Morphogenesis

Paul Bourgine · Annick Lesne Editors

Morphogenesis

Origins of Patterns and Shapes

123 Editors Dr. Paul Bourgine Dr. Annick Lesne CREA CNRS École Polytechnique Laboratoire de Physique Théorique de la Rue Descartes 1 Matière Condensée (LPTMC) 75005 Paris Université Paris VI France place Jussieu 4 [email protected] 75252 Paris Cedex 05 France [email protected]

Translation from the French language edition of Morphogenése c 2006 Editions Belin, France

ISBN 978-3-642-13173-8 e-ISBN 978-3-642-13174-5 DOI 10.1007/978-3-642-13174-5 Springer Heidelberg Dordrecht London New York

Library of Congress Control Number: 2010936323

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Springer is part of Springer Science+Business Media (www.springer.com) Preface

This book has been first published in French by Belin in 2006. It originates in an interdisciplinary Spring School devoted to morphogenesis and held in Berder Island (Morbihan, France) in March 2002. Although the topics were not directly focused on morphogenesis, we should also mention the ensuing annual sessions of this Berder CNRS Thematic School, organized by one of the editor of the book (A. L.), where most of the authors of the book met and interacted. This initial event has been fol- lowed by two 1-day meetings, “Journées Complexité” that we organized in Paris at the Institut Henri Poincaré in November 2003 and November 2004, and again specially devoted to morphogenesis and the specific interdisciplinary approaches required to reach a full understanding. These meetings have been among the launch- ing events founding the Institut des Systèmes Complexes de Paris-Ile-de-France. Several other events, mostly organized by ISC-PIF, reinforced the links between the authors and the motivation to put on the paper and share with readers all the ben- efits and challenges of an interdisciplinary approach of morphogenesis and pattern formation. The collective enterprise that led to the present book is exemplary of the spirit of this institute and its activities. Morphogenesis has been specially focused among the main issues arising in the science of complex systems, due to the intrinsic interdisciplinarity of the topic. The reader will discover in this book the range of objects where similar questions about the formation and persistence of their shape arise, and the wealth of complementary concepts and methods involved in their study. All the different facets have been considered together to really grasp what is morphogenesis. The ambition of this book is to offer such a multiple account. It aims to present a collective work rather than a compilation of independent papers, in which authors interacted and mutually influenced each other, and shared a similar vision about morphogenesis although substantiated in (very) different instances and contexts. To complete the cohesion and scope of the book, we propose an overview of the central questions raised by morphogenesis and a presentation of the contents in the introduction (Chap. 1). We acknowledge the support of the European Community for the translation of this book, as being one of the outcome of BioEmergences, a NEST-Measuring the impossible project coordinated by one of us (P.B.) and of Embryomics, a NEST- Adventure project coordinated by Nadine Peyriéras, author of Chap. 9.Weare much grateful to the wonderful job done by Richard Crabtree, who has to face the

v vi Preface challenge of translating 18 chapters with different styles and technical terms from as many different disciplines. It was a pleasure to work with him. We hope that both the authors and the readers will appreciate the final result!

Paris, July 2010 Paul Bourgine Annick Lesne Contents

1 Introduction ...... 1 Annick Lesne and Paul Bourgine 1.1 Fundamental Issues ...... 1 1.1.1 The Notion of Shape ...... 1 1.1.2 Some Paths to Explore the World of Shapes ...... 2 1.1.3 Shapes and Their Causes ...... 3 1.1.4 Modelling Morphogenesis ...... 3 1.2 Morpho-Genesis ...... 4 1.2.1 Shape-Generating Mechanisms ...... 4 1.2.2 Equilibrium, Out-of-Equilibrium and Far-from-Equilibrium Shapes ...... 4 1.2.3 Irreversibility...... 5 1.2.4 Self-Assembly and Self-Organisation ...... 5 1.3 Instabilities, Phase Transitions and Symmetry Breaking ...... 6 1.3.1 Phase Transitions, Bifurcations and Instabilities ...... 6 1.3.2 Symmetry Breaking ...... 7 1.3.3 Emergence ...... 7 1.3.4 Fractal Shapes ...... 8 1.4 Inanimate or Living Shapes ...... 9 1.4.1 Some Questions ...... 9 1.4.2 Are Living Shapes Special? ...... 10 1.4.3 Functional Shapes...... 10 1.4.4 Genetic Programme, Self-Organisation and Epigenomics .. 11 1.4.5 The Robustness and Variability of Living Shapes ...... 12 1.5 Book Overview ...... 12 References ...... 13

