthening response within about 15-20 min that results in an increase in the amount of tension that cells exert on their ECM adhesions (Lotz et al., 1989). The resulting changes in the CSK cause the isotropic actin network that stretches between different focal adhesions at the cell base to reorganize into linear bundles, and cell flattening results. The possibility that cell spreading is driven by CSK tension is supported by studies using malleable silicone rubber substrata which show that cells actively pull on their basal adhesions during all phases of cell attachment and spreading (Harris, 1982). Also, as described earlier, depletion of ATP prevents cells from spreading (Bereiter-Hahn et al., 1990). Studies using silicone rubber substrata also reveal that cells apply the greatest tension on their ECM a few microns behind their leading edge (Harris, 1982). In other words, the ruffling lamellopodia at the front end of the spreading cell does not drag the entire cell forward. Instead, cells

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appear to first tension mold their CSK by pulling against their fixed ECM adhesion sites. They then extend small portions of their CSK forward using the entire mass of the rear-lying CSK lattice as an internal tensionally stiffened support. But how could this work? How does the cell remodel its actin lattice within the leading edge so that forward movement results? Is cell migration primarily driven by chemical modifications, as was often assumed in the past (Stossel, 1989), or do mechanical forces also play a critical role? A clue to the mechanism by which cells spread and move comes from analysis of the geodesic dome-like structures that appear within cells during the early phases of spreading. The vertices of this actin geodome (the only regions that are free of myosin and tropomyosin) appear to serve as nuclei for actin polymerization during assembly of filopodia (Lazarides, 1976; Rathke et al., 1979). Filopodia are thin cytoplasmic protrusions that extend outward from the lamellopodia at the leading edge of spreading and migrating cells. The large MF bundles that extend outward from vertices on the surface of the actin geodome form the core of each filopodium, although they also interconnect with the rear-lying CSK lattice via surrounding MF nets (Fig. 12A). Filopodia may nucleate preferentially on exposed vertices of the actin lattice near the leading edge because this is where new ECM contacts are forming. We have recently shown that adhesion to ECM induces synthesis of phosphatidylinositol-bis-phosphate (McNamee ef al., 1993). This inositol lipid can compete with actin for binding to gelsolin and profilin and thereby release free actin monomer (Janmey et al., 1987; Janmey and Stossel, 1987; Goldschmidt-Clermont et al., 1990). Thus, formation of new ECM adhesions could increase the local concentration of actin monomer available for polymerization at the cell’s leading edge. Assembly of filopodia is one place where actin polymerization, either acting alone (Tilney and Kallenbach, 1979)or facilitated by osmotic forces (Oster and Perelson, 1987), may actively drive the cell membrane outward and upward. The large MF bundles that form the core of filopodia may be able to resist local compression produced by the limiting plasma membrane and submembranous CSK because of their geometric arrangement (close side-to-side packing of MFs) combined with a high degree of crosslinking. However, to produce outward extension of the membrane, the proximal end of the MF core must be fixed in place. Otherwise, the filopodium would be pushed inward rather than outward. Key to this mechanism is that the proximal end of the M F core is connected to the vertex of the actin geodome. Although the rear-lying actin lattice is contractile, it can resist external compression because of its geodesic (tensionally integrated) arrangement. (Man-made geodesic domes are known to exhibit incredibly high load-bearing capabilities with a minimum amount

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FIG. 12 A tension-molding mechanism for cell spreading and motility. (A) The continuous actin CSK tensionally stiffens and remodels into basal stress fibers and an apical dome as a result of transmitting force across the cell’s basal focal adhesion sites and to the compressionresistant ECM. Increased binding of cell surface integrin receptors at the leading edge of the cell results in increased inositol lipid (PIP,) synthesis and subsequent release of free actin monomer (not shown). Vertices on the dome that are free of tropomyosin and myosin act as nucleation sites for actin polymerization and result in the extension of MF bundles that form the core of a newly formed filopodium. Contraction of loose MF nets that interconnect this MF bundle with basal stress fibers and the rear-lying apical dome cause the filopodium to move down and up. (B) Greater tension within the basal CSK pulls the filopodium downward, using its point of attachment to the tensionally stiffened dome as a fulcrum. Fixation of the tip of the exploring filopodium to the rigid ECM substratum as a result of ECM receptor binding shifts the CSK force balance. The trailing CSK lattice is pulled downward and slightly forward by continuous tension molding. The downward motion of the actin dome exposes new vertices and formation of a second filopodium begins. (C) Tension molding continues and the surrounding MF nets within the lamellopodium are pulled forward along the stiffened filopodial MF core. MFs within these nets also tend to align and interconnect with the rear-lying basal stress fibers. Flattening and forward movement of the actin dome continues, as does growth and extension of the newly forming filopodium. (D) The flattened filopodial core merges with the rear basal stress fiber, a new focal adhesion forms closer to the new leading edge, and the older focal adhesion dissolves. The system is recocked and the second filopodium begins its own exploration of the substratum. Reiteration of this process would cause cell spreading and net forward motion (see the text for a more detailed description). Note that only the actin CSK is depicted. ECM, extracellular matrix; solid black rectangles, focal adhesion complexes.

of building materials .) Thus, actin polymerization may promote outward extension of the cell membrane and formation of the filopodium through a combination of local thermodyamic alterations, osmotic changes, and, most important in the present context, global structural stabilization. Once the filopodium forms, contraction of the MF nets that stretch from the filopodial MF core to the basal stress fibers (Rathke et al., 1979) would be resisted by the fixed focal adhesions that lie just behind the leading edge (Harris, 1982; Felder and Elson, 1990) and tend to cause downward movement of the extended filopodium. However, at the same time, forces

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FIG. 12 (continued)

that are generated within the net that connects the filopodial MF core to the apical actin geodome would act to oppose this force. These opposing forces, combined with use of the rear-lying, tensionally stiffened actin geodome as a fulcrum (Lazarides, 1976; Rathke et af., 1979), would cause the filopodium to waver up and down (Fig. 12A). A similar tensegrity mechanism is the basis for the development of oscillatory movements in the bones of our arms when we pull them outward to their fullest extension using tension generated within the surrounding muscles (neural servomechanisms normally suppress this oscillation). In cells with less well-developed apical MF domes, tensionally stiffened bands of MFs that are associated with the cell’s basal focal adhesions may act as the fulcrum (Heidemann et af., 1990). If the adhesivity and rigidity of the ECM substratum is high, then the net tension vector would be directed downward. Thus, on average, the filopodium would be more likely to explore the ECM substratum than to be pulled upward toward the cell apex. A small but permanent increase in cell extension will result once receptors on the tip of the exploring filopodium bind to immobilized ECM ligands and become fixed in place (Fig. 12B). Direct measurements of filopodia within living cells confirm that they are contractile, that is, they exert tension on their points of insertion on the ECM (Heidemann et al., 1990). The resulting increase in isometric tension (due to pulling against a fixed ECM attachment site) will be transmitted throughout the interconnected CSK lattice, causing further tension molding of the adherent filopodium as well as the MF nets that interconnect it with the rear-lying actin lattice. Downward movement of the filopodium and increased alignment of MF within the surrounding actin nets will result (Fig. 12C). Continued contraction of the opposing MF nets will also tend to pull the MF meshwork within the lamellopodium forward along the filopodial core, much as a sail is raised up on a mast. At the same time, transmission of tension to the rear-lying actin geodome will cause

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flattening and forward extension of the entire CSK lattice (Fig. 12C,D). Progressive tension molding will eventually result in merging of the ventral stress fibers with what was originally the filopodial MF core (Fig. 12D). At the same time, new vertices of the geodome will become exposed to the chemical microenvironment of the leading edge, causing new MF bundles to nucleate and filopodia to form (Fig. 12B-D). In other words, the motive mechanism will be “recocked. ” Cell flattening and incremental forward motion of the entire MF lattice relative to its fixed attachments at the rear would then result from reiteration of this adhesion-tension molding-polymerization cycle. While MTs and associated IFs are not required for spreading, they may provide additional internal supports which further stabilize the new extension and hence increase the efficiency of spreading (reviewed in Ingber, 1993a). To briefly summarize, the tensegrity paradigm suggests an alternative mechanism for cell spreading and movement that is largely mechanically based, although it also incorporates chemical forms of CSK regulation. Extension of the leading edge and forward locomotion would be produced through a series of integrated steps (Fig. 12): 1 . Tension molding following cell attachment results in formation of an interconnected tensile MF network containing basal stress fibers, suprabasal polygonal nets, and apical triangulated domes. 2. Formation of new ECM adhesions at the leading edge releases chemical messengers that in turn increase the availability of free actin monomer. 3. Geometric determinants within the triangulated apical actin lattice (e.g., vertices on geodomes) provide nucleation sites for actin polymerization. 4. Newly extending MFs bundle, stiffen, and push outward against the plasma membrane through a combination of actin polymerization (Tilney and Kallenbach, 1979), changes in local osmotic pressures (Oster and Perelson, 1987), and global structural stabilization (i.e., pushing against the tensionally stiffened MF geodome). 5 . Actomyosin filaments within opposing MF nets that link the filopodial MF core to the rearward actin lattice contract. 6. The rear-lying actin dome or a basal tensionally stiffened MF band is used as a fulcrum, resulting in upward and downward movement of the extending filopodium. 7. When the tip of the filopodium binds to ECM and becomes fixed, net downward and forward pulling on the trailing CSK lattice results. 8. The surrounding MF network is then tensionally stiffened and dragged outward as a lamellopodium. 9. Continuous tension molding results in merging of the filopodial MF core with ventral MF bundles, causing forward extension and linearization of stress fibers.

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10. Downward pulling of the apical triangulated lattice exposes new actin nucleation sites (vertices on the geodome) and the cycle begins once again. While cell spreading and cell motility are closely related, they are not the same. Movement requires the establishment of a net directional force vector which itself assumes a polarized distribution of adhesion contacts (integrin binding) as well as localized release of chemical messengers within a cell that generates centripetal tension. In fact, even epithelial cells that commonly spread in a nonpolarized way will take on bipolar forms and polarize their lamellopodia to opposite poles if the ECM topography is varied so as to inhibit cell attachment along lateral cell borders (Domnina er al., 1985). Cells will also migrate up an increasingly dense gradient of immobilized ECM ligands (Brandley and Schnaar, 1989). In general, rigid ECM substrata that are very highly adhesive result in generation of isometric tension, promote formation of large stress fibers, increase cell growth, and suppress cell locomotion. In contrast, changing the CSK force balance by decreasing cell adhesivity results in generation of more isotonic tension, fewer stress fibers, a lower growth rate, and enhanced motility (for further discussion, see Couchman er al., 1982; Opas, 1987). Thus, the ECM-resisting substratum can direct cell spreading and guide locomotion, even though the motive force is generated intracellularly. The immobilized ECM ligands both induce changes in intracellular chemistry (e.g., inositol lipid synthesis) and act as mechanical elements which resist cell tractional forces and thereby support tension molding of the continuous CSK lattice. It is possible that growth factors could also alter cell motility during development by modulating both signalingmechanisms (i.e., mechanical as well as chemical). U. Integration of Cell, Cytoskeletal, and Nuclear Structure

1. Microtubules as Compression-Resistant Struts Tension molding may also pertain to the MT system. For example, druginduced disassembly of MTs induces cell retraction in neurites, but only under conditions in which active tension is generated within the surrounding M F network (Solomon and Magendantz, 1981;Joshi er al., 1985). These studies and others (Dennerll et al., 1988, 1989; Lamoureux et af., 1989) suggest that both the stability of axonal form and active neurite extension result from the action of tension which is generated within the continuous MF lattice and locally resisted by internal MT struts (Fig. 13). The MT struts and ECM tethers also provide complementary and interchangeable load-bearing functions in these cells (Lamoureux et af., 1990). For these reasons, a tensegrity mechanism has been used to explain

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.MT or MF Bundle

MF or IF

FIG. 13 A diagramatic representation of a simple tensegrity microdomain. MT struts (or cross-linked MF bundles) hold out the cytoskeleton against centripetal tension that is generated within the interconnected network of contractile MFs. IFs may also serve as tension elements in this system.

how changes in MT and MF extension are orchestrated in growing neurites (Heidemann and Buxbaum, 1990). Tension molding provides a plausible mechanism to explain why the MT organizing center of endothelial cells is oriented toward the heart (i.e., toward the direction in which wall distension is greatest) in both arteries and veins, even though the orientation of blood flow differs (Rogers er al., 1985). Many other cells (Tomasek and Hay, 1984; Domnina er af.,1985;Travis and Bowser, 1986; Bereiter-Hahn, 1987; Vasiliev, 1987; Madreperla and Adler, 1989; Bailly et al., 1991) and tissues (Burnside, 1971; Gordon and Brodland, 1987) similarly maintain stable morphology by establishing a balance of mechanical forces between competing MT struts and contractile MF networks. This is usually most clear in cells that exhibit an asymmetric or elongated shape. Disrupting MTs in polygonal cells (e.g., epithelial cells) only partially inhibits cell flattening (Middleton er af.,1988), although it does decrease the rate and efficiency of spreading (Domnina er al., 1985; Vasiliev, 1987). It is interesting that polygonal cells that normally do not require intact MTs to spread become dependent on MTs when they are forced to elongate in a bipolar fashion by altered ECM topography (Domnina et al., 1985). Taken together, these studies support the concept that MTs normally act as internal struts that hold the cell outward against pull of the contractile MF network (Fig. 13). However, relative to MFs (Fig. 12), they may

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play a redundant or secondary supporting role in polygonal cells and in elongated cells during the initial phase of spreading. Mechanical measurements of living cells also show that disruption of MTs results in an increase in the amount of force that is transferred outward across the cell membrane and to the ECM (Dennerll er al., 1988; Danowski, 1989; Kolodney and Wyslomerski, 1992). This result is consistent with a tensegrity array in which MTs and ECM provide interchangeable compressive load-bearing functions. In fact, it is probably because of their complementary load-bearing functions that MTs are most critical in elongated cell processes that have a lower density of stable ECM adhesions (Domnina er al., 1985). Tensegrity-based force interactions between MTs, MFs, and the ECM also provide an efficient mechanism for local regulation of CSK filament polymerization. A thermodynamic model that incorporates the tensegrity paradigm has been published (Buxbaum and Heidemann, 1988). Analysis of isolated CSK filaments confirms that MTs have a much greater ability to withstand compression than MFs, whereas individual MFs are much better at resisting tension (Mizushima-Sugano er al., 1983). Instituting multiple tensile guy lines along the length of MTs (Brodland and Gordon, 1991), as IFs appear to do in living cells (Schliwa and Van Blerkom, 1981; Heuser and Kirschner, 1980), can further enhance their compressive load-bearing capabilities (Fig. 14). Bundling and cross-linking

FIG. 14 An enlarged image of one vertex from a tensegrity array similar to that shown in Fig. 13. IFs are also shown; they are laterally stabilizing the MT struts against lateral bending and compression. (Based on Brodland and Gordon, 1991.)

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of any CSK filament will increase its rigidity (because of greater resistance to lateral distortion) and hence its ability to resist compression (e.g., MTs in cilia and flagella; MFs in microvilli and filopodia). Thus, at times, MFs may be able to act as rigid struts and replace MTs in a tensegrity array (Fig. 13). IFs also may replace MFs as tension elements. Complementary force interactions between compression-resistant MTs and interconnected tension elements also may be critical for mitotic spindle function during cell division. In v i m studies using isolated chromosomes and microtubules made from purified tubulin suggest that depolymerization of MTs moves chromosomes toward the pole of the spindle during anaphase (Koshland et al., 1988). One possible explanation for this observation is that the MT strut that connects to the chromosome kinetochore on one end and the spindle pole on the other normally resists a potential restoring force that is exerted by an undefined elastic element that interconnects with this system (Koshland et al., 1988) (Fig. 15). Owing to the presence of a mechanical force balance, stored elastic energy in the system would cause a net poleward motion of the chromosome when the MT strut shortens as a result of depolymerization (Fig. 15). The use of an interconnected structural element that generates active tension rather than a passive elastic element would produce the same result. If either one of these structural arrangements were used, it would represent another example of tensegrity at the molecular level. During cytokinesis, the MTs that emanate from the centrosome appear to provide a more complex form of global structural integration by linking

ffinetochore Microtubule ( Compression element )

Net Poleward Movement FIG. 15 A theoretical tensegrity-based mechanism for chromosome movement within the mitotic spindle. Depolymerization of MTs at the kinetochore would result in poleward movement of the chromosome if the spindle pole were linked to the chromosome by an additional series of tensile elements that could generate elastic restoring forces. (Based on a model depicted in Koshland et a / . , 1988; see the text for more discussion.)

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up with the actomyosin band that is responsible for formation of the cleavage furrow (Rappaport, 1975) and possibly with the nucleus as well (Rappaport, 1991). The functional significance of this structural integration can be made clear by using a micropipette to move the centrosome within a dividing cell (Rappaport, 1975). A repeated change in the location of the centrosome results in coordinated movement of the overlying cleavage furrow. As long as the centrosome is not held in one place for more than 4 min, cytokinesis will not progress to completion and the cleavage furrow can be moved once again. In other words, the centrosomes appear to position the formation of the cleavage furrow and to coordinate karyokinesis with cytokinesis by acting as physical anchors from which MT struts can extend and push. The centrosomes may also use the submembranous actomyosin ring as an external stabilizing support in order to facilitate physical separation of the spindle poles during telophase. Microtubules may be involved in other forms of structural integration as well. For example, axonemal regeneration experiments reveal that if a pair of flagella are amputated in the same cell, the rate of repolymerization of MTs in one is sensitive to the extent to which MTs are polymerized in the other (Coyne and Rosenbaum, 1970; Raff, 1979). Taken together, these observations suggest that cell and nuclear division requires global structural integration within the CSK and that MTs play a key role. This possibility is supported by the observation that initiation and progression of embryological development requires the presence of a functional centrosome (the principal MT organizing center), whether it is preexisting or induced de nouo (Fulton, 1971; Tournier et af., 1991). Centrosomes can also induce parthenogenesis when they are microinjected into unfertilized eggs (Picard et al., 1987; Klotz et al., 1990). 2. Intermediate Filaments as Tensile Stiffeners Intermediate filaments (IF) are relatively stiff-coiling filaments that interweave with MFs and MTs to form the intact CSK (Fig. 1). The IF network stretches from binding sites on the cell surface (e.g.. desmosomes, focal adhesions) to the surface of the nucleus (Lehto ef al., 1978; Fey ef al., 1984; Green et al., 1986; Bershadsky et af., 1987; Georgatos and Blobel, 1987). Intermediate filaments are also held out in an extended array through the action of MTs which oppose the inward pull exerted on IFs by contractile MFs (Hollenbeck et al., 1989). Kinesin motors appear to be capable of pulling the IF lattice outward along these MT struts (Gyoeva and Gelfand, 1991). Recent studies using antisense oligodeoxynucleotides suggest that IFs are needed to maintain mechanical rigidity within living tissues (Torpey et al., 1992).Our measurements with the magnetic twisting device confirm that IFs are at least partly responsible for maintaining CSK integrity and stiffness (Wang et al., 1993).

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Intermediate filaments have been shown to act as filamentous coils which harden at high strains (Janmey el al., 1991).Thus, they are excellent candidates to act as guy lines or tensile stiffeners that could hold separate parts of the CSK in place (Figs. 1, 13, and 14). Intermediate filaments that stretch from the cell surface to the nucleus might also act to stabilize nuclear form and integrate cell and nuclear structure (Hansen and Ingber, 1992). In contrast, the continuous MF lattice would provide the motive force that drives shape changes. Intermediate filaments also may stabilize the nucleus against rotational movements, just as they are thought to resist MT bending (Brodland and Gordon, 1991) since IF disruption has been shown to induce nuclear rotation in certain cells (Hay and DeBoni, 1991). Intermediate filaments also appear to orient mitotic spindles in epidermis (Bereiter-Hahn, 1987)and position nuclei within syncytia ( Wang er al., 1979). Because IFs stretch from nucleus to junctional complex to nucleus, they could provide a direct path for mechanical and harmonic information transfer within whole tissues (Ingber and Jamieson, 1985; Pienta and Coffey, 1991).

3. Nuclear Tensegrity It is important to clarify that tensegrity can be used to provide structural stability on any scale. Furthermore, smaller and larger tensegrity systems can be structurally and functionally integrated simply by providing tensional continuity. The simplest example of this is the construction of a tensegrity cell model that contains a tensegrity nucleus which is interconnected with the cell surface through a series of tension elements. In this tensionally integrated structure, the cell and nucleus undergo coordinated alterations in shape when the cell flattens (Ingber and Jamieson, 1985; Ingber, 1993a),just as they do when living cells attach and spread (Ingber er ai., 1987; Ingber, 1990). Construction of these models raises the possibility that the nucleus may itself be constructed as a tensegrity structure. Isolated nuclei contain actin and myosin, but it is not clear that nuclei actively generate tension. Yet, the nucleus of a spread cell does appear to exist in a state of isometric tension. For example, extended nuclei rapidly retract and round when the cell’s ECM anchors are dislodged (Ingber and Folkman, 1989~).Furthermore, similar effects can be obtained by increasing the level of tension within the CSK of membrane-permeabilized cells (Sims et al., 1992). If the nucleus does use tensegrity for its organization, then individual chromatin fibers that contain tightly wound coils of DNA might represent compression-resistant elements. These compressed coils would be interconnected with a surrounding scaffolding of nuclear matrix, composed of proteins and heterogeneous nuclear RNA (hnRNA) (Berezney and Coffey ,

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1975); Nickerson et al., 1989; Pienta et al., 1991) that is under continuous tension. However, the nuclear matrix is also structurally interconnected with the remainder of the CSK (Fig. 1). Thus, expansion of the nucleus would require a change in the force balance within the entire extended CSK. Nuclear extension could result from tension that is generated withill the interconnected actin lattice (Osborn and Weber, 1977; Fey et al., 1984). In other words, the nuclear matrix could be pulled outward if the cell’s ECM adhesions were fixed and capable of resisting CSK tension. Intermediate filaments that physically interlink the nuclear matrix with MF, MTs, and the cell surface could help focus this force and thus more efficiently integrate changes in cell and nuclear form. Structural integration between the cell and nucleus also could provide a mechanical basis for the expansion of nuclear pores and the associated increase in nucleocytoplasmic transport rates that accompanies cell spreading (Feldherr and Akin, 1990; Hansen and Ingber, 1992). Conversely, disruption of this system for structural integration could be responsible for the uncoupling between cell and nuclear shape as well as the deregulation of nuclear functions (e.g., nuclear transport) that accompanies neoplastic transformation ( Jiang and Schindler, 1988; Boyd et al., 1991 ; Pienta and Coffey, 1992). These observations, in combination with the recent finding that RNA processing (transport and splicing)occurs in specific locations within the nucleus that are in close proximity to the gene that is being transcribed (Carter et al., 1993; Xing et al., 1993), emphasize the potential significance of understanding the mechanical basis of nuclear shape control.

VII. The Cytoskeleton as a Mechanical Signaling System A. Convergence of Chemical and Mechanical Signals within the Focal Adhesion

How do mechanically induced changes in CSK structure alter cellular biochemistry? To answer this question, we must go back and analyze how changing the density of ECM attachment sites and shifting the CSK force balance alter cell growth and differentiation. In a series of studies first initiated in collaboration with Dr. Martin Schwartz (Scripps Institute), we found that ECM molecules exert their effects by binding to specific integrin receptors on the cell surface and activating many of the same chemical signaling pathways that soluble growth factors use (Ingber er al., 1990; Schwartz et af., 1991a,b; McNamee et al., 1993). Essentially, we and

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others have shown that cell binding to purified ECM molecules and associated integrin clustering activates tyrosine kinases, stimulates inositol lipid turnover, turns on the Na+/H+ antiporter, triggers calcium release, and induces early growth response genes, without a cell shape change (reviewed in Schwartz, 1992; Hynes, 1992). However, CSK tension may even play a role in this shape-independent signaling. For example, an ECM ligand must be presented in an immobilized form that can both cluster integrins and physically resist internalization in order to produce sustained activation of the N a + / H + antiporter (Schwartz et al., 1991b). Receptor internalization results from CSK tension. Thus, this is one point at which changing the balance of forces across integrin receptors could alter the chemical signaling events that are required for progression of the cell cycle. Recent studies have revealed that many of the molecules that are responsible for these early chemical signaling events rapidly become physically associated with CSK elements within the focal adhesion complex. Signaling molecules that are recruited to the focal adhesion complex and activated within minutes following ECM receptor binding include c-src, FAK kinase, inositol lipid kinases, phospholipase C, and the Na+/H antiporter (Plopper et al., 1991; McNamee et al., 1993; and in preparation). In other words, the CSK microdomain that we refer to as the focal adhesion complex may also represent a localized chemical signaling complex. A change in the balance of forces that are transmitted across ECM receptors would therefore be expected to result in tension molding of the CSK scaffolding as well as changes in the distribution of chemical signaling molecules within the focal adhesion complex. Force-dependent changes in focal adhesion organization could alter the proximity between enzymes (e.g., kinases) and substrates or expose different molecular binding sites and thereby influence chemical signaling in the absence of a global shape change. In support of this hypothesis, recent studies confirm that application of apical shear stress to intact endothelium rapidly induces both the release of chemical second messengers (Nollert et al., 1990) and remodeling of basal focal adhesions (Robotewskyj et al., 1991). +

B. A Global Mechanism for Long-Range Signal Transfer It is important to emphasize that while integrin-activated (and growth factor-induced) chemical signaling events are required for growth, they are not sufficient. Most cells must also undergo large-scale mechanical deformations and literally change shape in order to grow (Folkman and Moscona, 1978; Ben Ze’ev et al., 1980; Ingber, 1990; Mooney et af., 1992b). If CSK tensegrity plays a fundamental role, then forces that are

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transferred across ECM receptors and are responsible for changes in cell shape would produce global rearrangements within the CSK lattice as well as in the nuclear matrix. Mechanically induced CSK rearrangements in the cell cortex might drive mechanochemical conversion by activating stretch-activated ion channels on the cell surface (Sachs, 1989). The function of other chemical signaling molecules (e.g., protein kinase C) also could be modulated because of their ability to physically associate with internal CSK filaments (Murti et al., 1992). It even has been suggested that physical extension of contractile MFs could directly convert mechanical forces into chemical information by reversing the energy transformation reaction that drives actomyosin filament sliding (Ulbrich and Ruegg, 1976); however, this proposal remains unproven. Alterations in the CSK force balance also may change local thermodynamic parameters (e.g., critical concentrations for tubulin or actin) and thereby alter chemical polymerization of CSK filaments (Hill, 1981 ;Ingber and Jamieson, 1985; Buxbaun and Heidemann, 1988). The dependence of MT polymerization on a tensegrity-based force balance has been clearly demonstrated in cultured neurites (Joshi et al., 1985; Dennerll et al., 1988; Buxbaum and Heidemann, 1988; Heidemann and Buxbaum, 1990). We have recently found that altering the number of ECM attachments that can resist ECK tension also results in a dose-dependent change in the concentration of free tubulin monomer within hepatocytes (Mooney et al., 1991). Associated changes in CSK monomer levels could, in turn, modulate chemical signaling mechanisms. For example, tubulin has been reported to modulate G-protein-associated signaling events (Roychowdhury et al., 1993) whereas monomeric actin competes with inositol lipid intermediates for binding to gelsolin and profilin (Janmey et al., 1987; Goldschmidt-Clermont et al., 1990). In theory, mechanical forces could similarly regulate other types of chemical polymerization events inside the cell as long as the molecule was physically interconnected with the CSK and load bearing. It is interesting that much of the cell’s metabolic machinery (e.g., mitochondria, polyribosomes, mRNA, glycolytic enzymes, protein kinases) has been shown to be associated with the CSK (reviewed in Ingber and Jamieson, 1985; Ingber and Folkman, 1989~).Even the critical regulators of cell cycle progression, the cyclins, appear to alter cell shape as well as the structure of the CSK and nucleus as part of their action (Nurse, 1990; Lamb et al., 1990; Luscher et al., 1991). Tensegrity cell models predict that the CSK also provides a molecular path for direct communication of regulatory information, in the form of mechanical forces, from the cell surface to the nucleus. Tension-dependent changes of nuclear matrix structure could alter nuclear functions, such as gene expression and DNA replication, by changing the arrangement of

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associated nuclear regulatory proteins, releasing mechanical constraints to DNA unwinding, or by changing the size of nuclear pores. DNA synthesis occurs on the nuclear matrix scaffolding (Berezney and Coffey, 1975) and both DNA unwinding and nuclear expansion have been shown to be prerequisites for entry into the S phase (Yen and Pardee, 1979; Moser et al., 1981; Nicolini et al., 1986; Ingber et al., 1987; Roberts and D’Urso, 1988). While the effects of mechanical stress on the arrangement of the nuclear matrix remain to be demonstrated, changes in physical interconnections among specific genes, transcriptional regulators, RNA splicing assemblies, and distinct elements of the nuclear matrix are known to be critical for control of gene expression (Getzenberg and Coffey, 1990; Dworetzky et al., 1992; Xing er al., 1993; Carter et al., 1993). Furthermore, it has been shown that nuclear pores physically expand in size and that nuclear transport rates increase when cells change from round to spread (Feldherr and Akin, 1990). Mechanically induced increases in nuclear transport, combined with decreased mechanical resistance to DNA unwinding, could at least partly explain why nuclear expansion is required for entry into the S phase. Thus, transmembrane force transfer to the CSK may represent the first step in an intracellular mechanical signaling cascade that drives global CSK rearrangements and simultaneous mechanochemical transduction events at many locations inside the cell. This type of cell-wide structural rearrangement could provide a mechanical basis for the global modulation (immobilization) of all surface receptors that follows local ligation of a subset of receptors (Yahara and Edelman, 1975). This mechanical signaling system would be based on maintenance of tensional continuity and thus it differs greatly from alternative mechanochemical transduction models which rely upon local distortion of the plasma membrane or deformation of individual CSK filaments at the site of mechanical force transfer. In this type of system, it is the change in distribution of physical force which accompanies cell shape changes, rather than a specific cell morphology, that provides regulatory information to the cell. For this reason, the balance of mechanical forces that preexists within the CSK before an external mechanical load is applied (e.g., whether a cell is round or spread) may be one of the most critical determinants of the subsequent cellular response. C. Structural Inheritance within the Cytoskeleton

The concept of global structural integration within the CSK becomes even more interesting when the possibility of structural inheritance is considered. For example, when a small region of the cell surface containing

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a cortical arrangement of consistently oriented cilia is inverted microsurgically in Paramecium, this inverted patch of beating cilia is inherited consistently for thousands of generations over a period of more than 10 years (Sonnenborn, 1970a,b). There is no evidence of similar inheritance of complex CSK structure in multicellular eukaryotes. However, it is important to emphasize that the specialized MT organizing centers which are known as centrioles, basal bodies, and centrosomes are duplicated in every cell cycle (Sluder and Rieder, 1985). Thus, these specialized CSK templates undergo self-directed assembly in the cytoplasm much as nucleic acids do in the nucleus. Futhermore, in some somatic cells, centrosome duplication is actually required for cell cycle progression as well as cell division (Maniotis and Schliwa, 1991). Thus, the concept of structural inheritance within the CSK deserves more study in the future.

VIII. Conclusions and Implications for Development

Hopefully, it has become clear from this discussion that the problem of cell and tissue organization is a question of three-dimensional design rather than one of chemical composition. The molecular constituents of all cells and tissues undergo continual turnover. Thus, it is the integrity of molecular pattern that is maintained and that we recognize as “life.” Tissue development must therefore be viewed as the process by which complex networks of molecules and cells are assembled and arranged within a structural hierarchy to provide specialized form as well as function. In this type of system in which structure dictates function, an understanding of the rules of architecture is critical. It is now clear that mechanical forces play a critical role in the development and maintenance of tissue pattern. In this chapter, we have focused on the role of the CSK and its extensions (ECM and nuclear matrix) in morphogenesis because this structural continuum provides a molecular path for transferring mechanical stresses throughout cells and tissues. We showed that specific CSK patterns as well as the CSK response to stress can be modeled using the rules of tensegrity architecture. If cells use this form of architecture to organize their CSK, then individual support elements will be extremely sensitive to tension, and alterations in the CSK force balance will drive a global remodeling cascade at the molecular level. Changes in cell shape and migration would result from tension molding of the CSK, and internal oscillatory transformations between locally stable and unstable architectural states. In cellular tensegrity systems, the critical support elements would include internal compressionresistant struts (MTs and MF bundles in certain locations), suspensory

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ligaments (IFs and M F nets), and external tethers (ECM adhesions, junctional contacts) as well as a system for generating and distributing tension to all interacting parts (actomyosin filament sliding). In tissues, highly cross-linked collagen bundles and clusters of hydroscopic proteoglycans may resist compression locally, whereas ECM fibrils (collagen, fibronectin) and basement membranes may transmit tension that is generated within their constituent cells (Harris et al., 1980; Ingber and Jamieson, 1985; Klebe, 1989; Ryan, 1989). In this organic tensegrity hierarchy, the molecular composition of individual struts may vary and even the mechanism of tension generation may change (e.g., MT vs. MF-based motors; Goldstein and Vale, 1992). There also may be structural redundancies in order to further stabilize cell and tissue form (e.g., MTs in polygonal cells). Nevertheless, the structural network will remain a tensegrity structure as long as tensional integrity is required to maintain structural stability and not compressional continuity. If tensegrity exists in living tissues, then we will need to change our frame of reference in studies on morphogenetic remodeling to include the concept of prestress. This will require us to transform our image of tissue architecture from a rigid, static view that is largely based on local molecular binding events into one that is mechanically based, globally integrated, and dynamic. For example, morphogenetic changes in tissue form may be guided by varying ECM mechanics locally, not only by gradients of soluble signals (Ingber and Jamieson, 1985). In other words, positional information and pattern-generating signals would exist in this architectural scheme in the form of underlying structural forces. Global changes in tissue structure would therefore alter the CSK force balance locally and hence elicit an integrated cellular response. In this manner, entire societies of cells (e.g., an entire epithelium) may be guided and orchestrated during morphogenesis simply by remodeling a common structural scaffolding, such as the basement membrane (Ingber and Jamieson, 1985). Also inherent to tensegrity architecture is a mechanism for transfer of mechanical information (Ingber and Jamieson, 1985; Pienta and Coffey, 1991; Hansen and Ingber, 1992; Ingber et af., 1993), thermodynamic regulation (Ingber and Jamieson, 1985; Buxbaum and Heidemann, 1988), and hierarchical integration that is based entirely on tensional continuity. By hierarchical integration we do not mean a system of cataloging biological structures by size or complexity, as has been done in the past. Rather, we refer to a building method in which similar rules of stabilization (tensional integrity) are used regardless of the size of the structural component. Furthermore, each structural element is linked to the other (e.g., nucleus to the CSK) using the same tension-dependent mechanism for stability. This type of building approach not only produces a structural hierarchy, as can be seen in many compression-dependent structures (e.g., the Eiffel

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tower; Lakes, 1993), it also permits global rearrangements without loss of structural integrity (e.g., Fig. 6). It is difficult to envision another type of building system that could explain how tissues that contain interconnected cells, CSKs, and nuclei (Fig. 1) can undergo enormous deformations, such as that observed during gastrulation in the embryo, without producing structural breakage or disconnection. From the standpoint of chemical regulation, it is critical to emphasize that the tensegrity model does not make biochemical signaling pathways any less important; rather, it provides a mechanical context that may help us understand how these signals actually influence cell form and function. Specifically, the CSK provides an internal scaffolding or template which can both facilitate chemical reactions (e.g., bring substrates and enzymes into close proximity) and make these reactions sensitive to external mechanical stress. In this manner, CSK tensegrity may provide a simple mechanism for integrating both types of signals, chemical and mechanical, that are responsible for guiding development and maintaining functional tissue form. In contrast, mechanical manipulation of the CSK in the absence of concurrent chemical signaling events would likely do little to influence cell behavior. To summarize, these observations suggest that transfer of force from the ECM, across integrins, and to the CSK may represent a proximal step in an intracellular mechanical signaling cascade that leads to global CSK rearrangements and simultaneous mechanochemical transduction events at multiple locations inside the cell. If cells use a tensegrity-based transduction system, then mechanical signal transfer throughout the entire cell would be essentially instantaneous and thus more rapid than any diffusionbased signaling system. A simple way to visualize this type of signaling mechanism would be to think of the CSK as if it were a guitar string. Strumming would do little if the string were isolated and had no prestress. However, plucking the same string under tension would generate sound and transmit information. Furthermore, the type of information conveyed (tone) would vary, depending on the level of prestress and where along the string one placed their fingers (i.e., the spacing between the points of string fixation). In a similar manner, transmembrane receptors that physically join ECM to the CSK, such as integrins, are perfectly poised to control mechanical signal transfer across the cell surface, modulate the CSK force balance, and thus tune the cellular response to force. If this mechanochemical vision of cell and tissue development is accurate, then future experiments must be designed in which mechanical as well as soluble factors can be varied in a controlled manner, just as developmental morphologists attempted to do over a century ago. However, this time we will have the modern tools of molecular cell biology available to analyze the molecular basis of the changes we observe. If the

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tensegrity paradigm is correct, then we will also have an architectural context in which these molecular alterations can be placed. Thus, understanding and predicting complex tissue interactions as well as engineering artificial tissues (Ingber, 1993b) may be a possibility rather than a dream.

Acknowledgments We would like to thank Drs. J. Folkman and R. Cotran for their continued support, Dr. M. Bernfield for the gift of the tensegrity building kit, and Drs. M. Schwartz, J. Butler, and J. Fredberg for their collaborative contributions and helpful suggestions during the course of these studies. This work was supported by grants from National Aeronautics and Space Administration Space Biology (NAG-9-430). National Institutes of Health (CA-45548 and HL-46491), and the American Cancer Society. H. McNamee is a recipient of a graduate student research fellowship from NASA. S. Karp and J. Sims were recipients of medical student fellowships from the Johnson & Johnson Research Fund and the Stanley J. Sarnoff Foundation for Cardiovascular Research, respectively. Dr. Ingber is a recipient of a faculty research award from the American Cancer Society.

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Mechanics of the Cytoskeleton and Morphogenesis of Acetabularia 8. C. Goodwin and C. Briere Developmental Dynamics Research Group, Department of Biology, The Open University, Milton Keynes MK7 6AA, United Kingdom; and Laboratoire de Biologie Biotechnologie et AmClioration des Plautes, CNRS ENSAT, Toulouse. France

1. Introduction

Acefubulariu is a single-celled alga that undergoes a characteristic pattern of morphogenesis to produce a giant cell of distinctive form. Because of its basic simplicity, this organism lends itself to experimental and theoretical studies of the components that make up the morphogenetic field, and their dynamic properties. The dynamics of the cytoskeleton and its interaction with calcium are intimately involved in the changes of shape that occur during development in this species. A mathematical description of this basic eukaryotic system and a finite-element simulation of its behavior are presented which show that spatial patterns generically similar to those observed in the alga arise naturally, suggesting that normal morphogenesis can be described as an attractor of a moving boundary process. The implications of this possibility in relation to morphogenesis in related species are considered.

II. Growth and Morphogenesis The giant unicellular green alga, Acetabularia, has been recognized for many years as an exceptionally favorable organism for studying basic problems of cell and developmental biology, notably nucleo-cytoplasmic interactions and the molecular biology of cell differentiation (Brachet and Bonotto, 1970; Puiseux-Dao, 1979). This cell is now proving to be equally useful for studying the dynamic properties of the cytoskeleton and the Inrernolionol Reuiew of Cytology, Vol. 150

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cell wall that underlie the sequential transformations of cell shape observed during growth from a zygote, or in the process of regeneration of apical structures. The basic characteristics of the life cycle of Acetabularia acetabulum (formerly A . rnediterranea), whose habitat is the shallow waters around the shores of the Mediterranean, are shown in Fig. 1. Isogametes fuse to produce a roughly spherical zygote which breaks symmetry, producing a growing stalk and a branching rhizoid that anchors the alga to the substratum and houses the nucleus in one of its branches. When the stalk reaches a length of about 1-1.5 cm after several weeks of growth, a ring of small bumps arises around the tip, growing into a whorl of hairs or verticils that branch successively as they grow. The tip renews its growth from the center of the whorl and, after a few days during which the stalk grows several millimeters, another whorl is produced. This process repeats itself until a cap primordium is generated (Fig. 2). This is a structure with the same circular symmetry as a whorl but consisting of many rays joined together into a disc-shaped structure, the cap. This grows radially and

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FIG. 1 The life cycle of Acetabularia acerabulum.

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FIG. 2 Formation of a cap primordium, after three whorls.

the whorls drop off, resulting in the morphology of the adult: a rhizoid (still containing the nucleus), a stalk 3-5 cm in length and about 0.5 rnm in diameter, and a cap whose diameter is approximately 0.5 cm-a giant differentiated cell (Fig. 3). The alga is also capable of regenerating a cap after a cut through the stalk. It does so following the same sequence of shape changes as in normal growth. After the cut has healed with the production of a new cell wall, a tip emerges, grows, produces a series of whorls, and then generates a cap. After the whorls have dropped off, the regenerate with the rhizoid is indistinguishable from the original mature alga. In this chapter we discuss the dynamic processes responsible for the characteristic sequence of shape changes during normal development and regeneration.

111. Calcium-Cytoskeletal Dynamics Our attention was drawn to the importance of calcium in morphogenesis by studies which showed that changing the concentration of this ion in the sea water in which the algae develop causes dramatic changes of

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morphology (Goodwin et al., 1983). These changes could be duplicated by adding to the sea water ions (Co2+ or La3+)which block calcium channels, so the effects of reduced calcium are not simply on the mechanical properties of the cell wall but extend inside the cell. The wavelength of the whorl pattern can also be systematically altered by changing the calcium concentration in the medium (Harrison and Hillier, 1985; Goodwin et al., 1987). Calcium is known to have significant effects on the mechanical state of the cytoskeleton (Kamiya, 1981; Menzel and Elsner-Menzel, 1989). It changes the viscosity and elastic modulus of the cytopolasm by influencing the state of polymerization of actin and tubulin, and by activating actomyosin contraction and enzymes such as gelsolin which cut actin filaments. Some of these influences are shown schematically in Fig. 4. In order for morphogenesis to occur, it is necessary to have a medium in which spatial patterns are generated spontaneously. The most likely candidate for this in a cell is certainly the cytoplasm. It was established by Turing (1952) that coupled biochemical reactions combined with diffusion can produce spatially nonuniform patterns of reactants which he called morphogens. These reaction-diffusion systems have been extensively used by Meinhardt (1982) and by Murray (1989) to model morphogenetic processes in a variety of organisms, and they have been considered by Harrison and Hillier (1985) and by Goodwin and colleagues (1985; see also Murray, 1989, for Acetabularia morphogenesis). However, the morphogenetic effects of calcium and its influence on the cytoskeleton suggest that this system itself might play the role of primary patterngenerator. The first step in explaining this possibility was to derive equations that describe the mechanical properties of the cytoskeleton, the cytoplasmic regulation of calcium, and their interaction. This was done by Goodwin and Trainor (1985) and the coupled equations were shown to have the property of spontaneous bifurcation for particular ranges of the parameters. Within this range, spatial patterns of cytosolic free calcium and mechanical strain in the cytoplasm develop from random perturbation of the system from a spatially uniform initial condition. The reason for this behavior lies in certain basic properties of the calcium-cytoskeleton interaction, which will now be described. Cytosolic free calcium is regulated in eukaryotic cells at concentrations of 100 nM or so by plasmalemma pumps; by a sequestration mechanism involving the endoplasmic reticulum, vesicles, or vacuoles; and by binding

FIG. 3 Morphology of the mature alga, showing rhizoid, stalk, and cap. The whorls have dropped off.

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MP

FIG. 4 Schematic diagram showing structural compounds of the cytoskeleton. AM, actomycin; F, fibrin; G, gelsolin; MF, microfilament; MP, membrane protein; MT, microtubule.

to cytoplasmic proteins and chelating agents such as calcitonin and calmodulin. Studies of actin gels have shown that as calcium rises above 100 nM, it induces gel breakdown and solation by activating enzymes such as gelsolin. At higher concentrations, calcium initiates contraction of actomyosin filaments so that the cytoplasm becomes more resistant to deformation (Nossal, 1988).At calcium concentrations above about 5 p M , depolymerization of filaments and microtubules and the progressive action of gelsolin result in the cytoplasm becoming progressively solated. A qualitative description of this behavior in terms of changes in the elastic modulus of the cytoplasm as a function of calcium is shown in Fig. 5. This describes how calcium affects the mechanical state of the cytoplasm. We deduce that the mechanical state of the cytoskeleton acts reciprocally on free calcium concentration. It is assumed that strain or deformation of the cytoplasm results in release of calcium from the bound or sequestered state to free ions. Therefore, regions that happen to have elevated strain will also have elevated free calcium levels. However, increased free calcium causes gel breakdown and solation. This results locally in more strain (deformation) since the cytoplasm is assumed to be

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under tension, and hence in further calcium release. The result is a positive feedback loop in the regions of calcium concentration where the slope of the elastic modulus curve as a function of calcium is negative (see Fig. 5 ) . A local, random increase of calcium above the steady-state level initiates a runaway calcium release and increase of cytoplasmic strain. However, this is stabilized by the effects of diffusion, which tend to reduce the calcium gradients, and also by the opposing effects of calcium on actomyosin contraction, which increase the elastic modulus and so decrease the strain (region of positive slope, Fig. 5 ) . The argument also works in reverse: where calcium levels are decreased, the strain is also reduced since the cytoplasm is more gel-like (higher elastic modulus) and so free calcium will be bound or sequestered, decreasing it still further. In terms of reaction-diffusion dynamics, calcium plays the role of a short-range activator while mechanical strain is like a long-range inhibitor. The result of the interactions is that spatial patterns of calcium concentration and strain can arise spontaneously from initially uniform conditions when the equation parameters are in the bifurcation range. The model is qualitatively similar to that discussed by Oster and Ode11 (1984). A brief description of the calcium-cytoskeleton equations is given in Section 1 of the appendix.

IV. Cell Wall Dynamics

The properties of the cytoplasm described above give it the characteristics of an excitable medium which can spontaneously generate spatial patterns, both stationary and dynamic, that is, propagating waves. This is sufficient

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FIG. 5 Variation of elastic modulus with free Ca2+concentration (micromolar). Qualitative relations only.

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to initiate pattern, but morphogenesis involves changes of geometry. In the case of Acetabularia and many other developing organisms, morphogenesis is linked to growth, so the cell wall must undergo localized changes of shape together with elongation. The wall is described in the model as a purely elastic shell (about 2 p m thick) whose state changes as a function of strain in the underlying cytoplasm, which is a thin shell about 10 p m thick closely apposed to the wall, the plasmalemma separating them. This functional coupling is assumed to arise through strain-activated pumps in the plasmalemma that cause the wall to soften by excreting protons or hydrolases. The large vacuole in the center of the cell is an osmotic organelle which is separated from the cytoplasmic shell by another membrane, the tonoplast. The vacuole exerts a pressure that is resisted by the wall. Patterns of strain in the cytoplasm are thus reflected in the elastic modulus of the wall, which undergoes elastic deformations as a result of the outward-directed osmotic pressure. A growth process was introduced into the model whereby new wall material was added wherever wall strain exceeded a threshold value so that elastic deformations led to plastic changes, in accordance with experimental evidence (Cleland, 1971; Green et af., 1971). Growth of the cytoplasm was coupled to wall growth, while vacuolar pressure remained constant. The details of the growth algorithm are described in Section 2 of the appendix, while the cytogel-wall coupling is presented in Section 3. These relations are also described in Briere and Goodwin (1988).