2 Ferrofluids: A Model System of Self-Organised Equilibrium ...... 15 Jean-Claude Bacri and Florence Elias 2.1 Introduction: Situation with Regard to the Other Chapters ...... 15 2.2 Physical Systems in Self-Organised Equilibrium ...... 15 2.2.1 Examples of Self-Organised Physical Systems ...... 16

vii viii Contents

2.2.2 The Origin of Order ...... 19 2.2.3 The Bond Number ...... 21 2.2.4 Domain Size and Choice of Pattern ...... 21 2.2.5 Summary ...... 22 2.3 Morphologies in Ferrofluids ...... 22 2.3.1 Ferrofluids: A Model System for Studying Structures ..... 22 2.3.2 Stripes and Bubbles, Foams and Rings in Ferrofluids ..... 26 2.3.3 The Influence of History: Initial Conditions and Conditions of Formation ...... 28 2.3.4 The Source of Patterns: Instabilities ...... 31 2.4 Conclusion ...... 37 References ...... 38

3 Hierarchical Fracture Networks ...... 41 Steffen Bohn 3.1 Introduction ...... 41 3.2 The Formation of Hierarchical Fracture Networks ...... 42 3.3 The Fracture Network as a Hierarchical Division of Space...... 44 3.4 A Characteristic Scale ...... 45 3.5 Conclusion ...... 47

4 Liquid Crystals and Morphogenesis ...... 49 Yves Bouligand 4.1 Shells and Series of Arches ...... 49 4.2 Helicoidal Plywood ...... 51 4.3 Cholesteric Liquid Crystals and Stabilised Analogues ...... 53 4.4 Specificity and Diversity of Liquid Crystals ...... 54 4.4.1 Mesogenic Molecules ...... 55 4.4.2 Structure of Liquid Crystals ...... 56 4.4.3 Phase Transitions ...... 57 4.5 Liquid Crystals and Stabilised Analogues in Biology: A Widespread Phenomenon ...... 58 4.5.1 Muscles ...... 58 4.5.2 Myelinic Figures and Fluid Cell Membranes ...... 59 4.5.3 Stabilised Membranes ...... 60 4.5.4 Nematic and Cholesteric Analogues ...... 60 4.5.5 The Limits of a Widespread Phenomenon ...... 60 4.6 Liquid Crystalline Self-Assemblies ...... 61 4.7 Curvature and Structure ...... 62 4.7.1 Diversity of Curvatures in Liquid Crystals and Their Analogues ...... 62 4.7.2 Geometry of the Different Curvatures ...... 64 4.7.3 Elastic Coefficients and Spontaneous Curvatures ...... 68 4.8 Lyotropic Systems and Cell Fluidity ...... 69 Contents ix

4.9 Liquids with Parallel Surfaces and the Geometrical Origin of Forms 72 4.9.1 Caps and Saddles: Elliptic or Hyperbolic Surfaces ...... 73 4.9.2 Dupin Cyclides in Liquid Crystals ...... 74 4.10 Germs and Textures of Liquid Crystals: Their Biological Analogues 77 4.11 Topological Nature of Liquid Crystalline Textures ...... 81 4.11.1 Möbius Strips ...... 81 4.11.2 Pairs of Interlocking Rings ...... 82 4.12 Liquid Crystals and Mechanical Clock Movements ...... 84 References ...... 84

5 Biological Self-Organisation by Way of the Dynamics of Reactive Processes ...... 87 James Tabony 5.1 Self-Organisation by Dynamic Processes in Physical Systems...... 90 5.2 Self-Organisation in Colonies of Living Organisms ...... 92 5.3 Self-Organisation by Reaction and Diffusion: Stripes in a Test-Tube 93 5.4 Microtubule Self-Organisation ...... 97 References ...... 103