V. Simulations of Acetabularia Morphogenesis

The calcium-cytogel and cell wall equations were used for a finite-element simulation of growth and morphogenesis. Parameters were adjusted so that the calcium-cytoskeleton equations were in the bifurcation range, making spatial patterns possible. The shape that developed depended on the characteristic wavelength of the pattern, and also on the parameters that describe wall growth. Simulations started with uniform initial conditions, on a dome representing a regenerating apex (Fig. 6). The first stage of pattern formation that typically occurred was the formation of a gradient of cytosolic free calcium that increased to a maximum at the apex. This is shown in Fig. 7. On the left is the outline of the shape of the tip along one of the longitudinal elements of the dome, from base to apex, while the other graphs show different variables of the cytogel as a function of distance from the base. Strain is measured both in the latitudinal (solid line) and longitudinal (dotted line) elements, showing the anistropy; this was also done for the elastic modulus of wall elements (incorrectly labeled

233

ACETABULARIA CYTOSKELETON AND MORPHOGENESIS

FIG. 6 Computer simulation of regeneration in which the cytoplasm and the cell wall are described as shells made up of finite elements which obey equations describing their dynamics as mechanochemical or elastic media, respectively.

elasticity). All variables start off spatially uniform (flat) and spontaneously develop a pattern, calcium rising to a maximum at the tip, as does the gel strain. The result is that the wall softens in this region and there is an elastic deformation. A three-dimensional view of this is shown in Fig. 8: a tip is produced. Shape

2.0

Wall strain

Gel strain

;:p

0.04

-

0.02 1.5

-

0.02

0.00

Wall elasticity

Calcium

100

10

80

60 40 20 0

Radius

0.4 0.8 1.2 1.6 2.0 DistanceIBase

2L 0.4 0.8 1.2 1.6 2.0

Distance/Base

FIG.7 Section through the mesh describing the regenerating tip, showing shape, wall strain and elastic modulus, cytogel strain, and free calcium concentration as a function of distance from base (origin, 0, on the abscissa of the graphed variables, radius 1 in the curve showing shape). A gradient in calcium forms spontaneously, with a maximum at the tip.

6 . C. GOODWIN AND C. BRIERE

234

FIG. 8 Tip initiation in the model, resulting from spontaneous symmetry-breaking of the cytogel-calcium dynamic, gradient formation with maxima of strain and calcium at the tip, and wall softening as a result of interaction between cytoplasm and the wall.

This is the first stage of the regenerative process, shown schematically for the real alga in Fig. 9. A characteristic feature of whorl formation is the flattening of the conical tip just prior to the appearance of the ring of hair primordia that initiates a whorl. This was something we had never understood. The model gave us an explanation. As growth occurs at the tip with plastic changes of geometry following the elastic deformations, there is an interesting interaction between the shape generated and the dynamic behavior of the calcium-cytogel system. After an initial stage of growth, the calcium gradient with the maximum at the tip becomes unstable and transforms into an annulus, with the maximum level of calcium occurring away from the tip. The region of maximum cytogel strain also changes in a similar manner (Fig. 10). Wall softening is now greatest in this annular region, resulting also in maximal wall curvature proximal to the tip, with consequent flattening of the tip itself, where the elastic modulus of the wall is now larger than in the annular region. As the tip grows, the amplitude of the annulus increases. A calcium annulus of this type was perturbed to see if it could spontaneously generate a pattern similar to that of a whorl. It did so, producing a

.

.

OLD CELL WALL

FIG. 9 Representation of the rnorphogenetic changes taking place during regeneration of Acetabularia. From left to right: hemispherical dome, tip formation, growth, tip flattening, and whorl formation.

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ACETABULARM CMOSKELETON AND MORPHOGENESIS

2.0 0.02

0.00

0.00

I .5

Calcium

Wall elasticity 140 1 20 100 80 60 40 20

0 Radius

I I

0.4 0.8 1.2 1.6 2.0 Distance/Base

0.4 0.8 1.2 1.6 2.0

Distance/Base

FIG. 10 Later stage of regeneration: The maximum of cytosolic free calcium is now displaced from the tip to the region of maximum curvature of the wall shape where the wall elastic modulus is reduced. In three dimensions, this defines an annulus.

ring of peaks of calcium that can be interpreted as the initiator of the whorl pattern (Fig. 11). Unfortunately the finite-element program is not yet sufficiently robust to allow us to study the growth of such small elements, breaking the axial symmetry of the growing tip. This work is in progress. However, the sequence of pattern changes observed, namely, gradient and tip formation, elongation, annulus formation, and tip flattening, and the bifurcation of an annular pattern to a ring of calcium peaks, provides a very natural dynamic explanation of a basic morphogenetic sequence. These observations suggest that we may be dealing here with an attractor in the moving boundary process, a whorl being a natural form. As the apex elongates, the annulus itself becomes unstable and intermittently collapses back to a gradient with a maximum at the tip, an annulus then reforming and growing in amplitude. This occurs with a rather irregular frequency, which is suggestive of the somewhat irregular frequency of successive whorl initiations as the alga grows. So we seem to have here another dynamic aspect of the morphogenetic process that occurs spontaneously, without any parametric change. These aspects of the moving boundary process again suggest that the basic generative dynamic is robust and fundamental to this type of growth and morphogenesis. We return later to this issue in relation to higher plant phyllotaxis, where a

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FIG. 11 The pattern in the simulation corresponding to the state of tip flattening described in Fig. 2, with a well-defined annulus of calcium at the region of maximum curvature in the shape. This annulus then spontaneously breaks into a series of peaks, which are assumed to initiate the whorl pattern.

multicellular meristem undergoing growth and morphogenesis commonly generates whorled patterns of leaves. Hairs in Acetabularia are basically simple leaves. They even fall off-in the adult. So they appear to serve no function. From a neo-Darwinian or functionalist perspective, this poses a problem: Why are useless structures generated? The dynamic analysis presented suggests that whorls are produced because they arise naturally

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237

(generically) as an accompaniment of growth in this type of morphogenesis. We will not pursue this aspect of the analysis here, which bears on evolutionary issues, but refer the interested reader to a more extended discussion elsewhere (Goodwin, 1990). Our simulations have so far failed to produce a cap. This requires another pattern of growth which we have approached, but never achieved, in which lateral growth exceeds longitudinal growth. The conditions for cap formation appear to require more anisotropy in the strain field than is currently in the model. The results reported here are preliminary but very encouraging. What is surprising is how comparatively easy it was to find parameter values that result in a series of shape changes that simulate remarkably closely the morphogenetic sequences of normal growth. Tip formation and elongation can be obtained equally readily starting from a sphere rather than a hemisphere, so the boundary conditions of the latter do not impose artificial constraints on the process. However, it is necessary to make a systematic study of the range in parameter space which results in the sequence observed, in order to characterize the robustness of the model. Although it is computationally complex, it is biologically extremely simple: cell wall, cytoplasm, and vacuole, modeled at their simplest. We may be looking at a basic eukaryotic morphogenerator.

VI. Variations on a Theme

Acetabularia belongs to a group of giant unicellular marine algae called the Dasycladales, all of which have basic morphological features in common. Some species are very similar to Acetabularia acetabulum, with slight variations of whorl and cap morphology. An example is A . crenulata, in which the rays of the cap are separated so that the overall form has spherical rather than circular symmetry, the rays emanating from the apical end of the stalk like radii from the center of a sphere. Related species have no caps, the hairs of the whorls becoming large and bulbous and serving as gametangia, where the gametes are produced. These and other forms can be “phenocopied” in A. acetabulurn by environmental influences; that is, this species can, without any change of genotype, be induced to take on phenotypes similar to those of other species simply by altering the environment. For example, Goodwin and colleagues (1983) found that changes in the concentration of calcium in the sea water caused characteristic changes of form. If the normal 10 mM Ca2+ was reduced to 3 mM, the algae failed to make caps so that the cells produced a series of whorls only. However, no gametes were produced under these

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conditions, so these cells are reproductively sterile. When the calcium is reduced to 2 mM, the algae cease making whorls and the stalk simply continues to elongate. At 1 mM, a bulbous tip is produced which stops growing. By altering the elastic modulus of the cell wall in the model, this bulbous form can be simulated, suggesting that there is a direct relationship between calcium in the medium and the mechanical properties of the wall, which is to be expected because of the role of calcium as a hardening agent in cell walls. Algae grown in the calcium range 2-4 mM often have bulbous hairs in whorls and no caps, “phenocopying” other species with this form. However, no systematic study of these variants by parametric modification of the model has yet been carried out.

VII. Conclusion

The essential simplicity of Acetabularia morphology and its amenability to experimental study are attractive features for investigating growth and form. The model of morphogenesis described depends upon fundamental properties of the cytoskeleton in interaction with calcium, encouraging the view that this may be a primary pattern generator in the eukaryotes, as argued elsewhere (Goodwin, 1989). What our studies have shown is that when the state of this excitable cytoplasm is coupled to the mechanical properties of the cell wall in ways that simulate experimentally deduced processes of deformation and growth, the cell undergoes patterns of morphogenesis that reveal generic qualities of the normal sequence of shape changes. This encourages the view that there may be general dynamic principles underlying morphogenetic sequences in Acetabularia and its relatives in the taxonomic group Das ycladaceae. An extension of this idea is that the essential dynamic properties of the morphogenetic field described for Acetabularia may be applicable, with modification, to the higher plant meristem. What encourages this is the observation that the whorl is one of the basic forms of leaf phyllotaxis. The other two, distichous and spiral, can be seen as transformations of whorls, all possibly arising from a similar generative dynamic in the meristem as a morphogenetic field. Each of these patterns may be a distinct morphogenetic attractor of the moving boundary process of the growing meristem. This view has been persuasively argued by Green (1987, 1989). Our own studies of asymmetric pattern initiation in the Acetabularia model support this. These speculations require further detailed investigation, which is in progress, but they point to the possibility of a remarkable unification of pattern-forming principles across a wide taxonomic range of organisms. Once again Acetabularia proves itself to be a model organism for studies which have very wide applications and implications.

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Appendix

A.

Viscoelastic Equations

The first equation describes the displacements of the cytogel (cortical cytoplasm containing the cytoskeleton) near an equilibrium state. The variables to consider are the displacement 5 from this equilibrium and the calcium concentration x (in this theory the cytogel is represented as a continuum). From the displacement field, we can calculate at any point the strain tensor E and the strain rate tensor d, which account for the elastic deformation and for the viscous motion, respectively. The stress tensor a, whose elements are the components of the forces per unit area exerted in the three principal space directions, depends on the strain and strain-rate tensors and on the mechanical properties of the cytogel. Since these properties depend on the local calcium concentration, we can write at any point M: a(M) = u [ & ( W ,&(MI,x (MI1

A linear expansion of a about the equilibrium stress tensor a. gives: a = a.

+ S . E + A.E

(1)

In general, A and S are fourth-order tensors (calcium dependent). However, for an isotropic material (which we assume for the cytogel), the 81 components of S can be expressed in terms of just two elastic moduli, the Lame coefficients h and p; similarly, in the theory of simple liquids, the 81 components of A can be expressed in terms of two coefficients, the shear viscosity, 5 and the bulk viscosity, q. Consider now a very small unit element of cortical material, with a volume density p; it accelerates according to Newton’s second law in response to the various elastic, viscous, and mechanical forces acting on it such that d i v u + f = p - d25 dt2 where div a accounts for the elastic and viscous forces andfdescribes the external forces. From Eq. (1) we have d i v a = divao + div(8.E)

+ div(A.&)

But, since a. depends on the calcium concentration duo . (Vx) div v0 = dX

(3)

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C. GOODWIN AND C. BRIERE

then divcr

=

S.V E

+ A. V E + 0acr . ax

(".ax

0 +~

E

+

Replacing S and A by the elastic moduli and viscosity coefficients, and expressing E and & in terms of the displacement and the velocity vectors 5 and 5 , we finally get the Goodwin and Trainor equation for viscoelasticity

where

F is a calcium-dependent second-order tensor and the external force term RE stands, in a linear approximation, for the restoring forces due to structural components (e.g., microtubules) which resist local displacement of the gel. It can be assumed (Goodwin and Trainor, 1985)that the contribution of the acceleration term is negligible, so that the left-hand side of ( 5 ) is zero.

6. Calcium Kinetics The Goodwin and Trainor calcium equation describes the simplest aspect of calcium kinetics. These authors assume a reaction with a stoichiometry n between calcium ions and a macromolecule C.

where C* represents the complex of n calcium ions bound to the macromolecule C . Assuming that the total concentrations of the binding macromolecules and of calcium are constant, a straightforward derivation leads to the kinetic equation.

dx = k,(K dt

-

x> - K,(P + x)x"

where x represents the concentration of free calcium, and p , K are constants. [Note: /3 + K = nC (total concentration of calcium-binding macromolecules).] In order to take account of stretching or compression ef-

ACETABULARIA CYTOSKELETON AND MORPHOGENESIS

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fects on calcium release or calcium binding, the rate constant k , was assumed to be a function of strain. Expanding this function to first order, this gives

k, = a

+ aV-ati

aXj

Finally, the Goodwin and Trainor equation for calcium kinetics is:

where a term for the diffusion of calcium, with diffusion coefficient D, has been added.

References Brachet, J., and Bonnotto, S. (1970). “Biology of Acetabularia.” Academic Press, London and New York. Britre, C., and Goodwin, B. C. (1988). Geometry and dynamics of tip morphogenesis in Acetabularia. J. Theoret. Biol. 131, 461-475. Cleland, R. (1971). Cell wall extension. Annu. Reu. Plant Physiol. 22, 197-222. Cosgrove, D. J. (1983). Cell wall yield properties of growing tissues. Evaluation by in vitro stress relaxation. Plant Physiol. 78, 347-356. Goodwin, B. C. (1989). Unicellular morphogenesis. In “Cell Shape. Determinants, Regulation and Regulatory Role” (W. D. Stein and F. Bronner, eds.), pp. 365-391. Academic Press, San Diego. Goodwin, B. C. (1990). Structuralism in biology. In “Science Progress,” Vol. 74, pp. 227-244. Blackwell, Oxford. Goodwin, B. C., and Trainor, L. E. H. (1985). Tip and whorl morphogenesis in Acetabularia by calcium-regulated strain fields. J. Theor. Biol. 117, 79-106. Goodwin, B. C., Skelton, J. C., and Kirk-Bell, S. M. (1983). Control of regeneration and rnorphogenesis by divalent actions in Acetabularia mediterranea. Planta 157, 1-7. Goodwin, B. C., Brikre, C., and O’Shea, P. S. (1987). Mechanisms underlying the formation of spatial structure in cells. I n “Spatial Organization in Eukaryotic Microbes” (R. K. Poole and A. P. J. Trinci, eds.), pp. 1-9. Green, P. B. (1987). Inheritance of pattern: analysis from phenotype to gene. Am. Zoo/. 27, 657-673. Green, P. B. (1989). Shoot morphogenesis, vegetative through floral, from a biophysical perspective. In “Plant Reproduction: From Floral Induction to Pollination” (E. Lord and G. Barrier, eds.), Vol. I , pp. 58-75. Am. SOC.Plant Physiol. Symp. Series. Green P. B., Erickson, R. O., and Buggy, J. (1971). Metabolic and physical control of cell elongation rate. In vitro studies in Nitella. Plant Physiol. 47, 423-430. Harrison, L. G., and Hillier, N. A. (1985). Quantitative control ofAcetabularia morphogenesis by extracellular calcium: A test of kinetic theory. J . Theor. Biol. 114, 177-192. Kamiya, N. (1981). Physical and chemical basis of cytoplasmic streaming. Am. Rev. Plant Physiol. 32, 205-236.

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Lockart, J. A. (1985). An analysis of irreversible plant cell elongation. J. Theor. Biol. 8, 264-275. Meinhardt, H. (1982). “Models of Biological Pattern Formation.” Academic Press, London. Menzel, D., and Elsner-Menzel, C. (1989). Induction of actin-based contraction in the siphonous green alga Acetabularia (Chlorophycea) by locally restricted calcium influx. Bot. Acfa 102, 164-171. Murray, J. D. (1989). “Mathematical Biology.” Springer-Verlag, Berlin. Nossal, R. (1988). On the elasticity of cytoskeletal networks. Biophys. J . 53, 349-359. Oster, G. F., and Odell, G. M. (1984). The mechanochemistry of cytogels. Physica 12D, 333-350. Puiseux-Dao, S. (1970). “Acetabularia and Cell Biology.” Logos Press Ltd. Turing, A. M. (1952). The Chemical basis of morphogenesis. Philos. Trans. R. Soc. B . 237, 37-72.

The Chemical Basis of Diatom Morphogenesist Richard Gordon* and Ryan W. Drum$ * Departments of Botany, Radiology, Physics, and Electrical and Computer Engineering, University of Manitoba, Winnipeg, Canada R3T 2N2; and 4 Island Herbs, Waldron Island, Washington 98297

An examination of the artificial diatoms shows that purely chemical and physical considerations will account for the varieties of pattern we notice in natural diatoms, and their living structure appears only to provide the conditions under which the silicious precipitation takes place, according to the ordinary laws of chemical action and molecular coalescence. . . . [I have tried] to make the subject more intelligible to that, I fear, very numerous class of microscopists who have not paid to Schultze's (1863a,b) artificial diatoms the attention they deserve. (Slack, 1870)

The external form of crystals is prismatic, and bounded by straight surfaces which cut each other at certain angles. But the same form is seen in the skeletons of many of the protists, especially the flinty shells of the diatomes and radiolaria; their silicious coverings lend themselves to mathematical determination just as well as the inorganic crystals. (Haeckel, 1905)

1. Introduction Diatoms (Bacillariophyceae) are single-celled eukaryotic algae responsible for about 25% of the world's net primary production (Werner, 1977). In addition to the vast deposits of diatomaceous earth (Cummins and Mulryan, 1937), their fossil record includes 1000 km algal mats (Anon., 1993; Kemp and Baldauf, 1993). Their silica shell (or frustule)' consists of two nearly often identical valves and associated girdle bands which fit together somewhat like a petri dish and its lid. There are 12,000 (Werner, 1977) to 60,000or more species (Eugene F. Stoermer, personal communication), which are classified by their wide variety of graceful forms and fine details 7 Dedicated to the memory of Judith Georgia Colburn, botanist, and her love for plants. See glossary at end of chapter.

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International Reuiew of Cytology. Vol. I50

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Copyright 0 I994 by Academic Press, Inc. All rights of reproduction in any fonn reserved.

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of the frustules and girdle bands (von Stosch, 1975), from the rows of striae just visible with a light microscope (cf. Roeder and Sharpe, 1991), down to the ornamentation of the pores or punctae (areolae) seen in ultrastructural studies. (There is no better way to appreciate the design in diatoms than to browse through the boxed sets of micrographs in the series “Diatomeenschalen im elektronenmikroskopischen Bild,” Helmcke and Kneger, 1962a,b; Geissler et a f . , 1961, 1963; Okuno, 1964, 1970,1974; Drum er al., 1966; Gerloff and Helmcke, 1974,1977; Krammer, 1982; cf. Round et al., 1990; Gaul et a f . , 1993.) What is intriguing is that these apparently regular structures are not formed out of a crystalline material (as once suggested: Desikachary and Dweltz, 1961; Drum et a f . , 1966), but rather appear to consist of fully amorphous silica (Bailey, 1856; Liebisch, 1928; Kamatani, 1971). This is an important distinction for us because it is easy to see how structure can arise by self-assembly when the molecules are arranged in a regular, bricklike fashion, as in crystals; however, the very word “amorphous” means “formless.” It reminds us more of the mystery of the origin of the universe. Pickett-Heaps and colleagues (1990) question the amorphous nature of the silica in diatoms: Amorphous silica . . . is not truly amorphous, since it contains regions of local order at the atomic level or in extremely small crystals. T. V. Desikachary (personal communication; cf. Desikachary and Dweltz, 1961) has also suggested that silica in diatoms is initially microcrystalline. While some local atomic order is to be expected for even completely amorphous substances, due to the hard core diameter of each atom (Ziman, 1979), it is indeed, “difficult to prove conclusively that . . . loss of the third peak in the RDF [radial distribution function, ascertained by x-ray or neutron diffraction, is] . . . inconsistent with . . . perturbed microcrystal disorder” (cf. Mason, 1968). (All quotes in this paper are as in the original.) What may be important here is to determine the scale of such microcrystallinity, if any, compared with the smallest features of diatom shells. A number of techniques are available: “although silicate structures have been determined mainly by X-ray diffraction, magic-angle spinning nmr using 29Siand ”Al is useful for microcrystalline and amorphous solids and glasses” (Cotton and Wilkinson, 1988). Nuclear magnetic resonance (cf. Farnan et a f . , 1992) has yet to be applied to diatoms. Another approach is Raman scattering (Boukenter et af.,1986; cf. Gaskell et a f . ,1983). Some crystallinity is found in dead diatom shells that have been heated or are fossils (Hurd, 1983). Since modern methods apparently have yet to be applied to just-formed diatom shells, we will proceed on the assumption that the latter are fully amorphous, and hope that someone will settle this old question soon.

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Thus the problem we address, simply stated, is: How do diatoms create such beautiful forms from at least effectively amorphous (formless) silica? We will see that the fundamental ideas that permeate the general morphogenesis problem in biology clash here, in this microcosm (cf. Gordon, 1994). Is there a prepattern determining where silica is placed (preformationism) or does the pattern of silica arise spontaneously (epigenesis)? Prepatterns have always struck us as ideas to be anathematized, since they smack of infinite regression, just like the old concept of the homunculus (Gardner, 1972). On the other hand, epigenesis has had a bad press because of its association with vitalistic forces (Driesch, 1929, 1933; Haraway, 1976; Gordon, 1994). In this paper, we confine ourselves to the earliest stage of diatom morphogenesis: the formation of the embryonic valve. We focus on our hypothesis (Gordon, 1981a,b) that the initial patterns are primarily a result of instabilities in the diffusion-limited precipitation of silica, resulting in a space-filling branching pattern (cf. spacing patterns in Wolpert, 1972; Bonner and Hoffman, 1963). For most diatoms, these patterns give but a crude first approximation. However, the fact that they are reasonably accurate for some diatoms suggests to us that this first approximation captures and represents the essential first step of diatom valve morphogenesis. First we summarize important features of diatom shells and discuss the generally observed stages of their morphogenesis. This will establish the chronology of pattern formation and help us identify any physical and/or cellular components that must be considered in a model. Next we undertake a critical review of the present theories and speculations offered to explain diatom pattern formation. Then we present electron microscope observations of aberrant diatoms and a preliminary heuristic model that they inspired. This is followed by an outline of our proposed molecular model based on the assumption that diatom pattern formation is basically the result of diffusion-limited precipitation. Details of the computer implementation of the model and its results are shown for the case of irreversible precipitation. Finally, we look at the roles of sintering, the colloidal nature of the silica, and the possible roles of the cytoskeleton in diatom shell morphogenesis. An odd convergence occurs here: the cytoskeleton apparatus associated with diatom shell morphogenesis is uncannily similar to the cell state splitter (Gordon and Brodland, 1987; Gordon et af.,Appendix, this volume). Perhaps they have a common origin. Preliminary accounts of our work were given in the review by Katchalsky (1974) and in Gordon (1981a), Gordon and Aguda (1988), and Gordon and Brodland (1990), and presentations were made at various symposia (Gordon 1980a,b, 1981b, 1985;Gordon and Drum, 1982). The fractal nature of the patterns was apparent early on, by comparison with the work that consolidated over a century of research on objects with fractional

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dimensions (Mandelbrot, 1977, 1982). In the meantime independent work on the formation of fractal patterns by random aggregation or diffusionlimited precipitation has arisen in physics, biology, and metallurgy (e.g., Witten and Sander, 1981, 1983; Meakin, 1983, 1986; Garik, 1985; Stanley and Ostrowsky, 1986; Freeman, 1987; Cusack, 1987; Feder, 1988; Family and Vicsek, 1990; Vicsek, 1992), though none of these addressed the diatom morphogenesis problem. The earliest work on pattern formation (branching fibrils) by irreversible precipitation may be that of Sutherland (1967; cf. Iler, 1979; Sutherland and Goodarz-Nia, 1971). Our major conclusions may be summarized as follows:

1 . The diatom shell forms within a flat membrane bag called the silica deposition vesicle (SDV) by irreversible precipitation of silica 2. Precipitation starts on a nonsiliceous nucleating structure of unknown composition inside the SDV 3. Because the source of the silica is initially along the margin of the growing silicalemma (the membrane of the SDV), conditions are set up for instabilities 4. These instabilities lead to branching patterns 5. Migration of the silica over the surface of the precipitate structure smooths (i.e., sinters) it and also leads to greater regularity of spacing of the developing silica dendrites 6. In the case of pennate (i.e., typically bilaterally symmetrical) diatoms, the regularity of spacing usually leads to a comb-like structure, masking the underlying tendency to form a branching pattern 7. Because the silica is amorphous, branching dendrites (costae or ribs to the diatomist) do not show fixed, crystallographic angles 8. Many centric (i.e., radially symmetric) diatoms contain areolae vesicles of unknown composition that adhere to fresh plasmalemma, act like a bubble raft through and around which the silicalemma and the branching silica precipitation must wend, and leave the shell in the form of a more or less perfect hexagonal honeycomb 9. The formation of hexagonal honeycomb patterns by colonies of Escherichiu coli bacteria, by a mechanism that may be mathematically analogous to silica precipitation, places in doubt the necessity of the areolae vesicles for pattern formation 10. The colloidal nature of the silica speeds precipitation immensely compared with what would happen if the silica were monomeric 1 1 . Any freshly exposed plasmalemma surface (i.e., not adhering to a mature silica shell) forms a silicalemma by an unknown mechanism 12. Silica enters the cell either through vesicles pinched off from the plasmalemma and/or via a silica ionophore 13. The silica is packaged in gel (low molecular weight) form in silica transport vesicles (STV)

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14. The STV are formed in an unknown place by an unknown mechanism, perhaps with the help of the Golgi apparatus 15. The silica transport vesicles make their way to any freshly exposed plasmalemma, perhaps by assistance of microtubules and/or by diffusion, where they are encountered by the margin of the expanding silicalemma 16. The silica transport vesicles contribute both their silica content and their membrane to the silicalemma when they fuse with it 17. A change in pH and/or ionic composition from the inside of the silica transport vesicle to the silicalemma occurs, sometimes causing the silica to form a small sphere within the silicalemma before it diffuses to and precipitates onto the growing shell 18. Unknown substances in the mother liquor within the silicalemma affect the kinetic parameters of the silica precipitation, causing species to differ 19. As the silicalemma completes the extension of its margin, precipitation of silica over the whole face of the silicalemma begins by an as-yetto-be observed transport process, perhaps involving lower adhesion and/ or fusion rates of silica transport vesicles, compared with the silicalemma margin, or perhaps involving a silica ionophore 20. The shell thickens considerably often incorporating mitochondria in the process, and generates an elaborate three-dimensional structure by unknown mechanisms which may include precipitation instabilities 21. The mature diatom valve acts as an antenna for scavenging silica from the medium

II. The Diatom Shell and Observed Stages of Its Morphogenesis There are two main forms of diatoms: pennate and centric (Fig. 1). The pennate diatoms are elongated and generally have parallel striae arranged normal to the long axis (Fig. Id). The striae are furrows or rows of holes (puncta) in the silica. The silica ridges between the striae are called costae (Hendey, 1959) or ribs (Lee, 1980). Centric diatoms are nearly radially symmetric, with approximately radial, branching costae. Branches of costae are rare in pennate diatoms. They nevertheless occur (Fig. lej,k). Finally, those centric diatoms that look like honeycombs (Fig. 2) also have an underlying, branching arrangement of costae: Evidently the basic pattern of lightly silicified valves is radial, with many species showing bundles or areolae with rows parallel to the central radial row in a fasciculated pattern. In cells that have more heavily silicified valves, the full pattern, such as a linear [perfectly hexagonal] or eccentric array, is shown. (Fryxell and Hasle, 1977)

a

FIG. 1 Examples of main forms of pennate and centric diatoms. (a) An aberrant valve of Licmophoru sp. with a nearly normal midrib which has a side branch. Note the fan of radial costae and the “suture” lines where costae run into one another. The cross-costae are thin and somewhat regularly spaced. (b) A Licmophoru valve in which the midrib is split in two parts. Note the front of mutual stoppage of growth of the costae along what may be a fusion zone (Li and Volcani, 1988). The long, thin, girdle band, partially separated above, has a structure somewhat similar to that of a normal pennate epivalve or hypovalve. (c) A Licmophoru valve whose aberrant midrib somewhat resembles the midring of centric diatoms. Id) A normal valve of Nauicufu sp. Note that two costae terminated early, and that the cross-costae are regularly spaced. (e) A Nuuicula sp. in which the midrib is short. Note the

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branching of the costae and the local nature of the alignment of the cross-costae to them. (f) A centric diatom, Cyclotella pseudostelligera. with an irregular branching pattern. Note the midring. (From Lowe, 1975, with permission.) (g) A centric diatom, Thalassiosira eccentrica, exhibiting well-defined domains of parallel costae. Note the small midring. (Kindly provided by Gretha R. Hasle.) (h,i j) Three partially formed raphes of the pennate diatom Pheodactylurn tricornatum, arranged in a presumed time sequence showing growth of the costae. (From Borowitzka and Volcani, 1978, with permission.) (k) Two naviculoid diatoms in which the abnormal one exhibits multiple branching and irregularities similar to those found in our computer simulations of irreversible precipitation (Fig. 9). Bars for h , i j = 0.5 pm. Bars for the others = 10 pm.

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FIG. 1 (continued)

This suggests that all diatoms use the same basic morphogenetic mechanism. Before proceeding with a disucssion of diatom shell morphogenesis, we need to decide which component is laid down first. This is a nontrivial question, whose very answer has depended on the kind of theory of morphogenesis one is pursuing: if preformationist, the organic component, and if epigenetic, the inorganic silica component. Let us try to separate the evidence from the interpretations. Dissolution of the silica of the mature valve with hydrogen fluoride (HF, or hydrofluoric acid) leaves organic material that preserves as much detail as the valve itself (Drum, 1963; Reirnann et al., 1965; Volcani, 1981; von Stosch, 1981; Pickett-Heaps et al., 1990): In the living cell the interior of the valve is covered with an organic layer that stains strongly with ruthenium red (see also Liebisch, 1929; von Stosch and Reimann, 1970), is resistant to hydrofiuoric acid (Schmid, unpublished observations),and is probably identical with the “subfrustular zone” of Drum et al. (1966). (Schmid and Volcani, 1983)

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FIG. 2 Tilted view of a portion of a centric diatom, Thalassiosira turnida, with a hexagonal valve face. Note the strutted processes and irregular pores at the short margin, and the girdle bands with and without small pores. Bar = 5 pm. (From Fryxell er a/., 1986, with permission.)

It has been observed that this material completely coats both the outer and inner surfaces of the mature valve of Cylindrotheca fusiformis (Reimann, 1964; Reimann et al., 1965), Nauicula pelliculosa (Reimann et al., 1966), and other diatoms (Drum, 1963; Drum and Pankratz, 1964a; Stoermer el al., 1965a). It has been presumed, therefore, that the organic material may function to retard the dissolution of the amorphous silica component of the wall (Cooper, 1952; Kamatini, 1971; Lawson et al., 1978; Pickett-Heaps et af., 1990). On the other hand, Hedy J. Kling (personal communication) suggests that dissolution begins while the cell is still alive, implying that there is no lasting protective covering. (She suggests that dissolution may even be essential to open pores occluded during valve formation.) Crawford (1981a) finds: Sections of mature epivalves . . . show no membrane to the outside. The organic layer . . . is the only non-siliceous component found between the new valve and the plasmalemma.

The answer to the question of whether there is organic matter embedded within the silica has oscillated. Reimann and colleagues (1965) suggest that their “findings [on Cylindrotheca fusiformis] are contrary to earlier ones . . . in which the organic material (called pectin) was considered either to be chemically bound throughout the silica structure (Mangin,

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1908a) or to exist as a layer beneath the silica layer (Liebisch, 1928, 1929).” The latter case is evident in the electron micrographs of Coornbs and Volcani (1968b). No organic matter can be seen in the spaces left by HF removal of the silica. These authors suggest that “apparently, macromolecular organic components are sequentially added to the periphery of the developing wall immediately preceding Si deposition.” The possibility has further been raised that “fibrillar organic material from the water itself. . . could also be a contributor to organic films on diatom cell walls” (Rosowski er al., 1986).This is possible, if our antenna hypothesis is correct. The search for organic matter within the silica, driven by the idea of an organic matrix on which the silica deposits, persists: Extraction of the frustule with hydrogen fluoride (HF), first performed by Von Mohl (1861) and Mangin (1908b) [leaves] . . . the organic investment which displays much of the fine detail originally present in the silica. Whether this result absolutely eliminates the possibility that the siliceous component of the frustule contains a polysaccharide skeleton, is still open to dispute . . . What is needed is a similar HF extraction of valves that have had all external polysaccharide removed. (Pickett-Heaps et al., 1990)

This very experiment has now been done by Swift and Wheeler (1992) who find that a fraction (f = 20-40%) of the dry weight inside the silica of diatom valves is protein and carbohydrate: The soluble material appears to contain glycoproteins with relatively high levels of serine and glycine . . . we suggest that the materials we have extracted are specific to and intimately associated with the mineral and thus represent a potential class of regulatory molecules for biosilicification.

Such a conclusion may be premature. Volcani (1982) also demonstrated by electron microscopy the presence of organic matter within what would appear to have been the solid silica of diatom valves. However, the fine, lacy, curved structure of this material suggested to us that it may have been present on the surface of the original colloidal silica spheres from which the valve probably precipitates, and may, in effect, be a trapped impurity (Chernov et al., 1984). Indeed, if we assume that a silica sphere of radius r and density p is surrounded by an organic shell of thickness s and density (T,then we can calculate:

Equation (l), with p = 2 g/cm3 (Iler, 1979) and u = 0.8 g/cm3, yields s / r = 0.39 to 0.46 for the rangef = 20-40%. Thus it is not unreasonable

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that the organic matter is a separate coat on a pure silica particle, and that these coats merely get trapped within the sintered silica as the particles coalesce during shell morphogenesis. If these coats have any structural rigidity, we can anticipate that they will have a spherical structure of appropriate diameter, if they were reconstructed by serial sectioning (Stevens and Trogadis, 1984). The problem is that the purported silica spheres have never been identified prior to their precipitation, and so we do not know if they actually carry an organic coat into the precipitation process. On the other hand, let us suppose they were delivered to the morphogenetic apparatus bare. Silica is covered with hydrogen bonds, and strongly adsorbs and even denatures protein (Iler, 1979). Indeed, this is why colloidal silica is a common packing material for high-performance liquid chromatography (HPLC) (Fallon et al., 1987). As soon as bare silica makes contact with any organic portion of the diatom cell, it is likely to acquire an organic coat. We thus see that the question of the relationship of organic matter to the silica depends on how the silica enters the cell, and not just on how the valve morphogenesis is accomplished. Unfortunately, the problem of how the silica is extracted out of the environment and concentrated in the cell from 40 (Azam and Volcani, 1974) up to 250-fold (Sullivan, 1976, 1977) is still unsolved. Two silica transport systems, “a high affinity-low capacity system and a low affinityhigh capacity system” (Azam and Volcani, 1974; cf. Roth and Werner, 1978), appear to be involved. These could be responsible for the initial formation of the valve and its subsequent thickening, respectively. The cell acquires most of its silica during valve formation (Volcani, 1981). This active concentration of silicic acid, Si(OH),, uses “a carrier-mediated membrane transport system which conforms to Michaelis-Menten type saturation kinetics” (Azam and Volcani, 1974; cf. Sullivan, 1976, 1977; Sullivan and Volcani, 1981). Immediately after cytokinesis, but before cell separation, each daughter cell of a diatom lays down a flattened membrane bag, the silica deposition vesicle (SDV), within which its new valve is formed (Reimann, 1964; Drum and Pankratz, 1964a,b; Lewin et al., 1966; Reimann er al., 1965; Drum et al., 1966; Dodge, 1973). The membrane of the SDV is called the silicalemma. The silicalemma is adjacent to the plasmalemma, is coated with microfilaments, and probably has an array of microtubules against or near it, emanating from a microtubule organizing center attached to the nucleus (Pickett-Heaps er al., 1990). Li and Volcani (1988) make the observation that, some of the sibling cells without nuclei could form normal valves. . . . this finding indicates that an unknown organelle might be responsible for the initiation of the SDV. This organelle could be the LPA [labiate process apparatus].

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Formation of a valve within the SDV sometimes takes only 10 to 20 min (Reimann, 1960; Reimann et al., 1965; Geissler, 1970; Jeremy D. PickettHeaps, personal communication). it continues to thicken for 1-3 hr or more (cf. Sullivan and Volcani, 1981). Volcani (1978) suggests that, from the first pair of [silica deposition]vesicles, additional vesicles on either side are sequentially formed by extension and enlargement of the previously formed vesicles, and are filled with silica as they form, until the entire valve is completed. All vesicles extend the full length of the cell. In this case, the valve would develop as a set of corrugations parallel to the midrib, for which there is apparently no evidence. Pickett-Heaps and colleagues (1990), drawing an analogy with mittens versus gloves, distinguish two cases. in one the silicalemma is convex, effectively the “visual hull” (Meister and Ulam, 1967; Beyer and Ulam, 1968) of the silica precipitated so far. In the other case, the silicalemma forms a contour around the growing valve and one may get “lateral fusion of the [silicalemma] membranes” (Schmid, 1986b) when cross-costae form. (These may explain the corrugations suggested by Volcani, 1978.) The single silicalemma in a daughter cell surrounds the entire developing valve (Plate 517 in Drum et al., 1966). A good example of what has been observed during the sequential wall development is provided by the work of Chiappino and Volcani (1977) on the pennate species Navicula pelliculosa. Following cytokinesis, they identify the following four stages (cf. Schmid, 1984a): 1. Formation of a primary central band (PCB) inside the SDV; the earliest PCB they observed already extends the length of the cell with a central nodule (CN) in the middle 2. In-turning of the PCB and differentiation of the CN, which involves growth of secondary arms and appearance of mounds or knolls in the central region of the CN 3. Approach of the PCB extensions and the secondary arms which ultimately fuse, forming the raphe rib (in this stage, the growth of transapical ribs is apparent) 4. Growth of cross-bridges and loss of the mounds of the CN.

For this species, the silicalemma is observed as one continuous membrane that closely follows the configuration of the valve throughout the development of the wall. The concomitant biochemical events during wall formation are summarized by Coombs and colleagues (1967a): 1. “uptake of silicon from the medium 2. synthesis of the constituents and the macromolecules comprising the silicalemma

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3. translocation of silicon from the cytoplasm into the silicalemma 4. polymerization of the silicon within this membrane system 5 . synthesis of any organic material added secondarily to the wall” The sequential order of the last two steps was changed to “concurrent” in Volcani (1978). Toman and Rozsival (1948), in what is perhaps the earliest electron microscopic study of nascent valves, found that in Nitzschia amphibia: 1. The costae first grow to their full length and “do not cohere. Therefore these stages are most liable to mechanical injury” 2. Small bumps appear on both sides of each costa 3. “[Cross] costae begin to unite . . . [and] keep uniting” 4. The pores so formed partly fill in and round up: “The connecting bands are provided with one row of holes” We interpret this as a clear indication that, in this diatom, the processes of costa formation, cross-costa formation, and pore formation are sequential, the latter two requiring silica available over the whole face of the developing valve. A number of poorly understood events occur subsequently: thickening of the valve in both vertical directions, interaction of the valve thickening with various organelles, such as mitochondria, and the construction of other silica structures, such as girdle bands, spines, etc. (Pickett-Heaps et al., 1990). In some pennate cases the whole SDV moves before the two-dimensional growth phase is complete, so that the costae mostly grow from just one side of the central rib (Pickett-Heaps et al., 1990). In this review we focus on the first, essentially two-dimensional phase, on the assumption that it must be understood first.

111. Theories and Speculations on Shell Morphogenesis A. Mold Prepattern Hypothesis

1. Molds in General The concepts of “template” and “mold” have not been clearly distinguished in the diatom literature. Our division of some of the existing theories for diatom morphogenesis into these categories is thus a little arbitrary. We will take “mold” to mean a container into which silica is placed, so as to fill it. We take “template” to mean a guide along which the silica pattern is nucleated. In neither case is the silica itself supposed to cause pattern formation.

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Lewin and colleagues (1966) have asked: How is the specific form of the diatom shell controlled? Since the silicalemma is presumably flexible, we may assume that its shape conforms in some way to a cytoplasmic matrix, perhaps by changes in the sol-gel configuration of the cytoplasm which could serve as a semiflexible mold for the silica shell.

(Compare Stoermer ef al., 1965a,b.) This is the common embryological notion of a prepattern or preformation (Gould, 1977). Hendey (1964) implies a similar mechanism: The pH of the interior of most diatoms is acid, for example, that of Surirella sp. is 6.8 approx. Silica dissolved in sea water of pH 8.2 entering such a cell would be precipitated, probably in a highly hydrated gel form, and oriented upon the plasmatic layer.

(See also Hendey, 1959.) Pickett-Heaps and colleagues (1979a) also suggest a prepattern: “A patterned wall can be created either by different cytoplasmic regions secreting wall material at different rates, or else by such regions beginning their secretion at different times (or a combination of these possibilites),’ ’ and hint (1979b) that the endoplasmic reticulum may have this role because “its positioning corresponds to some extent with the . . . pattern of fine, presumed newly formed wall [silica] fibrils. ” Stoermer and colleagues (1965a) suggested that “the silica deposition vesicle appears to act as a mold in determining the final morphology of the valve.” Their observation that “the outer membrane of this silica deposition vesicle infolds and approaches the inner membrane in areas that will become the puncta in the mature valve” does support this view. Lacalli (1981) suggests that each costa is wrapped in membrane in some diatoms (cf. Li and Volcani, 1984). However, the possibility exists that the silicalemma may collapse onto the mature valve when valve growth is complete, giving the appearance of a mold, although Crawford (1981a) finds, to the contrary, that the silicalemma and plasmalemma above the valve deteriorate even before valve maturation. Reimann and colleagues (1966) support the hypothesis that the SDV is a mold, despite their evidence to the contrary: The newly deposited silica is not tightly surrounded by a rnembr$ne, but instead there is an irregular space, sometimes as much as [600 A] wide, between the silica and the membrane that surrounds it; thus, this membrane does not exactly follow the contours of the silica. It is difficult to imagine that a structure as complicated as a diatom shell could be formed without direct contact with inductively acting cell structures. We therefore suggest that this space visible between the silicalemma and the siliceous structures is artificially produced during the fixation and embedding procedures.

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2. Bubbles in Particular

A theory “by Helmcke (1959) [in which] the foamy structure of areolae, should be the result of gas-vesicles, which arise from the chemical process of the precipitation of silica” was dismissed in Schmid and Schulz (1979), but reconsidered in Schmid (1984a, 1986b) via “spacer vesicles” (liquid-filled; Schmid, personal communication) who gives some evidence for the functional implication of areolae vesicles in valve pattern formation in the centric diatom Coscinodiscus waifesii. She finds what she calls a prepattern of radially organized “areolae vesicles . . . about 1.0 to 1.6 p m in width of unknown origin” (Schmid, 1986a) that precedes growth of a bifurcating and anastomosing SDV that appears to wend its way between these vesicles. Schmid (1986b) hypothesizes that “certain recognition sites for the small vesicles . . . and the primary prepattern, that is the signal for the AV-[areolae vesicles] and ER [endoplasmic reticulum]- mitochondria1 distribution, could already be created during cleavage. ” This prepattern scenario is taken as sufficient evidence that “the hypothesis of the ‘space filling branching pattern’ (Gordon and Drum, 1982) proposing that the basic valve patterns are effected by instabilities in the precipitation of silica, is strictly contradicted.” However, “an interesting riddle, still waiting to be solved, is the absence of areola vesicles during areolae formation in Thalassiosira eccentrica (though they are found in Pinnularia, Nitzschia sigmoidea, and Achnanthes longipes; Schmid, personal communication). Although rather unlikely, it can’t be completely excluded that this is due to insufficient fixation” (Schmid, 1984a). On the other hand, in her preparation of Coscinodiscus wailesii, Schmid (1984a) indicated “fixation is still dreadful in comparison with other objects.” While the prepattern of areolae vesicles may be real, the author’s obvious concern for artifacts on both sides of the question makes us desire further investigation. The purported prepattern itself was only demonstrated in fixed material in which the “DAB-cytochrome-oxidase reaction was applied to identify mitochondria in LM [light microscopy]. Demonstration in the living diatom would be preferable (perhaps requiring confocal microscopy). Thus this intriguing hypothesis, supported by mechanical considerations (Bach and Burkhardt, 1984),remains a plausible alternative whose correctness and universality need testing. A critical experiment might be to eliminate the areolae vesicles. Badour (1968), obtained full lateral valves in the absence of cytokinesis in the centric diatom Cyclotella cryptica. These cells lacked intercellular, valvar plane plasmalemmas and thus may have generated valves at arbitrary positions around the (perhaps new) lateral plasmalemma without ”

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any benefit of a plasmalemma-associated prepattern. These lateral valves, except for mechanical distortion and a small bit of extra branching, often look like normal valves (cf. Oey and Schnepf, 1970). Hasle and Lange (1992) show a centric Coscinodiscus concinnus “valve under development. . . . Radial strings are first laid down as ‘spaghettilike’ structures” which both branch themselves and work their way around branching (though unconnected) rows of areolae. This suggests that the areolae are secondary obstructions to a primary, branching silica deposition mechanism. The branching structure of the growing silica may create a branching pattern of the areolae as it works its way past them (cf. Kimball and Frisch, 1991). Perhaps areolae and the silica strands can actually move a bit before the latter sinter together. If so, the combined mechanism may be what is responsible for the near perfection of hexagonal patterns in some diatoms (cf. Hasle and Syvertsen, 1985), which seem to preserve no record of any aberrations in the course of their morphogenesis. It would explain the correlated zigzags of adjacent costae in some centric diatoms (Fig. l l a in Hasle and Fryxell, 1977) and possibly the competition between square and hexagonal patterns in some pennate diatoms (Van Heurck, 1890). The cases of imperfections, which look so much like the domain structures with crystallographic dislocations in bubble rafts (Helmcke, 1984; cf. frontispiece in Smith, 1981; Howell et al., 1974), are thus explicable, as are, perhaps, the cases of groups of nonradially parallel costae (Fig. lg). A hint of this local, adjusting motion can be seen in the following description of the development of cross-costae, before they sinter into a hexagonal pattern obscuring its origin: The cross-extensions branch from the radial silica strings at a narrow angle . . . [and] curve to meet the extensions from the opposing radial strings, thereby forcing the radial strings to curve outwards between the two

branching points. . . . the opposing cross extensions have joined . . . forming the round outline of the prospective areolae. (Schmid and Volcani, 1983)

Perhaps some form of micromanipulation, such as dielectrophoretic levitation (Kaler and Tai, 1988), or analysis of their Brownian motion (Mizushima-Sugano et al., 1983) could be carried out in the large centric diatom used for this work (Coscinodiscus wailesii, up to 500 pm in diameter), to measure the bending modulus of the silica strands. Similarly, the mechanical stiffness of the areolae vesicles needs to be known, as shown by simulations of analogous patterns in which the “repulsion is soft, more akin to the magnetic ball model than to the bubble-raft model . . . popular to visualize dislocations and grain boundaries” (Rivier et al., 1984; cf. Stein and Gordon, 1982).