6 Dunes, the Collective Behaviour of Wind and Sand, or: Are Dunes Living Beings? ...... 107 Stéphane Douady and Pascal Hersen 6.1 Discovery ...... 107 6.2 The Wind Drives the Sand . . . Which Steals the Wind’s Force as It Flies ...... 107 6.3 The Minimal Dune ...... 108 6.4 The Wind Runs Over the Dune . . . and Pushes It Along ...... 109 6.5 Does the Wind Flow Make the Dune? ...... 109 6.6 Understanding the Barchan Shape ...... 111 6.7 The Paradox of Corridors . . . or the Problem of Dunes Among Themselves ...... 114 6.8 The Wind is Never Constant ...... 114 6.9 Dunes are Not Isolated ...... 115 6.10 The Grain of Sand, the Dune and the Corridor of Dunes . . .What About the Individual, the Flows and the Form? ...... 116 References ...... 118

7 Morphodynamics of Secretory Endomembranes ...... 119 François Képès 7.1 Some Preliminary Reminders ...... 119 7.2 Introduction ...... 120 7.2.1 Cell Membrane and Translocation ...... 120 7.2.2 Eukaryotic Secretory Pathway ...... 121 7.2.3 Other Eukaryotic Compartments ...... 123 x Contents

7.2.4 Cytoplasm, Cytoskeleton and Compartmentalisation ...... 123 7.3 Morphodynamics of Membranes ...... 123 7.3.1 Biological Membranes ...... 123 7.3.2 Segregation ...... 124 7.3.3 Fission ...... 126 7.3.4 Fusion ...... 131 7.4 Functional Models ...... 133 7.5 Conclusions ...... 136 7.5.1 Themes ...... 136 7.5.2 Evolutionary Perspectives ...... 136 7.5.3 Questions ...... 137 7.5.4 Prospects ...... 138 References ...... 138

8 From Epigenomic to Morphogenetic Emergence ...... 143 Caroline Smet-Nocca, Andràs Paldi, and Arndt Benecke 8.1 Genetic Inheritance, Regulation of Gene Expression, and Chromatin Dynamics ...... 145 8.1.1 Gene Transcription and the Regulation of Gene Expression 145 8.1.2 Genomic Structure and its Impact on Transcriptional Regulation ...... 146 8.2 Epigenetic Mechanisms, Epigenetic Inheritance and Cell Differentiation ...... 149 8.2.1 DNA Methylation: Epigenetic Marker of Transcriptional Repression ...... 149 8.2.2 Structural and Functional Organisation of Chromatin: Spatio-Temporal Regulation...... 152 8.3 The Link Between Epigenetic Information and the Regulation of Gene Expression ...... 158 8.3.1 The Link Between DNA Repair and Transcription ...... 158 8.3.2 CBP/p300, HATs Involved in Cell Growth, Differentiation and Development...... 160 8.3.3 Epigenetics and Oncogenesis ...... 161 8.4 Morphogenomics ...... 163 References ...... 166

9 Animal Morphogenesis ...... 167 Nadine Peyriéras 9.1 The Acquisition of Cell Diversity ...... 169 9.1.1 Heterogeneity of the Egg: What Is Determined from the Moment of Fertilisation? ...... 170 9.1.2 The Interaction Between Cells and Their Environment and the “Inside-Outside” Hypothesis ...... 171 Contents xi

9.2 The Anatomical Tradition of Embryology, Identification of Symmetry Breaking and Characterisation of Morphogenetic Fields ...... 171 9.2.1 Symmetry-Breaking in Early Embryogenesis ...... 172 9.2.2 Formation of Boundaries and Compartments During Organogenesis ...... 175 9.3 The “Bottom-Up” Approach of Developmental Biology ...... 176 9.3.1 Dynamics of Molecular and Genetic Interactions in the Formation of Patterns ...... 178 9.3.2 The Concept of Morphogen and Pattern Generation Through the Threshold Effect ...... 179 9.3.3 The Formation of Somites in Vertebrates: A Model of Coupled Oscillators ...... 181 9.4 The Reconstruction of Cell Morphodynamics and the Revival of the Anatomical Tradition of Embryology ...... 184 9.4.1 Cell Movements and Deformations in Morphogenesis . . . . . 184 9.4.2 Cell Adhesion and Biomechanical Constraints in the Embryo ...... 185 9.4.3 The Tensegrity Model ...... 185 References ...... 187