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6 . Template Prepattern Hypothesis

Hecky et al. (1973) analyzed the amino acid and sugar composition of six diatom species and built on it a prepattern hypothesis. They found that the cell wall contained from 0.7% to 28% dry weight of amino acids and from 0.06% to 0.3% dry weight of hexosamines. They found that the cell wall protein contains up to 25.2 mole percent of serine in Cyclotella cryptica, “the highest of any biological material known to us.” Since Coombs and Volcani (1968a,b) had “observed a marked increase in protein concentration in cell walls during Si-deposition” according to Hecky et al. (1973), the latter proposed a mechanism for silicification in which the serine in this protein, presumably exposed on the inner surface of the silicalemma, acts as a template for epitaxial condensation of silicic acid. Volcani (1978) elaborated: Silicification itself. . . may result from changes in pH or concentration, or from binding to specific sites in the silicalemma followed by polymerization. Such binding could be produced by hydrogen binding (Holt and Yates, 1953), ionic concentration (Holt and Yates, 1953), or condensation by hydroxyl groups (Cotton and Wilkinson, 1966; Fessenden and Fessenden, 1967).

Similar template suggestions had been made previously: The occurrence of 3,4-dihydroxyproline in the proteinaceous components of the diatom wall suggests that the new amino acid may be a determinant of the molecular structure of the organic matrix associated with silicification. (Nakajima and Volcani, 1969) One may conceive o f . . . mechanisms, such as deposition on an organic surface which has a pre-established topography and which serves as a template for the final pattern. (Lewin, 1962).

Other researchers have also considered the prepattern to be in the silicalemma. Duke and Riemann (1977) claim that: It is one of the particular features of the silicalemma that it possesses sites where silica is preferentially deposited within the vesicle which it forms and other sites where no silica deposition takes place . . . the membrane of a site exhibiting a particularly high activity of silica deposition extends into a membrane part which is morphologically identical but is totally inactive relative to silica deposition.

Pickett-Heaps and co-workers (1979a,b) have observed fine microfibrils associated with growing parts of the valve. These were reduced where endoplasmic reticulum was juxtaposed with the silicalemma. They interpret their micrographs to show “fine strands of template (presumably polysaccharide) created by the silicalemma, on to which the siliceous matrix is precipitated.” Some fibrils appear to consist of small particles

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of the order of 100 A wide. The fibrils coating the forming costae have the same electron density as the silica shell. Thus they may consist of silica particles (Pickett-Heaps, personal communication). Brief treatment with HF removes such fibrils, leaving no evidence of a template (Drum et al., 1966). On the other hand, Schnepf et a f . , (1980) and J. Kiethe and B. E. Volcani (Volcani, 1981) found that some fibrils remained after HF treatment. The organic material may, however, merely represent an organic coat on precipitated colloidal silica particles that survives HF treatment and remains as a cast of the original silica fibrils that the coagulated colloidal particles formed, as discussed earlier. Anderson (1975) observed the Golgi near the silicalemma in growthresumed resting cells of Amphora coffaeforrnis, and concluded that they form templates: The electron-dense deposits in the golgi resist HF treatment and therefore are not silicon. The golgi vesicles may fuse to form the cisterna and the “organic plates” could act as templates for silicon deposition, thus explaining regulation of frustule form.

Finally, Lacalli (1981) has suggested that the template prepattern could be in the plasmalemma: The pattern could be laid out in advance in two dimensions in the adjacent cell membrane, and growth of the silicalemma follow this as a template.

C. Critique of Prepatterns

If the prepattern is placed outside the silicalemma (organic plates: Anderson, 1975; endoplasmic reticulum: Pickett-Heaps et a f . , 1979b), we have to concern ourselves with how it gets inside. We need a mold of the mold or a template of the template, which is not impossible, but is another step to be elucidated. It is important to note that in some cases the organic material is tightly pressed only to the inside surface of the frustule (Chiappino and Volcani, 1977). It does not always form an organic casing, “which consists as a rule of a structurally undifferentiated layer, 8-10 nm thick” (Volcani, 1981; cf. Schmid e f a f . , 1981). Crawford (1974a) found that “organic material and siliceous scales in the auxospore [of Melosira sp.] . . . are present as two distinct components” that form at different times and some distance apart. Borowitzka and Volcani (1978; cf. Volcani, 1981) show that Phaedactylum tricornatum can form a daughter cell entirely lacking silica. Its cell wall shows only randomly oriented sets of ridges that in no way resemble the costae of normal valves. “Nonsilicified protoplasmic

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masses have been reported in diatom cultures . . . . Such naked cells were enclosed within a tenuous membrane, probably the organic part of the cell wall, but they bore no markings characteristic of the species (Hendey, 1945)” (Lewin, 1%2; cf. Hendey, 1946). Thus the t h i n g of formation of the organic walls (mostly after silica deposition), their occasional displacement relative to the silica (“newly formed organic wall attaches to the edges of the siliceous portion of the valve”: Borowitzka and Volcani, 1978), and their lack of structure when they form without silica present, make their role as a mold for the silica questionable. Conflicting evidence that an organic matrix is present within the SDV (reviewed by Volcani, 1981) will have to be resolved. Schmid (1986a) believes that “evidence for a complicated functional and structural interaction of nearly all cell organelles during valve formation . . . exclude[s] hypotheses such as . . . the suggestion that the silicalemma itself could be the moulding compartment (Stoermer et al., 1965; Dawson, 1973; Chiappino and Vocani, 1977; Lacalli, 1981).” Bacterial colonies (none other than E. coli !) can also form hexagonal honeycomb patterns when the culture medium is thin (Budrene and Berg, 1991), with nothing comparable to the areolae to guide them. The startling similarity of some of these patterns to those of some centric diatoms was noted by Natalie K. Bjorklund (personal communication). With the use of a Petri dish, the thin medium required is morphologically similar to the silicalemma in centric diatoms. The mathematical bases of the patterns may be similar, precipitation corresponding to the loss of motility. This observation places in doubt the logical necessity of the areolae vesicles for such pattern formation, even acting only as bubble rafts. Both living organisms-diatoms and E. coli-humble us, for we are not yet able to simulate the richness of patterns that they can generate, in the absence of the directional biases of crystalline precipitation processes (Langer, 1989). A simple objection can be raised to any prepattern hypothesis: if there

is a prepattern for diatom shell morphogenesis, then why are the branching patterns of costae on three individual valves from the same clone of the centric diatom Thalassiosiru bulbosa (Figs. 14, 15, and 19 in Syvertsen and Hasle, 1984, with only a 20% spread in valve diameters; cf. Figs. 94-95 in Hasle, 1978; Schmid, 1990) entirely different from one another? Reimann and colleagues (1965) observed that “every part of the silica shell is tightly enclosed by organic material . . . . The surface of the organic material on the outside as well as on the side towards the cell interior is completely smooth, i.e., without a patterned structure.” Presumably they meant that the organic material looked the same everywhere. This speaks against the template prepattern hypothesis.

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A number of observations indicate that the pattern of a new diatom valve is not based on the existing valve as a template: 1 . The pattern is not transferred from the old valve of a daughter cell to its new valve, since in some species both valves have different patterns (Drum et al., 1966) 2. When a cell is crenated (Kiister-Winkelmann, 1938) or a resting spore is formed (Fig. 21 in von Stosch and Fecher, 1979), both new valves reform within the old ones 3. In “rapid size reduction, the cytoplasm first separates . . . [from] the valve” (Kling, 1993) 4. There is no ultrastructural evidence for a pattern echoing the costae in the cytoplasm adjacent to the silicalemma (Drum et al., 1966) 5. Moreover, the naked protoplast of an auxospore can form its own diatom shells de nouo (Bold et al., 1987) 6. This is also true in vegetative extrusion and enlargement Unexpected morphogenetic forces are demonstrated by which cells with irregular cross-sections give rise to almost regularly radiate forms in the course of vegetative propagation (Ditylum). This result cannot be explained solely by mechanical membrane “inheritance.” (von Stosch, 1965)

One argument against the prepattern hypothesis of Hecky et al. (1973), that epitaxial growth of silica is involved, is that the direction of cyrstallization of what are probably cubic salt crystals within the silicalemma, is always parallel to the silicalemma surface, but at random orientation otherwise (Gordon and Brodland, 1990). The problems with the very concept of a prepattern are (1) we have to identify what (usually invisible) structure it consists of and (2) how that structure is formed into a specific pattern. What is the prepattern of the prepattern? Either we must eventually stop and decide to explain the “initial” pattern, or accept the concept of infinite regress (the homunculus). Since the existence of atoms eliminates infinite regress, at some point we must be intellectually prepared to tackle the formation of the initial pattern, whatever it is, however it is formed. If we apply Occam’s razor, “Do not multiply hypotheses more than is necessary” (Wiener and Noland, 1957), then we should get on with seeing what silica itself can do. D. Physicochemical Mechanisms

Thompson (1942) has discussed formation of “the very minute and astonishingly regular pattern of hexagons which we see on the surface of many diatoms.” He cited FitzGerald (Larmor, 1902) who “thought diatom patterns might be due to electromagnetic vibrations” set within the defined

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boundary of the cell. These could be analogous to standing waves on drums or coffee in cups (Friedman and Youtz, 1965). Other physical mechanisms leading to hexagonal patterns include BCnard instabilities (Chandrasekhar, 1961; Prigogine, 1980; Rivier et al., 1984) and the growth of crystals in the presence of impurities (Chernov et al., 1984). Were we to conclude that hexagonal patterns are fundamental rather than secondary, these mechanisms might be well worth reviving, especially since at least one is under consideration for limb morphogenesis (see Forgacs and Newman, this volume). Hendey (1959; cf. Hendey, 1954) has made an analogy between diatom patterns and the “boundary layers or interfaces between complex immiscible systems.” Recently, Fiedler and Fiedler (1984) also embraced the assumption that the great variety of diatom patterns are mainly due to physicochemical causes: When one looks for analogous or similar shapes among the macroscopic phenomena which are accessible to analysis one finds parallels mainly in the flow patterns of free convection and in the agglomeration patterns of bubbles or drops. Both phenomena are in principle conceivable as basic models for the formation mechanism of diatomaceous shells.

They went on to investigate a free convection current (FCC) mechanism which requires “the existence of a dielectric layer having free charge camers (silicalemma).” Their conclusion: The FCC model based on electroconvection supplies a possible explanation for the formation of the characteristic chamber forms in diatomaceous shell. This model does not, however, explain the consolidation and hardening of the chamber walls, i.e., the formation of the skeleton itself. An answer to this question may be found in colloid chemistry.

It is also interesting to note that Fiedler and Fiedler (1984) eliminated Marangoni-type convection although the Marangoni effect has been suggested as a possible mechanism for initiating periodic finger formation in asymmetric membranes (finger formation due to the transport of a third component) (Ray et al., 1985). Pattern formation in reaction-diffusion systems has also been taken as a possible explanation for diatom morphogenesis. Lacalli (1981) has suggested that diatom patterns are generated by a Turing (1952) mechanism which operates along the growing edge of the silicalemma. Such models require two or more substances interacting in a reaction-diffusion mechanism. Suggestions as to the nature of these substances, their reactions, or their relationships to the precipitated silica are yet to be proposed. The very first concrete indication that the basic diatom patterns can be explained mainly by using physicochemical considerations came from the work of Schultze (1863a,b) (Fig. 3). He noted the similarities between vapor-precipitated silica and diatom shells with regard to morphology,

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2.

FIG. 3 Sketches of artificial diatoms made of silica precipitated by Schultze (1863a,b).

amorphous constitution, specific gravity, and form birefringence. He stated that nonuniform deposition during precipitation “chiefly on the elevations” can lead to pattern formation [cf. Rehbinder and Vlodavets, 1971, who report “condensation structures at the phase boundaries of silica gels, which, because of the colloid structures, also show typical hexagonal forms” (Fiedler and Fiedler, 1984)l. A quantitative understanding of such instabilities in precipitation processes was not available for another hundred years (Mullins and Sekerka, 1963). The pattern formed by the vapor-precipitated silica was three-dimensional. Schultze’s work was further discussed by Slack (1870, 1871, 1874) and Morehouse (1876). References to his diatom work appear to be entirely lacking in the literature of our century. Our hypothesis of instabilities in diffusion-limited precipitation is essentially a rediscovery and elaboration of Schultze’s hypothesis. E. Does the Golgi Play a Role?

Sullivan and Volcani (1981; cf. Mehard et al., 1974; Volcani, 1978) have used electron microprobe analysis in an attempt to locate the intracellular

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pool of silica. No sharp localization was found. Mitochondria, the nucleus, Golgi vesicles, and every other organelle seemed to have its share of silica, with more in the mitochondria. Quantitative experimental discrimination between cytoplasmic and Golgi vesicle pools of silica has yet to be made. The active mechanism concentrating the silica may reside in the Golgi membrane rather than the plasma membrane of the cell. A gel character of the silica in Golgi vesicles, and its consequent solubility, may explain why Dawson (1973; cf. Drum et ul., 1966) was unable to alter the Golgi’s ultrastructural appearance with HF. The frustule dissolves away by this treatment. On the other hand, Schmid and Schulz (1979) observed “cytoplasmic vesicles with a diameter of 300-400 A, which are possibly derived from the Golgi apparatus [which] . . . have an electron-dense content.” These “silicon-transport vesicles” were observed “fusing with the silicadeposition vesicle during valve formation.” Coombs and co-workers (1968a), however, observed: vesicles with dark electron dense contents in the region of the nucleus, apparently increasing in size as they move towards the developing wall. . . . However, treatment with HF failed to remove the dark centre as should have occurred if the contents were silica . . . . It would appear thus that such structures are lipid drops derived from disintegrating membranes.

Chiappino and co-workers (1977) also observed dense vesicles in Nuuicula alba: “In the presence of [Ge]/[Si]of 1 .O . . .vesicles usually surround the nucleus in the area normally occupied by the Golgi apparatus.” (This observation is consistent with these vesicles actually being at least part of the Golgi apparatus.) The vesicles were also only partially extracted with H F treatment and “appear to be disc-shaped, approximately 100 x 50 nm in size and ca. 20 nm thick and are always membrane bound.” The visibility of the silica in diatoms treated with teratogenic Ge could be explained by assuming that Ge shifts the pH dependence of the balance between gel and sol states of silica (Fig. 4) toward the sol state, and either that the gel state is sufficiently electron transparent so that its contrast is not changed by HF, or that ordinary fixation and embedding of Ge free diatoms removes silica in the gel state before sectioning. [Note that the pH of the medium alters the Ge effect (Lee, 1980).]If the silica is ordinarily in the gel state in these vesicles, this may be because the pH within the vesicles is acidic, pH < 7 (Fig. 4). [Note the opposite suggestion in Volcani (1978) which would require high salt.] Lysosomes, for comparison, have a pH of 5 compared with a cytosol pH of 7.2 (Alberts et al., 1989). An alternative or complement to an acidic pH for creating a gel state of silica in silica transport vesicles would be a change in electrolyte concentrations (Fig. 4) (cf. Allen and Matijevic, 1969). Our suggestion that the silica in the silica transport vesicles is low molecular weight is consistent with the observation “that large Si pools are maintained in cells at all times . . . (and) that 48% of the water soluble

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I

DIMER

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CYCLIC pH< 7 or

i

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IOOnm

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FIG. 4 “Polymerization behavior of silica. In basic solution (B), particles in sol grow in size with decrease in numbers; in acid solution or in presence of flocculating salts (A), particles aggregate into three-dimensional networks and form gels” (Iler, 1979). Copyright 0 1979. Reprinted by permission of John Wiley & Sons, Inc.

pool Si is reactive as a blue-colored silicomolybdate complex and is thus monomeric Si(OH),” (Sullivan, 1980). Schmid (1986a) suggests a shift in the nature of the vesicles after the two-dimensional growth of the silica is over: The SDV enlarges by coalescence of what appears in cross-section as small vesicles, about 35 to 50 nm in diameter, which are obviously derived from the distal cisternae of the dictyosomes . . . . At the time of cribellum formation the dictyosomes of the entire cell switch to produce a different and very characteristic type of vesicle, about 90-100 nm in diameter, containing electron dense material in its center with a surrounding clear zone. HFextractions made clear that this electron dense substance is organic . . . . These vesicles fuse with the proximal silicalemma and the dense material appears within the SDV.

The vesicles may be typical coated vesicles: In Synurapetersenii(Schnepfand Deichgraber, 1969) . . . “coated” vesicles, apparently derived only from the Golgi apparatus have also been found to be incorporated in the SDV. (Schmid et al., 1981)

Fulton (1984) notes that microtubule tubulin has been found associated with clathrin-coatedvesicles (Pfeffer et a!., 1983). This may be important

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in the transport of vesicles to the silicalemma, and could also explain why microtubules are seen near the silicalemma. It is possible that one role of the microtubules underlying the SDV is to bring the silica transport vesicles to the outer edge of the silicalemma, where they would contribute to the initially strict two-dimensional growth of the silica. This process could be analogous to the motion of pigment granules (Gras and Weber, 1977; Schliwa, 1981) and Golgi cisternae (Alberts et al., 1989) along radially organized microtubules. A number of mechanisms are available for transport along microtubules (Allen et al., 1981; Allen, 1987; Darnell er al., 1990). Chiappino and co-workers (1977) were able to observe silica precipitated in the Golgi vesicles in diatoms poisoned with the chemical analog Ge(OH),. The germanium may alter the equilibrium for the sol-gel transformation toward the gel phase. This premature precipitation of the silica in the Golgi vesicles may partly explain the morphological alterations caused by germanium, which include shorter, wider costae (called “transapical ribs” by Chiappino er al., 1977) which never reached the normal length. Germanic acid has been found to concentrate at the surface of the silica in diatoms (Werner and Petersen, 1973), where it could have a marked influence on sintering and percipitation rates, and alter costa spacing. “Deposition does continue, however, producing a thick, abbreviated valve” (Chiappino et al., 1977), suggesting that the second stage of valve thickening proceeds on top of whatever is available from the truncated first stage. Unfortunately, the coprecipitation of Si(OH), and Ge(OH), apparently has not been investigated by chemists (cf. Brace and Matijevic, 1977). It does not appear in the comprehensive review by Iler (1979). The surface concentration of germanium (“predominantly bound to the silica shells, but only at the surface and incompletely; Werner and Petersen, 1973) could be due to coprecipitation with silica followed by migration of the germanium to the surface (cf. Lagues and Domange, 1975). This may partially account for the observation: “In the presence of [Ge]/[Si] of 1.0 . . . in the electron microscope electron probe microanalyzer . . . granules contained both Si and Ge in different proportions (e.g., Si/Ge 8 to 63)” and for the faster dissolution of Ge than Si from heated shells of Coscinodiscus asteromphalus (Werner and Petersen, 1973;Werner, 1977). Given the evidence of silica in the Golgi vesicles during germanium poisoning, it seems reasonable that these vesicles are, perhaps, involved (cf. Drum and Pankratz, 1964b), contrary to the opinion of Pickett-Heaps and co-workers (1979b) (cf. Stoermer et al., 1965a,b; Chiappino and Volcani, 1977): How the silicalemma arises and grows is obscure. Some (particularlyDawson, 1973) claim that it arises from, and grows by continuing fusion with, Golgi vesicles. Although this matter cannot yet be decided, we remain quite unper-

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suaded that this happens, either from our own or past published data . . . . Golgi vesicles and the silicalemma can manufacture intricately formed scales or valves. We believe, therefore, that the silicalemma is equivalent to a giant, highly evolved “golgi” vesicle, not necessarily functionally associated with or derived from, the more typical golgi bodies. Such golgi bodies usually appear equally active whether or not a diatom is secreting wall material and their function remains enigmatic.

In discussing the possible evolutionary origins of diatoms, Round and Crawford (1981) point out that: Two groups of heterotrophs living today also elaborate siliceous scales in vesicles closely associated with the nucleus and Golgi apparatus; these are the testate amoebae (see Hedley and Ogden, 1973,1974) and the choanoflagellates (see Leadbeater, 1981, for a review).

Rather than regard the silicalemma as a specialized Golgi vesicle, we could consider the possibility that it is derived from the Golgi by fusion of smaller Golgi vesicles, as are lysosomes (Alberts et al., 1989). Since lysosomes are formed both from Golgi vesicles and endocytotic vesicles derived from the plasmalemma, we could suggest a similar double source for the silicalemma (cf. Anderson, 1992). The possibly complex traffic in vesicles is described by Schnepf and Deichgraber (1969): Coated vesicles . . . seem to bud off the Golgi cisternae and fuse with cytolysosomes (which also may be derivatives of the Golgi apparatus), or with young “scale forming vesicles,” or with the ER [endoplasmic reticulum], or with the plasmalemma.

and Schmid (1988): The production of “scale vesicles” is not unusual since scales occur constantly during the formation of auxospores (e.g., von Stosch, 1962, 1982)and it has been demonstrated . . . for [the] . . . centric diatom, Thalassiosiru, that anti-MT [anti-microtubule] drugs can induce scale formation (Schmid, 1984b). The surprising observation in Coscinodiscus wailesii is the dissociation of the Golgi stacks and that the “scale vesicles” possibly represent single cisternae of the former complete dictyosomes.

Golgi-derived vesicles in diatoms are likely to be of many types and have many functions, including excretion of mucilage (Crawford, 1973) and providing the raphe fluid used in motility (Gordon and Drum, 1970; Edgar and Pickett-Heaps, 1984b; Gordon, 1987). Ultimately, these kinds of vesicles will have to be distinguished from silica transport vesicles. The initial formation of the silicalemma continues to be a mystery, although its close association with a microtubule organizing center and the nucleus (Pickett-Heaps et al., 1990) may provide some hints: In the present study and that on valve development in Hantzschia (PickettHeaps and Kowalski, 1981), the earliest stage of the valve morphogenesis

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recognizable was the appearance in each daughter cell of a narrow tubular SDV devoid of siliceous content. (Edgar and Pickett-Heaps, 1984a)

Similarly, in Surirella Pickett-Heaps and co-workers (1988) find that The SDV arises as a small, densely stained tube. . . . The origin of this membrane in unknown. . . . A bundle of MTs [microtubules] appears lying around the cell periphery, in close proximity to the region to be occupied by the SDV. In spite of considerable effort, we have not been able to ascertain an exact sequence of events and so we cannot say whether MT growth precedes or follows the initial appearance of the SDV. Neither is it clear precisely where these MTs . . . originate.

Li and Volcani (1985b) find, in centric diatoms, an initially toroidal SDV: Valve formation starts prior to the completion of cytokinesis. The earliest seen silica deposition vesicle is located beneath the newly exposed plasmalemma and next to the nucleus. . . . It is a ring-shaped, flat bag that grows both inwards and outwards by fusion with vesicles about 27 nm diameter. The fact that the developing valve inside the silica deposition vesicle is also ringshaped at the earliest stage, suggests that the primary silicification sites might be the labiate process regions.

Since many auxospores form multiple silicalemmas, perhaps they would be the best place to begin. Aberrant centric diatoms present another opportunity: In Thalassiosira tumida . . . some clones showed a high incidence of valves with multiple centers, that is, valves with two or more centers of areolar radiation. Valves with multiple centers were seen in six of the ten clones and reached a frequency of 25% . . . . [They have the] appearance of two fused scales grown into one valve. (Wood et al., 1987)

Hedy J. Kling (personal communication) finds that severe limitations on nutrients in Arctic, ice-covered freshwater lakes leads to two centers in Cyclotella bodanica, and Cox (1891) noted: “Deformed diatoms [with] . . . double or multiple center in the scheme of marking” (cf. Cox, 1890). Schmid (1984b, 1987) suggests that scale vesicles formed in the centric diatoms Thalassiosira eccentrica and Coscinodiscus wailesii grown in the presence of microtubule inhibitors possibly represent single cisterna of the Golgi stacks, which may explain the origin of auxospore silicalemmas (Schmid, 1987). Can Golgi blow smoke rings, or at least toroidal membranes? Germanium also causes the formation of multiple valves (Azam e f al., 1973). When cytokinesis is inhibited using colchicine, lateral valves form (Badour, 1968), but mostly in narrower cells (Sam Badour, personal communication) and not in pennate diatoms (Darley, 1974), maybe due to valve buckling.

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Of course, the silicalemma could itself actively concentrate silicic acid (Duke and Reimann, 1977), which might explain Sullivan’s (1977) observation of a 10-fold higher transport rate during cell division, presumably while the silicalemma is growing. Sloughing of the silicalemma and/or its fusion with the plasmalemma (Crawford, 1981a) would stop the transport. In this case, the Ge observed in Golgi vesicles may be in the process of being removed as a substance toxic to the cell. Perhaps the intracellular colloid is so highly hydrated that its electron opacity is significantly reduced. One consequence of sintering inside the silica deposition vesicle may be to remove this excess water. If the silica enters through the new plasmalemma, can it go directly to the silicalemma, especially where the silicalemma abuts the plasmalemma, or does it have to first go around it, perhaps toward or to the Golgi? These questions are of obvious importance to understanding how the asymmetric three-dimensional thickening of the diatom valve occurs. Perhaps isolation of the purported silica receptor and preparation of fluorescent antibodies to it, in conjunction with confocal scanning microscopy, could provide direct answers. In the meantime, an experiment by Cohn and co-workers (1989a) can be interpreted to suggest that the Golgi is not involved in silica transport (cf. Badour, 1968): When [Hanfzschia amphioxys] cells are treated with cytochalasin earlier during valve formation (15 minutes after cytokinesis) for . . . 55 minutes . . . the raphe canal formed in a wavy pattern around the midline of the valve face . . . we find that deposition of valve material proceeds in the presence of both colchicine and cytochalasin, suggesting that the process of silicificationrequires neither MTs [microtubules]or actin. (Cohn et al., 1989a)

Despite the presence and obvious penetration of cytochalasin during early valve deposition in this experiment, the costae (albeit branched) are fully formed (their Fig. 32). At worst, “several pores are often merged into abnormal oblong pores,” suggesting a slight silica deficit when crosscostae are formed, and a few three-dimensional inward protrusions form, which are probably aberrations of wall thickening. Now it has been shown recently that microtubules are often (if not always) involved in Golgi vesicle transport (Duden et al., 1990; Schroer and Sheetz, 1991; Guma et al., 1992). Thus we may conclude either that the silica vesicles are transported from the Golgi to the margins of the silicalemma before silicalemma growth occurs, or more likely, since silica transport occurs throughout valve morphogenesis, that the Golgi is not involved or essential. Unfortunately, the critical observations called for have not yet been made: Transport of silicon in microvesicles, as suggested by Stoermer, Pankratz and Bowen (1965b), would appear unlikely in Navicula pelliculosa, since . . . electron dense material in such vesicles is resistant to HF. . . . Some of our electron micrographs strongly suggest incorporation of Golgi derived

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vesicles into the silicalemma. However, this cannot be confirmed without autoradiographic studies. (Coombs et al., 1968a)

IV. Instabilities in Diffusion-Limited Amorphous Precipitation of Silica Generate Space-Filling Branching Patterns

A. Branching Costae in Aberrant and Normal Diatoms First, we would like to report some of our own electron microscopic observations of aberrant diatoms. These aberrations may shed some light on the patterning mechanism. Diatoms of the genera Licmophora (Fig. la,b,c) and Navicula (Fig. ld,e) were obtained from cloned cultures maintained by Paul E. Hargraves in enriched seawater at the Narragansett Marine Laboratory of the University of Rhode Island. Shells were isolated by ultrasonic cleaning and prepared for electron microscopy by Drum’s method (1967). Photographs were taken with the Marine Laboratory’s Zeiss EM-9 electron microscope. All valves seen were photographed, for a total of 55 Licmophora and 55 Navicula. An example was printed in Katchalsky (1974). Similar, subsequent work has been reviewed by Pickett-Heaps et al. (1990). We found that aberrant valves of pennate diatoms contain branching costae (Figs. la,b,c,ej). (Compare van Heurck, 1896, who drew a deformed “Navicula permagna, the half of the raphe of which is wanting, whilst in the same part of the valve the striae are radiant.” See also Plate 129 in Schmidt, 1874, and Fig. 32 in Cohn et al., 1989a; cf. Hostetter and Rutherford, 1976; Fig. 7 in von Stosch, 1965.) We subsequently learned that branched costae occur in some normal pennate diatoms (Anon, 1974, Plate I, D; Schmidt, 1874, Plate 214; Schoeman and Archibald, 1976-see their figures for Navicula cloacina and N . pseudohalophila; Helmcke and Krieger, 1962a,b; Medlin, 1985; etc.).

5. Preliminary Heuristic Modeling of Branching The observation of branching costae in both centric and pennate diatoms suggested to us the following simple mechanism of accretionary growth and branching (cf. Cohen, 1967; Prusinkiewicz and Lindenmeyer, 1990). In this model, the costae grow continuously until they reach the margins of the cell. During this growth, when the separation between adjacent costae starts to increase, at least one costa branches. This serves to

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provide it with a neighbor and thus fill in the space into which it is growing. On the other hand, if the tip of one costa is crowded by its neighboring costae, it stops growing before reaching the cell margin. These two rules were incorporated in a Fortran computer simulation. The costae are considered to be just lines of material that grow (or branch) at their tips when certain thresholds of distance from neighboring costae are crossed. They form a space-filling branching pattern (Fig. 5). Such a pattern would give the diatom a rigid structure covering the whole cell. As long as enough material is provided, a space-filling branching pattern simply grows until it occupies the whole available space. Similar two- and three-dimensional patterns also occur in lung growth (Judson, 1980), breast ducts, blood vessels, river deltas, and drainage networks (Scheidegger, 1966, 1967; Dacey and Krumbein, 1976). Other examples are dendritic crystal growth and frost, tree growth (Honda, 1971; Leopold, 1971), root growth, the venation of some leaves (e.g., gingko), fish scales and fin rays, Acetabularia caps (Bold and Wynne, 1978; Goodwin and Briere, this volume), fossil dendroids (Urbanek, 1973), corals (cf. Stevens, 1974),and limestonebuilding algae (Johnson, 1961). The properties of space-filling branching patterns have been described for diatoms as follows: The results of the cytochalasin treatments of Hantzschia arnphioxys also confirm what is evident in Achanthes (Boyle et a/., 1984); the overall valve shape is independent from the position at which the valve raphe forms. The expansion of the SDV (and the nascent valve) continues until it reaches the

FIG. 5 Computer simulation of costal growth and branching by the heuristic model. The dots are time markers along the costae placed equidistant along the costal arcs from their starting points. Each costal tip branches into two costae if the sum of its perpendicular distances to the two adjacent costae exceeds a threshold. If the same sum is, instead, less than another lower threshold, the growth of the tip ceases.

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correct marginal site which determines the edge of the new valve. The lateral expansion of the nascent valve does not continue for only a predetermined fixed distance from the initial raphe ribs. This result is in concurrence with the findings of Schmid (1979b), who concluded that the mantle-building interstitial ribs will spread out as far as they are allowed to, and that their orientation and convergence are directly influenced by the space available. (Cohn et a/., 1989a).

We next turned our efforts from this preliminary work on a heuristic branching model to a search for a molecular basis for the branching and stopping behavior of growing costae.

C. The Structure of the Nucleating Structure

In pennate diatoms the presumptive midrib of the new valve (the PCB), which is inside the SDV, may act as the nucleating structure. The costae usually appear to grow from the midrib out (Fig. l h j j ) , though there are apparently exceptions, which are reviewed by Volcani (1981). In these cases there may be other structures serving as nucleating structures. Alternatively, they may simply be explained as a result of movement of the whole SDV to one side of the cell before much silica deposition occurs (Pickett-Heaps et al., 1990). Crawford’s (1981b) observation that in Melosira, “the process occurs evenly over the entire valve,” may be the secondary thickening of the valve. The distinction between the initial twodimensional growth of the valve and its three-dimensional thickening may be visible in, for instance, Fig. 17 of Dawson (1973), which shows a line of new silica from which feathery lines emanate in the perpendicular direction. The midrib itself elongates in a complex manner, which explains a minor feature of pennate diatom morphology called the “Voigt discontinuity” (reviewed by Pickett-Heaps et al., 1990): Geitler (1932) and Chiappino and Volcani (1977) illustrate the creation of this double rib in Epithemia zebra and Navicula pelliculosa from a single rib that grows to the end of the cell and then curves back sharply upon itself to meet a second shorter rib growing from the centre alongside the first . . . . Mann (1981) correlates the Voigt discontinuity (Voigt, 1943, 1956) with the site at which these two ribs meet.

This is not incorporated in the simulation. To do so, we would need to simulate a whole pennate diatom instead of a small segment of the raphe and the costae growing from it, and would need data on the rates of growth of the four ends of the raphe rib, which have never been sought. One thing seems clear: this growth is not, in the first instance, a silica precipitation (although the silica follows it), because the nucleating structure is anisotropic with respect to the deposition of silica. Otherwise, the

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costae would form on both sides of it, precluding the ability of the ends of the raphe rib to meet after the 180” turns occur. This anisotropy thus tells us something important about the unknown nucleating structure. Since midrings in centric diatoms precipitate silica both inward and outward, this anisotropy is present only in pennate diatoms, or else in centrics the polymer, whatever it is, is indeed anisotropic, but is twisted into a helix, effecting isotropy. It could be that one side of the nucleating structure in pennate diatoms is simply inaccessible to the silica, being bound to something else, such as the microtubules associated with the raphe (Pickett-Heaps et al., 1990). The nucleating structure may be homologous to the mechanism that deposits “extracellular cellulose . . . parallel to cortical microtubules . . . anchored to the plasma membrane” (Alberts et al., 1989; cf. Lloyd, 1982). There is perhaps an exploitable similarity between the indirect role of microtubules in valve morphogenesis and in plant morphogenesis: The general conclusion is that a preexisting orientation of [cellulose] microfibrils can be propagated, even in the absence of microtubules, but that any change in the deposition of cellulose microfibrils requires that intact microtubules be present to determine the new orientation. . . . The direction in which the [cellulose] synthase complexes move could be restricted by microtubule-determined boundaries in the plasma membrane that act like the banks of a canal to constrain movement of the synthase complexes to a parallel axis. This . . . model has the advantage that cellulose synthesis is viewed as an activity that is independent of microtubules,being constrained spatially only when cortical microtubules are present to define membrane domains within which the enzyme complex can move. . . . It is worth recalling that the cytoskeleton of an animal cell likewise determines the orientation of extracellular matrix components that the cell secretes and that elongated proteins such as collagen and fibronectin are laid down by these cells in close association with their plasma membrane. (Alberts et al., 1989) We could, in fact, build a whole theory of valve morphogenesis on channels between microtubules (cf. “Transverse section of. . . seta showing MTs [microtubules] spaced between ribs of silica . . . [in] micrographs [of Chaetoceros armaturn] supplied by Dr. Kent McDonald”; Pickett-Heaps et al., 1990), but they are only universally present and required for normal shaping of the raphe, not the costae, and there is a “need for caution in generalizing” (Pickett-Heaps ef al., 1990). In centric diatoms, the very center may contain a generally circular nucleating structure (Li and Volcani, 1984, 1985b), which we shall call a midring (Fig. lf,g). This midring may be homologous with the midrib of pennate diatoms. In our aberrant pennate Licrnophora cells, structures that could be called midrings are sometimes found (Fig. lc). Some of the experimentally produced aberrations of the pennate Nauicula saprophila also show crude midrings (Fig. 9 in Blank and Sullivan, 1983). The midring has been given other names:

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The overall structure of the valve appears to emanate from a more or less clearly defined “pattern centre” (Mann, 1984) from which silicification proceeds centrifugally outwards (Schiitt, 1896, 1899; Peragallo, 1907; Geitler, 1932). The pattern is also synonymous with the “primary silicification site” (the terminology of Schmid, 1979a, 1980, 1984b, . . . ), where one can first detect the silica of a the new valve. . . . [In] . . . Melosiru uuriuns . . . Schmidt (1923) described . . . initiating silicification in the form of a circular disc; later, in Chaetoceros, von Stosch et al., (1973) showed that it is a circular band. This band was called the “annulus” by von Stosch (1977, 1980) who noted that the central space of the annulus was later filled in during silica secretion. . . . the annulus is common to most, perhaps all, centric diatoms . . . (Round and Crawford, 1981; Mann, 1984) . . . electronmicroscopy shows that silicification commences at the future valve centre . . . (Schmid and Schulz, 1979; Schmid and Vocani, 1983; Schmid, 1986a,b). (Pickett-Heaps et a f . , 1990) Drum and co-workers (1966), Chiappino and Volcani (1977), and PickettHeaps and colleagues (1979a,b) have obtained electron micrographs of the newly forming midrib of pennate diatoms, which already extends the entire length of the cell (cf. Volcani, 1981). This nascent midrib “is uniform in structure along its entire length except for a slightly enlarged . . . primordial central nodule” (Chiappino and Volcani, 1977). The width of the silica is about 200 A. Usually, the earliest midrings seen are already full silica rings (Li and Volcani, 1984).

D. Modeling t h e Morphogenesis of Diatom Shells The following are the major ingredients of our model: a linear or circular nucleating structure onto which the diffusing silica particles precipitate, and a concentration gradient of silica particles that decreases from the linear or circular edge of the advancing silicalemma to the nucleating structure. We assume that the nucleating structure is uniform in its properties and that the migrating silica particles adsorb to it preferentially (essentially exclusively) compared with sticking to each other and to the inner surface of the silicalemma (in contrast to template models). Despite the uniformity of all conditions, we assume that the pattern formed is induced by random fluctuations caused by the Brownian motion of the silica particles adsorbing to the nucleating structure. Thus we simulate that Brownian motion directly in the computer program instantiating the model by using random numbers in a Monte Carlo simulation (Gordon, 1980~). As precipitation of silica proceeds, we hypothesize that concentration gradients of diffusing silica form in the horizontal plane of the SDV (Fig. 6). These gradients are formed by removal of silica from the medium within the SDV by precipitation. Thus the concentration inside the SDV would, on average, increase with distance from the nucleating structure (Mullins and Sekerka, 1963; Delves, 1975). The overall effect is a growth

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276

SILICALEMMA

DIFFUSING SILICA

GROWING COSTAE

PARTICLES

FIG. 6 Schematic drawing of the initial precipitation of silica in the silica deposition vesicle of a pennate diatom. The silicalemma (rectangle) contains diffusing silica which precipitates onto the midrib. This process sets up a concentration gradient whose mean increases with distance from the midrib. The costae that, as a result of chance fluctuations in arrival of the silica, grow and jut further out into the SDV, are exposed to a higher average concentration of diffusing silica. Thus their growth is further accelerated relative to the shorter costae.

rate for the precipitate that is diffusion-limited (cf. Ham, 1959). The concerns of Sullivan (1980) that “purely chemical reactions, which are uncoupled from cellular metabolism, cannot completely account for Si(OH), polycondensation during silica frustule morphogenesis in the diatom” are not warranted for the reactions occurring inside the silicalemma. There it is easy to imagine attaining “supersaturated aqueous solutions (>3.5 mM) of monomeric Si(OH), [that will be] spontaneously polycondensed (autopolycondensed) to form amorphous or colloidal silica. It is also reasonable to suppose that energy is required to get the silica to and into the silicalemma (Coombs et al., 1967c; Sullivan and Volcani, 1973a, 1974; Okita et al., 1976). It is certainly required to get it into the diatom cell (Raven, 1983), though with great efficiency: ”

Only 2% of the energy budget of the cell is used in the production of silicified frustules which (with a whole cell S K atomic ratio of 0.25) comprise some 20% of the cell dry weight. . . . On a volume basis, . . . the energetic advantage of SiO, . . . amounts to some 20-fold for lignin and I0-fold for polysaccharide. When the “glove” configuration of the silicalemma occurs, we would have to postulate that the gradient of silica exists in the cytoplasm itself, perhaps in the form of a concentration gradient of small vesicles bearing silica. This gradient could be directly observable with electron microscopy, or even in uivo, if we learn what coats the silica transport vesicles and could label them with a vital fluorochrome.

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As a result of Brownian motion, small fluctuations should occur in the amount of precipitation from one position to another along the nucleating structure. Some parts of the precipitate will then jut out further into the concentration gradient than others (Fig. 6). These protruberances are exposed to higher concentrations of diffusing silica and grow faster, forming the diatom’s costae. Were it not for these fluctuations, precipitation would occur uniformly. Since the fluctuations grow and amplify themselves, mathematically one speaks of instabilities relative to an otherwise uniform precipitation. Each growing costa alters the concentration gradient within the SDV by continued adsorption of the silica. We may think of this gradient as forming a zone around each costa which is nearly depleted of diffusing silica. Other costae cannot grow far into this zone of reduced concentration. On the other hand, they can grow right up to the zone (or at least until their zones begin to overlap). The inhibitory zones will have a characteristic width that depends on the rate of diffusion. Thus the nearly regular spacing of the costae may be accounted for. This also explains why some portions of the silicalemma are adjacent to precipitated silica, while others are not, without invoking an assumption that the silicalemma itself varies from place to place, as in Duke and Reimann (1977). The computer simulation was carried out as shown in Fig. 7 for pennate diatoms and Fig. 8 for centric diatoms. When the precipitation is irrevers-

t

EDGE OF SILICALEMMA

----------

ENTERING PARTICLE

SOURCE LINE

DIFFUSING PARTICLE

DIRECTION OF SDV GROWTH

1-

f

.. ... .... . ... ....... .. ’0

------

. ....

PRECIPITATE

0 . .

MIDRIB

FIG. 7 Schematic drawing of the computer simulation for pennate diatoms. The particles are shown entering at the edge. Entrance at any vacant site over the silicalemma (“face” arrival) is also permitted. Entrance at the dashed source line is numerically equivalent to entrance at the edge of the silicalemma.

RICHARD GORDON AND RYAN W. DRUM

278

I I

PRECIPITATE

.) FIG.8 Schematic drawing of the computer sirnulation for centric diatoms. The inside portion of the midring is not simulated.

ible, the surface is veritably covered with branches (Figs. 9, 10, and 1 1 ) . Yet, only a few branches succeed in competing for the diffusion-limited substrate and continue to grow. On the other hand, at least one branch succeeds in entering any open space. Simple irreversible precipitation therefore provides an explanation for space-filling branching patterns. It partially fills the call for “a mechanism that, in its spatial and temporal course, is strictly controlled by a non-reversible sequence of instructions” (Schmid et al., 1981), although we could hardly speak of instructions being given to the diffusing silica. In centric diatoms, as the precipitating structure expands, the distance between the existing costae increases. Thus centric diatoms (Fig. 10) have more main branches than pennate diatoms (Fig. 9). E. Computer Implementation of the Model

1. Description In order to test our hypothesis that irreversible precipitation could produce diatom-like patterns, we constructed a computer simulation of the process

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THE CHEMICAL BASIS OF DIATOM MORPHOGENESIS /

FIG. 9 Computer simulation of totally irreversible precipitation, in which each particle sticks where it hits. In this simulation of a pennate diatom, a moving source line was kept 10 units above the highest protruberance. The starting structure is a straight line (midrib). Periodic boundary conditions are used horizontally on the 960 x 960 m a y , with 145,583 particles precipitated. The graph shows the average concentration gradient of diffusing particles as a function of distance from the moving source line. Note that most of the precipitation occurs in a relatively narrow region near the source line. Thus the structure below this zone is essentially fixed for all time (except for possible sintering, which was not included in this run).

at the molecular level (cf. Gordon, 1980a,b, 1981a,b). We modeled the diffusion of silica in solution (inside or adjacent to the SDV) as a simple random walk. In this random walk model, for convenience, a square lattice is used on which a particle moves with equal probability in all four directions. 'The use of such a random walk on a square lattice as an approximation to the diffusion equation is discussed by Brown (1956) and Crank (1956). When a silica particle encounters the bottom row of the lattice, representing the midrib of a pennate diatom, it is deposited at that location (adsorbed or precipitated). A particle is also adsorbed when it hits the growing precipitate, which consists of previously adsorbed particles. Periodic boundary conditions are used in the horizontal direction to avoid edge effects (cf. Gordon, 1968a,b). The precipitate itself was represented as 1s on the same square lattice of computer bits. Only a small fraction of a diatom shell can be represented, since it contains, say, 100 pg Si/cell (Werner, 1977), or 10l2 SiOz molecules.

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FIG. 10 Simulation of a centric diatom with a moving circular source on a 960 x 960 array. The starting structure is a circle (midring). Note the similarity to Fig. If.

The thinness of the SDV in some diatoms, as little as 300 A (Coombs and Volcani, 1968b, their Fig. 2), permits us to carry out our computer simulation in two rather than three dimensions. Thus we are effectively simulating the projection of the actual three-dimensional process onto a plane. Schmid and Schulz (1979) suggest that the valve forms first as a twodimensional structure, then thickens. As we shall see later, this twodimensionality is essential to forming a planar branching pattern. It may be important in this regard to note that “it is impossible to detect a space between the membrane part facing the inside of the [silicalemma] vesicle and the polycondensed siliceous structure itself” (Duke and Reimann, 1977). The “reduction of dimensionality in biological diffusion processes” is not just for efficiency of collecting molecules (Adam and Delbriick,

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FIG. 11 Simulation of irreversible precipitation within a midring. The silicalemma is assumed to be toroidal and 5 pixels smaller in radius than the most inwardly jutting structure.

1968), but also leads to the formation of patterns that would not occur otherwise.

2. Spatial Distribution of Sources and Sinks of Silica In any nonequilibrium diffusion problem, one may speak of a “source” and “sink” for the particles involved (Carslaw and Jaeger, 1959). These are the locations where the diffusing particles begin and end their Brownian motion. The surface of the precipitate of the growing valve acts as a sink. The sink for diatoms is thus a well-defined geometric shape. It merely presents the mathematical inconvenience of being a complicated and growing shape. The shape or distribution of the source of silica can only now be obtained by an educated guess. One possibility is that the dissolved silica arrives at the silicalemma from a spatially uniform source. If the silicalemma itself concentrates silica, then the rate of supply inside could be the same everywhere. The vertical thickening of the costae observed by Drum

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and colleagues (1966), Pickett-Heaps and colleagues (1979a), and others, suggests such a spatially distributed source (cf. Schmid and Schulz, 1979; Crawford, 1981a,b). It is not known whether the spatial distributions of the two silica transport systems postulated by Azam and Volcani (1974) are the same. The apparent inward growth of costae into the midring of some centric diatoms (cf. Schmidt, 1874) also suggests that at least some of the silica is available everywhere over the face of the silicalema. The pattern within a midring can be similar to (Stephanodiscus astraea, Fig. 315 in Geissler et al., 1963) or different from (Arachnoidiscus ornatus, Fig. 223 in Geissler et al., 1961) the face of the valve. Of course, without knowing the precise diameter of the individual diatom’s nucleating midring, it is hard to distinguish such inward-growing patterns from nonuniform, outward-growing patterns, so this interpretation must be taken as tentative. We show a simulation of inward irreversible precipitation in Fig. 12. It might be thought possible that there is a concentration gradient of

A

h

C

FIG. 12 Frames from a movie of a computer simulation of a pennate diatom on a 180 x 180

array with edge arrival of silica particles. (A) Frame 2 of the movie after 129 particles were adsorbed that together took 99,871 random diffusion steps (mean of 774 steps) to get from the source line-kept 17 raster units above the outermost structure-to the growing precipitate. (The bar represents the initial midrib.) (B) Frame 18, 1420 particles, 1,698,580 diffusion steps, 1196 steps/particle. (C) Frame 85,4183 particles, 8,395,817 diffusion steps, 2007 steps/ particle. (D) Frame 169, 6529 particles, 16,741,728 diffusion steps, 2564 steps/particle.