10 Phyllotaxis, or How Plants Do Maths When they Grow ...... 189 Stéphane Douady 10.1 Discovery ...... 189 10.2 Why? ...... 190 10.3 How? ...... 192 10.4 Van Iterson’s Tree . . . Pruned! ...... 194 10.5 Dynamics ...... 196 10.6 Conclusion ...... 197 References ...... 198

11 The Logic of Forms in the Light of Developmental Biology and Palaeontology ...... 199 Didier Marchand 11.1 Introduction ...... 199 11.2 Palaeontology and Time ...... 200 11.3 From the Cell to the Multicellular Organism: An Ever More Complex Game of “Lego” ...... 201 11.4 The Major Body Plans: In the Early Cambrian, Quite Everything Was Already in Place ...... 202 11.5 The Phylum of Vertebrates: A Fine Example of Peramorphosis . . . . . 204 11.6 The Anomalies of Development: An Opening Towards New Morphologies ...... 205 11.7 The Brain as the Last Space of Freedom ...... 207 xii Contents

11.8 Conclusion ...... 208 References ...... 209

12 Forms Emerging from Collective Motion ...... 211 Hugues Chaté and Guillaume Grégoire 12.1 Introduction ...... 211 12.2 Towards a Minimal Model ...... 213 12.2.1 The Ingredients ...... 213 12.2.2 Formalisation ...... 214 12.2.3 The Results of Vicsek et al...... 216 12.3 Forms in the Absence of Cohesion ...... 218 12.3.1 Moving in Self-Organised Groups ...... 218 12.3.2 Microscopic Trajectories and Forms ...... 219 12.4 When Cohesion Is Present: Droplets in Motion ...... 220 12.4.1 Phase Diagrams and Form of Droplets ...... 220 12.4.2 Cohesion Broken During the Onset of Motion ...... 221 12.5 Back to Nature ...... 222 References ...... 223

13 Systems of Cities and Levels of Organisation ...... 225 Denise Pumain 13.1 Three Levels of Observation of the Urban Fact ...... 226 13.1.1 Emergent Properties at the City Level ...... 226 13.1.2 The Structure of the System of Cities ...... 228 13.2 A Functional Interpretation of the Hierarchical Ordering ...... 231 13.2.1 Daily Life in the City ...... 232 13.2.2 The Functions of the System of Cities ...... 233 13.3 The Interactions that Construct the Levels ...... 235 13.3.1 The Constituent Interactions of City Forms ...... 237 13.3.2 The Constituent Interactions of Systems of Cities ...... 239 13.4 Complex Systems Models for Urban Morphogenesis ...... 242 13.4.1 Cities as Spatial Objects ...... 243 13.4.2 Cities and Fractal Objects ...... 244 13.4.3 From Support Space to Relational and Conforming Space . 245 References ...... 246

14 Levels of Organisation and Morphogenesis from the Perspective of D’Arcy Thompson ...... 251 Yves Bouligand 14.1 Games of Construction ...... 252 14.1.1 Chemical Syntheses and Biosyntheses ...... 252 14.1.2 Supramolecular Assemblies and their Lattices ...... 254 14.1.3 Molecular and Supramolecular Models ...... 256 14.2 Water Games ...... 256 Contents xiii

14.2.1 Hydrostatic Forms ...... 257 14.2.2 Hydrodynamic Figures...... 258 14.2.3 Morphological Adaptations to the Hydrodynamics of the Environment ...... 259 14.3 The Fragile Architectures of Diffusion ...... 260 14.3.1 Hydrostatic Diffusion ...... 260 14.3.2 Hydrodynamic Diffusion ...... 261 14.4 Stabilisation and Reorganisation of Forms ...... 262 14.5 The Problem of Strong Local Curvature and New Prospects ...... 263 14.6 Particular and General Morphogenetic Theories ...... 265 14.6.1 The Direct or Indirect Role of the Genome in Morphogenesis ...... 265 14.6.2 Symmetry Breaking and Differentiation ...... 267 14.6.3 New Prospects in Morphogenesis and the Concept of Viability ...... 270 References ...... 271

15 The Morphogenetic Models of René Thom ...... 273 Jean Petitot 15.1 General Content of the Model ...... 273 15.2 Morphodynamics and Structural Stability ...... 275 15.3 The Theory of Dynamical Systems ...... 276 15.4 The Theory of Singularities and “Elementary” Morphogenetic Models ...... 279 15.5 The Principles of Morphodynamic Models ...... 280 15.6 The Models of Morphogenesis ...... 281 References ...... 281