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silica in the cytoplasm, or of Golgi vesicles, silica transport vesicles (Schmid and Schulz, 1979), or mitochondria (Sullivan and Volcani, 1981) carrying silica to the silicalemma. This intracellular, three-dimensional silica source would be locally depleted as the silicalemma expands and passes by it. At the edge of the expanding silicalemma the depletion would be least. Along the surface of the silicalemma, the adjacent intracellular silica concentration will increase from the nucleating structure to the edge of the silicalemma. From the point of view of the silicalemma surface, we thus anticipate a gradient in the source of silica particles, always highest at the growing edge of the silicalemma and lowest at the nucleating structure. However, there is a problem with this view. As we shall see below, the fact that the SDV is thin is essential to the generation of instabilities. This may explain why silica is not accumulated in the cytoplasm prior to valve formation but rather peaks during valve formation (Sullivan and Volcani, 1981): if silica were accumulated in advance, at least in the bulk of the cytoplasm, it would be available over the whole face of the SDV, and instability patterns would not be generated. We therefore accept the view that the purported silica transport vesicles (Schmid and Schulz, 1979) contain silica, and are situated along freshly exposed plasmalemma, perhaps prior to silicalemma growth. This confines the source of the silica to the margin of the silicalemma. Cytoplasmic movement, cytokinesis, or electrophoretic motion could alter any intracellular gradient. Such effects are likely to be secondary, because at the size scale of diatoms, diffusion gradients should come to steady state rapidly enough to keep up with these movements. This can be seen by a simple dimensional argument. The units of the diffusion coefficient D are length2/time. Thus the characteristic time f for diffusion over the width w of a diatom is w 2 / D . Taking w = 1 p m and D = 3.2 x cm2/sec for colloidal silica (to be derived below), we obtain f = 3 msec. This is much smaller than the time for growth of the shell discussed above (10 min o r more). This calculation also indicates that the silica transport vesicles, if they stick to freshly exposed plasmalemma, should be able to arrive there shortly after their synthesis. If we assume that they fuse preferentially with the margin rather than with the flat part of the silicalemma, then their synthesis need not precede silicalemma growth, but could also be concurrent with it. When silicalemma expansion is complete, the margin may no longer be available (either by some unknown alteration or by fusion with the plasmalemma), and fresh plasmalemma is no longer available for their preferential adhesion. This could explain the switch to fusion of silica transport vesicles over the face of the silicalemma, resulting in thickening of the valve.

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We will consider two concentration profiles in the source of silica: uniform and monotonically increasing. We choose two source distributions to represent these extremes: (1) a line source at the growing edge (margin) of the silicalemma and (2) a uniform (plane) source over the whole face of the silicalemma adjacent to the cytoplasm. The latter is included to show the effects of a three-dimensional source on reducing instability patterns. A linear combination of the two distributions is also permitted in our computer simulation. To simulate a line source in pennate diatoms, we introduce particles at random only along a horizontal line of the lattice. This line is kept at a fixed distance ahead of the most advanced growing tip of the silica precipitate (Figs. 7 and 9). Centric diatoms were simulated by changing the geometry of the source and nucleating structure to circles (Fig. 8). A nucleating midring is represented as a circle in the center of the lattice. The line source for pennate diatoms is replaced by an expanding circle concentric with the midring. The concentration gradient at some distance above the highest or outermost precipitate formed so far (beyond its inhibitory zone) will be reasonably uniform. We thus take a source line or circle a small distance beyond the furthest jutting precipitate (for pennate or centric diatoms, respectively). This boundary is taken as the source of particles (dashed source lines in Figs. 7 and 8 and the solid straight line in Fig. 9). We also treat it as a reflecting boundary for the diffusing particles, to increase the efficiency of the program, and because that is what we would anticipate physically. Since each particle has a much shorter distance to diffuse, on the average, before precipitating, we thus achieve an immense reduction in computing time (cf. Brown, 1956). This approach is also discussed by Vicsek (1992), though without use of the reflecting boundary condition. Real diatoms may also use this device of having the silicalemma grow in width or diameter just beyond the already precipitated silica, to speed precipitation: The continued incorporation into this [ silicalemma] protein of I4C assimilated during the Si-uptake period also suggests that the silicalemma is not complete at the time Si is reintroduced. This is consistent with electron microscope studies of isolated developing walls and thin sections of Si-starved cells, in which the silicalemma is seldom found to extend a significant distance beyond the deposited silicon (Volcani and Kiethe, unpublished data 1. Apparently, macromolecular organic components are sequentially added to the periphery of the developing wall immediately preceding Si deposition. (Coombs and Volcani, 1968b)

The simplest way to achieve this coordination is perhaps for the silica transport vesicles to be the sole source of new membrane.

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3. Results

Our computer simulations of precipitation of silica generate fine, feathery branching patterns (Figs. 9 and 10). These patterns resemble the feathery deposition observed transiently in forming diatom valves (Drum and Pankratz, 1964a; Stoermer et al. 1965a; Dawson, 1973; Volcani, 1981). When the simulations are carried out for many particles, for a pennate diatom, they lead to costae that grow in a direction that is on average perpendicular to the nucleating structure and toward the silicalemma (Fig. 9). On some occasions, in real diatoms, costae appear to branch in the wrong direction (Malone et al., 1973, their Fig. 2k; Drum, 1969, his Fig. 6; Coombs et al., 1968b, their Fig. 2b). This may be explainable as fusion of two costae after one of them stops growing. Such fusions occur in our molecular simulation (Figs. 9 and 10). They are also apparent in some aberrant diatoms (Figs. le,k). In our heuristic simulation, Fig. 5 , branching can occasionally go in the wrong direction because the directionality of the source of the silica is not represented. The number of costae still growing at a given distance from the midrib of simulated pennate valves diminishes rather rapidly, roughly by a factor of 2 for every doubling in distance (criteria for counting are somewhat subjective, and thus left to the reader). Costae which terminate early in real pennate diatoms may be seen in Fig. la,b,c,dj,k (cf. Plate 940 in Gerloff and Helmcke, 1977; Fig. 7 in Krammer, 1979) and in real centric diatoms in Figs. 29 and 32 of Hasle & Heimdal(l970). It is not known if the continual reduction in the number of growing simulated costae would stop at some final costal spacing or would go on indefinitely, if the silicalemma could expand indefinitely. An argument can be made for the latter, since there is always a small (but decreasing) probability that a given branch will grow too close to another and be hindered from further growth. If the reduction of the number of branches continues indefinitely, this pattern would be self-similar at all scales of demagnification and would thus (except for its atomic basis) fully qualify as a fractal (Mandelbrot, 1977, 1982). The fractal nature of these kinds of precipitation patterns has recently been analyzed (Witten and Sander, 1981; Meakin, 1983, 1986; Vicsek, 1992). Such a pattern is not at all that predicted by linear perturbation analysis (Mullins and Sekerka, 1963; Sekerka, 1973; Delves, 1975) and thus shows the limitations of perturbation theory in predicting the course of instabilities once they start growing. Our simulation thereby confirms the caution expressed by Doherty (1975) about the quantitative application of perturbation theory to dendritic growth. Glicksman (1985) warns that: progress has not been uniform, but required a sequence of major developments from both experiment and theory, as well as overturning plausible, but incorrect concepts.

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When the silica particles are allowed to arrive over the face of the silicalemma, the parts of the structure laid down early are obliterated by the additional precipitate that accumulates near the midrib (Fig. 13). Despite this, distinct costae persist. A combination of edge and face arrival of the silica yields an intermediate result (Fig. 14).

F. Further Considerations Sufficient information on the ultrastructural changes accompanying diatom shell formation is now available to enable us to propose specific models for this morphogenetic process. However, the physicochemical conditions during the process are not yet known. In lieu of the scarce experimental work being done in this direction, some progress toward unraveling the mystery of this pattern formation can be made using computer simulations, as we have illustrated here. The simple mechanism presented by us is able to generate the spacefilling branching patterns that are commonly observed in centric diatoms. The formation of costae and their direction of growth toward the margin of the silicalemma is also exhibited by this crude model. Round and

A

B

n

C

FIG. 13 Pennate diatom simulation with silica particles arriving over the face of the silicalemma. The parts of the structure laid down early are obliterated by the additional precipitate that forms near the midrib. Despite this, distinct costae persist. (A) Frame 2, 237 particles, 99,763 diffusion steps, 420 steps/particle. (B) Frame 9, 1271 particles, 798,729 diffusion steps, 628 steps/particle. (C) Frame 41, 6240 particles, 3,993,760 diffusion steps, 640 steps/particle. (D) Frame 81, 14,936 particles, 7,985,064 diffusion steps, 535 steps/ particle.

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A

B

D

C

FIG. 14 Pennate diatom simulation with silica particles arriving at both the edge and face of the silicalemma, yielding results intermediate between those of Figs. 12 and 13. (A) Frame 2, 72 particles from the edge, 96 particles from the face, 99,832 diffusion steps, 594 steps/ particle. (B) Frame 9, 344 edge arrivals, 718 face arrivals, 798,938 diffusion steps, 752 steps/ particle. (C) Frame 39, 976 edge arrivals, 3213 face arrivals, 3,795,811 diffusion steps, 906 steps/particle. (D) Frame 77, 1574 edge arrivals,7379 face arrivals, 7,591,047 diffusion steps, 848 steps/particle.

Crawford (1981) have attempted to identify the “ur-diatom” and the fundamental pattern of its scales. Their suggestion which is supported by many excellent micrographs, is that: there is a pattern that is very similar to that in the auxospore scale of Mefusiru. This is a central circle [or] annulus . . . of silica from which ribs radiate. . . . in some diatoms other structures are superimposed so that the basic pattern is only visible in immature valves (e.g., in Melosira and Hyalodiscus). Nevertheless, a large number of micrographs have been published that illustrate this pattern, for example Bacterosira, Detonila, Porosira (Hasle, 1974),Hemidiscus (Simonsen, 1972), Stephanodiscus (Lowe and Crang, 1972), Stictocyclus (Round, 1978a)and Chrysanthemodiscus (Round, 1978b).Other genera in which it has been shown include Coscinodiscus,Stephanopyxis, Cyclotella, Dactyliosolen and Leptocylindrus.

Our computer simulation thus matches the “ur-pattern” for centric diatoms. However, the periodic or almost periodic costae along the midrib of pennates have not been generated by our computer simulation. These periodicities appear when we include sintering, such as by surface diffusion (Gordon and Aguda, 1988; cf. Vicsek, 1984; see the later discussion). Ultrastructural ornamentation besides the costae, such as the fine spines

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observed on Tricerutiumfuuus (Miller and Collier, 1978), the silica arches (fibulae) seen by Reimann and co-workers (1969, or labiate processes and setae (Li and Volcani, 1984) will require explanations going beyond our theory. The use of a square lattice (anisotropic) for the randomly walking particles is known to affect the patterns generated by Monte Carlo simulations (e.g., Kertesz and Vicsek, 1986; Vicsek, 1992). Future work should reconsider this carefully and use either a hexagonal lattice, which has reduced directional bias, or nonlattice ballistic simulation (Vicsek, 1992), or direct representation of the amorphous structure of the precipitated silica (discussed later).

V. The Role of Sintering

A. Possible Sintering Mechanisms We next make the assumption that when silica is deposited on silica, it does not ordinarily stop moving, that is, that there is a continuing process of surface migration, at least during valve formation. A vivid description of the immense molecular activity involved in surface migration in general is given by de Boer (1968). He concludes: We cannot expect the molecules to establish a dynamic equilibrium with the gas [or solution], involving a great probability of any individual adsorbed molecule escaping from the surface without there being an even greater probability of the same molecule's moving along the surface.

This implies, by the way, that surface migration should be more important than dissolution and readsorption in the reshaping of costae. The migration rate rn of monomers hopping over a surface, according to de Boer's (1968) theory, should be

m = K A (kT/h)q p [sec-'1

(2)

per monomer, where

p

=

exp( -fdkT)

(3)

is a modified Boltzmann factor and E is the adsorption potential. K is the transmission coefficient (dimensionless), A is a lattice factor ( = 3 for hexagonal close packing), h is Planck's constant (6.6254 x erg sec), k is Boltzmann's constant (1.3805 x erg/"K), T is the absolute temperature, q is the statistical mechanical partition function for vibration: q = exp[-V/(2T)l/[l - exp (-V/(2T)I

(4)

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V is the characteristic temperature, and f i s the fraction of the adsorption energy which gives the activation energy for surface diffusion. Both de Boer (1968) and Blakely (1973) estimate f at between 0.5 and 1 . Withf = 1, then b = u = 3 x if we choose E as an interfacial energy of 100 ergs/cm2 (Iler, 1979). Thus we obtain a migration rate of 5.7 x 10’4 (sec-’). Since covalent bonding is involved, the characteristic temperature for vibration of silica monomers, V, is likely to be in the range of 300 to 3000 O K (Hill, 1960), for which q = 1.5 down to 1.5 X lo-’. Thus each surface monomer hops at least 8.5 x lo4times per second. If we consider a 10.2-nm diameter silica particle with 7.2 OH groups/nm2 (Iler, 1979) or 77 monomers on its surface, the surface configuration is changing 6 x lo6times per second. The very formation of silica as colloidal spheres (Iler, 1979) rather than irregularly shaped particles indicates considerable surface activity which is not likely to be only internal condensations. Surface migration of silica on silica has yet to be studied by physical chemists (A. C. McLaren, personal communication). Unfortunately, reasoning of this type, derived from absolute rate theory (Glasstone et al., 1941), can be off by as much as a factor of los. “One reason [for this failure] is that absolute-rate equations contain no surface parameters except as they operate collectively through the activation energy” (Clark, 1970). Blakely (1973) states flatly: “At present the mechanism of surface self-diffusion has not been established with certainty for any particular surface.” On the other hand, an error of los either way would not alter our conclusion from the above argument that surface migration can be a significant sintering mechanism on the time scale of diatom shell morphogenesis. Fortunately, Monte Carlo and quantum mechanical calculation methods are now available to refine such estimates (Doll and Voter, 1987). The strongest argument favoring surface diffusion as an ever-present sintering mechanism is given by Blakely (1973) (cf. Herring, 1950; Mullins, 1959). He considers the flattening of a sinusoidally corrugated surface of wave number K = 2 m/A, where A is the spatial wavelength, and calculates the rates of various mechanisms as a function of K”: 1 . Viscous flow ( K ) 2. Evaporation/condensation (Ostwald ripening or readsorption) ( K 2 ) 3. Bulk diffusion ( K 3 ) 4. Vapor phase diffusion (diffusion through the solution) ( K 3 ) 5. Surface diffusion (K4)

The amplitude of the corrugation is proportional to exp ( - aKn), where a is a constant depending on the process. Clearly, for high enough values of K , corresponding to the smallest bumps, surface diffusion will predominate. This explains the extreme smoothness of mature frustules at the

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greatest electron microscope magnifications. [Note that if the viscosity within colloidal silica is comparable to glass, 10l2poise according to Lontz (1964), viscous flow will in any case be insignificant.] Kingery (1960) gives precisely the same power relationships for the radius dependence of the sintering of two identical spheres, where K is replaced by their radii. Further evidence for a predominance of surface diffusion is given by the: experimentally determined diffusion spectrum for fcc [face centered cubic] metals, as deduced by Gjostein (1973) . . . at temperatures significantlylower than TM [the melting temperature] D, > Db > D, . . . > D, where D,, Db, D,, and D, represent surface, grain boundary, lattice dislocation, and lattice diffusivities, respectively. These results are consistent with our intuitive feeling that the constraints placed upon atomicjumping should increase . . . and . . . the diffusivities should therefore decrease [in this order]. (Balluffi, 1984)

Iler’s (1979) data on the rate of precipitation of monomeric silicic acid argues against an evaporation-condensation (readsorption) sintering mechanism, since the rate of condensation would be too slow to form the nascent diatom valve. Although the solubility of small silica particles increases (Alexander, 1957; Iler, 1979), no direct demonstration of the growth of large silica particles at the expense of smaller ones (Ostwald ripening) (Sugimoto, 1978) appears to have been made, although Ostwald ripening is experimentally indicated (Righetto et al., 1987). It is of some interest to note that the behavior of silica migrating, adsorbing, or desorbing on the surface may be affected by the bulk silica within. Ostwald ripening is generally presumed to be caused by either an increased fraction of edge molecules on the surface of smaller crystals, or increased average exposure of surface molecules to the solution, or increased surface stress, etc. Bikerman (1948) questions the existence of a surface energy or surface tension for solids, on which the Gibbs-Thomson equation is based (solubility over bulk crystals proportional to the purported surface tension divided by radius of curvature). Unlike a liquid, the surface energy proper is not the only kind of energy which varies when the extent of a solid surface is varied. It is impossible to extend the surface of a crystal without upsetting its lattice, and the lattice energy is involved in every change of surface area. Therefore, even if there is no basic difference between the surface energies of a liquid and a solid, their observable manifestations are very different indeed. These remarks ought to apply equally well to amorphous solids such as silica. Iler (1979) finds, for instance, that the interfacial energy must be much higher for smaller silica particles to explain their solubilities. Bikerman (1948) further suggests that:

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the curvatures of the surface of a small solid may be greater or smaller than, or equal to, the curvatures of a large solid body. They depend only on the degree and kind of roughness which is not related to the microscopic dimensions of the specimen.

This is especially true of an amorphous solid which will not have the extended edges and faces of an ordinary crystal. Thus both the existence and mechanism of Ostwald ripening are called into question. Moreover, whereas small silica particles may exhibit, for instance, high solubility, this does not mean that small bumps which are covalently integrated with a larger precipitate, such as the growing diatom shell, will do the same. The lattice strains they are under may be significantly different. Empirically, the solubility of even the smallest silica particles we need concern ourselves with is low enough for them to last weeks to months (Lawson et al., 1978; cf. Hurd, 1983), well beyond the morphogenetic time scale of 10 min to 10 hr. Existing data on sintering of silica in the presence of water vapor (Chertov et al., 1965; Iler, 1979), when extrapolated by us to 20°C suggests that no significant amount of sintering will occur by any mechanism (area loss of 6 x loF8A */set per particle). However, Chertov and co-workers aged their silica gel 2 days before carrying out their experiments. Their silica thus may have already fully sintered by mechanisms available at ambient temperatures, or may have had a minor contaminant. There is apparently no understanding yet of the mechanism by which soft silica, as in a gel or floc, can harden at room temperature. By hardening we mean the following: a pile of glass marbles is soft in the sense that the marbles can readily flow aside if pushed on. However, if sintered together, they form a rock-hard mass. This hardening process in colloidal silica at ambient temperatures may take weeks to go to completion (Krauskopf, 1956), which is obviously too long to be of use to diatoms. Again, we must question the state of the silica used in this experiment. Barrer (1941) gives many examples of substances with high rates of surface migration at room temperature, and evidence that the rate of surface rearrangement of silica colloids at 22°C peaks sharply at pH 7 is given by Righetto and co-workers (1987): Another factor to consider is the surface pH of the bilayer membrane of the silicalemma, which is in close proximity to the precipitating silica particles. If there is an ordinary membrane potential across the silicalemma, the surface pH could be raised 3 to 4 units above that of the fluid within (Tewan and Lee, 1975; cf. Danielli, 1937; Geissler, 1958). This might have a catalytic effect on sintering processes. Direct measurement of the pH within the silicalemma may be possible using fluorescent indicator dyes.

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Glicksman and Schaefer (1967) have suggested that dendrites should appear at low supersaturations, whereas they will fuse laterally to form scalloped or quasi-planar structures at high supersaturations. This shows another mechanism by which smooth girdle bands could form. B. The Molecular Basis of Sintering

Since silica is a covalently bound block polymer, it is not clear what chemical species could be responsible for surface migration. We can, however, conceive of silica monomers migrating either by a hydrationdehydration mechanism or by breaking and making hydrogen bonds: There is ample evidence . . . that silica sol particles are strongly hydrated . . . [and] their surface consists predominantly of silanol groups ( = S O H or =Si (OH),). . . . In this respect they differ from quartz, glass and “Aerosols” (sols whose particles are formed in air) where a substantial fraction, or, in some cases, most of the surface consists of unhydrolyzed, relatively inert, siloxane groupings (=Si-O-Si=). Since the adsorption forces for water on a silanol surface are stronger than van der Waals forces, it has been concluded that hydrogen bonding is responsible for the adsorption. (Allen and Matijevic, 1969)

Hydration and dehydration may proceed as in Fig. 15, where the three stationary Si atoms represent a portion of the surface. This plausible reaction scheme for surface migration was suggested to us by Fig. 6.1 in Iler (1979), which shows various states of hydroxylation of the silica surface. Iler (1979) notes that the first monolayer of “strongly hydrogenbonded water becomes more highly dissociated and thus able to attack the siloxane bond and open it.” Thus adsorbed water is ideally localized to enhance monomer surface migration by this mechanism. The alternative mechanism of hydrogen-bonded surface migration of silica may be visualized by analogy to that of water. Iler (1979), emphasizes: “As water is a unique liquid, so is amorphous silica a unique solid. They are much alike, both consisting mainly of oxygen atoms with the smaller hydrogen on silicon atoms in the interstices.” Kingery (1960) found that the freezing together of ice particles at temperatures as low as -25°C is due to rapid surface diffusion of H,O molecules: The high surface mobility of molecules on the surface of ice is not unreasonable in view of the unique structure of the ice. Each oxygen in the crystal is tetrahedrally coordinated to other oxygen ions by means of hydrogen bonds in which hydrogen atoms alternate between equivalent positions. Molecules on the surface are presumably bonded to the crystal by two hydrogen bonds in which the hydrogen atoms also have two equivalent positions. These hydrogen bonds provide a reasonable mechanism by which rapid mobility of surface molecules might be anticipated. Murphy (1953) . . . proposed that

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THE CHEMICAL BASIS OF DIATOM MORPHOGENESIS OH

HO \

/

Si / 0 I

\ 0 l

Si

H 0 l

Si

+ H , O o

Si

/ I \ /, \ /, \

0 0 0 0 0 0 0 H 0 I

0-Si -OH H I 1 0--H 0

H 0

I

l

l

si

SI

si

/I \/I

‘\/I

e

\

0 0 0 0 0 0 0 H 0 I HO-Si-0 H I I H 0 0 H--0 I l l

Si Si /I \/I

Si \

%\

0 0 0 0 0 0 0 HO \

OH /

SI

H 0

/

I

0 l

SI

SI

/I \ / I

\

0 l

+

SI

\/I

H 2O

\

0 0 0 0 0 0 0

FIG. 15 Dehydration and rehydration mechanism for surface migration of silica monomers on bulk silica. “--”represents a hydrogen bond.

the swinging of hydrogen bonds from one lattice oxygen to another gives rise t o a “bipedal walk” surface diffusion mechanism.

For silica, the analogous bipedal walk could be what we propose in Fig. 16.

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RICHARD GORDON AND RYAN W. DRUM HO \

OH / S1 / \ HO OH

..

..

H 0

H 0

I S1

s1

H 0 l

l

51

/I \/, \/I \

0 0 00 00 0

OH

HO \

/ S1

/ HO

..

H 0 I 81

\

OH

..

H 0 l

H 0 l 51 SI /I \ / I \ / I \

0 0 0 0 00 0 FIG. 16 Hydrogen bond mechanism of silica surface migration. ":" represents a hydrogen bond.

Kingery (1960) also found that an a priori calculation of the surface diffusion rate for water was low by four or five orders of magnitude. Thus we will not attempt to calculate the relative rates of surface migration by the covalent and hydrogen-bonded mechanisms above. Both are plausible mechanisms and both could be taking place simultaneously. [A third mech-

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anism involving transient binding of five oxygen atoms to silicon atoms (Pennisi, 1991) can probably be eliminated because of the energy barriers.] It is interesting to note that the surface diffusion constant of water over silica depends on the surface concentration gradient of water (Kruckels, 1973). This is likely to be true of the hydrogen-bonded mechanism of silica surface diffusion, further complicating both the theory and experimental measurement of the rate of sintering. The role of cooperative interactions between cyclic polymers of water molecules is considerable in the freezing of supercooled water (Stillinger, 1980). Analogous polymers occur in silica (Iler, 1979). We could anticipate furthermore that surface migration on both ice and silica may involve such polymers. Perhaps some of these questions can be settled by molecular dynamics computer calculations (cf. Ladanyi and Skaf, 1993). Techniques for handling the surface diffusion of small clusters of atoms, instead of just single atoms, are now available (Doll and Voter, 1987).

C. Chemistry of the Silica Surface in Diatoms Because empty diatom shells persist longer in the ocean than they ought to, their rate of dissolution has been carefully investigated. “It can be concluded that certain adsorbed inorganic cations decrease the rate of dissolution of diatomaceous silica. In living diatom cells there may be an additional mechanism for stabilizing silica walls” (Lewin, 1961; cf. Jgrgensen, 1955; Kamatini, 1971; Hurd, 1983). The aluminum ion is significantly adsorbed by diatom frustules, so that their surface may actually be protected from dissolution: The fact that the amorphous silica on the ocean floor, found in enormous deposits of skeletons of diatoms, does not dissolve in seawater, has been a mystery. . . . When only one aluminum atom was absorbed on the surface as an anionic aluminosilicate site per 2 nm2, at which point only 5% of the surface was occupied, the rate of dissolution as well as the equilibrium solubility of the surface were drastically reduced. (Iler, 1979)

Such a mechanism would effectively “poison” dissolution and perhaps readsorption, analogous to the way catalysts are poisoned. It is likely to have a similar effect on surface migration. Those diatoms which might bring this mechanism into play during morphogenesis of the shell would be expected to have reduced sintering. It is interesting in this regard to note that “the solubility of the silica shell in water can vary with nutritional conditions” (Werner, 1977). Azam and colleagues (1973) showed that germanium, which has chemical properties similar to silicon, is incorporated into diatom shells through

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the same pathway. At high concentrations, multiple valves were laid down. (One might question, at Ge : Si of 1 : 1, whether the pathways remain identical.) Whether these involve multiple silicalemmas, as in many auxospores, or breakup of a single, initial silicalemma, may be worth investigating. Both aluminum and germanic acid may be excellent substances for introducing subtle changes in costa morphogenesis.

D. Assessment of Instability Theory Since we are interpreting diatom shell patterns as instabilities in amorphous precipitation, it is important to understand the status of that theory. Although crystals are referred to in the following excerpt from Cahn (1967), it should be realized that most mathematical treatments of diffusion-limited crystallization assume as isotropic surface free energy. [Jackson (1967) gives a criterion for growth of crystals without facets. Compare Sekerka (1973).] Thus all possible crystal faces are equivalent in terms of precipitation and surface diffusion rates, that is, the mathematician’s “crystal” is just an amorphous precipitate. In the past decade our concepts of the shape stability of a growing crystal have been themselves rather unstable. Prior to this the idea that a protrusion on the surface of a growing crystal would be a position to collect more material and hence would grow more rapidly was a widely accepted qualitative explanation for the origin of dendrites. . . . However, the elegant mathematical paper of Ham (1958) seemed to show clearly that a growing ellipsoid was shape preserving. . . . These correct results were loosely interpreted to imply general shape stability, and the origin of dendrites was for a time without explanation. The next reversal in our concepts occurred . . . with the already classic work of Mullins and Sekerka (1963, 1964). . . . By analyzing in terms of spherical harmonics the diffusion around a sphere with a slightly perturbed shape, they found a shape instability that was a function of the order of the harmonic. Second harmonics which distort a sphere into an ellipsoid were indeed shape preserving, but all higher harmonics could grow faster than the sphere. If the equilibrium concentration at the interface was constant, the shape was always unstable. Consequently Mullins and Sekerka introduced isotropic capillarity. . . . This condition stabilized the shape of small particles only until they reached a size or order of magnitude larger than the critical radius for nucleation. This size is often very small and raises the question of the existence of other stabilizing factors in the boundary conditions that might operate to keep a particle stable to large radii. The main [new concept] is to introduce interface diffusion. This has been done by Nichols and Mullins (1965) and by Coriell and Parker (1966) and can lead to stabilization to larger radii. (Cahn, 1967)

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Langer (1980) suggests: Despite its apparent success in the interpretation of experimental results, the stability theory of dendritic growth is fundamentally incomplete. The stable operating point of a dendrite seems to be a complex, dynamic, essentially nonlinear state of the system: and I must emphasize that we do not understand this state at all yet. . . . Until we understand . . . we shall not know whether the stability criterion is exact, or is just an approximation with a limited range of validity, or really whether it makes any sense at all. Nor shall we know how to compute a number of interesting quantities, most particularly, the amplitudes and ultimate spacings of the sidebranches. Thus we cannot simply apply the results of the instability theory of dendritic growth to diatoms. We must expect to have to contribute to the advancement of that theory. Moreover, the diatom valve apparently involves not just growth of a dendritic pattern, but, for structural strength, also anastomosis between adjacent costae, usually (though not always: Fig. 2 in Coombs et af., 1968b) by cross-costae formation, a phenomenon apparently not dealt with in the crystallographic literature.

E. Status of the Theory of Growth of Dendrites A common approach to asking why a process follows a particular pathway is to say that it seeks to optimize some function (Rosen, 1967). Our task is then to find that function, such as rate of entropy production (Glansdorff and Prigogine, 1971). Doherty (1975) has pointed out that The crystalline dendrite by virtue of its extended surface has a considerably increased surface free energy compared to the equilibrium shape. The origin of the dendrite must therefore result from the kinetics of crystal growth. The origin of the kinetic advantage of a dendritic growth is now universally recognized as arising in diffusion controlled growth processes. Thus the optimization function is definitely not merely a drive toward chemical equilibrium. Bolling and Tiller (1961) assumed that the physically realized shape of a crystal or precipitate would be the solution to the diffusion equations whose steady-state growth rate was a maximum. This was shown experimentally by Glicksman et af. (1976) to be an order of magnitude too fast. Langer and Miiller-Krumbhaar (1978a,b) and MiillerKrumbhaar and Langer (1978) then presented an instability theory which accounted for these results. With the velocity of tip growth as u and the radius of curvature of a dendrite tip as r, most theories only obtain u$ = constant, which is inadequate to obtain u or Y alone. These authors found that the velocity and morphology of the dendrite tip growth depends on a dimensionless parameter:

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where D is the bulk diffusion coefficient of the solute, and y is the surface tension. The conclusions of Miiller-Krumbhaar and Langer may be summarized as follows: 1. Larger values of s imply sharper and faster growing dendrites 2. For any finite s, a perturbation at the tip always generates a train of growing deformations which moves down the dendrite at just such a velocity as to remain nearly stationary in the laboratory frame of reference. In other words, any isolated dendrite will form side branches 3. For low or zero values of s, the dendrite has a tip-splitting instability. “New dendrites of relatively small tip radii appear to emerge from a region localized at the tip of the original parabola [representing the dendrite]” (Langer and Miiller-Krumbhaar, 1978b). Above a certain critical s*, this instability disappears, but the side-branching instability persists. In other words, with y > 0, an isolated dendrite will continue to grow. However, it will continually produce side branches 4. There appears to be a nonlinear coupling between the side branches and the velocity of tip growth such that an isolated dendrite will grow at a rate and tip radius governed by s = s* 5. This coupling appears, however, to be weak, so that the dendrite tip is only marginally stable against fluctuations in the tip radius and velocity of growth. 6. The side-branch spacing may depend on the velocity When the surface tension y is zero, such as in our simulations of irreversible precipitation, then the mathematics are exactly soluble and predict the tip-splitting instability. Except for the bilateral symmetries imposed by the mathematical analysis, this result is consistent with the multitude of fine dendrites seen in our simulations. On the other hand, we did not find that “the dendrite is growing very slowly with a very large tip radius” (Langer and Muller-Krumbhaar, I978a). These observations of Miiller-Krumbhaar and Langer and their limitations, given above, have the following consequences for diatom patterns: 1 . If we compare centric diatoms, such as those seen in Fig. 17 and 18, we see that some costae grow quite straight, while others appear to be more irregular. The former may have larger values of s . For instance, Chaetoceros diadema has a quite irregular branching pattern. At high resolution, considerable roughness of the costae is apparent (Hargraves, 1972, his Figs. 4,5, and 8; see also Figs. 26-31 of Subsiliceu frugilarioides in von Stosch and Reimann, 1970). Highly irregular branching is found in the hemispheric initial valve of many centric diatoms (Hedy J. Kling,

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FIG. 17 Reasonably straight, branching costae on a partially dissolved valve of the centric diatom Stephanodiscus hantzschii. (Courtesy of Hedy J . Kling.) Bar = 5 pm.

personal communication). We could suggest that the value of s changes through subsequent cell cycles 2. The lack of side branches in pennate diatoms may be due to lateral interactions between the growing costae. This effect cannot be explained by the above theory, which deals only with an isolated dendrite (cf. Jaeger, 1960) 3. Secondary effects not accounted for by this theory may significantly alter the costa width, since r and u are sensitive to perturbations. Thus, for instance, an increasing concentration of impurities as silica precipitates could alter D or y or the rate of surface diffusion (also not accounted for) and thereby change s 4. It is important to measure not only the width and spacing of the costae, which are probably proportional to r, but also the velocity of costa growth u, if we are to attain a quantitatively accurate theory of diatom valve morphogenesis. This could be done in uiuo by differential interference contrast (DIC) light microscopy, X-ray microscopy (Parsons, 1980; Hoover et al., 1991), or with a wet stage for the electron microscope (Parsons, 1974; Parsons et al., 1974)

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FIG. 18 Irregularly branched valve of the centric diatom Cyclotella stelligera. (Courtesy of Hedy J. Kling.) Bar = 2 pm.

5 . Some diatoms, such as the centric Chaetoceros diadema (Hargraves, 1972), show highly irregular spacing of their costae. This irregularity may be due to the marginal stability of dendrite growth. It is interesting to note that irregularities in the spacing of costae in auxospore scales seem to correlate with the development of multiple rows of pores between the costae (Crawford, 1974a, Figs. 15 and 16; Drum, 1969, Fig. 1). This suggests that the cross-costae cannot continue to grow perpendicular to the costae if the latter are too far apart. Instead they themselves branch and form a finer division of the space between adjacent costae. (Alternatively, areolae vesicles may be involved.) 6. We cannot now predict the spacing between dendrites. This means that we cannot be certain of the fundamental cause of the species differences in costal spacing 7. “The addition of the capillarity term [ y ] . . . has made it impossible for us to progress further by analytic methods . . . in order to explore the rich structure . . . we have had to resort to numerical techniques”

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(Muller-Krumbhaar and Langer, 1978). The same will probably be true for now for diatom patterns The theory of dendritic growth continues to advance (Glicksman, 1985): Stability methods combined with thermal and solutal transport theory now clearly show that dendritic growth is inherently a dynamically unstable process. We can anticipate a two-way interaction with the theory of diatom morphogenesis, as appropriate researchers cross disciplines, and we try to understand how diatoms control such an unstable process, producing multitudes of (generally) recognizable, different species. Theoretical crystallographers interested in dendritic growth need to generalize their work to amorphous materials (cf. the Journal of Non-Crystalline Solids) and learn a bit about diatoms, and diatomists have to learn what parameters are necessary to test alternative theories of diatom morphogenesis, and create ways of measuring them, while experimental crystallographers need to see if they can synthesize reasonable facsimiles of diatom valves in abiotic conditions.

F. The Number of Costae in Pennate Diatoms One prediction of our proposed precipitation mechanism is that for diatoms of the same species, smaller individuals should have fewer costae. Fortunately, because of the unequal cell divisions caused by the petri dish structure of the frustules, clones are available with cells of varying size. There is no correlation with cell size (van Heurck, 1896). The independence of costal spacing from cell size in the pennate diatom Nitzschia cylindroformis is vividly apparent in Figs. 1-12 in Hasle and Booth (1984). On the other hand, the costal spacing can vary considerably between species of the same genus (Hasle and Lange, 1992). The spacing of costae in Entopyla australis var. gigantea is 7.5 p m (Prasad and Fryxell, 1991) while that in oval cells of Phaeodactylum tricornatum is 0.10 p m (Lewin et al., 1958), showing that whatever the mechanism of precipitation, it is capable of a 75-fold or greater variation in costal spacing (cf. the scaling of sintering phenomena in Herring, 1950). The large diatoms with wide costal spacings present opportunities for time-lapse work on shell morphogenesis. G. Formation of Cross-Costae

The formation of cross-costae is similar to the coalescence of neighboring dendrite tips that has been discussed by Doherty (1975). Chiappino and

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Volcani (1977) claimed that: Cross extensions between the transapical ribs [costae] appear along their length. These extensions are laid down successively, the first appearing at the origin of each rib. . . . The extensions directly appose each other, and with continued growth, they ultimately meet and fuse, becoming bridges. On the other hand, in some silica-starved centric diatoms, hexagonal tesselations occur only at the margin, suggesting either that cross-costae form there first or that more silica is available there (cf. Paasche, 1973). We thus see that the sequence of appearance of cross-costae may reflect the spatial and temporal distribution of the source of silica (or some other more subtle factor). As we saw earlier, a planar source of silica can lead to the formation of irregular cross-costae. Sintering keeps them smooth (see later discussion). Since cross-costae require extra material, we may conclude that a planar source provides the material and sintering controls the shape. Since the cross-costae are the silica boundaries of the pores (in the direction parallel to the raphe in pennate diatoms), a difference in transport mechanism for the initial growth of the valve and costal formation may account for the observation that “The pore-pore distance within striae of vegetative cells is maintained in initial cells, although the distance between striae is not” (Cohn et al., 1989b). Even without the addition of more material, a long, linear structure breaks up into a row of drops under the action of surface tension (Gordon et al., 1972, 1975). Two neighboring costae forming such drops could fuse laterally. The breakup of drops can be highly regular (Rayleigh, 1879) or irregular (Rayleigh, 1892; cf. Rayleigh, 1964). If this model proves applicable, it could explain regular (Fryxell et al., 1990) and irregular (Fig. 15b in Fryxell et al., 1986) spacing of cross-costae. The formation of cross-costae by such a sintering mechanism could thus proceed to some extent even without the addition of any silica. It would therefore be important to measure total silica in nascent valves before, during, and after costal formation. It is not clear now whether the initiation of costae depends on a shift from a marginal to a face source of the silica entering the silicalemma. Crawford (1974a) shows a presumed sequence of siliceous scales of the auxospore of Melosira uarians in which feathery cross-costae may be seen growing out from the costae in a well-spaced, but irregular fashion. They link, form a somewhat regular arrangement of pores, and become sharper in outline (his Figs. 14-17). These changes in cross-costae morphology are probably a direct consequence of sintering. Another beautiful sequence of micrographs, which can be interpreted as steps toward full sintering of the mature valve, can be seen in Schmid and Volcani (1983).

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H. Roles of Impurities in Diatom Morphogenesis

1. The Formation of Punctae The openings (punctae) between cross-costae are often small and have shapes characteristic of each species. The serine-rich protein (Hecky e? al., 1973)or other organic constituents possibly in the solution in the silica deposition vesicle may be responsible for keeping the puncta of the valve open. These components could include parts of the silicalemma itself, which is reported to stay close to every portion of the silica surface during costal growth (Volcani, 1981).The distinctions between membraneembedded, membrane-bound, and free in the interior of the silicalemma may not be important while the silicalemma is still of macromolecular thickness. As precipitation proceeds, any organic material which is not trapped or will not coprecipitate with silica will be driven to higher and higher concentrations (unless it passes out through the silicalemma). If there is any protein, etc. within the silicalemma, we would then predict that, at least upon completion of the shell, much of this material would be found in the puncta. The high local concentrations in the forming puncta may locally inhibit further silica deposition: These tiny pores usually appear filled with mucilage or other material in fixed and embedded cells. . . . The mucilage probably offers little barrier to the diffusion of many ions, gases and metabolites, which therefore have free access to the selectively permeable plasmalemma through the silica wall. A large proportion of the cell’s mitochondria are thus favorably situated for rapid gas exchange with the environment. (Pickett-Heaps et af., 1979a)

(Compare Plate 583 in Drum e? al., 1966.) Schmid (1988) suggests that the mother liquor is deliberately filled with organic material as the valve matures: Dictyosomes not only contribute membrane and content of their vesicles to the SDV which is attached to the plasmalemma while the siliceous wall parts are formed, but upon their completion a new population of dense Golgi vesicles is produced and integrated into the SDV. Their organic content coats the siliceous wall parts, in this way probably arresting further silica deposition.

The diatom may, of course, have a mechanism for later removing the material from the puncta in order to provide freer access to the environment. For crystals, different habits occur in different regions of a plot of supersaturation versus impurity concentration (cf. Doherty, 1975). Analogous phenomena may occur for amorphous precipitation, giving costae of varying dimensions and spacing. Since the impurity concentration may

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increase as precipitation proceeds, there could be systematic changes in costal morphology during valve morphogenesis. Little impurity may be needed: Minor additionsof certain solutes can have a dramatic effect on the micromorphology of a growing ice crystal. . . M . . .NH41 solute seems to suppress the long wavelength instabilities and cause a general roughening to appear. Glicksman (1977) Some centric diatoms show an abrupt change in costal morphology versus radius (for example, Cestodiscus; J. Fenner, personal communication). This may sometimes reflect an abrupt change in the mother liquor, which might be attributable to a phase transition of one of its constituents or spatial or temporal variations in the supply of silica over the silicalemma during valve maturation. In some cases these changes occur at radii shorter than that of the valve margin (Cyclotella pseudostelligera, Fig. 312 in Geissler et al., 1963; Thalassiosira JEuuiatilis, Fig. 106 in Helmcke and Krieger, 1962b; Cyclotella cryptica, Fig. 738 in Gerloff and Helmcke, 1974), suggesting that something other than an angle change as the silicalemma grows around the margin is involved. Such nonstationary patterns may be caused by increasing concentrations of impurities as the silica precipitation proceeds. These impurities are subject to their own complex diffusion dynamics (Chernov et al., 1984) and can get trapped (Geguzin and Krivoglaz, 1973). Some diatoms form resting spores that look similar to the vegetative cells, except that the puncta appear to be completely closed (von Stosch and Fecher, 1979). In some cases the increased silicification is accompanied by pattern changes (Syvertsen, 1985) or even gross changes in valve morphology (Hasle and Sims, 1985). The cell seems to intentionally isolate itself from the environment. In the simplest cases the mechanism need only be silica precipitation that is permitted to go closer to the extreme of completely filling the silica deposition vesicle. Fritsch (1971) has similarly noted that “while the valves are usually ornamented in a characteristic manner, the connecting bands (girdle) are commonly smooth.” Both of these altered morphologies could be accomplished by a mere reduction in or lack of proteins added to the silica deposition vesicle forming a girdle. There is some dispute about the role of “granules which occur between the organic material and the silica of the first girdle-band” of unknown composition (Crawford, 1981a; cf. Lewin, 1961). The girdle bands often have puncta of their own (Hendey, 1959; Round et al., 1990), suggesting they are formed by essentially the same mechanism as the valves. Some girdles have branching and stoppage patterns (Figs.19, 23, and 24 in Crawford, 1971), the latter at the corners of what

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would appear to be a T-shaped nucleating structure. Their nascent nucleating structures have yet to be observed in whole cell preparations, but Round and Crawford (1981) point out that “many girdle bands have a distinct line running along their length” which we suggest may be homologous with the midrib in pennate diatoms. They also find that: the form of the areolae (valve pores) and the siliceous plates within the areolae are very similar, and in some it is very difficult to decide from isolated fragments which is valve and which is girdle band (e.g., in Zsthmia, Thalassiosira, Amphiphora, Rhizosolenia and many others that we have examined. . . . Almost complete similarity suggests a similar rate of coevolution of the two parts.

We would rather conclude that in one and the same diatom, the physicochemical conditions of silica precipitation are usually the same in the valve and girdle silicalemmas. 2. The Shapes of Punctae

The cribae (finely perforated siliceous layers at the inner surface of an areola) themselves often contain smaller pores (poroids) about 1000 A in diameter arranged in rosettes that vary from irregular to a hexagonally close-packed array (Fryxell and Ashworth, 1988; cf. Miiller, 1898). Some exhibit branching patterns (Fig. 51a in Hasle and Fryxell, 1977; Round, 1984), while others have pores hierarchically within pores (Schmid and Volcani, 1983). These openings are clearly too large to be spaces created by single protein molecules. They may, however, represent condensation products of protein molecules forced to high concentrations. Silica can actually cross-link and denature proteins (Iler, 1979), and thus may also contribute chemically to the formation of condensed protein spheroids. Denaturation of protein, supposedly by a hydrogen bonding mechanism, requires colloidal silica with a diameter above 50 A (Iler, 1979). Even mechanical interactions between such protein spheroids packed into the small area of a pore could lead to the observed close-packed structures of some poroids. The systematic orientation of elongated punctae, silica bars separating punctae (Jackson and Lowe, 1978), and other details may require the intervention of other macromolecular mechanisms. The parallel alignment of these bars may be due to their local orientation to the costae (cf. Wall et al., 1978), rather than any global effect, such as orientation of liquid crystals in an electric field. The hexagonally arranged, floral-shaped punctae seen in some diatoms, with the “petals” aligned from one punctum to the next (Fryxell and Hasle, 1974), will take more imagination to explain away.

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Since mitochondria enter the locules in some diatoms (Pickett-Heaps et al., 1979a; cf. Drum and Pankratz, 1964a; Li et al., 1990), they may

also influence the formation of punctae. An advancing front of silica precipitation may actually be able to push objects, such as protein spheroids, that might occur in the mother liquor of the silicalemma. Such a mechanism would be similar to the phenomenon of freeze front motion of protein-coated beads, which is used to measure the surface tension of proteins (Omenyi et al., 1981a,b). Depending on the surface tension, some beads get trapped in a moving front of a freezing aqueous solution, while others are pushed ahead. It is a common observation in tissue culture laboratories that a drop of dried culture medium exhibits dendritic cystals. Careful examination of some of these reveals what appears to be completely unfaceted dendrites (Gillian Arden, personal communication). The serum protein impurities may be responsible for this change to an isotropic, if not amorphous, habit.

3. The Mother Liquor In the course of the 10 min of silicalemma growth, dramatic changes in the concentration of nonsilica substances in the mother liquor should occur, sometimes leading to systematic changes in the pattern of precipitation of the silica (perhaps by altering the rate of surface diffusion of the silica). Cohn et al. (1989a) have observed different pore spacings between the valve mantel and the valve face in Hantzschia amphioxys, concluding that “pore-pore spacing is determined not by position on the valve face or mantle, but by position relative to the raphe.” (Cf. Round et al., 1990.) While both sides of the valve in this pennate diatom are formed within the same silicalemma, precipitation starts at different times because the raphe is finished on one side of the valve before the other (Chiappino and Volcani, 1977; Schmid et al., 1981). Thus the mother liquor may have aged between times, causing a different pore spacing between the two “bilateral” halves. Changes over the life cycle in the initial contents of the mother liquor in the silicalemma may account for the following conundrum: The distance between striae is considerably larger in initial valves than in gametangial and post-initial valves. . . . It seems unlikely that the change from one precise interstrial spacing to another could be controlled simply by the absence of MTs [microtubules]. . . . It is difficult to explain why the stria-stria spacing differs dramatically in the intial cell (as compared to the vegetative cell). . . . At this point it is impossible to know what part of the valve morphogenetic machinery is affected in the initial cell to cause the change in strial spacing. Yet, it is possible that this one part of valvar pattern formation can be altered independently from the others. (Cohn et al., 1989b)

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The “others” refers to a preserved pore-pore or cross-costal spacing. As the latter, in our model, may be a later step in valve morphogenesis, it may indeed be somewhat independent of costal (striae) spacing. While the contents of the silicalemma during two-dimensional valve growth have never been measured by means other than standard transmission electron microscopy, it may be possible to chemically and physically manipulate the mother liquor. As mentioned in a study of the effects of Al+3, which reduces cell size and increases silica shell thickness (Gensemer, 1990): Morphological features of the diatom frustule also exhibit variation in response to external environmental factors. Changes in cell morphology and silica cell content have been observed for diatoms in response to changes in environmental factors including inorganic nutrient dynamics, salinity [cf. Schultz, 1971; Schmid, 1979b; Gordon and Brodland, 19901, temperature [cf. Fryxell, 19881, and light (Tilman et al., 1976; Paasche, 1980; Turpin and Harrison, 1980; Theriot and Stoermer, 1984; Taylor, 1985; Conley et al., 1989).

Isolation of nascent valves under these various influences would indicate which were worth pursuing because of their effects on costal growth, if any. In sorting out these effects, one must look only at freshly divided cells, since older cells may alter morphology through dissolution (Hedy J. Kling, personal communication). For those agents that are chemical elements, energy loss electron microscopy (Henkelman and Ottensmeyer, 1974) could be used to examine their coprecipitation, if any, in the nascent valves. Aluminum changes the Michaelis-Menten parameters for Si uptake (Gensemer et af., 1993) and is adsorbed on diatom shells (Stoffyn, 1979). Lewin (1962) gives the following summary: A chemical analysis of diatom walls from marine plankton indicated 96.5%

SiO, and only approximately 1.5% of A&03or Fe203;no titanium or alkaline earth metals could be detected (Rogall, 1939). Desikachary (1957), however, found that acid-cleaned walls of Desmogonium guyanense contained aluminum, as indicated by spectroscopic and microchemical tests.

(See “Addendum” for a continuance of this section on p. 421.) VI. Modeling of Sintering A. An Attempt a t Exact Modeling

1. Modeling an Amorphous Precipitate We have shown how the patterns of diatom shells can be approximated by irreversible precipitation of amorphous silica. However, while the fine

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feathery patterns we obtained in our computer simulations resemble the first formed silica fibrils seen by electron microscopy, they only grossly resemble the structures of most mature valves. We would like to show now how sintering can be simulated to produce structures that better resemble mature diatom shells. Our modeling of sintering was at first quite complex, because we tackled the problems of representing a smooth, amorphous substance on a square grid, using a model based on chemical kinetics. This approach was set aside because of biases introduced by random number generators (cf. Ferrenberg et al., 1992) and because a simpler method became available (Vicsek, 1984, 1992). The latter will ultimately have to be abandoned, since it does not get past the anisotropy of the lattice (Vicsek, 1992). We thus record some of our chemical kinetics considerations here. For the future, the best approach to representing the tetrahedral network in silica may be molecular dynamics simulations based directly on computer representation of amorphous tetrahedral networks (Weaire, 1985). These have previously been handled as physical models, such as in Ordway (1964; cf. Alben and Boutron, 1975): The ideaof acontinuous random network, denoted by CRN, based on covalent bonding was put forward . . . by Zachariasen (1932) in a paper which has been regarded as one of the most influential in the history of glass science. . . . In the 1960s some ball-and-spoke models were built in this way with several hundred tetrahedral units (Evans and King, 1966; Bell and Dean, 1966). . . . These models are in the Bernal tradition of building an “essentially irregular assemblage” [cf. Bernal et al., 19641 but they are in the Zachariasen tradition of determining the SRO [short range order] by maintaining the chemical bonding. It appears possible to build such CRN to indefinite size without including unsatisfied bonds. They may be held to represent ideal glassy structures. Real materials like vitreous silica may approximate to the ideal but contain defects just as crystals depart from perfection. (Cusack, 1987) Even line defects are possible in amorphous structures (Venkataraman et al., 1989).

Because of memory restrictions, we represent the silica precipitate in the computer as a set of contiguous points or sites on a two-dimensional square lattice, each occupying just one bit of memory. The distance between neighboring sites is taken as the molecular diameter of Si(OH),, approximately 6 A. On a square lattice, if one were to use ordinary nearest neighbor rules in calculating the positions of minimal energy for migrating molecules (Gordon, 1980c), any attempt at rounding up would actually produce “squaring up.” We thus had to find a way to avoid this problem and attempt to retain the amorphous, anisotropic properties of the precipitate, even though we represent that precipitate as a figure on a square lattice. At first we did this by approximating the region about each surface molecule by a best-fit, straight line segment. The best site for its relocation

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by surface migration was chosen using a square well potential, as detailed later (cf. Leontovich et af., 1975.) The migration or diffusion of molecules over a surface is a complex affair. A quantitative description requires that values be estimated for a number of difficult-to-measure parameters. The limited speed and memory of present-day computers places limitations on the realism with which we may represent molecular activity on a surface of any extent. In this section we present the best representation we have been able to achieve to date for the migration of silica molecules on an amorphous silica surface (cf. Faivre, 1983). Undoubtedly, more accurate representation will be possible. We suggest, however, that the present representation captures the essence of the problem. Migration events were initiated in two circumstances. When the simulated, freely diffusing species is a monomer (colloidal particles are introduced later), it migrates upon adsorption to the existing precipitate. [This is analogous to “surface migration or gliding during the act of condensation of a metal atom from the vapor phase”; reviewed by Muller and Tsong, (1969).] Otherwise, any surface monomer is allowed to migrate at a specified rate. The choice of monomer is random. Since the hole that an already adsorbed monomer would form would cause an irregularity in the surface, it is replicated without leaving a hole. When the extra increase in mass equals one surface monomer layer on the average, the whole surface is shrunk uniformly by one unit. When a surface molecule has been chosen, we use a boundary tracing algorithm (cf. Rosenfeld and Kak, 1982) to list the coordinates of all nearby surface molecules (called “perimeter molecules”) and their neighboring empty sites (called “boundary sites”) within a certain maximum migration distance R in either direction of the starting site of the migrating molecule. A bivariate straight line (Burington and May, 1958, expressed in a symmetric normal form) is fit through these perimeter molecules, which we regard as the actual or best fit surface. The distance r of each neighboring empty boundary site to this line is calculated. (Other boundary tracing algorithms, say, using larger search neighborhoods, would undoubtedly have some effect on which sites were regarded as providing a contiguous surface for migration.) Since the precipitate is approximately two-dimensional, its relevant surface is actually the perimeter around the precipitate. Thus the terms “surface” and “precipitate” will usually be used interchangeably in this section. The straight line would badly represent the local surface if it were extended too far. Thus it is fit to only a small group of consecutive perimeter molecules within a certain distance t from a given boundary site. The lines may then be called “running tangents.” One running tangent is thus associated with each boundary site, and is used in calculating the distance

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r of the site from the surface. Empirically we found that the minimum distance c or “tangent range” that gave a smooth fit was three molecular diameters in each direction. The minimum radius of curvature of the growing structure is essentially governed then by the tangent range. Larger values would create larger curvatures. They also improve smoothness somewhat. Because of the large improvement in smoothness from a tangent range of three to four molecular diameters, the latter value is preferable. Values greater than four molecular diameters were not explored because of substantially increased requirements for computer memory and time. We assume that their primary effect is a linear scaling of the pattern. The centroids of consecutive groups of perimeter molecules used to calculate the running tangents define an arc along the surface. The accumulated distance between these centroids is approximately the arc length of a smooth curve through them. We take this sequence of centroids to represent the amorphous surface. The probability that a boundary site is chosen for adsorption depends, in part, on the arc length that it occupies along this curve. This was calculated as one half of the sum of the distances from the centroid of the boundary site to the centroids of the boundary sites to its left and right.

2. Choice of the Adsorption Potential In general, we may assume that the newly adsorbed molecule has an adsorption potential u ( r ) (Hill, 1960; Davidson, 1962) with respect to its distance r from the surface, which is represented by its running tangent. Using absolute rate theory (Glasstone et al., 1941),we take the probability of choosing a given empty site as proportional to the Boltzmann factor (cf. Tolman, 1938; Gordon, 1968a,b, 1980~):v = exp [ --u ( r ) / ( k T ) ]where , T is the absolute temperature and k is the Boltzmann constant ( k = 1.38044 x ergs/”K). Experimental values for the interfacial energy of amorphous silica range from 50 to 200 ergs/cm2(Iler, 1979). With 7.8 OH groups/nm2(Iler, 1979), and 100 ergs/cm2, we obtain E = 1.3 x ergs per molecule (cf. Eq. 3). At T = 20 “C or 293 OK, this yields a Boltzmann factor of v = 0.04. If the interfacial energy were 50 ergs/cm2, v would be 0.2. At first we tried taking u ( r ) as the Lennard-Jones potential, which is commonly used for adsorbed molecules (Hill, 1960). The narrowness of this potential appeared, however, to bring out some of the discrete structure of the square grid used to represent the amorphous precipitate. Thus we turned to a square well potential (Hill, 1960), varying the width of the well until these discrete effects were masked. The ideal width of the square well potential was ascertained empirically by setting up aritificial surfaces that macroscopically corresponded to

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straight lines of various slopes. Such a surface is microscopically a staircase. This staircase effect is obviously an artifact of the square lattice. The purpose of finding an appropriate width to the square well potential is thus to mask this artificial staircase structure from the simulated molecules migrating over the surface. For all boundary sites along the staircase to be treated equally as potential sites for adsorption of the migrating molecule, we found that the square well had to extend from r = 0.5 to 1.5. This range was adequate for straight lines at all angles. (A geometric proof of this observation could undoubtedly be found.) We then have u (r) = E for r in this range, and infinite outside. The Boltzmann factor v is constant within the square well (meaning all boundary sites within the well are treated equally), and zero outside. On an amorphous surface, we should expect a variety of binding energies (cf. Gordon, 1968a): Since the silicon atoms on the surface of amorphous silica are, by definition, not in an exactly regular geometrical arrangement, it is obvious that the hydroxyl groups attached to these silicon atoms will not be exactly equidistant from each other. They are therefore not all equivalent either in their behavior in adsorption or in chemical reactions. (Iler, 1979)

Thus surface migration may continue until a particularly low potential well is encountered, as in low-temperature studies of the migration of adsorbed atoms on metals (Muller and Tsong, 1969). For low values of v, such adsorption sites are particularly favored. We might even anticipate that on an amorphous surface there may effectively be channels of adsorption sites of lower than average potential along which most of the surface migration may occur. The proportions of high and low energy adsorption sites could then dramatically affect the rate of surface migration through a percolation bond effect (cf. Hammersley and Handscomb, 1964; Gordon et at., 1972, 1975; Zallen, 1983): “In silica glass the network is irregular and some more open diffusion paths result” (Barrer, 1978).These channels cannot be represented in a two-dimensional model of valve growth, since the surface for migration is approximated as the one-dimensional perimeter of the projection of the precipitate. For this reason, we include no variation of u (r) from site to site, although it should be included in a full threedimensional computer simulation. Since the bonds in amorphous silica are in a constant state of vibration, it may be that each one on the surface has the same time average binding energy. This would justify using the same binding energy E and the same potential u (I-) for each site. The probability that a monomer will migrate an arc distance s along the surface during a given migration event will decrease with increasing s. In order to approximate this effect, we consider migration as a random walk

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along the perimeter, with equal probabilities of jumps in either direction from the starting site (cf. “Kinetics 1” in Gordon, 1968b.) (Correlation effects are ignored; cf. Wolf, 1983.) This one-dimensional perimeter diffusion may be described by a probability of migration proportional to the Gaussian exp[ - 2(s/R)*)]. This is a form of the one-dimensional diffusion equation (Crank, 1956)in which R may be considered as the characteristic distance of migration in a given amount of time. This time is just the reciprocal of the rate of initiation of movement of the monomers (Gordon, 1980~).To eliminate unnecessary computations, the probability is truncated to zero when s exceeds two standard deviations (i.e., the probability is nonzero for the range of s: R> s> - R ) . The probability of a given boundary site being chosen as the stopping point for a migrating silica molecule is then proportional to the product of three factors: (1) the Boltzmann factor v, (2) its associated portion of the arc length, and (3) the probability that a molecule would migrate to the arc distance s from its starting position. B. A Simpler, but Anisotropic, Approach t o Sintering

We describe here a simpler, if physically less realistic, computer simulation of the initial growth of costae in pennate diatoms. [A condensed version of the work in this section was reported in Gordon and Aguda (1988).] A uniformly adhesive nucleating structure is assumed. Periodic vertical boundary conditions are used to eliminate edge effects. All the calculations were programmed by Baltazar D. Aguda on a Macintosh using the language Modula-2 implemented by Microsoft. A bitmap of 101 x 144 pixels (= height X width) is used for the picture of the growing shell. The initial distance between the silicalemma and nucleating structure is chosen arbitrarily. A concentration field (of silica particles) is set up between the silicalemma and the nucleating structure. It is assumed that this concentration field attains a steady state rapidly in comparison with the silica deposition on the nucleating structure. The stead-state condition is given by the Laplace equation V2C = 0, where C is the concentration. A steady-state concentration profile from the nucleating structure to the silicalemma is approximated in the following way: The concentration along the silicalemma is fixed at 1 and the occupied sites (which are now of a different phase) are fixed at 0 concentration. The concentration at a given pixel in the mother liquor is then calculated by averaging the concentrations of its four nearest neighbors (Meakin, 1986). This calculation is iterated several times until the concentrations no longer change significantly.

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The growth process is simulated in the following way: A growth site is chosen at random. The sticking probability P at this growth site is calculated according to the formula (Vicsek, 1984): P = A(ni - no)

+B

(6)

where ni = N i / s 2 ;Ni is the number of occupied sites in an s X s square of pixels centered on the chosen growth site; no is the value of ni for a flat interface and is equal to (s - 1)/(2s). The difference ni - no is an approximate discrete measure of the local curvature at the growth site. A and B are non-negative parameters, the former allowing us to vary the influence of curvature (or surface tension) on the sticking probability. The length of the square, s, is another parameter of the program that allows us to change the characteristic wavelengths of the ensuing patterns. Another factor that we expect to affect the rate of growth is the local concentration gradient at the growth site. Most of the analytic treatments of diffusion-limited growth at interfaces assume that the velocity of growth at a given tip is directly proportional to the concentration gradient at that site. As a first approximation of V’C, we take CIC,,, where C is the silica concentration at the growth site calculated as described above and C,, is the highest concentration of silica among all of the growth sites available. This give V2Ca range of 0 to 1 and speeds up the computations. The final adsorption probability used in our program is then: The following criteria for adsorption are then followed, after a number R between 0 and 1 (inclusive) is generated at random: 1. If P < R, then another growth site is chosen at random 2. If P > R, surface sites adjacent to the present growth site are checked for their surface potential energy (in our program, this is equal to the number of occupied pixels adjacent to a given site) and if one is found that has a lower potential, then it is chosen as the adsorption site. Otherwise the growth site is occupied

This simple algorithm roughly approximates silica surface migration. In our program, only immediately adjacent sites are checked for their potential values; one could easily also check the second-nearest, third-nearest neighbors, etc. to extend the range of surface migration. After a pixel is occupied, the interface has changed and the program goes back to the very first step, i.e., calculating the steady-state concentration field. The results that will now be shown assume that the silicalemma has a constant distance from the highest tip of the growing precipitate. Figure 19 shows that sintering is, indeed, capable of generating the regular spacing pattern of costae. The development of this pattern is shown

314 . . . ... .....

..... ........... ...... .................................. . . . . .

RICHARD GORDON AND RYAN W. DRUM ...... .............................................................................. ........

FIG. 19 Irreversible precipitation simulated with sintering, after 3050 particles have been precipitated. The contour lines show the concentration gradient for the free, diffusing silica. Note that these lines are closer at the growing tips, and that the rate of growth is thus fastest at the tips. Nevertheless, because of the smoothing effect of sintering, a regular spacing is obtained. This corresponds to the regular spacing of costae in most pennate diatoms. Cois the source concentration (at the silicalemma), g is the gap between silicalemma and the highest tip of the growing precipitate, A and B are the parameters in Eq. (7), and s is the scaling parameter. Values here are Co = 1.0, g = 10 pixels, A = 6.0, B = 0.5, s = 7. The distance between adjacent contour curves represents a difference of 0.2 concentration unit.

in Fig. 20. An identical run, with a different sequence of random numbers, is given in Fig. 21. The six costae grow more or less at the same rate, and with fairly equal widths and spacings. Figure 22 demonstrates how the low concentration between two costae inhibits growth of a costa between them. As we lower the parameters for sintering in Fig. 23 and 24, dendritic and irregular patterns begin to appear. The addition of surface migration to the molecular simulation had a dramatic effect (Fig. 19) compared with simple irreversible precipitation (Fig. 9). The more widely spaced costae have far fewer branches and have a greater tendency to be straight. These simulations essentially repeat the work of Vicsek (1984), summarized in Fig. 9.5 of Vicsek (1992). A similar simulation for the geometry of centric diatoms is shown in Fig. 25. The costae are of irregular widths, indicating that we have achieved at best a crude approximation to diatoms with this kind of modeling. The shortcoming may be in the oversimplified representation of surface migration, which is why we have retained our description of a more accurate approach in the previous section. Have we explored the full range of parameters? Do new ones need to be measured and incorporated? What is the effect of alternative geometries for the silicalemma (glove versus mitten), or the compressive force of the microfilament ring? As in other morphogenetic work (Jacobson and Gordon, 1976; Gordon and Jacobson, 1978), an interplay of the development of numerical methods with experimental observations, applied to a particular organism, may be what is needed for success.

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Particles

3436

4657

FIG. 20 Time sequence for the same simulation of precipitation with sintering as Fig. 19. The straight line represents the moving margin of the growing silicalemma.

C. Physical Simulations An alternative to computer simulation of precipitation with sintering may be an actual physical simulation. Williamson and Chalmers (1967) have demonstrated that supercooled water can have “branched crystals . . . [that] have a random appearance which does not reflect the hexagonal symmetry of the crystal structure of ice . . . [a] random, noncrystallographic growth morphology” (cf. Lindenmeyer and Chalmers, 1966). It would be interesting to know if this ice is amorphous. Perhaps it is: Not surprisingly, vitreous ice, deposited from the vapour on a surface below - 160°C, is thought to be analogous to vitreous silica (Fletcher, 1970; Alben and Boutron, 1975). (Ziman, 1979)

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Particles

4501

5538

6987

10001

FIG. 21 Duplicate run, with the same parameters as used in Fig. 20, but with a different sequence of random numbers, in order to test the reproducibility of the patterns generated by irreversible precipitation with sintering. Comparing this sequence (at 4501 particles) with the previous (at 4657 particles), we see that both have six costae that are growing at about the same rate (although eventually the two middle costae of this run fuse; however, it seems that the second rightmost costa split into two later). We can see that both runs, using exactly the same parameters of the computer program, generate qualitatively the same pattern despite the random beginning of the pattern formation.

'THE CHEMICAL BASIS OF

31 7

DIATOM MORPHOGENESIS

Particles 224

-.I

663

1482

2585

................................... .........

FIG. 22 Simulation of irreversible precipitation with sintering, with decreased gap g between the silicalemma and the maximally extended precipitate, which effectively increases the concentration gradient of the diffusing silica particles. We also have increased the sintering range s, which means that we have extended the range of surface curvature calculation. This explains why there are now only two smooth bumps. Two of the pictures are magnified to show the concentration profile and how a low concentration gradient, as exhibited between the two fast-growing bumps, can inhibit the growth of costae. C, = 1.0, g = 5 pixels, A = 6.0, B = 0.5, s = 11.

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Particles

___." ..__._._." ..---..I.__I......................................... ...."--.........

2166

3531

5068

FIG. 23 The sintering is weaker in this simulation. A dendritic structure is generated. Notice that one costa shows runaway growth. This nicely demonstrates the instability inherent in a diffusion-limited growth process. There are also six smaller costae that are more or less of the same height and spaced somewhat regularly, but, most likely, would shortly cease growing for lack of access to silica. Co = 1.0, g = 5 pixels, A = 50.0, B = 1.0, s = 3, that is, a very high value of A and a low value of s.

Particles

2442

3774

4659

7022

FIG. 24 Another simulation with little sintering, sharp tip growth, and runaway growth of one tip. C, = 1.0, g = 10 pixels, A = 1.0, B = 0.5, s = 7.

319

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FIG. 25 Irreversible precipitation with sintering, growing in a fashion similar to centric diatoms. (Reprinted from Vicsek, 1992, with permission.)

One could also imagine using silica itself, confined between two suitably coated plates and nucleated with a fragment of precipitated silica (such as a chip of a diatom valve), to see if diatom-like patterns were formed. This would be a continuation of the experiments of Schultze (1863a,b), but with the now known geometry of the silicalemma incorporated. It might even be possible to carry out the precipitation within artificial bilayer membrane vesicles (Berndl et al., 1990; Miao et al., 1991). It is interesting to note that a start toward such experiments has already been made: Geissler (1958) showed that the silica walls of diatoms adsorb positively charged colloids to the s a m e degree as d o dried silica gels. (Lewin, 1962)

Experiments on crystal growth between rough plates (to force microcrystallinity and thus an approximation to amorphous precipitation) and on thin films are reviewed in Vicsek (1992).

VII. The Colloidal Nature of the Silica

A. Formation of Colloidal Silica

The nature of the migrating silica particles has been ignored in these preliminary simulations. This may affect the patterns obtained, if only by

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altering the ratios of the kinetic processes and the scaling. Lauritis e t al. (1968) showed “empty vesicles, in the vicinity of silicon-deposition, beneath the plasmalemma” slightly flattened parallel to the plasmalemma, of roughly 500 A x 1000 A, “which could coalesce to form the silicalemma.” Schmid and Schulz (1979) have suggested that 300-400 A silica transport vesicles fuse with the silicalemma, providing spherical particles of silica in this colloidal size range. Li and Volcani (1984) have been unable to confirm the presence of silica in these vesicles and have suggested that they merely provide the membrane material for the expansion of the silicalemma: “The silica deposition vesicle expands by the fusion of small vesicles (16 nm in diameter) along its margin” (Li and Volcani, 1985a). They also report vesicles of 27 nm and 35 nm in diameter (1985b). Edgar and Pickett-Heaps (1984a) doubt the importance of these vesicles: In the present study [on Nauicula cuspidata,] . . . in Hantzschia (PickettHeaps and Kowalski, 1981), . . . and in Pinnularia (Pickett-Heaps et al., 1979b), all pennate diatoms, there is no evidence suggesting that the SDV arises by fusion of vesicles in contrast to studies on two centric diatoms (Schmid and Schulz, 1979; Schnepf et a/., 1980) which describe vesicle fusion in SDV formation. . . . N . cuspidata . . . conforms to the “hands in glove” analogy. Accompanying this early development of the central ribs, small electron-dense vesicles (possibly dictyosome-derived) were apparent near the SDV, and in short rows some distance from its growing edge. These were equivalent in size (30-50 nm) to the silicon transport vesicles described by Schmid and Schultz (1979). . . . We feel it unlikely that addition of a siliceous material throughout valve growth occurs by fusion of these vesicles with the SDV since they become sparse later even where the valve is undergoing extensive thickening (e.g., at the central nodule). We cannot discount, however, their involvement in early valve growth.

Although preparation techniques are better today, we may do well to heed the technical advice of Reimann et al. (1965): The loss of opacity of silica in the presence of [the common electron microscopy stain] uranyl acetate was unexpected and is certainly worthy of further investigation.

Perhaps here lies a reason silica is not seen in the small vesicles. The lack of vesicles during valve thickening is another indication of a different transport mechanism at this stage of valve morphogenesis. The fusiform cell of Phaeodactylum tricornatum, which “lack any organized siliceous structures, yet contain as much silicon per cell as do the partially silicified oval cells of this species (Lewin er al., 1958)” (Darley, 1974), may be blocked at the step of fusion of the silica transport vesicles and/or formation of a silicalemma: When oval cells were digested with nitric acid . . . only the valves remained, thereby confirming their silicious nature . . . with a raphe, a central and

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polar nodules, and 60 rows of pores or striae (equivalent to 95 in lop). . , . Both oval and fusiform cells contained approximately the same amount of silica (0.4-0.5% of dry weight). This was unexpected, since no silica walls have ever been observed in the fusiform cells. . . . [which] after nitric acid digestion . . . when examined with the electron microscope [the precipitate] . . . appeared to be composed only of structureless debris, comprising irregular particles of various sizes, plainly not derived from silica walls. (Lewin et af., 1958)

Weighing these comments and their caveats, it seems reasonable to tentatively conclude that silica transport vesicles do line up under the plasmalemma and fuse with the silicalemma as it grows and encounters them. The contents probably include silica in low molecular weight form. On the other hand, valve thickening (which probably requires little, if any, additional membrane for the silicalemma) may not involve silica transport vesicles, but rather the direct action of the plasmalemma and/or silicalemma, perhaps using a silica ionophore (Bhattacharyya and Volcani, 1980, 1983; Sullivan and Volcani, 1981) or a coupling to organic Si cornpounds involved in general metabolism (Werner, 1966, 1967; Werner and Pirson, 1967) but no such intermediates have been reported (Volcani, 1978; cf. Werner, 1978). Centrifugation experiments might distinguish STV from ionophore silica transport.

6. Diffusion of Colloidal Silica In order to carry out a future quantitative simulation of silica precipitation and sintering in the diatom, we need to derive a few properties of silica either from experimental data or a priori. All quantities will be expressed in centimeter-gram-second units and indicated in brackets. The diffusion constant for a spherical silica particle of radius r [cml is given by: D = kT/(2d my) [cm2/sec] (8) The viscosity 7 [poise] is that of the fluid inside the silicalemma. Equation (8) is the Sutherland-Einstein equation, assuming no significant effect of counterions (Jacobs, 1967), modified to account for the dimension d of the medium (Shewmon, 1963). [Iler (1979) estimates that the bound water adds 0.3 nm to r . ] For thin silica deposition vesicles we may take d = 2. The composition, and thus the viscosity, of the nonsilica fluid within the silica deposition vesicle is unknown. It is probably mostly water, so we take 7 = 0.01 poise. However, the presence of protein or polysaccharide could readily increase its viscosity one or two orders of magnitude, if not more: Lyophilic, or solvent-loving, sols are characterized by strong solvation of

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the colloidal particles. Examples are protein sols such as gelatin, starch sols and, in some instances, colloidal silica. . . . lyophilic sols have greatly enhanced viscosities, leading in many cases to the formation of gels at higher concentrations. . . . Lyophilic sols are not sensitive to small concentrations of electrolytes, but large concentrations may “salt them out” of solution. (Moore, 1955)

Perhaps our best estimate for now is the viscosity of protoplasm, 0.1 to 100 poise (Heilbrunn, 1958), although one must exercise some caution in interpreting such measurements (Brodland and Gordon, 1990). There is also an effect of the silicalemma and the deposited silica on the water itself that is in the mother liquor: The fluid between the apposed . . . membranes is likely to contain a large proportion of water whose structure will be influenced by the membranes. Peschel and Adlfinger (1970) have investigated the anomalous viscosity of water between hydroxylated fused silica surfaces. If, using their equatiqn (3,we extrapolate their highest values to a membrane separation of 100 A, the apparent viscosity of the water increases . . . fortyfold to 0.4 poise. (Gordon et al., 1972, 1975)

Using for now the viscosity of bulk water, with T = 293.16”K(20°C),for r = lo-’ cm (100 A) for example, we obtain D = 3.2 x cm2/sec. The diffusion constant D may be related to a random walk through:

< X 2 > = 2dDt (9) where <X is the mean-square-displacement of the particle at time t (Shewmon, 1963). If we simulate diffusion of such a particle on a square lattice, then we need its rate of hopping, a, from one site to another, a distance of one lattice site A. The mean time between hops is Xla (Gordon, 1980~).Thus we obtain: a = kT/ (my A*)

Note that the bulk diffusion coefficient D in Eq. (8) depends on kT in a linear fashion, while surface diffusion depends on kT exp ( - u / k T ) [Eqs. (2) and (3)], so that the ratio can vary with temperature and thus change diatom morphology as a function of temperature: Schumann (1867) deduced from his oft repeated researches that temperature was the most essential cause of variation in the striation. He established that for the same species the number of striae so nearly corresponds with the temperature that, for a given elevation, the temperature of the locality can be so accurately determined by the number of striae as to make a thermometer quite superfluous. (Van Heurck, 1896; cf. Heribaud, 1894a,b)

This linear relationship may be due to the linear dependence of the diffusion coefficient D on the absolute temperature T. (On the other hand, Hedy J. Kling found no variation of costal spacing with temperature in Cyclotella bodanica; personal communication.)

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C. Necessity for and Consequences of Colloidal Silica

Iler ( 1979) has calculated that monomeric silica can precipitate at room temperature at a rate of only 0.7 A per hour. If we consider a centric diatom of radius 10 pm whose shell forms in 10 min, its rate of silica deposition is approximately lo6 times faster. Thus it is likely that the silica particles which diffuse and precipitate inside the silica deposition vesicle are actually colloidal particles substantially greater in size than single molecules (Ralph K . Her, personal communication). Even crystalline quartz can grow by precipitation of amorphous colloidal silica (Iler, 1979). A number of observations have been made of colloidal-sized particles of silica in diatoms. Borowitzka and Volcani (1978) observed that the girdle region of fusiform cells of Phaeodactylum tricornatum contained silica bands that were made up of series of granules whose apparent diameter and spacing is 160 A. These may also be the individual silica particles that participate in pattern formation. The margin of girdle bands of Nauicula pelliculosa consists of highly pointed teeth 150 A wide (Reimann et al., 1966). Schmid (1979a) and Schmid and Schultz (1979) have made direct observations of 120-300 A particles forming the costae in some diatoms: Schmid (1976) hypothesized that in Anomoeoneis sphaerophora silica deposition might occur in small spherical units that are transported by small spherical vesicles whose membranes fuse with the silicalemma and release their silica contents into the SDV. Later observations suggest that indeed this may be the case (Schmid and Schulz, 1979). (Schmid et al., 1981)

Chiappino and Volcani (1977) observed close-packed, 300 to 500 A mounds in the central nodule of Nauicula pelliculosa. Their observation that “the interstitial spaces between the knolls are gradually filled until the knolls are completely obliterated [to the point that] . . . there is no evidence . . . that they ever existed” may be a direct result of sintering. This is reviewed in Schmid et al. (1981). In Subsilicea fragilarioides, a weakly silicified diatom, the incompletely formed cross-costae have a feathery appearance, suggesting a particle diameter of 500 or less (von Stosch and Reimann, 1970). In Gomphonema paruulum, “the sites of silica deposition are frayed or composed of regular 40-60 A wide channels between silica” with a particulate diameter about the same (Plate 583 in Drum et ai., 1966). This fine structure is the same as the microfibrillar texture of the forming wall seen by Pickett-Heaps et a f . (1979b). Li and Volcani (1985b) in their Fig. 25 show a cross-section of silica fibrils about 200 A in diameter. Schmid and Schulz (1979) note that:

A

The “growing zone” exhibits a loose assemblage of silica spheres . . . and the “compacting zone” has a rather homogeneous character. Growing zones never show the shattering of silica which is typically the result of sectioning. These two zones show transitional stages.

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(We would replace the word “compacting” with “sintering.”) In Thafassiosira mediterranea about 1000 A siliceous knobs at the areola corners on the outside face of valves have been seen (Hasle, 1990). Excellent micrographs of “silica-deposited in the form of small spheres of about 300-500 in diameter,” may be seen in Schmid (1979a). Further observations of silica spheres are summarized in Schmid et al. (1981) with the caveat:

A

Nothing is known of how these spheres are assembled and compacted to become the mature wall; the difficulty of investigating the problem is increased by the fact that in some diatoms such as Attheya decora the silicification process does not appear to involve preformed spheres. (Schnepf et al., 1980)

Sullivan (1979) has postulated that, “the extractable Si pool contains [in addition to Si(OH),] one or more silicon species as polymeric silica chains or as colloidal silica (Si02)xmacromolecules with molecular weights greater than lo6 daltons.” These would correspond to a colloidal diameter of more than 113 A, using Iler’s (1979) formula: log d = 0.333 log M

+

1.054

(1 1)

where M is the molecular weight in millions and the diameter d is measured in nm. The 5% soluble silica found in the macromolecular fraction by Azam et a f .(1974) may just be silica sol particles. Sullivan (1979) estimated that the pool of soluble silica in Nauicufa pelliculosa just before frustule formation is 500 to 700 mMlliter compared with the 5 mMlliter above which polymerization occurs (Alexander et a f . , 1954; Iler, 1979). The soluble silica is about 11% of the total in a cell (Sullivan, 1979), which means that only that fraction of the silica needed for the new shells is accumulated at any one moment during their formation. The surface area of diatom shells might be thought to provide information on the their colloidal nature. Microporosity of diatom silica has been demonstrated by N, adsorption (Lewin, 1961, 1962; Iler, 1979). While these authors imply that the 100 m2 surface area per gram of walls is a much greater surface area than that estimated from micrographs, direct measurements of, for instance, Coscinodiscus asteromphalus (Werner, 1977) indicate that all the surface is accounted for by the morphology. We thus have to conclude that sintering of the precipitated particles effectively fills the spaces between them; that is, at the scale of the valve morphology it does not consist of a microporous silica gel (Iler, 1979). The porosity of diatoms is reviewed in Hurd (1983). The formation of chains of silica particles, such as are seen in some girdle bands (Borowitzka and Volcani, 1978), as “spaghetti-like siliceous strings, 150-180 nm in diameter” (Schmid and Volcani, 1983), and in the fibrillar structure of just deposited silica in extending or thickening valves (Pickett-Heaps et al., 1979b; Li and Volcani, 1985b), may be due to an end growth precipitation mechanism. Very dilute gels of silica may owe

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their existence to particles with coordination numbers of 2 or 3 (Iler, 1979), lending credence to this suggestion. The fibrillar bundles in nascent valves (Plate 583 in Drum et al., 1966; Pickett-Heaps et al., 1979b; Li and Volcani, 1985b), may be formed by a similar end growth precipitation. The colloidal hypothesis has many implications for diatom morphogenesis besides accounting for the rate of silica deposition. It allows us to postulate what form the silica takes intracellularly. It leads to detailed postulates for the rate of diffusion of these colloidal particles and their mechanisms of adsorption (precipitation) and sintering. Their size and electrical charge may give them a role in the morphogenesis of the frustule.

VIII. Valve Morphogenesis in the Context of the Cell

A. Plasmalemma

Most of the cell components in diatoms are involved one way or another in valve morphogenesis. Changes occur in plasmalemma that is either new or freshly exposed to medium (i.e., not adjacent to the inner surface of a silica valve), such as in lateral wall formation (Badour, 1968) and plasmolysis: New silica valves are deposited on freshly exposed cytoplasmic surfaces not only during the process of cell division and after auxospore formation, but also when cells are plasmolyzed. Kiister-Winkelmann (1938) observed that when cells of Achnanthes longipes were placed in hypertonic media, the cytoplasm contracted, shrinking away from the cell wall, and new walls were deposited within the old frustule. (Lewin, 1962)

(These “Innerschalen” are often abnormal; Eugene F. Stoermer, personal communication.) The opposite process also leads to freshly exposed plasmalemma and new valve formation: Vegetative enlargement, i.e. partial or complete extrusion of a protoplast from its frustule followed by regeneration of new valvae, uses morphogenetic means and attains results (irregular shapes of valvae, more variable and lesser size) different from those of auxosporogenesis and should not be confused with the latter. (von Stosch, 1965)

The internal thecae of resting spores have a similar double morphology. Eunotia soleirolii forms a new shell, consisting of a number of components, entirely inside the old shell (von Stosch and Fecher, 1979): light micrographs of the process suggest that the plasmalemma may withdraw from the old shell all around, so that the whole of the plasmalemma may be freshly exposed. These changes to the plasmalemma may include vesicle formation (Plate 581 in Drum et al., 1966): “Vesicular profiles lying between new cells [of

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Gomphonema paruulurn] may represent surface activity related to silica deposition”) and a sudden rise “in the number of functional transport ‘sites’ in the plasma membrane” (Sullivan, 1977). We could suggest that these transport sites are capped or aggregated membrane receptor proteins that bind silica from the medium on the outside and participate in clathrin or other coated pit structures on the inner surface of the plasmalemma (cf. low-density lipoprotein receptor-mediated endocytosis; Alberts er al., 1989). They may be the membrane silica transport sites that have been found to be zinc dependent (Rueter and Morel, 1981) and copper sensitive (Rueter er al., 1981). As membrane proteins, they may be the silica transport site that is affected by repeated washing (Lewin, 1954; Lewin and Chen, 1968). A burst of synthesis of the receptors may explain the fact that “the transport system . . . depends on de nouo protein synthesis” (Sullivan and Volcani, 1981). Silica “uptake conforms to MichaelisMenten type of saturation kinetics” (Sullivan and Volcani, 1981), as mentioned earlier.

6. Silica Receptors

It may be possible to prove the specificity of the silica receptor: A substitutedorthosilicicacid, in which one hydroxylgroup has been replaced by a methyl group, is . . . inactive (Lewin, 1955). (Lewin, 1962)

We can speculate that exposed plasmalemma initially has a low surface concentration of silica receptors, which are perhaps the 1700 silica binding sites per square-micrometer found by Blank and Sullivan (1979). The transferrin receptor is an iron scavenging protein that could provide a model for the silica receptor (Alberts et al., 1989). However, unlike iron, most of the silica stays out of the cytosol, just as signaling ligands (hormones) do (Alberts er al., 1989). We thus postulate that binding of lowmolecular-weight silica (cf. Lewin, 1955; Sullivan and Volcani, 1981) triggers an allosteric conformational change in the silica receptor at its cytoplasmic end. This could activate a G-type protein and a signal transduction pathway to the nucleus that results in the synthesis of more silica receptors: “The addition of silicate to [silica] starved cells initiates the synthesis of at least four polypeptides, thus suggesting that silicate regulates gene expression in the diatom” (Okita and Volcani, 1980; cf. Reeves and Volcani, 1985). The same pathway could be involved in the silica dependence of DNA synthesis (Darley and Volcani, 1969; Sullivan and Volcani, 1976, 1981) and could be the basis for the correlation between CAMP (Borowitzka and Volcani, 1977; Lin and Volcani, 1989), DNA synthesis (Aline et al., 1984), nucleoside triphosphates (Coombs er al., 1967b), DNA binding proteins (Okita and Volcani, 1978), and wall forma-

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tion with phosphorylation which “increased 3- to 8-fold within 10 min of silicate addition, then decreased subsequent to this” in silica-starved Cylindrotheca fusifovmis (Reeves and Volcani, 1984). DNA polymerase is also silica dependent (Sullivan and Volcani, 1973b). C. Silica Transport Vesicles

Somehow the silica gets transported from the plasmalemma to either the Golgi or the mitochondria, where it is bundled into colloidal-sized particles in correspondingly small silica transport vesicles. There is a possibility that silica transport vesicles go straight to the silicalemma, though a trip to the Golgi could add sorting signals (Alberts et al., 1989) that target them for the silicalemma or the microtubules attached to the silicalemma. The problem with working out the transport pathway is that HF usually does not change the electron micrograph contrast of the vesicles. This suggests that the silica in vesicles is in a gel state, perhaps kept there by low pH within the vesicles (Fig. 4). The observation that colloidal silica ‘‘cannot serve as a source of silicon for diatoms unless it is first depolymerized (Lewin, 1955)” (Sullivan and Volcani, 1981) is consistent with the notion that the silica is in a gel state within vesicles, and suggests that the plasmalemma silica receptors and/ or acidic conditions within the vesicles are responsible for the depolymerization of the silica adsorbed from the medium. Since the medium has a very low concentration of silica (“typical ambient fresh water and sea water concentrations are approximately 100 pM and 10 pM, respectively”; Sullivan and Volcani, 1981), and silica is often the limiting nutrient for diatoms, it is ecologically reasonable to suppose that the adsorption mechanism accepts all silica in all degrees of polymerization, and converts it to a common form. However, Lewin, (1962) says: “There is evidence that more highly polymerized forms cannot be used,” without addressing the possibility of depolymerization. The gel state may be necessary to prevent premature solidification of the silica in the Golgi vesicles, which does occur when Ge is present. It could be that coated vesicles containing silica travel from the plasmalemma to the Golgi or to the lysosomes, where they acquire not only sorting signals, but also an H+ pump, to increase their internal acidity (Alberts et af., 1989). D. Silica lonophores

Another pathway by which silica may enter diatoms is via a silicate pump that includes one or two ionophores specific for a low-molecular-weight form of silica (Bhattacharyya and Volcani, 1980, 1983; Sullivan and Volcani, 1981):

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The nature of the transported silicon speciesis not known; however, increased uptake at higher pH (9.5) suggests that the species is some form of charged silicate ion, probably H3Si04-. Symport of one Na+ with one silicate ion best fits all the experimental data except that of increased uptake at higher pH. The model predicts the presence of a specific carrier protein with binding sites for silicate and Na+;the presence of a carrier is indicated by the finding that sulfhydryl reagent inhibits uptake, by the [Michaelis-Menten]saturation kinetics, and by the fact that increase of Si(OH)4 transport activity during the cell cycle requires protein synthesis (Sullivan, 1977). (Sullivan and Volcani, 1981) The problem with this pathway is that if silica is pumped into the cytoplasm, then it must be concentrated once again into either silica deposition vesicles and/or the silicalemma. The ionophore pathway does not take advantage of the polymeric nature of silica in natural waters, which can be accommodated in the vesicle transport mechanism by assuming acidic conditions within the transport vesicles. We include it here for completeness, though its relative importance for valve formation compared with micropinocytosis obviously needs to be ascertained. The requirement for protein synthesis does not distinguish the two pathways. Since the ionophores were investigated in isolated membrane vesicles (Sullivan et al., 1974), we cannot be sure of where they are located in the intact cell. They may have a role in providing monomeric silica for metabolic functions not directly related to shell formation (cf. Lewin, 1955; Werner, 1978). Given that polymeric silica is what is primarily available in neutral to basic natural waters, an ionophore transport mechanism may be of secondary importance. In acidic waters, an ionophore transport mechanism may be the primary one. While the pH of ocean water is about 8.3 (Huckstedt, 1973), the marine nonphotosynthetic diatom in which the silica ionophores were discovered, Nitzschia alba, is saprophytic (Lewin and Lewin, 1967; Bold and Wynne, 1978), and thus probably has an acidic microenvironment. E. Microtubules

A nucleating structure that is linear or a ring is formed in pennates and centrics, respectively, surrounded by a silicalemma. Microtubules may be involved. The silicalemma abuts the plasmalemma. A microtubule organizing center is generally found near the silicalemma (Pickett-Heaps et al., 1988a), centered on the nucleating structure. It arrives by passing (in 10 min) through a hole in the doughnut-shaped nucleus apparently left by the spindle apparatus (Pickett-Heaps, 1991): “The central hole . . . becomes cone-shaped later; this characteristic shape is maintained until the valve morphogenesis is complete” (PickettHeaps et a f . , 1979b; cf. the hole through a nucleus reconstructed in three

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dimensions by Stevens and Trogadis, 1984). The microtubule organizing center generates a radial array of microtubules covering the silicalemma (with some penetrating perpendicularly back through the hole in the nucleus; Pickett-Heaps et al., 1979b), which presumably grow in length before or as the silicalemma extends across the exposed plasmalemma. The microtubule array may extend over the whole inner surface of the plasmalemma (Wordeman et af., 1986; Wordeman, 1992). A number of functions can be imagined for the microtubules spread over the inner face of the silicalemma: 1 . They could be responsible for keeping the silicalemma flat, which seems to be essential for the development of an instability pattern during the initial silica precipitation. This could be done by passive attachment or by active stretching of the silicalemma along the radiating microtubules. The possibility that the microtubules are in position over the face of the plasmalemma before the silicalemma starts growing (Pickett-Heaps el af., 1988b) suggests this model 2. They could carry the purported silica transport vesicles to their ends, which may coincide with the margins of the silicalemma. Alternatively, the microtubule ends may extend beyond the margin of the silicalemma (Pickett-Heaps et al., 1988b; Wordeman, 19921, depositing the silica transport vesicles over that portion of the plasmalemma not yet underlain by silicalemma. When the silica enters the silicalemma at the margins, this would force the concentration gradient in colloidal silica within the silicalemma to be highest at its outer edge, which is the best guarantee of an instability pattern when the silica precipitates. Transport to the margins of the silicalemma would explain how “silica is deposited on both surfaces of the forming valve, not only at the inner, cytoplasmically-oriented surface” (Pickett-Heaps e? al., 1979b). If it comes in at the margin, it is available equally to both growing faces. (The later thickening of the fully extended valve may be asymmetric because silica may enter from only one face.) 3. They could precede the silicalemma, and be responsible for the prepattern of areolae vesicles seen by Schmid (1986a) 4. They could play a role in pore formation: The space between the costae is gradually silicified, leaving four or five rows of pores. However, prior to silicification of the inter-costae spaces, a row of regularly spaced microtubules can be seen in them, lying close to the silica deposition vesicle. Once silica deposition starts in the spaces, the microtubules disappear. Evidence for the microtubules is based on the fact that their diameter is 20 nm and on the aberration of the seta caused by colchicine (Li and Volcani, 1984). (Li and Volcani, 1985a)

On the other hand, pore spacing is affected little or not at all when microtu-

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bules are disrupted (Cohn et al., 1989a), except at high inhibitor doses (Schmid, 1980)

5. They could be involved in the initial centering of the microtubule organizing center and/or the nucleus on the face of the bare plasmalemma. To do this, they would have to extend at least to the margins of the plasmalemma ahead of the silicalemma (cf. Wordeman, 1992).[This extension of the microtubules may be the fundamental basis for the diminishing sizes of cells in successive generations and thus the ecology of sex and the life cycle in diatoms; reviewed in Jewson (1992).] A centering mechanism based on the extension and collapse of microtubules in dynamic instability would be especially effective, since “the mean excursion lengths may be of cellular dimensions” (Bayley and Martin, 1991). Appropriate microscopy observations would have to be made of the length versus time and the possible dynamic instability of the fan of microtubules (cf. Horio and Hotani, 1986;Cassimeris et af., 1988;Hotani and Miyamoto, 1990). At this time we have the following: After cleavage, the nucleus comes to rest below the plasmalemma in the center of the newly created surface, held in position by numerous cytoplasmic strings that radiate to the margin. (Schmid and Volcani, 1983)

6. The alignment of some of the microtubules in a bundle along what will become the raphe in pennate diatoms (reviewed in Schmid et al., 1981; Pickett-Heaps el al., 1979b), but not in centric diatoms (Tippit et al., 1975), could be a consequence of this centering mechanism operating in the asymmetric space defined by the old valve, in a manner similar to that postulated for the generation of microfilament rings (White, 1990). The role of microtubules in shaping the raphe slit has been reviewed by Pickett-Heaps ef al. (1990) 7. They could be involved in the motion of the whole silicalemma, before the nascent valve is complete (i.e., within the first 10 min or so), over to one side, in diatoms in which “the pseudoraphe is located near one edge of the cell,” although this involvement seems to vary among species (Boyle et al., 1984) 8. Since the microtubules that cover the silicalemma extend over most of the inner surface of the whole plasmalemma, including the portion beneath the old, mature valve (Wordeman et al., 1986; Wordeman, 1992), they could be involved in triggering silica transport by the latter F. The Nucleus

The peculiar shape of the nucleus and its relationship to the microtubules warrants some discussion. A funnel shape allows rapid exit of material

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from the nucleoplasm to the cytoplasm. It breaks the symmetry of the nucleus, so that if nuclear rotation, possibly involved in gene expression (see De Boni, this volume; De Boni, 1988; De Boni and Mintz, 1986; cf. Onyshko, 1989), were occurring, it would be restricted to a single axis and would have to be in one of two possible spin directions. While nuclear rotation has been reported, it is not clear if the karyoplasm moves relative to the nuclear membrane: The nucleus also stays focused on the MC [microtubule center], rotating as the MC moves around it . . . . When colchicine was added soon after cytokinesis . , . the MC disappeared and the nuclear rotation accompanying MC migration ceased. (Cohn et al., 1989a)

The microtubules through the hole could be used to transport gene products toward the silicalemma, where the fan of microtubules could then disperse them either over the surface of the silicalemma or to its margins. Traffic could be two way, using for instance kinesin and dynein, and involve the vesicles themselves (Alberts et al., 1989; Vale and Goldstein, 1990),although the membrane of the vesicles may be needed for expansion of the silicalemma, precluding their return. Pickett-Heaps (1983) has noted: “Examination of serial sections showed that sometimes a protrusion of the nucleus approached the newly formed silicalemma.” It is curious that there is no gene dosage effect in diatom shell morphogenesis. Artificially induced polyploidy makes for larger cells, but the costal spacing seems unaffected (Fig. 2 in Coombs et al., 1968b). Nuclear division is normally correlated with valve formation (cf. Badour, 1968; Oey and Schnepf, 1970; Li and Volcani, 1988). However, formation of girdle bands may proceed throughout the life cycle (cf. Round, 1972b; Chiappino and Volcani, 1977).

G. Microfilaments The silicalemma is apparently also coated outside with microfilaments, first on the inner facing surface, but “at some stage, a second group of microfilaments has appeared on the other side of the silicalemma, before it too, grew outwards . . . and these filaments remain in place through much-if not all-valve morphogenesis” and the silicalemma sometimes bears a microfilament ring around its periphery (Pickett-Heaps et al., 1979b). These microfilaments, especially the microfilament ring, could have the following functions: 1. They are contractile and thus tend to compress the silicalemma, providing a possible counter tension to the microtubule array. [PickettHeaps et al., (1979b) ascribe to the microfilament ring the opposite role of “moving the silicalemma outwards over the surface of the recently

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completed cleavage furrow.” See also Pickett-Heaps (1983).] The flatness of the silicalemma may depend on this tensegrity structure (cf. Ingber et d.,, this volume) which, as we have indicated (Gordon and Brodland, 1987), bears an uncanny resemblance to the cell state splitter (cf. Gordon et al., Appendix, this volume). The microfilament bundle shares the property of the microfilament ring in urodeles in that its total mass is conserved as it changes length (Burnside, 1971, 1973). “A reduction in bundle size and filament number appears to accompany valve growth.” (Edgar and Pickett-Heaps, 1984a) 2. The loss of inward microfilament ring tension, when the silicalemma turns the corner as it abuts the old valve, may be responsible for the branching patterns often seen on the margin of diatom valves after about a 90” turn (Figs. 26-28). (See also Fig. 1 in von Stosch and Reimann, 1970; Fig. 75 in Hasle and Lange, 1992; cf. the finer pores at the margins of Thalassiosira trifulta in Fryxell and Hasle, 1979aand the fully developed areola walls in the marginal zone in T. mediterranea in Hasle, 1990.)

FIG. 26 The centric diatom Stephanodiscus niagarae, showing different pore spacings on the face and mantle. The younger frustule has the pores occluded, suggesting that the pores become visible through dissolution of silica after valve morphogenesis. Bar = 10 pm. (Courtesy of Hedy J. Kling.)

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In Stephanodiscus alpinus Hedy J. Kling (personal communication) found that the costae terminated abruptly at the interface of the valve face and valve margin (Fig. 27). Even a diatom such as Coenobiodiscus muriformis, which is “exceptional in being ‘saucer’ shaped rather than ‘Petri dish’ shaped-the distinction into valve face and valve mantle is obscure,” shows a change in morphology at the margin (Round, 1972a) (cf. Fig. 28). Thus the change in angle rather than its sharpness seems to be the important parameter. Such effects could also be caused by changes in the mother liquor during initial silica precipitation, but then we would not expect a correlation with the angle. [Selective dissolution from the valve margin can also occur, as in Stephanodiscus hantzschii (Kling, 1992).1 An understanding of microfilament bundles may not come so easily. Edgar and Pickett-Heaps (1984a) reversed the conclusion of Pickett-Heaps et al. (1979b): Filaments appear first at one edge of the expanding SDV and then the other and maintain this relative position throughout development. This suggests

FIG. 27 The centric diatom Stephanodiscus afpinus, showing abrupt termination of the costae at the valve margin. Bar = 5 pm. (Courtesy of Hedy J. Kling.)

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FIG. 28 The centric diatom CycloreNa bodanica showing the outside of one valve and another

partially dissolved. Note the greater tendency for branching near the boundary of the valve face and margin, even though the corner is gradual. Bar = 10 wm. (Courtesy of Hedy J. Kling.)

they might be involved in the lateral expansion of the SDV (Pickett-Heaps and Kowalski, 1981; Pickett-Heaps et a[., 1979b), but just how is unclear. There is no evidence of bundles at the apical edges of the SDV and it is unlikely that the bundle forms an entire ring around the vesicle, as if functioning in a reversed manner to the microfilamentous bundle of the cleavage furrow. An incomplete microfilament ring sharply raises the question of what mechanical components, passive or opposing, the microfilament bundle is connected to. Ultrastructural studies need to be done with this question in mind. We would predict that, in order to prevent the microtubules from buckling because of the compressive force placed on them by the microfilaments, they are probably interlinked by intermediate filaments (Brodland and Gordon, 1990).

H. Membrane Fusion of Silica T r a n s p o r t Vesicles The silicalemma expands to full width at about 1 pm/min through accumulation of the silica transport vesicles. As the colloidal silica particles are

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released within the silicalemma, they diffuse at random until they strike already precipitated silica, whereupon they fuse to it. The silica structure grows either as a periodic pattern of costae (pennate diatoms) or as a branching pattern (centrics). The fact that the silica precipitates suggests that the pH and salt concentration within the silicalemma have appropriate values (Fig. 4). There is some evidence that the salt concentration is high since square holes (Idei and Kobayasi, 1989),perhaps due to NaCl crystals (Gordon and Brodland, 1990), are found in some diatom valves. If we assume that all silica transport vesicles contain low-molecularweight silica, then a potentially critical event occurs as the silica transport vesicle fuses with the silicalemma (Fig. 8 in Schmid and Schulz, 1979). At least in some cases, the silica forms into a sphere about the size of the vesicle, which is the form that precipitates (Schmid, 1979a). We could anticipate that in other cases the silica entering the silicalemma could form polymeric clusters significantly smaller than the vesicles, so that the nascent valves do not show assorted knobs of adsorbed and sintering spheres: We did not find any indication of a “compaction” of silicified structures by preformed spheres as described by other authors (Chiappino and Volcani, 1977; Schmid and Schulz, 1979). (Schnepf et al., 1980)

A flocculating agent may be present to promote formation of the silica spheres. At physiological pHs, possible candidates are cationic surfactants, basic metal salts (such as AlCl,), and cationic polymers (Iler, 1979). Coagulating agents, such as simple electrolytes, Na+ or K + , may be all that is necessary. Certain concentration ranges may favor precipitation on an existing silica surface over flocculation in the bulk fluid (Iler, 1979). This could ensure that the silica spheres and/or lower molecular weight forms do not precipitate before they reach the growing, nascent valve. In other words, flocculating agents could provide a mechanism to guarantee heterogeneous (Meakin and Family, 1989) rather than homogeneous (Skoog et af., 1990) nucleation of the silica precipitation. Alternatively, precipitation onto the already precipitated silica could be guaranteed just by the geometry: entering silica is never too far away from precipitated silica. This may be one reason that the silicalemma is not formed first, but rather grows as the silica precipitates.

I. Subcellular Mechanics The thickening and maturing of the valve takes 1 to 6 hr. In the course of it, considerable sintering (rounding and smoothing) of the valve structure occurs, as a result of further surface diffusion. The mechanical strength

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of the valve thereby increases. Pickett-Heaps et al. (1979b) note: “Fine microfibrils that end near either surface of the silicalemma become thicker as they extend to and merge with the central mass of the previously formed wall, which displays . . . the typical fracturing properties.” Thus the brittleness of the silica develops during what would appear to be sintering. As Iler (1979) points out, “sintering [of silica] . . . can increase the mechanical strength of a mass by widening the areas of contact between constituent parts.” An increase in mechanical strength in diatom valves does correlate with what we claim may be a continuing process of sintering as the valve matures: “Developing valves are very fragile and are usually broken in isolated preparations” (Chiappino et al., 1977). A beginning has been made on finite element analysis of the mechanics of diatom shells (Steucek and Schmid, 1988), which could be extended to developing and aberrant valves. Perhaps it will be possible to explain why so few of the latter are found in nature, and how auxospores lead to normal vegetative cells (cf. von Stosch, 1965). One physical manipulation would be to allow diatom valves to form in the presence of a standing sound wave. The costal spacing versus spatial wavelength might exhibit interesting forcing and resonance phenomena. Variation of the wavelength over time might show up as a record in the deposited silica. If the phenomena we predict do happen, then we would have another tool for dissecting the time course of silica deposition. The frequencies needed would be the highest generated for acoustic microscopes (Briggs, 1992), which could also be used to measure mechanical properties in passing. The effects could vary with the orientation of the growing costae with respect to the waves. We might even anticipate that the costae might align with the waves. J. Plasrnolysis

We do not yet know whether the silica from the medium enters through the pores of the old, mature valves, or through the new plasmalemma between the new daughter cells. The latter is suggested by the possible opening of a space between the cells, which are “held together at least for a time by girdle bands” (Round and Crawford, 1981): Peragallo (1907) reported that in the centric diatom, Biddulphia mobiliensis, the two daughter cells retract after cytokinesis, leaving an “empty” gap between them that is later closed when the cell again expands. This so-called “spontaneous plasmolysis” has been reported in many species in connection with valve formation (for references see von Stosch, 1967; Drebes, 1977; [cf. Cohn et al., 19891) but more recent investigations suggest that this retraction might, at least in the case of Attheya decora, be the result of a local secretion

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of “swelling mucilage” rather than a real plasmolysis (Schnepf et al., 1980) (Schmid et al., 1981).

On the other hand: In Surirella oualis, no plasmolysis occurs and the flat valve surfaces are compressed against one another during silica secretion, the “interactive” type of division defined by Mann (1984). (Pickett-Heaps et al., 1988b)

In related species plasmolysis creates a hemispheric valve (PickettHeaps et al., 1988b), suggesting that the primary purpose of plasmolysis is three-dimensional valve shaping, rather than access to silica in the medium.

IX. Discussion A. The Diatom as a Silica Antenna

How does the silica get to and into the silicalemma? If the mechanism is universal, then it cannot be directly through the plasmalemma above the silicalemma, because plasmolysis separating the daughter cells is not universal. Besides, the small gap created between some separating daughter cells by plasmolysis presents relatively little capture surface for silica in the medium. It seems obvious that the silica must come through the pores in the mature valve and girdle bands (or by facultative or temporary dissolution of part of the mature valve, perhaps precluded by the phenomenon of silica starvation synchrony). In most diatoms mitochondria are positioned in or under these pores, ready to provide the necessary energy on site. Why are the pores so ornate? Fine detail increases surface area, which may help adsorb silica from the medium. The organic coat may specifically aid silica adsorption (cf. Macrae and Edwards, 1972), while simultaneously preventing uncontrolled fusion of the adhered silica with the mature valve. The mature valve may be an “antenna” for silica (the way moth antennae collect pheromones: Adam and Delbruck, 1968; Kaissling and Priesner, 1970). At least small silica polymers could be expected to diffuse freely over its surface (van der Eerden et al., 1977), (which may be heterogeneous in its adsorption characteristics at the molecular level: Sparnaay 1968; Gordon, 1968a), and through the pores (Hill, 1956). The concept of the diatom as an antenna1 collector of silica may help explain why “in Bacillaria paradoxa [and Nauicula pellicufosa] the [growth] rate during logarithmic growth was found to be independent of the silicon concentra-

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tion down to about lop6gm-atom/l” (Lewin and Guillard, 1963). Werner (1977) has remarked on: the quality of silica structures (like silica gel) to adsorb various substances from low concentrations. Living diatoms are also more effective in uptake from very low concentrations of nutrients (inorganic and organic) than many other phytoplankton classes (Werner, unpublished results) . . . . the impressive inner surface area of the silica frustule of diatoms might also be involved in the competition for nutrients at low concentration.

The use of spines and other processes to reduce sinking rates (Patrick and Reimer, 1966) may have the further effect of greatly increasing the volume of water from which the diatom can collect silica by diffusion (cf. Kraus, 1964) from its hydrodynamic boundary layer: The laminar sub-layer which occurs next to the surface may be of some biological importance partly because in the transport of heat and matter between a surface and the surrounding medium, it can only support molecular diffusion. (Leyton, 1975)

This may explain why “It is doubtful whether form has much influence on flotation since the range is extremely great” (Round, 1973): buoyancy may be of secondary consequence compared with better scavenging of silica by extended forms. This is seconded by Vogel (1981): Out of curiosity, I’ve reanalyzed the data [of Smayda, 1970 on sinking rates] for diatoms (17 species, eliminating size from the surface-to-volume ratio by using a dimensionless surface-to-volume ratio, S”z/V’’3, and eliminating size from the sinking rates by referring each to the sinking rate of a sphere of the same size. A graph using these variables is pure scatter or very nearly so. Thus most of the variation in the original data is easily attributable to the size variation rather than to the shape variation of the diatoms. The results also imply that shape is much less important in setting sinking rates than is the density of the diatom relative to the medium.

In fact, the need for silica may be a predominant reason for spines and setae (along with colony maintenance): Neutral buoyancy may not be desirable at all (Lund, 1959; Smayda, 1970). A phytoplankter which doesn’t move with respect to the water may deplete the local nutrients (Munk and Riley, 1952) . . . , The reported increases in sinking rates of cultured diatoms as nutrients are depleted (Smayda, 1974; Titman, 1975)may be a deliberate, selected response, a result of some specific physiological mechanism rather than any passive physical or chemical change. (Vogel, 1981)

(Compare Lee, 1980). Of course, uptake of silica at constant cell volume would passively increase the cell’s density. If the antenna hypothesis is correct, then one should be able to track the surface migration of silica (or Ge) from the spines, etc., to the pores.

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Older valves show what appears to be silica loss from spines (Hedy J. Kling, personal communication) and pores (Kling, 1992). It is not known whether this lost silica goes into the medium or migrates along the surface into the cell. Newly formed valves may actually require silica directly from the medium for completion: Cell membranes are undoubtedly very versatile structures as the change from silicalemma to plasmalemma testifies but it is difficult to believe that after functioning as a cell membrane the material is then used as an amorphous protective layer . . . . deteriorating membranes with an incomplete valve, and the work of Stoermer, et al. (1965a) who report that the membranes are in fact lost before the pore plates are formed, suggest that the frustule maturation may be a long drawn-out process continuing well after division and the liberation of the new component to the outside of the cell. (Crawford, 1981a)

The ratio of the spacing of the pores to the pore diameter may also be important in the design of diatom shells, since in a boundary layer: the rate of diffusion [through a pore is] . . . much greater than would be expected from the area of the aperture . . . . the pores [should be] . . . sufficiently wide apart from each other for each to exercise its influence without interference (a minimum of about 10 diameters was suggested). (Leyton, 1975)

The latter condition is met by few diatoms, but the suggested criterion, developed for the spacing of stomata in leaves (Brown and Escombe, 1900), may not be the best function to optimize for diatoms. Directly under the ornate pores lies the plasmalemma. Perhaps it has receptors that can pinch off coated vesicles containing silica straight from the medium. Perhaps it contains a silica ionophore that pumps silica into the cytoplasm, where it is later packaged into small vesicles. Perhaps both. We simply do not know where the vesicles are made right now. The Golgi may have a role in the packaging, “addressing,” and/or transport of these silica-laden vesicles.

8. Silica Reserves It may be important to determine the total amount of intracellular silica available just before cell division, to see if it is sufficient for at least nascent valve formation. Figures of 5% (Azam et al., 1974) to 1 1 % (Sullivan, 1979) would seem quite adequate. The intracellular silica content below which silica starvation synchrony sets in may correlate with this amount. It is a general presumption that the silica needed for valve morphogenesis enters the cell when it is needed, but the following experiment suggests otherwise:

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Earlier experiments (Lewin, 1954) showed that silicon-deficient cells of [Nuvicula pelliculosu], when resupplied with silicate but prevented from normal growth by being kept in the dark in the absence of a nitrogen source, each take up just sufficient silicate for the formation of two new valves. Counts of individual shells in acid-digested material, made with the light microscope before and after such an uptake, established that no additional valves were formed, although the silica taken up had apparently become associated with the insoluble shell fraction. Lewin (1954) concluded that under these conditions the silica was deposited on the previously existing valves. (Lewin et al., 1966)

Lewin and Reimann (1969) withdrew the suggestion “that the original silica shells.must have become thicker” (cf. Lewin and Chen, 1968). The question of where this large reserve is kept deserves resolution (cf. Werner and Pirson, 1967). Sullivan’s (1979) results would suggest that it is not soluble. If it is in silica transport vesicles, then the uptake (“at a 10-fold increase in transport rates during the first 5 h of the cell cycle . . . [and an increase in] the number of transport ‘sites’ ”; Sullivan, 1977) that occurs during valve morphogenesis may not be for the valve under construction, but for the next generation. If this is correct, silica starvation experiments may have to be reinterpreted. (Of course, we would not expect that pools for “present” and “future” use would be kept separate. Compare Davis et al., 1978.) Similarly, the presumption that valve synthesis is timed rather than a response to the simultaneous availability of both freshly exposed, or newly synthesized, plasmalemma and a sufficient supply of silica transport vesicles, has to be questioned: Using a variety of inhibitors [Oey and Schnepf (197011 . . . showed that formation of lateral valves was independent of cytoplasmic growth, mitosis and cytokinesis. Thus the factors which control the timing of cell wall formation remain unknown. (Sullivan, 1977)

Diatom resting cells, which “can be distinguished with the light microscope by the presence of the condensed cytoplasmic mass in the center of the cell” (Sicko-Goad et al., 1989), may also warrant study of their silica reserves, if any.

C. A New Model for

lntracellular Silica Transport

It would be nice to have direct evidence that the vesicles contain silica in one form or another, but perhaps the most important thing we know about these vesicles is that they get to the place where they are needed, when they are needed, just below freshly exposed plasmalemma. How? Why do they stay put under the plasmalemma until the growing silicalemma encounters them?

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Perhaps all freshly exposed plasmalemma binds silica transport vesicles better than plasmalemma that is overlain by a mature silica valve. [Distinctions are made between these two kinds of plasmalemma by Schmid (1987). Mature, nonsilica wall may have to be taken into account, however (Schnepf and Drebes, 1977).] With that hypothesis, all of our concern about the use of microtubules for transport vanishes: diffusion of the vesicles to an adsorbing boundary, the plasmalemma, will get them there, albeit a little slower. Inhibition of microtubules will not stop vesicle transport. The Golgi could be involved in inserting the sorting signal that specifically binds silica transport vesicles to exposed plasmalemma. The diffusion rate of STVs to the SDV will depend on the plasmalemma fluidity (Darnel1 et al., 1990).

D. Formation of the Silicalemma

The remaining problem is how the tubular (pennate) or toroidal (centric) silicalemma, and its initial nucleating structure inside, get created on that same exposed plasmalemma. For pennate diatoms perhaps it is simply that microtubules also attach preferentially to exposed plasmalemma, form a centered bundle, and move a few silica deposition vesicles together so they coalesce into a tube. This would explain why the microtubules under the exposed plasmalemma vanish or move on as the valve matures. The creation of a toroidal membrane in centric diatoms is more problematic. The greatest detail has been provided for Attheya decora by Schnepf et al. (1980): The formation of a new hypotheca begins with the accumulation of small (diameter 30-80 nm), smooth vesicles under the new plasmalemma . . . . At first the small vesicles and also the silica deposition vesicle appear to be empty. Soon, the silica deposition vesicle contains fine structures which have the shape of the seive-like plate and the costae of the valva. Initially, they seem to consist of non-siliceous organic matter because they are not dissolved in HF . . . . By this stage, the labiate process is already rather well developed . . . . The outer membrane of the silica deposition vesicle is not parallel with the plasmalemma in the region where the labiate process will form the opening, but is deeply invaginated, together with the inner membrane of the silica deposition vesicle. The latter is symmetrically associated with plaques of electron dense material within the cytoplasm. An electron dense plug consisting of organic substances seems to connect locally the outer and inner membrane of the silica deposition vesicle. The “lips” of the labiate process are already silicified. There is only a slight accumulation of organic material in the other parts of the silica deposition vesicle in this very early stage.

Here we have a glimpse of the work that lies ahead to determine what the initial, presumably nonsiliceous nucleation structure actually is. Presumably it binds silica in such a way as to form at least a monolayer that

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is indistinguishable from bulk precipitated silica. The bound water on proteins, “roughly 2 water molecules per average amino acid residue . . . one third of the [monolayer of water] . . . surrounding the protein” (Creighton, 1984), may provide a clue as to what to look for, because water and silica properties are so close. A membrane protein jutting into the inside of the silicalemma could cause silica precipitation: Holt and Bowcott (1954) showed that silicic acid polymerizes to form a rigid network after the molecules have been adsorbed on a protein monolayer, presumably through the formation of hydrogen bonds between hydroxyl groups of the silicic acid and keto-imino groups of the proteins (Clark et al., 1957). (Lewin, 1962) Kling (1992) observes that in Stephanodiscus hanrzschii, while the labiate process may be present early in valve morphogenesis, it forms its mature siliceous tube toward the end of valve morphogenesis. The key to understanding the initiation of new valves may lie in the observations of whole new shells being formed de n o w , as in auxospores and resting cells. Ultrastructural work on this process may be just what is needed.

E. Alternative Mechanisms for Branching Patterns

Finally, we must ask, could diatom shell morphogenesis happen any other way? After all, noncrystalline branching patterns are formed by: 1. Erosion (rivers: Scheidegger, 1966, 1967) 2. Phase separation (lecithin in water: Brown and Wolken, 1979; or between immiscible glasses: Haller, 1965) 3. Injection of one fluid into another with which it is immiscible (viscous fingering: Feder, 1988; Vicsek, 1992; Bhaskar er al., 1992) 4. Lightning and other electrical discharges (Fig. 91 in Stevens, 1974) and breakdown (von Hippel, 1965; Fig. 3.13 in Smith, 1981) 5. Corrosion (Fig. 3.14 in Smith, 1981) 6. Shrinking during peeling of viscous fluids between plates (Figs. 176-177 in Stevens, 1974) 7. Shrinking during cooling (temmoku glaze of Figs. 9.13-9.14 in Smith, 1981) 8. Cracking (brittle Cu,Mg: Fig. 3.17 in Smith, 1981) 9. Wave motion (sand ripples: Fig. 179 in Stevens, 1974) 10. Dislocations in smectic liquid crystals (Venkataraman er al., 1989) 1 1. Droplet formation during splashing and spattering (Worthington, 1963; Figs. 77-79 in Stevens, 1974)

These are all physical processes, not biological analogies (paper nautilus shell, Fig. 57 in Portmann, 1952; Fig. 399 in Thompson, 1942; ocular

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dominance columns: Hubel et al., 1977; Lund, 1978; bacterial colonies: Matsuyama and Matsushita, 1993; trees, etc.: Prusinkiewicz and Lindenmeyer, 1990) that beg the question. The long list shows that mere appearances of similitude are not proof of mechanism. A simple demonstration that silica branches and forms diatom-like patterns by itself, without any of these other plausible or implausible processes guiding it, would be infinitely more convincing than our considered exposition of reasonableness of instabilities in irreversible precipitation of silica. Perhaps someone will pick up where Schultze (1863a,b) left off with this synthetic approach, while the theory we have formulated can guide the analytic approach toward the many intermediate steps that need to be elucidated. That great expositor of physical causes of morphogenesis, D’Arcy Thompson (1942), who may be excused for not knowing of its applicability to the relatively rare naturally branching costae in diatoms, was aware of instability in branching processes: It would seem that, if the supply of material to the growing cystal begins to run short (as may well happen in a colloid medium for lack of convectioncurrents), then growth will follow only the strongest lines of crystallising force. The crystal will have a tendency to become filiform, or “fibrous”; and the raphides of our plant-cells, and the needle-like “oxyotes” of sponges, are cases in point. Again, the long slender crystal so formed, pushing its way into new material, may start a new centre of crystallisation: whereby we get the phenomenon known as a “relay,” along the principal lines of force and sometimes along subordinate axes as well [Bowman, 19061.

F. Application t o Other Organisms

There are numerous organisms which may use pattern-forming mechanisms that are similar or identical to diatoms (Simpson and Volcani, 1981). The siliceous scales of Potarnodiscus kalbei (Gaarder et al., 1976) and Mallomonas (Siver, 1991), the calcareous scapholiths of Calciosolenia murrayi, and the cellulosic theca of Ornithocercus rnagnificus (Bold and Wynne, 1978; cf. Taylor, 1971), all bear uncanny similarities t o diatoms, suggesting that their patterns may have a common basis, whether or not they have a common evolution (Round and Crawford, 1981). The graceful rounding of the siliceous skeleton internal t o cells of the silicoflagellates (Bold and Wynne, 1978), the beading of siliceous sponge spicules (S. Inoue, personal communication; cf. Inoue, 1982; Gordon et al., 1972, 1975), and the “circular pores and gradual accretion at the rims resulting in some of the pores becoming nearly closed” in radiolaria (Anderson, 1983), suggest that sintering processes are involved in their formation. S. Inoue (personal communication) has suggested that our theory of pattern formation through instabilities in precipitation may be applicable

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to microtubule polymerization in dendritic cells, such as nerve cells and melanocytes. Even though the precipitate, consisting of elongated microtubules, is neither microscopically contiguous nor amorphous, nevertheless an instability mechanism operating during precipitation might account for the dendritic branches. Branching would be of bundles of microtubules, not individual ones. Microtubule branching could be the source of the prepattern suggested by Schmid (1986b).The numerous three-dimensional configurations of microtubules observed in cells (Dustin, 1984) may, in part, be explainable as instability patterns. Wood rays grow as columns of cells that apparently compete with one another, some growing out, and others staying back (Sinnott, 1960). The pattern is much like that of ice cylinders growing in supercooled water (Hardy and Coriell, 1968a,b, 1969). The generation of this pattern may involve an instability mechanism. Mammary ducts develop as a single epithelium branching as it grows into a fat pad. The branches are well spaced, and growth and branching continue until the whole fat pad is invaded. If two ducts start simultaneously in the same fat pad, their branching patterns stop when they abut (J. M. Williams, personal communication). Thus the mammary duct appears to grow analogously to the diatom shell, forming a three-dimensional space-filling branching pattern. There are at least two particles that may act analogously to the diffusing silica particles: growth factor protein and mesenchymal cells, both of which are found in a fat pad. Either protein molecules or cells, on diffusing or wandering to a duct, may locally stimulate duct growth and branching. Such stimulated growth becomes analogous to the diatom costal growth by precipitation. Growing parts of the duct jut out further into the gradient of protein or cells, leading to a positive feedback and thus instabilities. Abutting ducts exhaust the particles between them and thus cease growth. The analogy to sintering in the diatom may be the effect of curvature on the mechanics of tissue bending for the cells of the duct epithelium. For morphogenesis in general, rather than looking for rules for branching, we may find inherent instabilities in accretionary processes to be the prime cause of many branching structures.

G. Conclusion According to our silica precipitation hypothesis, there are three molecular processes responsible for the morphogenesis of diatom shells: 1. Diffusion of colloidal silica 2. Adsorption of colloidal silica 3. Sintering of the resulting silica precipitate

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Diffusion and adsorption together lead to instability phenomena adequate to explain branching costa patterns. Sintering gives them more realistic, smooth shapes and accounts for pore formation. We have tentatively suggested that the sintering mechanism is surface migration of silica monomers. Quantitative explanations will require further research on the surface chemistry of silica and the theory of dendrite growth. The variety of diatom shell patterns may be partly explicable as variations in the timing, placement, amounts, and rates of these three chemical processes. Our work could therefore help provide a rational basis for a new taxonomy of diatoms, which is in a confused state (Guillard and Kilham, 1977; Round et al., 1990), and has been for a while: “Considerations of this sort may assist us in reducing the enormous catalogue of species in the Diatomoceae, a consummation devoutly to be wished” ( J . D. Cox in van Heurck, 1896). Duke and Reimann (1977) have noted that: The uniformity with which the valve pattern of the vegetative diatom cell is repeated after every cell division challenges one to search for the biogenetic reasons for this consistency. In this respect, diatoms seem to offer most suitable test objects for ultrastructural and molecular genetic investigations.

With the molecular basis of diatom shell morphogenesis now possibly outlined, it should be possible to bridge the intellectual gap between the genetics and development of these organisms as we turn this multifaceted problem of microscopic beauty over in our hands. Acknowledgments The basic ideas in this paper were formulated during an extended visit by Ryan W. Drum to Richard Gordon at James F. Danielli’s Center for Theoretical Biology in 1972. We would like to thank the following people for their helpful comments and assistance in the long, if sporadic, course of this research: Baltazar D. Aguda, Nina S. Allen, Samir S. Badour, Robert Bender, Natalie K. Bjorklund, Barry Bunow, Sam Coriell, Hyman D. Gesser, James Henderson, Terrell L . Hill, the late Ralph K. Iler, Shinya Inouk, Hedy J. Kling, Kurt B. Luchka, Andrzej K. Mazur, Susan V. Meschel, Akshintala K. S. K. Prasad, Charles W. Reimer, Frank E . Round, Anna-Maria M. Schmid, Eugene F. Stoermer, Param H. Tewari, Allison Thurlbeck, and Elizabeth Lynn Whitmore. We would like to thank Paul E . Hargraves of the Narragansett Marine Laboratory, University of Rhode Island, for providing diatom clones and facilities for electron microscopy; Ralph K. Iler for suggesting the polymeric nature of the adsorbing silica; Gretha R. Hasle for donation of a micrograph; Hedy J. Kling for donation of micrographs and assistance with the glossary; Charles Reimer for use of the Limnology Department library at the Philadelphia Academy of Natural Sciences; Baltazar D. Aguda and Elizabeth Lynn Whitmore for unpublished computer simulations done while postdoctoral and undergraduate students, respectively, with R. Gordon; and Baltazar D. Aguda for the initial draft of Section VI,B. Computing was supported initially by Julius Kane of the Animal Resource Centre, University of British Columbia. We would like to thank the staff of the former University of Manitoba Computer Department for Health Sciences for their assistance.

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The Investigators were supported initially by a National Institutes of Health Grant to Robert Rosen. Further support was obtained from the Dean of Medicine, University of Manitoba, and grants to R. Gordon from the Canadian Medical Research Council, the Richardson Scientific Development Fund, the Control Data Corporation, the Winnipeg Childrens Hospital Research Foundation, the Manitoba Careerstart Program, the Spina Bifida Association of Canada, and the Natural Sciences and Engineering Research Council of Canada.

Glossary annulus, midring areola vesicle (AV), vesicle of unknown origin and contents in centric diatoms correlated with areola development, also called spacer vesicle (Schmid, personal communication) areola, “the regularly repeated perforation through the siliceous layer of a frustule” (Bold and Wynne, 1978) auxospore, “the zygote of diatoms” (Bold and Wynne, 1978), after swelling bristle, external extension made of silica cell wall, organic and siliceous material external to the plasmalemma central annulus, midring central circle, midring central nodule (CN), a wall thickening that divides the raphe into two parts central rib, midrib central ring, midring centric, “type of ornamentation arranged around a central point” (Lee, 1980) chamber, cavity in the frustule, bounded by costae connecting band, girdle connecting rod, siliceous spines that attach cells together in a colony costa, rod of solid silica cribellum, cribrum cribrum, a finely perforated siliceous layer at the inner surface of an areola cross bridge, cross-costa cross-costa, silica rib perpendicular to the nearby costae cross-extension, cross-costa epivalve, “the flattened or convex plate of a frustule opposite to the hypovalve and formed prior to the hypovalve and thus usually slightly larger” (Bold and Wynne, 1978) fasciculated, branching frustule, “silicified cell wall” (Lee, 1980) girdle band, “that portion of a diatom frustule between the valves” (Bold and Wynne, 1978) hyaline, “region of a frustule not penetrated by areolae or puncta” (Bold and Wynne, 1978) hypovalve, (see epivalve) interstitial rib, costa labiate process, “a tube or an opening located on the valve of a frustule, with a characteristic lip-like structure surrounding a narrow slit at the end of the internal portion” (Bold and Wynne, 1978); rimoportula (Ross and Sims, 1972) linear array, nearly perfect hexagonal arrangement of areolae

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loculus, “hexagonal chamber in the wall” (Lee, 1980) mantle, edge of a valve that is bent down, usually 90” from the valve face margin, junction of the valve face and mantle midrib, raphe rib midring, a ring of silica in the center of centric diatoms from which the valve seems to grow both outwards and inwards mother liquor, the fluid remaining after precipitation pattern center, midring or midrib pennate, “ornamentation arranged on either side of a central line (bilateral symmetry)” (Lee, 1980) pore, “a single hole” (Lee, 1980) poroid, “pore occluded by a plate” (Lee, 1980) primary central band (PCB), midrib puncta, “opening in the frustule, either a pore or a loculus” (Lee, 1980) raphe rib, the hyaline silica housing the raphe raphe, “longitudinal slit in the valve” (Lee, 1980) rib, costa scale, platelike silica structure on the surface of some auxospores seta, siliceous “elongated hollow wall extension” (Lee, 1980) silica deposition vesicle (SDV), “vesicle in which silica is deposited” (Lee, 1980) silica transport vesicle (STV), small vesicle presumed to contain silica, originally called “silicon transport vesicle” (Schmid and Schulz, 1979) silicalemma, “membrane of a silica deposition vesicle” (Lee, 1980) spine, pointed solid silica external protrusion attached at the margin stria, “row of punctae (pores or loculi)” (Lee, 1980) strutted process, pore through the full thickness of a valve supported by struts; fultoportula (Ross and Sims, 1972) theca, valve plus girdle bands transapical rib, costa valve, epivalve, hypovalve, or both together

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Appendix: Dialogue on Embryonic Induction and Differentiation Waves Richard Gordon,* Natalie K. Bjorklund,t and Pieter D. NieuwkoopS

* Departments of Botany, Radiology, Physics, Electrical and Computer Engineering, t Chemistry, and Microbiology, University of Manitoba, Winnipeg, Canada R3T 2N2; and 4 Netherlands Institute for Developmental Biology, Hubrecht Laboratory, 3584 CT Utrecht, The Netherlands

I. Introduction Embryology has reached a critical juncture. On the one hand, we are tripping over a mass of genetic and molecular biology “evidence” (Davidson, 1986; De Pomerai, 1990; Lawrence, 1992). On the other, the results of experimental embryology, garnered over the past 100 years, are crying out for explanation, while simultaneously being generally ignored (Gerhart, 1987). A central issue has been gastrulation, as expressed by Jonathan Bard (1991): “Gastrulation has a dual importance: not only is it the key event in development, but explanations for phenomena underpinning it would help to answer almost every other developmental question.” The three of us represent roughly three generations of embryological investigation: Pieter (P. D. Nieuwkoop) started his embryological research in 1938 as a student of Chris P. Raven (1954) at the University of Utrecht, obtaining his Ph. D., where he had also done his master’s and undergraduate work in biology. His work is summarized in four books: Nieuwkoop and Faber, 1975; Nieuwkoop and Sutasurya, 1979, 1981; Nieuwkoop er al., 1985). Dick (R. Gordon) entered embryology about 1965 via statistical mechanics, while he was a student of Terrell L. Hill (1960) at the University of Oregon, substituting interacting cells for interacting molecules (cf. Maruyama, 1963; Gordon, 1966). He graduated with a Ph.D. in chemical physics, after dropping out of molecular biology for philosophical reasons. Earlier, he worked as an assistant on quantitative chemistry solutions (with James S. Dwyer and Susan Meschel; Meschel, 1991, 1992; Meschel and Kleppa, 1991), a research assistant on DNA melting curves (with E. Peter Geiduschek; Geiduschek, 1991), and on organic matter in meteorites Inrernarional Review of Cytology. Vol. I50

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(with Edward Anders; Anders, 1989;Huyghe, 1991);he took an undergraduate degree in mathematics (University of Chicago, 1963). Natalie (N. K. Bjorklund) Upon entering university, Natalie’s original ambition to become a doctor was overtaken by her interest in embryology after she took an undergraduate embryology course taught by Hans Laale (1987). Since that first year she has worked as a research assistant in Dr. Gordon’s lab. She is in her last year of an undergraduate degree in biochemistry at the University of Manitoba. We have been corresponding for 3 years, and, as a result of sponsorship by the Netherlands University Foundation for International Cooperation, External Affairs Canada, Academic Relations Division, and the Spina Bifida Association of Canada, have been able to meet in Winnipeg. We did not expect to agree on everything. Thus we arrived at a structure for this discussion that leaves room for different opinions. We decided on the dialogue, a form going back in science at least to Galileo Galilei (1632): Salviati [advocate of the experimental method] and Simplicius [the Aristotelian] were to be set the task of vieing with one another to convince the third disputant, Sagredo, of the truth of their cause. (Ronan, 1974) There is no direct correlation between Galileo’s characters and our personalities. We view our dialogue as a synergistic meeting of minds that takes each of us beyond our individual predilections.

II. Authors’ Dialogue Natalie: We have now spent three delightful weeks together discussing all manner of subjects. I often feel my position is intermediate between the two of you. On the one hand we have classical experimental embryology with all its depth. On the other hand we have a purely theoretical and mechanical approach to understanding the embryo that appears to offer simple and easy solutions to old puzzles. I am standing with a foot in both worlds while simultaneously trying to juggle the biochemical and genetic approach I am learning in my course work. I hope we can share the wonderful flavor of our discussions during this visit with our readers. In this dialogue I have framed the successive questions and have added my time-lapse video observations to our discussion, hoping to bring Pieter’s experimentally based embryological data and Dick’s cell state splitter hypothesis closer together.

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1. What Is the Relationship between Genetics and Development? Natalie: Given all we are planning on discussing, this may seem a peculiar place to begin. However, I am learning to be a biochemist, and I naturally believe that the pursuit of genetic information is important to understanding the embryo. I am disappointed by a genetic approach in the literature that seems to be nothing more than a catalog of various genes being turned on and off at various points in development. I find it particularly frustrating that the actual function of many of these genes is a complete mystery. It would seem that knowing what genes are turned on where and when is not doing much to advance our understanding of embryology. What do each of you see as the role of genetics in development and where would you like to see genetics go in the future? Pieter: It does not help us very much to know what genes are turned on and off, but why are particular genes or better gene cascades turned on at a particular stage of development and why are they turned on in particular groups of cells in the embryo? What role do they play in the formation of the highly complex embryo? Genetics and embryology should go hand in hand and not develop as separate fields of research. Dick This problem was treated in a light-hearted manner by none other than the founder of modem genetics, Thomas Hunt Morgan, who started out as an embryologist (Morgan, 1897): It is significant that Morgan chose to write a book entitled Embryology and Genetics [1934] in which so little actual connection could be drawn between the two subjects. A story is told in which one of Morgan’s colleagues said that the title of the book had intrigued him, but that the contents had been a disappointment since no relationship was demonstrated about the genetic basis of differentiation. Morgan is reported to have said the man’s disappointment was his own fault: “After all, I did exactly what I said I would do in the title: I talked about embryology, and I talked about genetics.” This remark illustrates the basic problem with which Morgan tried to grapple. That he was unsuccessful is a result born of the complexity of the question itself (it is still unsolved). (Allen, 1978)

Cell state splitters (Fig. 1) give a tentative answer to the relationship between genetics and development. Imagine yourself inside the nucleus of a cell in a developing embryo, looking out. What can you see? I would suggest, not much. While there is some evidence that the nucleus has a mechanics of its own (see chapter by De Boni, this volume), and may be mechanically attached to the cell membrane by intermediate filaments and perhaps microtubules (Ingber and Folkman, 1989), it seems reasonable to regard its traffic with the cytoplasm as mainly biochemical. It thus must be “told” what is going on in the cell and at its surface, by molecules

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25w

w

80A microfilament bundle microtubule mat desmosome intermediate filament bundle

FIG. 1 In the ectoderm of the axolotl, we observe a cell state splitter consisting of a ring of microfilaments at the apical end of the cell, with a ring of intermediate filaments below it (Martin and Gordon, 1993a). Subtending these rings is an annular ring of microtubules, presumed to be in mechanical opposition to the microfilament ring. Desmosomes connect the cells, and microfilaments and microtubules impinge upon them from within. The vertical scale is about 30 times larger than the horizontal scale.

that the cell state splitter must transmit to the nucleus. The nucleus can respond chemically, presumably with specific mRNA synthesis. Natalie: For our readers unfamiliar with the cell state splitter model, please give us a short description. Dick: The cell state splitter is an unstable mechanical device, made of cytoskeletal components, which resolves into precisely two states: contracted or expanded. It consists of an apical microfilament ring and an apical mat of microtubules (Burnside, 1971, 1973),which are presumed to be in mechanical opposition (Gordon and Brodland, 1987), and an intermediate filament ring (Martin and Gordon, 1991, 1993a) that may be elastic in nature (Brodland and Gordon, 1990). The basic hypothesis regarding cell state splitters is that if they contract, one signal (probably biochemical) is sent to the nucleus, while if they expand, a different signal is sent: “the initial event can be mechanical, with gene products following” (Gordon and Brodland, 1987). A plausible molecular connection involving PKC pathways has been proposed that links such mechanical events to switching on of one of a pair of master genes (Bjorklund and Gordon, 1993). The contraction or expansion of the cell state splitter in one cell sets off the same event in the next cell, resulting in a wave of expansion or contraction. This wave phenomenon was predicted by Gordon and Brodland (1987) and subsequently reported by Brodland et al. (1993). Beloussov et al. (1990) have interpreted their

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experiments in which the whole ectoderm turns into neuroepithelium in terms of this model. Stretch-sensitive ion channels may play a role in propagation of these differentiation waves (Bjorklund and Gordon, 1993), though their lack of a physiological role to date (Morris and Horn, 1991) may make it necessary to turn to gap junctions or other cell-cell links for an explanation. To eliminate ambiguity, we have recently chosen to name each differentiation wave according to the tissue (or part thereof) that it travels through, with the word “expansion” or “contraction” appended, rather than for the stage it occurs in. Thus the former gastrula wave (Brodland et al., 1993; Bjorklund and Gordon, 1993) is now the presumptive notochordal mesoderm/ectoderm contraction wave. Pieter: Cell fate splitters may certainly play an important role in morphogenetic events. However, we must realize that at present we do not know whether they form a primary or a secondary event. I am inclined to consider them as secondary in inductive interactions set in action by biochemical signals between different parts of the embryo, parts which are in many cases brought into close adjacency by preceding morphogenetic movements. Natalie: I like cell fate splitters better. Seriously though, exactly how much evidence is there for the cell state splitter? Dick: The only evidence for its action at this time is ultrastructural (Martin and Gordon, 1993a) (Fig. 1) and circumstantial: we have timelapse videos of expansion and contraction waves. (Each wave discussed here has been seen in several embryos, and will be reported on in a series of papers in preparation.) Inhibitor and immunofluorescence studies and direct measurement of force generation are needed. It is also conceivable that we may be able to watch individual microtubules and the microfilament bundle in uiuo by epi-illumination and differential contrast (Allen et al., 1981; Inoue, 1986; Cassimeris et al., 1988). Natalie: Getting back to the question, what do you see as the central role for genetics in embryology? Dick: If differentiation occurs via cell state splitters, then all of the genes involved in development are organized in a hierarchical, bifurcating differentiation tree (Fig. 2). Furthermore, each intermediate, differentiated tissue may be characterized by a binary differentiation code. While this code is, for now, nothing more than our current best estimate of the sequence of kinds of waves going through a given cell (i.e., expansion or contraction), we hypothesize that it has a deeper meaning: different master genes are turned on depending on which kind of wave went through the cell, and thus different gene products are formed. Cells experiencing the same sequence of expansion and contraction waves should be essentially the same, no matter where they are located in the embryo.

invagination begins

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FIG. 2 The differentiation tree for the early axolotl embryo (Ambystoma mexicanurn), up until neurulation begins. The horizontal axis shows time and stage as indicated. The vertical axis indicates only the nature of the wave, upward for expansion and downward for contraction. The thick lines correspond to observed waves. They are labeled chronologically by letters, followed by arrows to the tissue type that differentiates after the wave passes. A, The dashed line indicates the presumed first expansion of the dorsal hemisphere of the fertilized egg to the animal cap of the stage 9 embryo. Many cleavage waves that have an unknown role in differentiation also occur in this long interval. B, The dashed line indicates the presumed contraction of the ventral hemisphere of the fertilized egg in the course of formation of the vegetal yolk mass of the stage 9 embryo. C, Vegetal yolk mass contraction wave that precedes the change of the vegetal yolk mass to yolk mass endoderm. D, Animal cap expansion wave (epiboly) that occurs when part of the animal cap changes to ectoderm, which then becomes the mesoendoderm expansion wave (F) that precedes the change of the mesoendoderm to mesoderm. E, Animal cap contraction “wave” that occurs when part of the animal cap becomes mesoendoderm. G, Presumptive pharyngeal endoderm-prechordal mesoderm contraction wave (first sign of dorsal lip of the blastopore) that occurs when the presumptive pharyngeal endoderm-prechordal mesoderm moves to the interior and becomes pharyngeal endomesoderm. H, Presumptive notochordal mesoderm contraction wave that occurs before the presumptive notochordal portion of the mesoderm invaginates and becomes (1) the ectoderm contraction wave that precedes the change of the dorsal hemisphere of the ectoderm to neuroepithelium (including sensory placodes). J , Presumptive lateral somitic mesoderm contraction wave (actually a pair of waves, the lateral lips of the blastopore) that may change the presumptive lateral somitic portion of the mesoderm to lateral somitic mesoderm. K, Presumptive notochord contraction wave when the presumptive notochord invaginates and becomes notochord. L, Mesoderm expansion wave (mesoderm that is encircled by the extending lips but moves to the interior without experiencing extreme contraction of bottle cell formation) which may change the presumptive lateral mesoderm portion of the mesoderm to lateral mesoderm. M, Presumptive ventral mesoderm contraction wave (formation of the ventral lip of the blastopore) that may change the presumptive ventral

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Natalie: This is a very specific prediction. Dick: Precisely. The entire cell state splitter model makes very specific and testable predictions. The tissues in sequence are:

Stage

Tissue name

9 9.5 9.5 10 10 10 10 10 10.5 10.75 11 11

Yolk mass endoderm Mesoendoderm Ectoderm Mesoderm Presumptive ventral mesoderm Presumptive pharyngeal endoderm-prechordal mesoderm Presumptive notochordal mesoderm Presumptive lateral somitic mesoderm Pharyngeal endomesoderm Neuroepithelium Presumptive notochord Lateral somitic mesoderm Notochord Lateral mesoderm Tailbud mesoderm Epidermis Ventral mesoderm

I1 11 1 1.75 12

12.5

Since the mesoderm has four distinct contraction waves go through it, we have subdivided it into four presumptive tissues. Another portion of the mesoderm, the presumptive lateral mesoderm, also experiences an expansion wave. I see the major task of genetics in development as that of working out the possible hierarchical relationship between genes that this model suggests, finding and characterizing the master genes that respond to cell state splitter events, and ascertaining the relationship of so-called housekeeping genes to the differentiation tree. Once we have differentiation trees of a few organisms, many interesting evolutionary questions can be addressed (Gordon, 1993, 1994; Martin and Gordon, 1993b). Natalie: But that will not tell us much about the critical events of embryology except as guideposts for when a differentiation has occurred or when a tissue is competent. If the cell state splitter model is essentially correct, then full understanding of the embryo will only come when the mesoderm portion of the mesoderm to ventral mesoderm. N, Ectoderm expansion wave (epidermal epiboly) that occurs during the change of the ventral hemisphere of the ectoderm to epidermis. 0, Neuroepithelium contraction wave that precedes the change of the most posterior portion of the neuroepithelium to tailbud mesoderm.

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nature of the cell state splitters and the mechanical forces that they generate and that act on them are elaborated. Genetics will end up playing a secondary role in embryology. Will this mean that the classical experimental approach will become even more important than it has been, as we manipulate forces experimentally to check the result? Dick Why do you think I have been after you to learn as much from Pieter as you possibly can in the lab? Natalie: Well it’s a lot more fun than running gels and looking at blots. Pieter: Let us stick to the descriptional observations of normal development and the experimental analysis of the successive morphogenetic events and try to link them to particular gene or gene cascade activity.

2. What Is Competence? Natalie: 1 understand competence to be that state when a tissue is prepared and able to become something else. An example is ectoderm reaching a state where it is competent to become either neural tissue or epidermis. Competence is something that occurs at a specific and a limited time, isn’t it? Pieter: Competence of a certain group of cells is the ability to be switched into different pathways of development. The choice is usually between two alternative ones but there may be situations in which the choice can be among three. Dick: Competence is the maintenance of the cell state splitter in a mechanically metastable state (Gordon and Brodland, 1987), paired with a biochemically metastable state in the nucleus (Bjorklund and Gordon, 1993). Because of the bistable nature of the cell state splitter (Fig. 3), the number of choices for a cell at each step of differentiation is precisely two. Natalie: This is an important difference. The cell state splitter model is based on only two possible choices for a competent tissue but Pieter has said there could be three possible choices. Can the cell state splitter model accommodate a three-way choice in any fashion? Dick When more than two choices seem to be present, I would suggest that two or more consecutive rounds of cell state splitting are involved. How do we know any of this? We don’t. I merely suggest that cell state splitters offer the first testable hypothesis for competence that explains all of its essential attributes. Pieter: But there are so many essential attributes for you to explain. Competence means a thoroughly prepared state, like, for example, neural competence, so that a rather unspecific stimulus, exerted by a different, but usually adjacent part of the embryo, is sufficient to switch it into that particular pathway. Without that stimulus the pathway in question remains closed (Nieuwkoop, 1958, 1973). Embryonic development is a one-way

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Exp a m i o h \

.-Ela2

-(Contraction Force due to MicrofilamentRing)

8.

G 0'

Apical Radius

FIG. 3 We can make a rough model showing why the cell state splitter is unstable. The xaxis is the radius of a cylinder approximating an epithelial cell (Figs. 1 and 4). We presume that the microtubule mat pushes outward. Since this force is likely to be generated by polymerization, it is approximately independent of the cell's apical radius, and is thus shown as a horizontal line. The force generated by a microfilament ring is contractile. By analogy with smooth muscle, it should generate a force proportional to its cross-sectional area (Gordon and Brodland, 1987), which is inversely proportional to the radius of the ring. The microfilament force is in the opposite direction, and so carries a negative sign to show it together with the microtubule mat force. Where they cross, the net force is zero, and the two forces are in balance. However, this equilibrium is unstable. If the radius of the cell becomes a little bigger than the equilibrium radius, the microtubule mat force exceeds the microfilament ring force and thus drives it toward greater expansion. On the other hand, if the radius of the cell becomes smaller than the equilibrium radius, the microfilament mat force exceeds the microtubule mat force and thus drives it toward an even smaller radius. This bistability of the cell state splitter is what we think is the basis for the binary nature of differentiation.

process, which is accurately timed. Different parts of the embryo go through different phases of competence, both for the production of certain stimuli and for the reactability to such stimuli. Particular parts of the embryo go, moreover, through successive phases of competence, each with a specific and limited time; for example, the competent ectoderm goes through a phase of mesoendodermal competence and then through a phase of neural competence. These phases partially overlap each other. Insight into the nature of competence is, in my opinion, essential for understanding embryonic development. Dick The successive phases of competence are probably the erection or rearming of a cell state splitter in each cell as it goes through consecutive events of differentiation. Where phases overlap, I would suggest that this is because of the slowness of the differentiation waves. For instance, the presumptive notochordal mesoderm/ectoderm contraction wave, which

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leaves in its wake the neuroepithelium, takes all of gastrulation: 9 to 12 hr in the axolotl. From the point of view of a single cell and its response to the consecutive waves in which it participates, there is no overlap. The lack of specificity is due to the metastable nature of the cell state splitter. Anything capable of triggering the metastability could induce competent tissue. Natalie: How could the cell state splitter’s metastability be achieved? Dick The metastability of cell state splitters may be maintained by cell-cell adhesions, perhaps through desmosomes (Gordon and Brodland, 1987)or CAMS (cell adhesion molecules; Edelman, 1988), or by the elastic restoring force of the cell state splitter’s intermediate filament ring (Martin and Gordon, 1993a) (Fig. 4). Natalie: The lack of specificity for Pieter’s competence would also account for the seemingly endless variety of substances that can induce neural tissue, correct? When it comes to mesoderm induction you, Pieter, cautioned a student at your lecture to be careful about substances that induce mesoderm in uiuo. You stated, “Almost anything you can take from your garbage can probably induce neural tissue. I am concerned that we are finding this to be the case in mesoderm induction as well.” Pieter: I don’t think mesoderm induction will be as completely nonspecific as induction of competent ectoderm seems to be. However, this is something I caution those who choose to study mesoderm induction about as a possibility. I find myself hesitating over new substances that are found to induce mesoderm (Nieuwkoop, 1973). Dick: A mechanical instability can be set off by anything that will generate a small force. In the case of an ectoderm cell, if this force is directed toward the axis of the cell, it will become a neural plate cell, while if it is directed outward, it will become an epidermal cell (Figs. 3 and 4).

3. How Does Competence Develop in a Cell? Natalie: This is more difficult. How does a single cell achieve competence? How does a whole tissue achieve competence? How is the timing of competence achieved? Pieter: Very recently an idea has been formulated of what may cause neural competence. Otte and co-workers (1988,1989,1990,1991), studying the difference in neural competence of dorsal versus ventral ectoderm in the Xenopus embryo, found it to be due to different isozymes of protein kinase C (PKC). Injection of Wnt-RNA in the ventral yolk mass not only leads to the formation of a second mesoendoderm-inducing center in the yolk mass (Sokol et al., 1991),but also to a change in the isozyme composition in the ventral ectoderm. Some type of message must precede and must spread in front of the mesoderm-inducing action originating from

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contraction

I

expansion

Ectoderm Cell

\

Epidermal Cell

Neuroepithelial Cell FIG. 4 If the microtubules in an ectoderm cell state splitter (Fig. 1, simplified) win the tug of war, the cell becomes an epidermal cell. If the microfilament ring wins, it becomes a neural plate cell. If a wave of contraction (mediated by microfilament rings) impinges on the cell, its own microfilament ring undergoes a stretch-activated contraction (Gordon and Brodland, 1987; Bjorklund and Gordon, 1993), propagating the wave (Luchka and Gordon, 1993). (It is less clear how expansion of the microtubules would be propagated from one cell to the next.) In the case of contraction waves, the contraction is transient, lasting about 10 min per cell (Bjorklund and Gordon, 1993). After this contraction, the cell relaxes back to its original shape. This is followed by further differentiation, resulting in columnarization and the cell undergoing the “final” change of shape. We presume that the gene cascade for neural plate cell differentiation is activated between the contraction wave and the final coiumnarization. An ectoderm cell is shown approximately to scale. Note that the cell state splitter appears effectively at the apical end, and that its thickness is inconsequential relative to the cell height (0.05 pm/50 p m = 0.1%). This makes the cell state splitter, from the viewpoint of a civil engineer, a thin shell or membrane element (Mollmann, 1981; Hinron and Owen, 1984), albeit an active one. Schematic final results of expansion or contraction are shown in proportion with the total cell volume and cylindrical shape held constant.

the second inducing center, leading to the formation of the right isozyme of PKC (Otte and Moon, 1992). Competence may develop partially (autonomously) during the aging (ripening) of the ectoderm in normal development of the embryo, but apparently also under the influence of spreading stimuli from adjacent parts of the embryo.

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Natalie: Your different PKC isozymes would, in our cell state splitter model, be part of the metabolic signaling pathway that connects response of the cell state splitter to the nucleus and the subsequent changes of gene expression (Bjorklund and Gordon, 1993). The connection to competence in the cell state splitter model would be that these isozymes are prepared as part of the synthesis of the cell state splitter. (Presumably the original PKCs were all the same, but increasing complexity required multiple copies, and genetic drift of the copies resulted in the different isozymes.) These isozymes would be needed to signal the potential master genes. Hence they would appear at the time a cell is competent and probably disappear after the period of competence is over. Putting isozymes in other places could indeed trigger gene cascades different from the expected ones, assuming the master genes for more than one cascade are present at different stages. This work may well provide us with key information on where and what the master genes are. Dick The problem arises as to why there are different PKC isozymes in the two hemispheres. If all ectoderm cells are equivalent in terms of their ability to become either neuroepithelium or epidermis cells, as the Spemann and Mangold (1924a,b) and related experiments (Holtfreter, 1944, 1945) show, then, if PKCs are involved in cell state splitters, differences would have to arise after the ectoderm contraction or expansion waves pass through each cell. Pieter: The Spemann and Mangold (1924a,b) and Holtfreter (1944, 1945) experiments were done on urodeles, where there are apparently no dorsoventral differences in neural competence. However, in Xenopus, a specialized anuran species, Gurdon (1989) found clear dorsoventral differences in neural competence of the gastrula ectoderm. Dick: Since the duration, at least of the ectoderm contraction wave, is the whole period of gastrulation, it is easy to confuse assays of anything relevant between the two hemispheres, if the location of the waves at the moment of embryo sacrifice for the assay is not known. Natalie: Whenever I hear of a gradient I always suspect a passing wave. Imagine a wave passing through a tissue taking several hours to travel completely through it. As the wave passes, it triggers a specific gene cascade, presumably the same one in each cell. The region that the wave passed through first would therefore have higher levels of specific gene products when compared with the region that the wave had just passed through. When attempting to interpret literature in light of the wave model, I must always have an exact description of the embryo stage, the shape of the blastopore, and so forth, so that I can estimate where the wave was. All too frequently, I find an assay was done midwave, making it almost impossible to interpret the results within the wave model. I am eagerly awaiting the opportunity to see waves on Xenopus embryos.

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Dick For competence, each cell must either erect a cell state splitter or reactivate an existing one. Some indication of the former is given by the appearance of an apical concentration of ribosomes just prior to the appearance of cell state splitters in the ectoderm (Martin and Gordon, 1993a). The simultaneous appearance of “armed” cell state splitters in each cell in a tissue presents a difficult problem for our theory. In the case of the ectoderm, a rising blastocoel and archenteron pressure may, somehow, provide the “global synchronizing mechanism” (Gordon and Brodland, 1987; Gordon, 1993). To me this is the least satisfactory aspect of cell state splitter theory, especially because it is not obvious how such pressure mechanisms could operate at each and every step of differentiation. A simple canulation experiment could deflate this part of the hypothesis. The flap grafting experiments of Nieuwkoop et af. (1952a,b) may have already removed pressure from serious consideration as a synchronization mechanism. Natalie: If not pressure then what else? Dick Two other possibilities present themselves. One, somewhat unsatisfactory, is a prewave of synchronization. Akin to a prepattern, it smacks of infinite regress. On the other hand, a prewave that crossed the whole of a tissue to set up cell state splitters need not be patterned at all, provided that contemporaneous tissues are set off from one another by compartmental boundaries that the prewave cannot cross (cf. Caveney and Safranyos, 1985). Since an increase in calcium concentration in the medium of cultured human epidermal keratinocytes has been shown to set up a cytoskeletal structure that looks like a cell state splitter (Zamansky et al., 1991), one could imagine calcium as somehow being involved in a prewave of global synchronization of the erection of cell state splitters in embryos. Another alternative is that synchronization does not actually occur, i.e., that a wave of contraction or expansion coming through a tissue activates the cells ahead of it, if they aren’t already activated. In this way, any stragglers are brought into readiness. These questions could be addressed by determining the spatial and temporal distribution of cell state splitters and their relationship to the expansion or contraction waves they become associated with. Natalie: It took Cris Marten almost 3 years of work to finally provide us with a detailed view of one cell state splitter! We have a joke in our lab. Dick likes to generate ten new Ph.D. problems each day. Dick: Well what could be better than to solve all of embryology? Pieter: But not in one lifetime or in one laboratory. Natalie: There is a secondary problem of keeping each cell state splitter from triggering off before all the others in a tissue are erected or armed. Dick: This merely requires that the mechanism of maintaining metasta-

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bility be erected prior to the cell state splitter itself. Appropriate observations on this sequence of events have yet to be made. Pieter: The Wnt-RNA injection experiments leading to the formation of a second mesoendoderm-inducing center as well as a change in competence of the reacting ectoderm, pleads, in my opinion, in the direction of the preceding spreading of a chemical or mechanical signal. Natalie: May I point out that high osmotic pressure in yeast is sufficient to turn on specific genes (Varela ef af., 1992). While yeasts are a long way from an embryo, we must have developed from much simpler forms of life (Margulis and Schwartz, 1987). If we assume that the cell state splitter model is correct, we must assume it was created out of preexisting abilities of our primitive single-celled ancestors such as yeast. A careful examination of all such abilities and comparison of these abilities with what is going on in the multicellular embryos is warranted. Dick: Now who is starting huge sets of Ph.D. projects? What do you suggest is going on? Natalie: Is it merely a coincidence that the embryo begins to swell up over the blastocoel at midblastula, precisely when the first zygotic mRNA appears? Is it likely to be simply coincidence that ionic and osmotic levels are also important to competence (Barth and Barth, 1969, 1972, 1974)? For the cell state splitter model to work, the first cell state splitters must be set up automatically by maternal mRNAs throughout different parts of the embryo. The global synchronization may arise from either chemical or mechanical signals. I favor mechanical in the earliest stages when the embryo is simple because they are easier for the embryo to use. But in later stages of extremely complex differentiations, such as in the final stages of brain development or learning in the brain, I see chemical signals being the important ones via receptor mechanisms. Dick: But what do you think triggers the setting up of the cell state splitter? Natalie: 1 see the first cell state splitter set up automatically after a specific number of cell divisions which have been coordinated by cleavage waves (Hara, 1971; Yoneda ef al., 1982; Boterenbrood e l al., 1983; Boterenbrood and Narraway, 1986). There is already evidence for this idea (Lund and Dahlberg, 1992). The first cell state splitter could be synchronized by rising blastocoel pressure and then activated. Of course that begs the question of what is going on in the bottom half. Perhaps that is where chemical differences present in the egg from before fertilization come into play. But then we are back to chemical instead of mechanical. Clearly, we have a long way to go in understanding competence. Pieter: In the amphibians, embryonic development starts with an egg consisting of two different moieties, an animal and a vegetal one. The first two (speculated) waves (A and B in Fig. 2) occur in these two separate moieties.

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4. What Is Embryonic Induction?

Natalie: In my embryology course I found the topic of induction to be both the most interesting and the most frustrating of all topics. We have covered competence. So we have tissues that are “competent.” They are then “induced” to become something else. I would like to see induction properly defined. Pieter: Embryonic induction is the mutual interaction of different parts of the embryo which have come into direct contact during morphogenesis of the embryo. The interaction is essentially a mutual one, although one way may be much more dramatic than the other one, e.g., archenteron roof jectoderm than neuroectoderm 3 archenteron roof (see next question). The natural stimuli in question may be chemical, physicochemical, and/or physical, and possibly all three at the same time or one after the other. This is still an open question. Dick Embryonic induction is the process of setting off a wave of activation of the cell state splitters. We don’t yet know how these waves get started, but from the point of view of cell state splitters, all we need is a force imbalance (Fig. 3). It is possible that the very act of adhesion of two tissues over an area of a few cells is sufficient to generate the tension needed for the force imbalance we are postulating (Pesciotta et al., 1989). Regarding the question of specificity of induction, I don’t see why we can’t “have our cake and eat it too.” The mechanism starting off a wave may be merely physical. However, because cell-cell adhesion is sometimes required to get the physical effect, and numerous specific molecules (fibronectin, collagens, CAMS, etc.) could be involved in setting up a very specifically localized cell-cell adhesion, specificity is possible. Pieter: You mention two types of possible apical wave phenomena: contraction and expansion waves. Apart from the question of whether these wave phenomena, as observed by Natalie and her colleagues in their time-lapsed films, are primary or secondary events in embryonic induction processes, they may also represent different types of phenomena. The early wave phenomena are characterized, as far as I understand, by a short-lasting contraction, immediately followed by a short-lasting relaxation, whereas the contraction and expansion phenomena associated with the first visible differentiation of the dorsal neural plate and the ventral epidermis have a much more lasting and definitive character. The cell state splitter hypothesis may be more particularly applicable to actual differentiation phenomena than to the early wave phenomena associated with the proceeding induction process. Natalie: I believe that this is the case in the expansion waves. The expansion waves correspond to well-established epiboly . The expansion differs from epiboly only in the sense that in time lapse you can see that the spreading motion begins at a point and spreads outward, with a wave

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front of moving activity through an entire presumptive tissue. The wavelike nature of the spreading is not included in the classical definition of epiboly. The expansion waves could indeed be the secondary result of a previous induction. But the differentiation could occur because the expansion wave has passed through a cell as well. Expansion waves, according to the cell state splitter model, involve microtubules which presumably lack the elastic component of microfilament rings. Expansion waves may be incapable of relaxation in the wake of the wave. Dick: I think this may be a bit more subtle: microtubules are essentially incompressible (Hill, 1987) and will not buckle if supported laterally by intermediate filaments (Brodland and Gordon, 1990), as they appear to be supported in cell state splitters (Martin and Gordon, 1993a). Thus, when an expansion occurs by polymerization, conditions would have to change to those permitting depolymerization if the nascent epidermal cells were to relax. For microfilaments, a rapid change in calcium ion concentration is all that is needed to reverse their contraction (Bjorklund and Gordon, 1993), a quicker process than depolymerization. Natalie: Yes, in the case of contraction waves we have a transient contraction of individual cells that lasts approximately 10 min per cell. It propagates through a cell and after the wave has passed, the cell returns to its previous shape. This includes those waves I have seen in the neural plate. They occur, pass through a tissue, then disappear. After they disappear, there are visible columnarization changes in the neural plate (such as the formation of eye placodes). One of the reasons a contraction wave is so hard to see without time lapse is that it leaves no immediately observable change in the cell, unlike an expansion wave, which shows epiboly. Differentiation occurs either after it has passed or during the actual contraction (as in the Drosophila ommatidia furrow: Ready er af., 1976) resulting in a change in the cell that becomes visible later. Dick: What frustrates me is the beautifully detailed molecular work subsequently done on the differentiation occurring in the Drosophila ommatidia furrow (Lebovitz and Ready, 1986; Tomlinson and Ready, 1987a,b;Tomlinson, 1988;Hafen and Basler, 1991),while the whole nature of the furrow itself and its possible role has been completely ignored, even though excellent genetic work on the wavelike propagation of the furrow was already available (Poodry et a f . , 1973; Suzuki, 1974; reviewed in Raff and Kaufman, 1991). Natalie: I would also like to point out that our observations do not (at least not yet) dispute the idea of a tissue being destined to become a specific tissue unless induced to become an alternative one. In two expansion waves we have seen to date, the expansion occurs well after a contraction wave has passed over the opposite region of the embryo. It is still possible, in the context of our observations, that ectoderm automatically becomes epidermis after a specific period unless it experiences a contrac-

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tion wave. If it experiences a contraction wave, it is induced to become neural tissue, But this raises the thorny question of how the ectoderm “knows” when enough time has passed and it should “give up” on waiting for neural induction and simply become epidermis. Why also would this “giving up” be expressed in a wave? The idea of opposing expansion and contraction waves eliminates having the cells needing to know anything except the sequence of the waves they have been a part of. That is why I prefer this model, even where I question it. It works better than anything I’ve heard of to date when I try to “think” as an individual cell.

5. When and Where Do Embryonic Inductions Occur? Natalie: Now that we have defined what induction is, I think we need to discuss where it occurs. However, I also think we should confine our dialogue to a manageable selection. Since early embryonic inductions lead to a number of cellular differentiations (see the later discussion), I should like to see these discussed extensively. These bring us to the end of neurulation, where we should probably stop, leaving further organ development for later consideration. Dick Besides, after neurulation, most of development is inside the embryo, rather than on the outside, necessitating creation of new ways of observing dynamic phenomena, such as differentiation waves (see Figs. 5-16). Thus, in particular, we will skip the somite stages of vertebrates that may correspond to segmentation in Drosophila (Lawrence, 1992). Drosophila accomplishes the early stages as a syncytium, and thus may not provide a model for early, presomite vertebrate embryogenesis. Pieter: The early induction processes are either preceded and/or followed by specific morphogenetic movements. The latter can best be classified successively as (1) pregastrulation movements, (2) actual gastrulation movements, and (3) the neurulation-associated movements. Since the surface contraction and expansion wave phenomena (Bjorklund and Gordon, 1993)are clearly associated with these different categories of morphogenetic processes, I would like to suggest that they be described under these headings. Dick A summary of the waves we have found on the external surface of the preneurulation axolotl embryo is given in Fig. 2. We have named each wave by the tissue it goes through. This convention means that a wave that passes from one tissue to another changes names. The tissue names were chosen by mutual agreement to conform as closely as possible to common usage. The animal cap contraction “wave” (Fig. 8a) is put in quotes because, so far, it appears to be a uniform contraction over the whole portion of the animal cap that becomes the mesoendoderm. Better time resolution and closeups may reveal an actual spatial progression to

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FIG. 5 The axolotl embryo (a urodele) after fertilization. At and before fertilization, the mature oocyte of an amphibian shows a sharp cortical boundary coinciding with abrupt hemispheric differences in visible pigmentation (darker on top, except in albinos), cortex viscosity (higher on top; Dictus e t a / . , 1984), and yolk content (higher density at the bottom). The orientation before spawning is arbitrary with respect to gravity. At activation, the vitelline membrane lifts slightly above the cortex, allowing rotation (due to the higher density of the yolky hemisphere) of the whole embyro, that is, cortex and contents, with respect to the vitelline membrane and jelly coat, so that gravity is down, as shown. The oocyte has a single vertical axis of symmetry.

FIGS. 5-16 (pp. 390-401) These are schematic diagrams of the newly discovered differentiation waves for the axolotl embryo up through the end of gastrulation. Staging and timing is for the axolotl using the staging Table 19-1 in Bordzilovskaya et al. (1989) (which has an erratum, specifying 29"C, instead of the correct 20"C, J. B. Armstrong, personal communication.) (The reader familiar with the Xenopus tables (Nieuwkoop and Faber, 1975) should note there are slight differences in the numbering of the stages between the axolotl and Xenopus.) Times are based on the average figures where a range is specified in the staging table. The stages specified in our figures are not precise because most of these diagrams show waves in progress between defined stages. The times in the figures have been chosen to match those in the differentiation tree, Fig. 2, to allow detailed comparison. The letters for the waves also match those in Fig. 2. Some sagittal sections are included for reader orientation. Labels are retained on the sagittal sections only for those waves that actually intersect the sagittal plane at the time specified. The outer surface diagrams should be consulted for their locations.

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cortica~rotation: 30”

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“yolk veneer

FIG. 6 Just before first cleavage. Stage 2 - (time 0). Three to 5 hr after fertilization, a cortical rotation of approximately 30” occurs, raising the yolk on one side (Neff et al., 1984; Gerhart el al., 1989; Neff et al., 1989; cf. Flint et al., 1990). The direction of the cortical rotation (always perpendicular to the cortical boundary) is approximately determined as opposite to the sperm entry point, at least in anurans (Vincent et al., 1986; Vincent and Gerhart, 1987; Gerhart et al., 1989). In urodeles, which do not prevent polyspermy (Elinson, 1986; Bordzilovskaya et al., 1989), it is not yet clear what determines the angle. The embryo is now bilaterally symmetric, and the cortical boundary now has two separated components: the yolk boundary (shown in sagittal section) and the pigment boundary (shown on the surface). We do not yet know what happens to the viscosity component of the cortical boundary, which may be labile and not simply follow either the pigment or yolk boundary. The yolk boundary is assumed to slosh as a result of: (1) a presumed adhesion to the cortex, raising at least a thin layer of yolk as shown on the right; (2) gravity, which raises the yolk boundary relative to the rotated pigment boundary, as shown on the left. The gray crescent is the portion of the cortex above the yolk boundary that is coated with a thin layer of yolk, which we call the yolk veneer. (Its crescent shape may be seen by tilting a bowl of water with ground pepper floating on it.) The first cleavage may occur before gravitational equilibrium, leaving the yolk boundary tilted as shown. (Note that all internal, noncortical structures in this and subsequent figures are represented as sagittal sections.)

this contraction. The reader will have to excuse the lack of details: discovery of all these new waves only began in April 1992. 6. What Are the Pregastrulation Movements?

Pieter:The pregastrulation movements (Nieuwkoop el al., 1985) comprise the epibolic expansion of the animal “ectodermal” moiety of the blastula/early gastrula and the slightly earlier starting contraction and involution of the vegetal “endodermal” moiety. The latter is characterized by a contraction wave and the former by an expansion wave in the cell state splitter model. Natalie: We should stress that all waves in this early portion of embryogenesis have been proven to occur only in those cells whose apical ends were on the outside at the time gastrulation began. The vegetal yolk

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vegetal yolk mass contraction wave (C) vegetal pole

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FIG. 7 Launching of the vegetal yolk mass contraction wave, leaving yolk mass endoderm in its wake. Stage 9 (21 hr at 20°C). A. Outer Surface. B. Sagittal section. Launching of the vegetal yolk mass contraction wave downward (arrow) starts from a circle at the surface of the embryo, whose origin may be related to a lowered position of the cortical boundary. The roof of the blastocoele is a monolayer epithelium and part of the animal cap. As the vegetal yolk mass contraction wave proceeds downward through the vegetal yolk mass (initially juxtaposed to the animal cap at the launching circle), it leaves in its wake the yolk mass endoderm. Note the gradient in cell sizes (cf. Gillette, 1944).

mass contraction wave starts as a large circle at the upper boundary of the vegetal yolk mass shortly after the midblastula transition (Fig. 7). It travels over the entire surface of the vegetal yolk mass toward the original vegetal pole of the egg in about 10 hr at 20°C (Figs. 7-11). This is a traveling furrow of contraction that can be seen to propagate from one cell to the next (Luchka and Gordon, 1993). In time lapse it looks like a circle that closes down. When the contraction wave has decreased by about one third of its original diameter (Fig. 9), several small problastopores appear on the original circle (Fig. 9). These are short-lived lines of contraction that appear in a random fashion around the circle. Dick: We have called the circle the “launching domain” of the wave. The launching domain is at the border of the vegetal yolk mass and the

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I r n ------

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k animal cap Contraction ”wave” (E)

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mass endoderm

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yolk mass vegetal pole

FIG. 8 Formation of the mesoendoderm in the wake of the animal cap contraction “wave” and launching of the animal cap expansion wave, which leaves in its wake the ectoderm. Stage 9.5 - (24 hr at 20°C). A. Outer surface. B. Sagittal section. The animal cap expansion wave is launched at the top of the animal cap by an unknown mechanism, along with movement (not shown) of the internal yolk mass endoderm up into the blastocoel cavity (Balinsky and Fabian, 1981), and expansion of the blastocoel presumably caused by an influx of water after an increase in Na+ levels in the blastocoel (Barth and Barth, 1972). The launching domain of the animal cap expansion wave may be related to the region of extrusion of the long-departed polar bodies. As this wave moves down (arrow) through the animal cap, it presumably leaves the ectoderm in its wake. However, before it reaches the yolk boundary, a contraction appears over the region of the animal cap underlain with yolk (including the yolk veneer), perhaps forming the mesoendoderm (shaded). Whether the animal cap contraction “wave,” over in about 0.5 hr, is an actually propagating wave, has yet to be determined. Thus we do not show where it might start and finish.

animal cap. Its location may have something to do with the sharp change in physical properties observed by Dictus et al. (1984). Natalie: Once the problastopores are visible, the animal cap expansion wave begins (Fig. 8). It starts at the original animal pole in the stage 9 + blastula. (All of our observations are of the axolotl, staged according to Bordzilovskaya et af., 1989.) This wave spreads as an uneven circle of increasing diameter traveling downward (Figs. 8-9) over the surface of

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FIG. 9 Formation of the mesoderm in the wake of the mesoendoderm expansion wave and appearance of the problastopores. Stage 9.5 + (24 hr at 20°C). As the animal cap expansion wave enters the mesoendoderm, we rename it the mesoendoderm expansion wave. Here it leaves in its wake the mesoderm. Note that the mesoderm is formed in what will be the dorsal hemisphere first, perhaps explaining the mesoderm’s dorsoventral polarity. Meanwhile, along what was the launching circle of the vegetal yolk mass contraction wave, problastopores appear and vanish, apparently at random.

the embryo to the boundary with the yolk mass endoderm, where it stops (Fig. 10). It is immediately followed by the appearance of the true dorsal blastopore at stage 10 on the launching circle of the vegetal yolk mass contraction wave (after which no further problastopores are seen). The dorsal blastoporal lip appears and the entire yolk mass endoderm begins invaginating. The closing circle of the vegetal yolk mass contraction wave is carried inward toward the dorsal lip and closes down to a point as it passes into the interior of the embryo, Pieter: These two pregastrulation wave phenomena correspond spatially with the initial dual composition of the amphibian egg (Nieuwkoop, 1969a,b; Dictus et af., 1984). They may play a role in endodermal and ectodermal specification, respectively. They do not apparently concern meso-endoderm induction. Natalie: They may. As the expansion proceeds, the region that matches presumptive mesoderm on the fate map of Pasteels (1942), the mesoendoderm, undergoes what appears to be a constriction (the animal cap contraction “wave”) that lasts for about half an hour. Once the constriction band disappears, the cells then participate in the animal cap expansion wave that is coming down from the top, whose name we change to mesoendoderm expansion wave as it moves through the mesoendoderm. This action of an apparent constriction simultaneously over the whole mesoendoderm rather than a propagating contraction wave is not predicted by our model. We are working on refining this observation to see if it has a discrete launching domain. Pieter: Mesoderm formation may also be associated with wave phenomena, but we will have to see if you produce convincing observations. The first known inductive interaction between the yolk mass-endoderm mass

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presumptive pharyngeal endoderm-prechordalmesoderm contraction wave (G)

pharyngeal endoderm

vegetal yolk mass contraction wave (C)

FIG. 10 Formation of the pharyngeal endoderm in the wake of the presumptive pharyngeal endoderm-prechordal mesoderm contraction wave (dorsal lip of the blastopore) and the beginning of invagination. Stage 10.5 (32 hr at 20°C). A. Outer surface. B. Sagittal section. Invagination begins. The tissues that invaginate are the yolk mass endoderm under the dorsal lip of the blastopore, and pharyngeal endoderm and a portion of the mesoderm over the lip. The upper boundary of the mesoderm moves down as the tissues below it invaginate. That the dorsal lip of the blastopore is a contraction wave (indicated by the thick line) is evidenced by the cells transiently taking on a bottle shape as they pass over the lip. Note that the arrow on each wave indicates its direction of travel relative to the tissue it goes through. In the case of the presumptive pharyngeal endoderm-prechordal mesoderm contraction wave (at present the dorsal lip of the blastopore), while the wave moves through the mesoderm, the mesoderm moves on the inside in the opposite direction, so that the presumptive pharyngeal endoderm-prechordal mesoderm contraction wave appears to be stationary in the laboratory coordinate system.

and the totipotent animal “ectodermal” moiety of the blastula leads to the formation of the main bulk of the mesoderm as well as the pharyngeal and dorsal intestinal endoderm of the embyro. These structures are all formed out of the animal ectodermal moiety. The center of the inductive interaction is located in the dorsal portion of the yolk mass-endoderm mass and is responsible for the formation of the dorsal axial mesoderm and the pharyngeal and intestinal endoderm (Nieuwkoop, 1969a,b, 1970, 1973; Nieuwkoop and Ubbels, 1972). The lateral and ventral portions of the yolk mass-endoderm mass induce only ventral mesodermal and endodermal structures (Boterenbrood and Nieuwkoop, 1973). Mesoen-

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presumptive notochordal mesoderm contraction wave (H)

presumptive notochord mass contractionwave (C)

yolk mass endoderm

presumptive notochordal mesoderm contraction wave (H)

presumptive notochord pharyngeal endoderm eta1 yolk mass contraction wave (C) ptive pharyngeal endoderm-prechordal rm contraction wave ( G )

FIG. 11 Launching of the presumptive notochordal mesoderm contraction wave, leaving in its wake the presumptive notochord. Stage 10.5+ (32 hr at 20°C). A. Outside surface. B. Sagittal section. The presumptive notochordal mesoderm contraction wave is initiated when the invaginated pharyngeal endomesoderm makes contact with the basal surface of some of the mesoderm cells. (The contact point is within that part of the mesoderm which is presumptive notochordal mesoderm.) The launching domain of the presumptive notochordal mesoderm contraction wave corresponds to the revised location of the “organizer” (Hama et al., 1985), which was originally thought to be the dorsal lip of the blastopore (Spemann and Mangold, 1924a,b; cf. Hamburger, 1988). The vegetal yolk mass contraction wave vanishes to a small termination domain just as the remaining vegetal yolk mass invaginates. (The relative timing of this vanishing versus invagination of the vegetal yolk mass varies slightly from embryo to embryo.)

doderm induction spreads very slowly, starting at the 32- to 64-cell stage (Nakamura et al., 1978), covering the anterior half of the presumptive marginal zone at the early gastrula stage (Kaneda and Hama, 1979; Kaneda, 1981) and only the entire marginal zone, except the tail somites, at stage 10.5 after an additional inductive interaction (see the later discussion). Nata1ie:Polarity in the embryo (according to the cell state splitter model) is created by the animal cap/mesoendoderm expansion wave. It travels downward in a horizontal fashion. But the ectodermlmesoendoderm boundary is not horizontal. It is higher at the future dorsal lip and lower

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over the opposite side (Figs. 7,8), possibly because of the precleavage cortical rotation (Neff et al., 1984, 1989; Gerhart et al., 1989; Flint et al., 1990) (Fig. 6). Owing to the trajectory of the animal cap/mesoendoderm expansion wave, first the area over the dorsal lip receives this second induction and then the induction reaches the other side of the mesoendoderm. If you looked only at the mesoendoderm, the induction would appear to start at the dorsal lip and move around to the other side. This could then provide a mechanically based explanation for the dorsal location of the mesodendoderm-inducing center (Boterenbrood and Nieuwkoop, 1973). By our system, mesoderm (first called mesoendoderm, then mesoderm) receives two distinct signals before gastrulation. The first appears simultaneously over the entire region. The second reaches the region first over the portion that will later correspond to the dorsal lip of the blastopore and then moves “backward” to the ventral portion because of the horizontal orientation of the animal cap/mesoendoderm expansion wave. Our model cannot explain evidence for the appearance of mesoderm induction occurring before the midblastula transition, at least not yet. Pieter: There are indications that a reciprocal action occurs between the freshly induced mesoderm and the yolk mass-endoderm, leading to the formation of flask cells in the peripheral cells of the yolk mass-endoderm as the initial step of the gastrulation process. The latter starts at the dorsal side and spreads by cell-to-cell contact through the lateral to the ventral side, reflecting the extending blastoporal groove (Doucet-de Brui‘ne, 1973; Nieuwkoop, 1973). Dick By our model, the reciprocal action is the mechanical action of the amval of the animal cap/mesoendoderm expansion wave in this area. The formation of the problastopores suggests that a mechanical stress is present in this region. This stress appears to be resolved by formation of the dorsal lip since the problastopores disappear as soon as the lip is formed. The problastopores may be transients in a mechanical instability mechanism involved in the development of bilateral symmetry from axial symmetry. We’ll have to have a closer look at them. The occasional failure of this instability mechanism may explain animals with two or three spontaneous axes (Nieuwkoop, 1973). 7. What Are the Gastrulation Movements? Pieter: The next known inductive interaction occurs between the invaginating dorsal mesoendoderm and the still uninvaginated and not yet induced ectoderm, changing the first from potential trunk inductor (chordamesoderm) into prechordal plate mesoderm (ultimate head inductor) and inducing the latter into chordamesoderm (ultimate trunkhail inductor) (KanCda, 1981).

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A ectoderm contraction wave (I)

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presumptive notochordal mesoderm contraction wave (HI presumptive pharyngeal endoderm-prechordal mesoderm contraction wave (GI

ectoderm contraction wave (I)

presumptive notochord pharyngeal endoderm dorsal lip of blastopore without bottle cells presumptive notochordal mesoderm contraction wave (H)

FIG. 12 The neuroepithelium starts forming in the wake of the ectoderm contraction wave, while bottle cell contraction at the dorsal lip of the blastopore transiently vanishes. Stage 10.75 (37 hr at 20°C). A. Outside surface. B. Sagittal section. That portion of the presumptive notochordal mesoderm contraction wave that enters the ectoderm is renamed the ectoderm contraction wave. The ectoderm contraction wave leaves in its wake the neuroepithelium (shaded). The presumptive pharyngeal endoderm-prechordal mesoderm contraction wave extends slightly into a circular arc, seen here edge on. The yolk mass endoderm, now fully formed, continues invaginating. As the presumptive notochordal mesoderm contraction wave encounters the dorsal lip of the blastopore, either the bottle cells there relax for about 0.5 hr, or no new ones are formed for that duration, over a small arc at the dorsalmost portion of the dorsal lip of the blastopore. Thus no bottle cells are shown. The extent of invagination has yet to be determined, and so is not shown distinctly.

Natalie: The gastrulation process includes a number of consecutive contraction wave phenomena in the blastopore region. Some of these may represent a single wave that travels through distinct presumptive tissues. These are described in Figs. 10-16. Pieter: I have the impression that you are describing the gastrulation process itself, distinguishing successive phases, since it is not clear to me whether these phases are actually preceded by separate contraction waves.

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FIG. 13 The notochord starts forming in the wake of the presumptive notochord contraction wave, and the center ofgravity starts shifting. Stage 11 (38 hr at 20°C). A. Outside surface. B. Sagittal section. The presumptive notochord is indicated in A by scalloping.The presumptive notochord contraction wave starts at the dorsal lip of the blastopore. Two rapid events occur as the presumptive notochordal mesoderm contraction wave reaches the end of the arced blastopore lip: the lip extends to a semicircle (thick arrow), and two crimps extend on both sides of the embryo, roughly along the dorsal-ventral equator, meeting opposite the blastopore. (Cellular resolution images of these crimps have yet to be obtained.) The region dorsal to the crimp will later become neuroepithelium; the portion ventral to the crimp will become epidermis. Because of subsequent events, we call the extension of the dorsal lip of the blastopore the presumptive lateral somitic mesoderm contraction wave. There are actually two presumptive lateral somitic mesoderm contraction waves, in bilaterally opposite positions. Finally, the whole embryo, in this and subsequent figures, begins rotating as a result of a change in center of gravity caused by invagination of the yolk mass endoderm.

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presumptive notochord

presumptive notochord contraction wave (K) presumptive notoc hordal mesoderm contraction wnve (H)

FIG. 14 The mesoderm expansion wave begins, leaving in its wake the internal lateral mesoderm and accelerating invagination. Stage I 1 + (39 hr at 20°C). The invagination of the mesoderm begins at a rapid pace. Part of this is through the presumptive lateral somitic mesoderm contraction wave, resulting in the lateral somitic mesoderm. The lower portion of the mesoderm is stretched at its visible surface as its passes into the interior of the embryo. Since this tissue passes into the embryo ahead of the presumptive lateral somitic mesoderm contraction wave without going over the lip (and undergoing bottle cell formation), this may constitute a mesoderm expansion wave for these cells. This new internal tissue (not sagittal, and thus not shown) corresponds to the lateral mesoderm of the fate map as the fate map invaginates. The crimp is now disappearing on the other side of the embryo.

ectoderm Contraction wave (I)

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e presumptive notoeliord contraction wave ( K )

yolk mass endode1-m c p r e s u m p t i v e lateral somitic mesoderm contraction wave (J) mesoderm expansion wave (L)

mesodermI FIG. 15 The ectoderm contraction waves sweeps across a hemisphere. Stage 11.5 (41 hr at 20°C). The ectoderm contraction wave accelerates along the now vanished crimp line, at least relative to its travel along the sagittal great circle, as indicated by a series of arrows of increasing length along the wave. Invagination continues over the three indicated waves. The blastopore is almost a complete circle.

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EMBRYONIC INDUCTION AND DIFFERENTIATION WAVES ,ectoderm contraction wave (I)

neuroepithelium contraction wave resumptive ventral mesoderm contraction wave (M) ectoderm expansion wave (N)

FIG.16 The epidermis is formed by the ectoderm expansion wave. Stage 12.5 (50 hrat 20°C). The ectoderm contraction wave is about to vanish as an ellipse (cf. Fig. 17). All tissues have invaginated through the blastopore, which is now circular, except for the tail bud (not shown) and about one-half of the ventralmost mesoderm. The lip of the blastopore is thus named the neuroepithelium contraction wave on the dorsal portion and the presumptive ventral mesoderm contraction wave on the ventral portion. The ectoderm expansion wave is launched by an unknown mechanism, producing the epidermis. (We suspect that invaginating lateral mesoderm, which may make contact on the interior at this time, acts to launch this wave.) We are now ready for the neural ridge to rise along the crimp line separating neuroepithelium and epidermis, and for shaping of the neural plate. The tissues on the inside may undergo further differentiation waves, but new techniques will be needed to observe these. We have seen waves on the neural plate, including one that splits into two shrinking circles to form the eye anlagen, and will report on them later.

Natalie: In this case, the blastopore itself, or rather the formation of bottle cells as the cells pass over the lip, is the actual contraction wave. Dick:Yes, if we compare any wave consisting of bottle cells in the blastopore lip with the presumptive notochordal mesoderm/ectoderm contraction wave, they have many similarities. Both show up as a pigment line and a furrow. Both involve an apical contraction of the cells and they relax after contraction. Each propagates parallel to itself, and, at least initially, increases its arc length. In fact, if the presumptive pharyngeal endoderm-prechordalmesoderm contraction wave is drawn as moving across the tissue it travels through (i.e., drawn in a tissue coordinate system rather than the laboratory coordinate system), it looks like a spreading arc, part of a circular wave. Finally, if we lump all the waves of the dorsal lip together, as the blastopore closes they close down to a point and vanish, just as the presumptive notochordal mesoderm/ ectoderm contraction wave does. Pieter: Bottle cell formation is an extreme contraction of the outer cell surface. Relaxation occurs after invagination and is followed by a strong expansion into flat archenteron bottom cells. It is a much more pronounced process than that in the yolk mass and ectoderm contraction waves.

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Dick Yes, it is correct that we cannot explain the quantitative difference in contraction between bottle cells and other contraction waves. But since the bottle cell contraction propagates from cell to cell, it is clearly a wave. Pieter: During the time you are watching the blastopore, the neural induction process takes place between the invaginating and forwardmoving archenteron roof and the downward-moving overlying ectoderm (epiboly). The prechordal plate mesoderm, moving in front, activates the overlying ectoderm to neural development, which ultimately leads to forebrain formation when no further inductive actions occur (Nieuwkoop et at., 1952a,b; Nieuwkoop 1958, 1963). Dick: It is here that I believe the cell state splitter model can best clarify “activation” and “inductive actions.” To my knowledge no one has ever satisfactorily explained just how this activation occurs and what the exact nature of the inductive actions is. In Gordon and Brodland (1987) I predicted that a wave of stretch-activated contraction of microfilament rings would explain the homoiogenetic component of primary neural induction. We subsequently discovered the presumptive notochordal mesoderm/ ectoderm contraction wave (Brodland et al., 1993). Pieter: Why not suppose that the wave turns inside and then expands forward (toward the animal pole) in the expanding roof of the archenteron? Outer and inner layers together are responsible for the formation of the dorsal axis in the form of notochord and somites (and prechordal meso- and endoderm) and overlying neural plate. This also explains the continuity of archenteron roof and neural plate in the form of the tail somites which develop out of the most caudal portion of the neural plate. Dick We would indeed like to be able to follow waves inside the embryos. Possible in uiuo 3-D techniques include confocal microscopy, X-ray microscopy (Howells er al., 1991), and magnetic resonance imaging microscopy (Cho er al., 1992). Natalie: The presumptive notochordal mesoderm/ectoderm contraction wave begins when the presumptive pharyngeal endoderm-prechordal mesoderm and prechordal mesoderm have invaginated, becoming pharyngeal endomesoderm and notochord, respectively. It starts at some distance in front of the dorsal lip of the blastopore and spreads first more or less concentrically until the expanding circle meets the blastopore. Here the circle breaks. The resulting arc now travels further over the dorsal half of the embryo. The left and right ends of this arc travel more quickly than the middle section and close as a circle in the presumptive forebrain area, where it finally ends as a point and vanishes (Brodland er al., 1993). The boundary of the ectoderm through which this wave passes extends slightly beyond the area of the presumptive neural plate. Pieter: Yes, but I said when no further inductive actions occur. However, the slightly later invaginating chordamesoderm transforms the poten-

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tial forebrain into hindbrain and spinal cord, the more caudal regions of the chordamesodermal archenteron roof exerting a stronger transforming influence than the more anterior ones (Nieuwkoop et af., 1952a,b). Since the median notochordal anlage attaches itself strongly to the overlying neurectoderm, induction starts at and spreads from this median region. Both activating and transforming inductive actions spread in the overlying ectoderm from cell to cell (homoiogenetic induction) in the mediolateral and activation also in the anterior direction (Albers, 1987; Nieuwkoop and Albers, 1990) till the corresponding competences run out, fixing the outer as well as regional boundaries of the neural plate. The transforming influence acts only upon activated neurectoderm and is restricted to the chordamesodermal area, hardly influencing the presumptive forebrain region of the neural plate (Nieuwkoop et al., 1952a,b; Nieuwkoop, 1992). The presumptive notochordal mesoderm/ectoderm contraction wave, though certainly there, cannot explain the regional nature of the induction. The wave may simply represent a visible manifestation of homoiogenetic induction and not be the cause of it. Dick: Yes, I fully agree, we cannot explain regional induction by a single wave. Until we resolve the question of regional differentiation of the neural plate, the salient fact is that the trajectory of the presumptive notochordal mesodermlectoderm contraction wave does correspond almost precisely (Brodland e? al., 1993) to the tissue that becomes neural plate. Pieter: The course of this neurectodermal contraction wave follows closely the neural activation processes which start where the invaginating anterior mesoendoderm makes contact with the overlying ectoderm, and it then follows the anterior expansion of the dorsal archenteron roof and the subsequent lateral and anterior extension of the neuralization process (Albers, 1987). These wave phenomena accurately cover the area of the neural plate plus surrounding placodal ectoderm and seem to precede their actual morphogenesis, like the wave phenomena of the pregastrulation movements. Natalie: The ventral launching of the ectoderm expansion wave (Figs. 16, 17) coincides with the end of the ventral mesoderm invagination. It travels in the form of an enlarging circle at the ventral side of the embryo and terminates at the boundary of the rising neural plate ridges, traversing the placodal ectoderm and the rising neural folds, where the epidermis overvaults the underlying neural crest. Pieter: Epidermal differentiation depends primarily upon the absence of mesoendodermal and neuralizing inductive influences, allowing the ectoderm to proceed along the intrinsic epidermal pathway. Epidermal differentiation finally requires the presence of a mesenchymal substrate of ventral mesodermal or neural crest origin for its apical/basal polarization.

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Crimp

FIG. 17 A diagram of the presumptive notochordal mesoderm-ectoderm contraction wave that forms the presumptive notochord and neuroepithelium during amphibian gastrulation. The dorsal surface of Ambystoma mexicanurn is shown. 20°C. The trough of the furrow is shown at 1-hr intervals. The presumptive notochordal mesoderm-ectoderm contraction wave appears at early gastrulation at a focus above, not coincident with, the dorsal lip of the blastopore, which was classically regarded as the organizer (Spemann and Mangold, 1924a,b; Hamburger, 1988). The initiation focus is probably underlain by an adhered tissue (Gordon and Brodland, 1987), most likely the pharyngeal endoderm (Hama et al., 1985), which is not mesoderm. This schematic diagram is an approximate composite made from a number of partial time-lapse sequences of the wave (Brodland et al., 1993). It does not convey the fact that, while the wave is traversing the dorsal ectoderm, a significant amount of invagination occurs as the blastopore changes from an arc to a circle, and then closes down nearly to a point. The presumptive notochordal mesoderm-ectoderm contraction wave takes 9 to 12 hr from start to finish. Updated from Bjorklund and Gordon (1993).

The ectoderm expansion wave seems to correspond with the expansion of the presumptive ventral and lateral plate mesoderm and overlying epidermis as compensation for the elevation and closure of the neural plate anlage and the dorsal convergence of the underlying chordamesoderm (Nieuwkoop, 1946). (It should be checked whether a real wave phenomenon precedes the actual morphogenetic movements or only reflects their spatial expression.) Natalie: As I explained earlier, in the case of expansion, the two may well be the same. However, I couldn’t agree more that we need more observations, many more.

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8. What Are the Neurulation Movements? Natalie: We are now reaching the final period where we have observed wave phenomena, which occur in the period of neurulation. These waves require more definition, and so are not represented in the figures. The first wave of neurulation is the posterior neural plate wave. The launching of the posterior neural plate contraction wave coincides with the closure of the blastopore and expands as an area from the tip of the slit-shaped blastopore of stage 13. It coincides with the extension of the underlying elongating notochord, distorting the forward-moving wave by pushing it forward in the middle, giving it a triangular shape. The wave ends at the tip of the notochord in the area which will later form the mid- and hindbrain. Pieter: Although the spatial extension of the posterior neural plate contraction wave coincides with the transformed area of the neural plate, the wave starts at a time (stage 13) that the transformation is already markedly on its way. Neural transformation starts at stage 11 to 12 (Nieuwkoop, 1973). (Thus instead of a preceding wave it looks as if we may have to do with a wavelike expression of posterior neural plate morphogenesis.) A reciprocal inductive influence is exerted by the neural plate upon the underlying archenteron roof, strengthening notochordal differentiation and consequently neural transformation (Weyer el al., 1978). Transformation essentially only leads to hindbraidspinal cord formation, the intermediate midbrain formation depending upon a later interaction between the spatially overlapping forebrain and hindbrain/spinal cord domains (Nieuwkoop, 1992).In the most caudal region of the archenteron, roof transformation leads ultimately to mesodermization of the overlying neurectoderm. Thus the tail somites form out of ectoderm which has first gone through the process of neural activation and subsequently through transformation via hindbrain and spinal cord, ending finally as tail somite mesoderm. Natalie: The eye anlage contraction wave begins as a circle on the edges of the rising neural ridges of the anterior neural plate at stage 14. Upon reaching the central area of the anterior neural plate, the circle breaks into an arc and the two ends close into two separate circles corresponding with the two eye rudiments. The circle vanishes and the region disappears laterally under the rising neural ridges. Pieter: Although the primary extension of this wave may correspond with the area with eye differentiation tendencies, the wave probably reflects true morphogenetic movements in the anterior neural plate. These wave phenomena, occurring during early embryonic development, represent characteristic, but still not understood, new supracellular phenomena. They show very interesting topographical and temporal relationships with

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later-occurring, well-known morphogenetic movements. The latter partially represent autonomous processes, like the pregastrulation movements, and are partially the consequence of preceding inductive interactions, leading to the initiation of new developmental pathways. The wave phenomena may either actually initiate these processes or may only represent early accompanying phenomena. A further analysis is highly desirable. Dick: We have indications that two waves in the neural plate (neuroepithelium) may split it into anterior/posterior portions, corresponding to known patterns of gene expression, but I do not yet regard our evidence as convincing. These need further time-lapse video microscopy, especially at higher resolution, using through-focus mosaic software (Gordon, 1983; Luchka and Gordon, 1993), which is needed to record waves on a highly curved surface through water immersion objectives. Given the probable existence of these waves, I suspect that regional induction is merely a case of further binary subdivision of tissues by discrete waves. The disagreement may be one of the resolution of different observation techniques: a hierarchical, binary, digital process can appear smooth if it is observed at low time and/or spatial resolution. You have raised questions of timing of our observations of waves with known inductions. I agree that further analysis is essential. Let’s hope the grant agencies agree (though I am skeptical; Gordon, 1993).

9. What Is the Role of the Inducing Tissue? Natalie: We now have when and where inductive interactions occur and what the inducing tissues are. So how does the inducing tissue induce differentiation? Pieter: A stimulus of chemical/physicochemical and/or physical nature spreads from the inducing tissue, releasing intrinsic developmental potentialities in the reacting tissue. I think there is little specific information in the inducing factors. However, they are not completely aspecific; the mesoderm-inducing factor is certainly different from the neural-inducing factor and the activating neuralizing influence is very likely to be different from the transforming factor acting upon a different substrate. Namely, the first acts upon competent ectoderm and the second upon activated neurectoderm. The inducing action ultimately leads to specific gene activity and subsequent cellular differentiation. Dick The specificity resides in the cell state splitters and their corresponding nuclear state splitters (Bjorklund and Gordon, 1993). The role of the inducing tissue is to set off a wave of contraction or expansion of the cell state splitters from an appropriate launching domain. How critical this must be is not clear. After all, some tissues are regarded as “autoin-

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duced” (reviewed by Gordon and Brodland, 1987),which is a euphemism that means that they don’t need a specific inducing tissue. Natalie: Then here you both agree that a mechanical explanation is one of the possible interpretations of the observed phenomena. 10. What Is the Role of the Responding Tissue?

Natalie: The tissue has been induced as you explained. Now please describe how the induced tissue responds. Pieter: The yolk mass endoderm responds by forming flask cells in its periphery zone, while the animal moiety spreads toward the reducing blastoporal anlage (epiboly). The mesoderm responds by changing cellular properties and by accumulating at particular sites (primarily the dorsal side) and by invaginating into the interior of the embryo. The chordamesoderm, in particular the mesoderm anlage, stretches in an anteroposterior direction, accumulating at the dorsal side and thus forming the axial structure of the embryo. The neurectoderm primarily contracts mediolaterally , its caudal portion extending caudally together with the underlying chordamesoderm. The epidermis spreads in all directions, compensating at the embryonic surface for the closure of the neural tube (Nieuwkoop, 1973). Dick: The initial response of a competent cell is an expansion or a contraction of its apical surface. The contracted cell relaxes and the contraction disappears visually. The cell has been changed, however, induced, if you like. An expansion wave does not disappear. The visible manifestation of this is the phenomenon of epiboly. The contraction or expansion wave a cell participates in is followed by a biochemical pathway within it that activates one master gene and represses another (Bjorklund and Gordon, 1993). This is followed (Gordon and Brodland, 1987; Bjorklund and Gordon, 1993) by the expression of particular gene products specific to the new tissue type. 11. What Is Regional Induction? Natalie: I am afraid this term loses me completely. Pieter: Regional induction refers to the formation of a regional segmental structure-for example, the dorsoventral segregation of the mesodermal mantle into notochord, somites, nephrogenous tissue, and lateral plate, and craniocaudal segregation into prechordal plate and chordamesoderm. The segregation of the neural anlage into the forebrain, midbrain, hindbrain, and spinal cord is another example-each with a different spatial distribution, as a result of successive inductive influences. Dick Regional induction is likely to be merely multiple inductions that we have not yet learned how to distinguish. As I mentioned earlier, each

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step of so-called regional induction is likely to be accompanied by differentiation waves. 12. What Is the Relationship between Induction and Specific Differentiation?

Natalie: Please give an example. Pieter: An inductive action is topographically linked to a specific competence of the reacting tissue, releasing a particular cascade of genes and leading ultimately to a particular cellular differentiation, for example, neural differentiation in answer to an inducing action of the anterior archenteron roof. Dick: Specificity resides in two possible places. (1) It is possible that there are specific molecules involved in binding the inducing tissue to the cells at the launching domain of a wave of homoiogenetic induction. (2) In the nucleus of the competent cell, a specific pair of master genes waits for the biochemical signal activating one master gene of the pair, which probably thereby represses the other in a mutual feedback mechanism (Bjorklund and Gordon, 1993). The pair that is ready depends on the cell’s specific history (sequence) of already activated master genes. Natalie: You obviously both agree on the result even if you disagree on the means.

13. What Is Homoiogenetic Induction? Natalie: As I understand it, homoiogenetic induction occurs when an inducing signal travels from a point of contact with an inducing tissue, through the tissue that is becoming induced, over a specific region within the embryo, and from one cell to another. Please give an example. Pieter: That is correct, see, for example, neural induction in attached, competent ectodermal strips. The process stops when competence to the inducing stimulus peters out (Nieuwkoop et al., 1952a,b; Nieuwkoop, 1958; Albers, 1987; Nieuwkoop and Albers, 1990). Dick: Homoiogenetic induction is the transmission of a contraction or expansion wave from one cell to another in a tissue of equivalent, competent cells. Pieter: Why does it stop at a certain boundary? Dick: We honestly don’t yet know, but I don’t think it “Pieters” out. We have been pursuing the idea that nonuniform strains in the surface, generated by invagination, may change the refractive index of the tissue for the presumptive notochordal mesoderm/ectoderm contraction wave in such a way as to make it go from one focus to another (Fig. 17), in effect, turning the embryo into a gradient index lens (Fowler and Pateras,

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1990) for this wave. However, we have just recently observed, at low spatial resolution, what we tentatively call a “crimp” (Figs. 13 and 14). It shoots across the embryo before this wave gets very far, and may somehow restrict the wave’s trajectory. We need close-up images of this strange phenomenon, which we have not seen at other stages. It may be our first evidence of an actual terminal boundary for a wave, other than another wave, and was not something we predicted. It appears to follow the floor of the archenteron. For all my chutzpah, the embryo may yet teach me some humility. Natalie: I hope so, but I rather doubt it. Dick: We are trying to sort out the role(s) of the crimp.

14. What Is Regulation? Natalie: I am afraid this term is another that loses me completely. Pieter: The term refers to the ability of the embryo to restore (wholly or partially) normal development after drastic experimental intervention. Dick: Regulation is probably a consequence of the as-yet-unknown mechanism by which differentiation waves are shaped within a tissue. As shown for the simple case of a wave that stops at or before covering one hemisphere (Gordon and Brodland, 1987), such shaping mechanisms could be robust, in the sense that they give the same morphology over a wide range of sizes of the tissue through which they travel. On a broader scale, Natalie has observed that the termination of one wave and the initiation of another sometimes seem to be correlated (Fig. 2). Perhaps wave-wave interactions are responsible for the coordinated development of the embryo, and thus for the near independence of the course of development over a wide temperature range (Duellman and Trueb, 1986).

15. What Is a Morphogen? Natalie: Please define and give an example. Pieter: A morphogen is the natural factor responsible for a particular inductive interaction. There may not be very specific morphogens or there may be quite a number of different substances and/or physical processes playing a role in the normal induction process. Dick: The concept of a morphogen goes back at least to Turing (1952), who showed how coupled chemical reactions and ordinary diffusion could produce spatial patterns of the chemicals, which he then presumed were amplified by cell growth, division, etc. (cf. Rashevsky, 1960; Murray, 1990; Winfree, 1990). It has since acquired a broader meaning as any molecule that causes a spatial tissue pattern to develop, and claims have

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been made for the actual existence of morphogens (Green, 1990; Slack, 1987), although their causal pathways have yet to be ascertained. If induction works by attachment of one small group of cells to another, by specific molecules, I would hesitate to use this term to describe those molecules, for they achieve no spatial distribution themselves. Given the beautifully complex shape of the physical ectoderm contraction wave (Fig. 171, there seems to be no need for an underlying, molecular prepattern. However, since Turing mechanisms (Turing, 1952), albeit sensitive to tissue shape (Arcuri and Murray, 1986), can also produce complex patterns (Murray, 1989; Peterson, 1992), we should remain open to the possibility that they provide the shaping mechanism. Natalie: I think you are both saying the same thing in different ways.

16. How Do Artificial Inducers Work? Natalie: I remember being quite shocked when Dr. Laale described how boiled guinea pig liver could induce neural tissue. I read in the book Of Scientists and Salamanders that Twitty (1966) noted that fly’s wings did not. It seems that the phenomenon of artificial inducers is like the childish magic of a fairy-tale world complete with nonsensical rules. I am most reminded of Alice in Wonderland with me as Alice. I would be interested in learning how artificial inducers work. Who started this type of work in the first place? How did this affect embryology as a science? Pieter: Artificial inducers are substances which can make a highly competent reaction system switch to a certain new developmental pathway. An inductive interaction may very likely be a highly complex chain reaction. Artificial inducers may act on different links of the chain reaction, setting off the entire chain. Holtfreter (reviewed in Holtfreter and Hamburger, 1955) looked for inductive factors in all kinds of animal (and even plant) tissues. Toivonen (1940) introduced the term “heterogeneous inducers.” Now the term “artificial” is used, to contrast them with “natural” inducers. The latter are further called “morphogens,” a rather unsuitable term. Dick: It is plausible that all substances tried for artificial induction fall into three categories: (1) materials that adhere to competent cells at their basal ends, setting off differentiation waves; (2) substances that cause competent cells to deposit actin and/or other cytoskeletal molecules at the inner surface of their exposed (usually basal) membrane; the contraction of this actin, for instance (Burnside, 1972), could set off a contraction wave; (3) materials to which no adhesion is possible; this would explain the lack of inductive effect by hydrophobic materials such as insect wings and banana peels (Brachet, 1974; Gordon and Brodland, 1987) and wax (Needham, 1950).

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Natalie: So you both agree that it is the response of the competent cell and not the nature of the inducer that is important. 17. What Is the Role of Morphogenetic Movements?

Natalie: Please define morphogenetic movement and give me an example. Once we are sure we are all talking about the same thing, we can discuss the role it plays. Pieter: The morphogenetic movements of for example, gastrulation, neurulation, eyecup evagination, etc., are extensive, specific coordinated movements of large groups of embryonic cells. These movements are responsible for bringing parts of the embryonic system in direct contact with each other, parts which were initially far apart from each other, differ markedly from each other, and may therefore cause inductive interactions by exchange of cellular products. Dick: More specifically, I would suggest that the role of a morphogenetic movement is to bring an inducing tissue into a small point of contact with a competent tissue, from which point a contraction or expansion wave can be launched. Other roles may include generation of shear to break cell junctions (Jacobson and Gordon, 1976; Gordon and Jacobson, 1978) and generation of tension over a tissue, which may shape a wave. 18. What Is the Cause of Morphogenetic Movements?

Natalie: What do we know about the cause of morphogenetic movements? Pieter: We simply don’t know! Changes in cellular properties are certainly involved. These may also be the consequences of inductive interactions. Dick: A popular hypothesis today, which seems plausible, is that the production of cell adhesion molecules causes cells to move relative to one another within cell sheets (Steinberg and Poole, 1982; Edelman, 1988). If this is correct, then morphogenetic movements are consequences of the gene cascades at each step of differentiation, and in no way the primary causes of differentiation. 19. What Is an Embryonic Field?

Natalie: How can we define an embryonic field? Pieter: An embryonic field is a part of the embryo which behaves as a unit, like, for example, the mesoderm or the forebrain area, and which can autonomously develop and segregate into a complex structure such as a forebrain with telencephalic and diencephalic structures and accompa-

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nying sense organs, or embryonic mesoderm, which aggregates into notochord, somites, nephrogenous tissue, and lateral plate. Dick: I would suggest that an embryonic field corresponds to the trajectory of an expansion or contraction wave.

20. What Is Positional Information? Natalie: This is another widely used, but, I think, dubious term. Pieter: A confusing concept, suggesting a direct relationship between cellular differentiation and spatial localization of the relevant cells within the embryo. Dick: When a tissue splits into two tissues at a given step of differentiation, the initially equivalent, competent cells split into two spatially separated groups. In a sense they have then acquired one bit of spatial information. However, the original concept of positional information required that the cell act on this information, that is, on its estimate of its own coordinates, and differentiate into whatever was somehow specified by those coordinates (Wolpert, 1969). In my view, differentiation comes first, and “positional information” is merely a handy, digital label we can apply to cells. On the other hand, since their subsequent actions may depend on the sequence of expansions and contractions to which they have been subject, and that “differentiation code” roughly corresponds to a spatial location in the embryo, we might yet say that the cells acquire positional information bit by bit. This sequential acquisition of positional information differs from the original concept, in which the information sprang fullblown in one step, so that every cell in the organism knew exactly what to do to make its contribution to the organism. Of course, one essential difference between a differentiation code and positional information is that the code is shared by all cells in a given tissue, whereas positional information is usually conceived of as potentially varying from one cell to the next in the same tissue. As I mentioned before, it is easy to blur these distinctions with low spatial or time-resolution observations. My 10-year-old son Chason, an aspiring poet, caused me to dust off this old skill: How does the embryo do it, Without positional information to get through it? It dimples with waves, And diligently saves, All the proteins and RNAs that accrue it.

Natalie: What was that you said about your level of intellectual development?

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21. Where Does Polarity Reside in the Embryo? Natalie: We may disagree on the possible definitions for the term “polarity.” I think you should both define polarity as it is in the embryo. After you define it, please describe where it resides. Pieter: Polarity refers to graded regional differences showing a certain directionality, as observed in an egg cell, an embryo, or portion of an embryo, for example, limb or wing. The egg starts development with an animal-vegetal “polarity” because of the presence of two different moieties along this axis. The dorsoventral polarity starts in the animal moiety of the fertilized egg as a result of the spreading of the sperm aster, leading to the formation of the gray crescent at the opposite side, except in polyspermic urodeles. The dorsal-ventral polarity is then transferred to the vegetal yolk mass (Nieuwkoop, 1969a,b, 1970, 1973; Boterenbrood and Nieuwkoop, 1973). We do not know how! With the induction of the mesoderm (mesoendoderm), the dorsal-ventral polarity is transferred to the induced mesoendoderm. The spreading of the inductive action from the boundary of the yolk mass of the embryo into the animal “ectodermal” moiety is responsible for the formation of the anteroposterior polarity, which is strongly accentuated by the dorsal convergence movement and anteroposterior stretching along the anteroposterior axis (Nieuwkoop, 1977). Dick: In terms of morphogenesis, I find it difficult to accept the notion of polarity: the concept of polarity implies that a cell “knows” which way is which in an embryo. Anisotropies certainly exist from cell to cell, and these undoubtedly have consequences, such as, perhaps, tension anisotropies in the shaping of waves, but I would not necessarily call these polarities. On the other hand, I am stuck: the cilia in early epidermis (Billett and Courtenay, 1973) have clearly defined orientations (Tung et af., 1949) whose origin, and morphogenetic importance we simply don’t understand. Thus I am forced to remain open about the possible existence and role of cell polarity in developing cell sheets.

22. What Has Been Solved in Embryology Thus Far and What Is the Most Important Problem Remaining to Be Solved? Pieter: I think it is that inductive interactions play a leading role in the development of the vertebrate embryo. In these interactions the rise and decline of specific competences in the reacting cells is of much greater importance than the nature of the inducing stimuli. In my opinion, the central question in embryology is therefore the nature of competence, its formation, climax, and decline.

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Dick: I think we are close to a complete solution of differentiation. We have to prove to everyone’s satisfaction that our waves are indeed differentiation waves (or disprove it, and assess the situation). The major problem without an obvious solution is what determines where and when they are launched. However, I would place “the most important problem” as the origin of consciousness, which does not fit our current paradigms. The plant morphogeneticist Sinnott (1960, 1962) has suggested that developmental biology may provide the essential clues, so maybe our work on differentiation will help. 23. What Is the Best Approach for Someone, for Whom Training Is Just Beginning, to Take in Solving This Problem?

Pieter: To work the remaining years of your life on the problem of competence and help to clear up a few of its questions. Dick Agreed! Just make sure you are not constrained by disciplinary boundaries, the mastery of techniques in search of problems, or a proclivity to make the embryo follow your preconceived ideas. (It won’t.)

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ADDENDUMTO The Chemical Basis of Diatom Morphogenesis Richard Gordon and Ryan W. Drum

Three-Dimensional Structure of Valves

There is a distinctive pattern in the costae from the inside of the cell out. Frequently, one side is nearly sealed with a thin layer of silica while the pores remain relatively open on the other. This reaches its extreme form in resting spores, which can be nearly solid silica on one side (von Stosch and Fecher, 1979). Some shells have two different sheets joined by perpendicular plates (Crawford, 1974a, Fig. 24). As Iler (1979) has pointed out, the charged nature of the silica particles can cause them to precipitate into two-dimensional sheets in the presence of a low concentration of an appropriate cationic surfactant: “Under these conditions the aggregate grows as a sheetlike layer of particles only one particle thick, since the particles can approach and attach themselves to the growing sheet only around the edges of the sheet where ionic repulsion is least.” These sheets then sinter together “so that an impervious flakelike particle of colloidal thickness is obtained.” Critical micelle concentrations need be only l o p 3 M and need cover only 5% of the silica particle surface. It seems possible, then, that the phospholipids forming the silicalemma could be available for such catalysis. This may explain how the cross-costal layer and porous plates form. Porous plates can be 50 to 100 A thick (Drum and Pankratz, 1963), corresponding well with the estimated diameter of the silica particles in diatom shells. The inner, porous plate tends to be thicker than the outer (Crawford, 1974b). The remarkable concentration of mitochondria against the silicalemma and their subsequent encapsulation in the valve in some species (Stoermer et al., 1964; Pickett-Heaps et al., 1979a) may be a major means of introducing asymmetries in the third dimension. The growth of the valve in the third dimension is thus a fascinating problem in itself. Basic twodimensional valve formation takes place over 10 to 20 min. However, lnrrrnurionul Rrurew of C y r o l o ~ Val. . I50

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Copyright 0 1994 by Academic Presi. Inc. All rights of reproduction in any form reserved.

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ADDENDUM TO THE CHEMICAL BASIS OF DIATOM MORPHOGENESIS

silica deposition continues for up to 3 hr (Darley et a f . , 1976) and possibly longer. This may represent subsequent thickening and elaboration of complexly shaped chambers in the valve. The work of Schmid and Schulz (1979) supports this time sequence. The total time for valve formation can be as little as an hour: In the centric diatom Ditylum brightwellii,wall morphogenesisoccurs during a 53-min period of the cell cycle (Eppleyet al., 1967), whereas in synchronized Nauicula pelliculosa cultures, it occurs in 2-3 hr or less (18% of the cell cycle time). (Sullivan and Volcani, 1981)

It is of interest that the thickness of the silica deposition vesicle is approximately equal to the spacing between costae, so that instability phenomena in the third dimension, themselves leading to asymmetries, may be anticipated. The 3-D structure of a diatom shell is similar to certain folded sheets that have greater structural strength than geodesic domes (Resch and Christiansen, 1973). Thalassiosira steffaris is a remarkable centric diatom in which “the strutted processes in the central ring are evenly spaced and located on the complete radial rows of areola . . . giving the stellate appearance for which the species is named” (Fryxell and IIasle, 1977). Their nearly symmetric patterns indicate some kind of interaction with the growing costae that grow in straight lines. The symmetry is lost in the related Thafassiosira weiss-ogii, which has a considerable degree of wobble of the costae. We have not explained the spines, hyaline rings, and numerous other siliceous structures that appear in and on (Fryxell and Hasle, 1979a) and internal to (Fryxell and Hasle, 1979b) the diatom valve. Harrison et al. (1977) note that in colonies of Skeletonema costaturn “the length of the connecting rods between cells was . . . almost zero for Si-limited cells.” This suggests that such structures may be formed last. The fusion of bristles, or setae, between adjacent cells in the colonial diatom Chaetoceros (von Stosch et al., 1973; Fryxell, 1978) suggests that sintering processes are involved in their morphogenesis. The suggestion that this “might indicate the beginning of a more complex organization” (Round and Crawford, 1981) may not be warranted if a simple physicochemical process is involved rather than a more complex genome.

INDEX

A Acanthamoeba, locomotion, 56 Acetabularia calcium in cytoskeletal dynamics, 227, 229-231 kinetics, 240-241 cell wall dynamics, 231-232 growth, 225-228 life cycle, 226 morphogenesis branching, 272 characteristics, 225-228 simulation, 232-237 phenocopying, 237-238 viscoelastic equations, 239-240 Acetabularia crenulata, morphology, 237 Actin, see also Contractile proteins; Microfilaments cytoskeleton models of cellular tensegrity, 189-196 tension molding, 196-201 in interphase nucleus, 165-167 lamellipodia assembly, 64 concentration, 39 retrograde surface transport, 47,49, 51-53 treadmilling, 61-65 treadmilling, as retrograde surface transport, 51-54, 61-65 Actomyosin, in retrograde surface transport, 47 Algae, see Diatom morphogenesis, chemical basis of; specixc species Amebae, see also speciJc amebae locomotion Amoeba proteus, 54-56,61 Dictyostelium, 57-61 Labyrinthula, 59-62 rolling membrane, 56-57 shelled amebae, 58-59

tissue culture cell locomotion comparisons, 35-36,61-62 y-Aminobutyric acid, chromatin reorganization by, 161-162 Amoeba proteus, locomotion, 54-56,61 Amorpha coffaeformis, template formation, 260 Amphibians, embryonic tissue, mechanical stress in cell surface angle measurement, 3-7 gastrulation, 29-31, 378 morphogenetic effects, 8-1 1 neural tubes affected by relaxation of stress, 10-11 neurulation, 29-3 1 , 378 relaxation of tensile stresses, 9 tissue dissection as detection method, 2-5 tissue stretching, 8 Antibodies, in retrograde surface transport, 47,49 Artheya decora, silicalemma formation, 342 B Basement membrane, associated proteins in retinal pigment epithelial cells phenotype expression role, 126-127 transdifferentiation role, 128-129, 131 Blebbing, tissue cell, definition, 40 C

Calcium Acetabularia cytoskeletal dynamics, 227, 229-231 kinetics, 240-241 in morphogenesis simulation, 232-236 phenocopying, 238 in transduction of mechanical forces with integrins, 85 Capping, definition, 41

423

424 Cell columnarization models, embryonic tissue, mechanical stress in, 23-24 Cell state splitters, 376 Cellular tensegrity, see Tensegrity, cellular Chaetoceros diadema, sintering, 298, 300 Chaos carolinense, locomotion, 54-56 Chromatin, in interphase nucleus gene expression, 150, 168 motion, 150-157 movement by contractile protein, 164-167 rearrangements, 160- 164 reorganization, I49 Chromosomes, in interphase nucleus patterns, 160-164 topology, 157-160 Coenobiodiscus mut$ormis, microfilaments, 334 Collagen, in matrix-driven translocation concentration, 141 percolation phenomenon, 145-146 Competence, embryonic induction definition, 380-382 development, 382-386 Contractile proteins, in interphase nucleus, 164-167 Contraction-stretching cell response, in embryonic tissue, 28-29, 376 Convection current, free, as mechanism in diatom shell morphogenesis, 263 Coscinodiscus asteromphalus, morphogenesis colloidal silica, 325 vesicles, 267 Coscinodiscus concinnus, valve formation, 257 Coscinodiscus wailesii, morphogenesis scale vesicles, 267 valve formation, 257 Cyclotella cryptica cell wall serine content, 259 valve formation, 257 Cytoskeleton Acetabularia calcium effects, 227, 229-231 characteristics, 225 cell state splitters, 376 extended, 177- 179 regulation of cellular tensegrity, see Tensegrity, cellular, cytoskeletal regulation Cytotomy, in embryonic tissue, 27

INDEX D Dendrites, growth theory, in diatom morphogenesis, 297-30 1 Developmental biology, finite element methods for, see Finite element methods, for developmental biology Development, embryological, see Embryological development Diatom morphogenesis, chemical basis applications to organisms, 344-345 branching patterns, alternative mechanisms, 343-344 characteristics of diatom, 245-247 definition of diatom, 243 shell, see Diatom shell morphogenesis, chemical basis silica colloidal properties, 320-326 diffusion, 322-323 formation, 320-322 precipitation, 271-275, 345 requirements, 324-326 reserves, 338-339 transport model, 341-342 silica antenna, diatom as, 338-340 silica deposition vesicle, 253-254 silicalemma characteristics, 253-255 formation, 342-343 sintering costae number in pennate diatoms, 301 cross-costae formation, 301-302 growth of dendrites theory, 297-301 impurities, role in, 303-307 instability theory, 296-297 mechanisms, 288-292, 346 molecular basis, 292-295 mother liquor, role in, 306-307 punctae formation, role in, 303-305 punctae shapes, role in, 305-306 silica surface chemistry, 295-296 sintering, modeling adsorption potential choice, 3 10-3 12 amorphous precipitate, 307-310 anisotropic approach, 312-320 physical simulations, 315, 320 space-filling branching patterns costae, 271 heuristic modeling, 27 1-273 nucleating structure, 273-275

INDEX

structural considerations, 243-244 terminology, 347-348 valve microfilaments, 332-335 microtubules, 329-33 1 nucleus, 331-332 plasmalemma, 326-327 plasmolysis, 337-338 silica ionophores, 328-329 silica receptors, 327-328 silica transport vesicles, 328, 335-336 subcellular mechanisms, 336-337 Diatom shell morphogenesis, chemical basis bubbles, 257-258 free convection current mechanism, 263 Golgi apparatus role, 264-270 models of space-filling branching patterns computer implementation, 278-286 future considerations, 286-288 procedure, 275-278 silica precipitation, 275-288 silica sources and sink distribution, 28 1-284 mold prepattern hypothesis, 255-258 patterns, 346 physicochemical mechanisms, 262-264 prepattern concept, 260-262 stages, 247-255 template prepattern hypothesis, 258-260 Dictyostelium, locomotion, 57-61 Differential adhesion hypothesis, experimental confirmation, 147 Differentiation, see also Transdifferentiation in embryonic induction, 408 muscle cell, see Muscle cell differentiation, mechanical stimulation and substratum mechanics, see Substratum mechanics, and cell differentiation Differentiation waves, 414 DifJIugia, locomotion, 58, 62 DNA in cytoskeletal mechanical signaling, 209-210,316 in muscle cell differentiation, gene regulation, 69-70

425 sequence analysis, in interphase nucleus, 149, 161-162, 167 synthesis, silica receptor role, 327

E Embryological development, mechanical forces, 175-176,377 Embryonic field, definition, 41 1-412 Embryonic induction artificial, 410-41 1 competence definition, 380-382 development, 382-386 definition, 387-389 differentiation waves, 414 embryonic field, definition, 41 1-412 gastrulation movements, 373, 397-404 and genetics, relationship, 375-380 homoiogenetic, 408-409 inducing tissue role, 406-407 interactions, 413 mechanism, 373-374 morphogenetic movements, 41 I morphogens, definition, 409-4 I0 neurulation movements, 405-406 occurrence, 389-391,414 polarity, definition, 413 positional information, definition, 412 pregastrulation movements, 391-397 regional, 407-408 regulation, definition, 409 related to specific differentiation, 408 responding tissue role, 407 Embryonic tissue, mechanical stress in absolute stress value range, 7-8 amphibians cell surface angle measurement, 3-7 morphogenetic effects, 8-1 1, 378 neural tubes affected by relaxation of stress, 10-11 relaxation of tensile stresses, 9 tissue dissection as detection method, 2-5 tissue stretching, 8 cell columnarization models, 23-24 hyperrestoration of preexisting stress hypothesis, 24-25 morphogenetic effects in amphibians, 8-11

426

INDEX

qualitative reconstruction of process, 29-3 I morphogenetic role, 1-2 morphomechanical situations intercalation capabilities, 27-28 intercalation capacities, lack of, 25-27 stretching-contraction cell relay, 28-29,376 superimposed cell sheets, 28 ontogenetic processes, 31-32 stress-force feedback cell columnarization models, 23-24 definition, 2 surface tension cellular level, 19, 22-23 mechanisms, 11-12 subcellular level relaxation of tension, 12-19 stretching, 19-21 tissue level, 19, 22-23 Epithelial cells, retinal pigment, see Retinal pigment epithelial cells Eunoria soleirolii, morphogenesis involving plasmalemma, 326 Extracellular matrix and cellular tensegrity actin cytoskeletal models, 192 focal adhesion, 207-208 mechanical stress response, 185-187 microtubules, 201-203 nucleus, 206-207 signal transfer, 209 tension molding, 196-201 cytomechanics, 120- 124 cytoskeletal force balance alterations, 179- 180, 182- 184 mechanical forces coupling with extended cytoskeleton, I78 resistance, 177 tension, 176 in muscle cell differentiation components, 71-12 interaction, 72, 84-85 role, 69, 71 structural changes, 174 Extracellular matrix proteins, in phenotypic expression, 129

F Feedback, in embryonic tissue intercalation role, 27-28

requirements, 1-2 stress-force cell columnarization models, 23-24 definition. 2 Fibers, stress. see Stress Fibers Fibroblast growth factors, and retinal pigment epithelial cells fate regulation, 127 transdifferentiation, 130-13 I Filopodia, in lamellipodia definition, 39-40 rearward traction forces, 41-42 in retrograde surface transport, 48. 53 Finite element methods, for developmental biology application, 100-101 approach, 98-99 definition, 95 formulataion assembly, 112-1 14 discretization, 107-108 element geometries, 103-105 equations, 102-103 external driving forces, 112-113 physical properties, 109-1 12 quantities, 103-104 shape functions, 104-106 solution techniques, 114 hourglassing, 110-1 11 modeling evolution, 100, 102 role of, 95-98 practical considerations, 116 recent advances, 116 time-dependent phenomena, 114-1 IS verification of results, 115 Free convection current mechanism, of diatom shell morphogenesis, 263 G Gastrulation, in embryonic induction, definition, 373, 397-404 Gel formation, in protein fiber networks, 140 Gene expression, in interphase nucleus, 150, 167-168, 376 Genetics, relationship to embryonic induction, 375-380 Golgi apparatus, diatom morphogenesis role, 264-270 Gomphonema parvulum, colloidal silica formation, 324

427

INDEX

H Hantzschia, valve formation, 268,270 Hantzschia amphioxys, sintering, 306 Heart hypertrophy decreased mechanical load effects, 81 myosin heavy chain isoenzyme transition during, 80 proto-oncogene expression in early stages, 79-80 RNA accumulation in early stages, 78 myocytes, see Myocytes, cardiac myofibrils, role of mechanical forces in formation, 75-76 in maturation promotion, 74-75 tissues, response to mechanical loading, 72 Heat shock proteins, synthesis during cardiac hypertrophy, 79-80 Homoiogenetic induction, embryonic, definition, 408-409 Hyalodiscus, locomotion, 56, 61 Hyperrestoration, in embryonic tissue definition, 25 preexisting stress hypothesis, 24-25 stretching in cell intercalation, 27

I Induction, embryonic, see Embryonic induction Integrins in protein-substratum linkage, 121-122 signaling role in transdifferentiation, 130-13 1 transduction in muscle cell differentiation, 72, 84-86 Intercalation movement, in embryonic tissue capabilities, 27-28 capacities, lack of, 25-27 hyperrestoration, 25 relaxation of mechanical stresses, 9 tissue compression, 29 tissue stretching as promotion method, 22 Intermediate filaments in cell state splitters, 376 mechanical load transport, 176 mechanical stress response, 187 morphogenesis regulation by, 173 as tensile stiffeners, 205-206 tension molding, 200

Interphase nucleus, as dynamic structure chromatin motion, 150-157, 167-168 chromosomes functional state of cells, 160-164 patterns, 160- 164 topology, 157-160 contractile proteins, 164-167 DNA sequence analysis, 167 gene expression, 167-168 intranuclear motor, 164-167 nuclear rotation, 150-157 spatial organization, 149- 150 Ischemia, effects on cardiac function, 82-83 L Labyrinthula, locomotion, 59-62 Lamella, leading, definition, 38-39.44 Lamellipodia actin, role in movement, 64 definition, 38-40 rearward traction, 41 retrograde surface transport, 44,46, 48-49,53 Licmophora, morphogenesis branching costae, 271 nucleating structure, 274 Lobopodia, of tissue cell definition, 40 rearward traction forces, 41 Long-term potentiation, interphase chromatin reorganization by, 163-164 M Matrix-associated regions, gene expression regulation role, 88 Matrix-driven translocation, see Translocation, matrix-driven Mechanical stress, in embryonic tissue, see Embryonic tissue, mechanical stress in Melosira uarians, cross-costae formation, 302 Membrane raking hypothesis, of locomotion, 48-5 I Microfilaments in actin cytoskeletal models, 192, 196 in cell state splitters, 376 in diatom valve morphogenesis, 332-335 mechanical forces stress response, 186 tension in tissue pattern establishment, 176

428 morphogenesis regulation by, 173 tension molding, 196-200 Microtubules in cell state splitters, 376 as compression-resistant struts in cellular tensegrity, 201-205 in diatom valve morphogenesis, 329-33 1 mechanical forces stress response, 187 in tissue pattern establishment, 176-177 morphogenesis regulation by, 173 stretch-activated channels, 86-87, 377 tension molding, 200 Mold prepattern hypothesis, of diatom shell morphogenesis, 255-258 Morphogenesis Acetabularia calcium effects, 227 growth, 225-228 simulation, 232-237 cardiac, role of mechanical forces, 73 cytoskeletal regulation identification of molecules in, 173 mechanism, 174 tissue pattern establishment, 177 transmembrane mechanical coupling, 178 diatom, see Diatom morphogenesis, chemical basis diatom shell, see Diatom shell morphogenesis, chemical basis movement, in embryonic induction, 409-410 in protein fiber networks liquidlike properties, 142- 143 model tissue system, 147 rearrangements based on interfacial forces, 146 Morphogens, definition, 409-410 Movement, see Intercalation movement; Neurulation movements; Pregastrulation movements Muscle cell differentiation, mechanical stimulation of cardiac myocytes development, 73-75 physiology, 76-71 cellular response to loading, 72-73 future experiments, 89 integrins, role in signal transduction, 84-86 load changes effects of decrease, 81-82

INDEX

pathophysiological, 82-83 in vitro, 82 myofibril formation, 75-76 nuclear matrix, 88 process, 69-72,88 receptors of mechanical force, 84 regulatory molecule response, 78-8 1 protein synthesis, 78-80 proto-oncogene expression, 78-80 RNA synthesis, 78 skeletal myocytes, 77-78 stretch-activated channels, 86-87 Myocytes, cardiac development, 73-75 load change effects pathophysiological, 82-83 in uitro, 82 physiology, 76-77 protein synthesis, 78 response to mechanical forces, 73-75,78 Myofibrils, cardiac, role of mechanical forces in formation, 75-76 in maturation promotion, 74-75 Myosin, in interphase nucleus, 165-167 N Nuuicula, morphogenesis branching costae, 272 nucleating structure, 273-274 Nuvicula alba, vesicle formation, 265 Navicula pelliculosa, morphogenesis colloidal silica, 324-325 nucleating structure, 273 stages, 254 vesicles, 270 Neural tubes, amphibian, relaxation of stress, 10-1 I Neurulation movements, in embryonic induction, definition, 405-406 Nitwchia amphibia, morphogenesis, 255 Nuclear matrix, in muscle cell differentiation, 88 Nuclear tensegrity, 206-207 Nucleus, interphase, see Interphase nucleus P Pelomyxa, locomotion, 54-55 Percolation, theory, in study of gel transition of protein fiber networks, 140-141, 145-146

429

INDEX

Phaeodactylum tricornatum, morphogenesis colloidal silica formation, 321, 324 nonsilicified protoplasmic masses, 260 Phenocopying, in Acetabularia, environmental effects on, 237-238 Phenotype extracellular matrix protein-regulated expression, 129 retinal pigment epithelial cytomechanics of expression regulation, 119-120 destabilized, 125 expression on basement membrane proteins, 126- 127 Plasmalemma, in diatom valve morphogenesis, 326-327 Plasmolysis, in diatom valve morpbogenesis, 337-338 Polarity, in embryonic induction, definition, 413 Positional information, in embryonic induction, definition, 412 Potentiation, long-term, see Long-term potentiation Pregastrulation movements, in embryonic induction, definition, 391-397 Protein fiber networks boundaries of immiscibility function, 146- 147 gel formation, 140 matrix-driven translocation definition, 140 percolation, 145-146 physical mechanisms, 143-146 process, 14 1-143 wetting, 143-145 model system, 140-141 properties, 139-140 Proteins basement membrane, and retinal pigment epithelial cells phenotype expression, 126- 127 transdifferentiation, 128-129, 131 and cardiac myocytes function, 83 growth, 80 physiology affected by synthesis rate, 76-78 contractile, in interphase nucleus, 164-167

decreased synthesis rate during cardiac atrophy, 81 extracellular matrix cytomechanics of adhesion, 121-123 phenotypic expression, role in, 129 focal contact, cytomechanics of adhesion, 120- 121 heat shock, synthesis during cardiac hypertrophy, 79-80 load-induced synthesis during cardiac hypertrophy, 79 tine, see Tine proteins Proto-oncogenes, expression in early stages of cardiac hypertrophy, 79-80 R Regional induction, embryonic, definition, 407-408 Retinal pigment epithelial cells cell fate choice regulation by soluble factors, 125-128 by substratum, 125-128 cell-substratum adhesiveness, 123-124 TPA effects, 124-125 transdifferentiation cellular mechanics, 128-131 process, 119-120, 122 Retrograde surface transport actin treadmilling, 51-54 definition, 41 future research, 62-65 hypothesis, alternative, 46-48 mechanism, 43-46 membrane raking hypothesis, 48-51 RNA, synthesis during myocardial growth messenger, 78 ribosomal, 78 Ruffling in actin assembly, 64 definition, 38,41 rearward traction forces correlated to, 41 in retrograde surface transport, 48

S Silica, in diatom morphogenesis colloidal properties, 320-326 deposition vesicle, 253-254, 269 diffusion, 322-323 diffusion-limited precipitation, 27 1-275 formation, 320-322 precipitation, 271-288, 345 receptor role in DNA synthesis, 327

INDEX

requirements, 324-326 reserves, 338-339 shell deposition vesicle, 275-277, 279, 283 diffusion-limited precipitation, 275-288 sources and sink distribution in models, 281-284 silica antenna, diatom as, 338-340 surface chemistry in sintering, 295-296 transport model, 341-342 valve ionophores, 328-329 receptors, 327-328 transport vesicles, 328, 335-336 Silica deposition vesicle, in diatom morphogenesis definition, 253 formation, 269 shell, modeling, 275-277,279,283 structure, 254 Silicalemma definition, 253 formation, 254-255,343 Sintering, in diatom morphogenesis, see Diatom morphogenesis, chemical basis Skeletal muscle, differentiation mechanical stimulation, 77-78 response to mechanical loading, 72 Stephanodiscus huntzschia, morphogenesis microfilaments, 306 silicalemma, 343 Stress, mechanical, in embryonic tissue, see Embryonic tissue, mechanical stress in Stress fibers adhesive plaque connection, 63 rearward traction forces on, 41 retrograde surface transport, 47 Stress-force feedback, in embryonic tissue cell columnarization models, 23-24 definition, 2 Stretching-contraction cell response, in embryonic tissue cell columnarization, 23 morphomechanical situations, 28-29 Subsiiicea frugilarioides, sintering, 298 Substratum mechanics, and cell differentiation cell type conversion, 119 cellular mechanics of transdifferentiation process, 128-132

cytomechanics, 120-125 retinal pigment epithelial cells cell fate choice regulation, 125-128 transdifferentiation process, I 19-120 Surface angle hypothesis, embryonic tissue, mechanical stress in amphibians, 3-7 stretched cell group formation, 25 Surface tension, in embryonic tissue cellular level, 19, 22-23 mechanisms, 1 1-1 2 subcellular level relaxation of tension, 12-19 stretching, 19-21 tissue level, 19, 22-23 Surface transport, retrograde, see Retrograde surface transport Surfing, in retrograde surface transport, 48 Surirella, morphogenesis, silica deposition vesicle formation, 269

T Template prepattern hypothesis, diatom shell morphogenesis, 258-260 Tensegrity, cellular, cytoskeletal regulation actin cytoskeleton models, 189-196 tension molding, 196-201 cell function control, 179-185 cell shape control, 179-185 development, implications for, 21 1-214 mechanical signaling system focal adhesion, 207-208 long-range signal transfer, 208-2 10 structural inheritance, 210-21 1 mechanical stress response, 185-189 mechanisms, 173-175 structural integration intermediate filaments as tensile stiffeners, 205-206 microtubules as compression-resistant Struts, 201-205 nuclear tensegrity, 206-207 tissue pattern establishment, 175-178 transmembrane coupling, 178-179 Tensegrity, nuclear, 206-207 12-0-Tetradecanoylphorbol-I 3-acetate, retinal pigment epithelial cell transformation by, 124-125 Thalassiosira bulbosa, morphogenesis, 261

INDEX Thalassiosira eccenirica, morphogenesis areolae formation, 257 scale vesicle formation, 269 Thalassiosira medirerranea, morphogenesis colloidal silica formation, 325 microfilaments, 333 Thalassiosira trifulra, morphogenesis involving microfilaments, 333 Thalassiosira tumida, valve formation, 269 Tine proteins in Difflugia movement, 62 in Hyalodiscus movement, 62 membrane raking function, 48-49, 51, 63 shelled amebae locomotion, 54 Tissue culture cells, locomotion ameboid locomotion in relation to, 35-36,61-62 future research, 62-65 mechanisms, 38-41 methods of study, 35-37 nomenclature, 38-41 rearward traction forces, 41-43

431 retrograde surface transport actin treadmilling, 51-54 hypothesis, alternative, 46-48 mechanism, 43-46 membrane raking hypothesis, 48-51 Traction, in tissue cells actin treadmilling role, 63 definition, 41 mechanism, 45-46 rearward forces, 41-43 Transdifferentiation, and substratum mechanics cellular mechanics, 128-132 cytomechanics, 120- 125 retinal pigment epithelial cells, 119-120 Translocation, matrix-driven, in protein fiber networks definition, 140 physical mechanisms, 143-146 percolation, 145-146 wetting, 143-145 process, I41 - 143 Transport, surface, retrograde, see Retrograde surface transport

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