16 Morphogenesis, Structural Stability and Epigenetic Landscape ...... 283 Sara Franceschelli 16.1 The Correspondence ...... 283 16.2 Delbrück’s Model ...... 286 16.3 Structural Stability and Morphogenetic Field ...... 287 16.4 Epigenetic Landscape: A Mental Picture, a Metaphor ...of What? . 288 16.5 Interpretations ...... 292 References ...... 292

17 Morphological and Mutational Analysis: Tools for the Study of Morphogenesis ...... 295 Jean-Pierre Aubin and Annick Lesne 17.1 Objectives ...... 295 17.2 Motivations ...... 297 17.2.1 Problems of Co-Viability ...... 297 17.2.2 Biological Morphogenesis ...... 299 xiv Contents

17.2.3 Image Processing ...... 300 17.2.4 Shape Optimisation ...... 300 17.2.5 Dynamic Economics ...... 300 17.2.6 Front Propagation ...... 301 17.2.7 Visual Robotics ...... 301 17.2.8 Interval Analysis ...... 301 17.3 The Genesis of Morphological Analysis ...... 301 17.4 From Shape Optimisation to Set-Valued Analysis ...... 302 17.5 Velocities of Tubes as Mutations ...... 306 17.6 Mutational Analysis ...... 306 17.7 Morphological Equations ...... 308 17.8 Embryogenesis of the Zebrafish ...... 311 References ...... 312

18 Computer Morphogenesis ...... 315 Jean-Louis Giavitto and Antoine Spicher 18.1 Explaining Living Matter by Understanding Development ...... 315 18.1.1 The Animal-Machine ...... 315 18.1.2 From Self-Reproduction to Development ...... 317 18.1.3 Development as a Dynamical System ...... 318 18.1.4 What Formalism for Dynamical Systems with Dynamical Structure? ...... 321 18.2 Rewriting Systems ...... 323 18.2.1 Introduction ...... 323 18.2.2 Rewriting Systems and the Simulation of Dynamical Systems ...... 325 18.3 Multiset Rewriting and Chemical Modelling ...... 326 18.3.1 Some Examples of Application ...... 328 18.3.2 Paun˘ Systems and Compartmentalisation ...... 329 18.3.3 In Parenthesis: The Application to Parallel Programming . . 331 18.4 Lindenmayer Systems and the Growth of Linear Structures ...... 332 18.4.1 Growth of a Filamentous Structure ...... 332 18.4.2 Development of a Branching Structure ...... 334 18.5 Beyond Linear Structures: Calculating a Form in Order to Understand It ...... 335 18.5.1 Simulation and Explanation ...... 335 18.5.2 Giving Form to a Population of Autonomous Agents...... 336 References ...... 337

Index ...... 341 About the Authors

Jean-Pierre Aubin is emeritus professor at the University of Paris-Dauphine, researcher at the CREA and the LASTRE (Applied Controlled Tychastic Systems Laboratory), and a specialist in viability theory and its applications. [email protected]

Jean-Claude Bacri is professor at the University of Paris-Diderot. His research lies in the field of soft matter: instabilities and structures, flows in porous media, and the physical properties of ferrofluids, particularly their use in the biomedical domain. [email protected]

Arndt Benecke is an experimenter and theorist working on genomic plasticity. He is principal investigator of Systems Epigenomics Group at the Institut de Recherche Interdisciplinaire and the Institut des Hautes Études Scientifiques. [email protected]

Steffen Bohn is a CNRS researcher at the Complex Matter and Systems Laboratory (UMR 7057 CNRS–Paris-Diderot) of the University of Paris-Diderot. His work in experimental and theoretical physics is centred on plant growth and more generally on the formation of structures. [email protected]

Yves Bouligand directed one of the teams at the Centre de Cytologie Expérimentale of the CNRS in Ivry-sur-Seine. He is now emeritus director at the École Pratique des Hautes Études. He has researched into tissues and cells displaying liquid crys- talline phases, including chromosomes and membranes, and stabilised analogues of a composite nature, components of skeletal formations. [email protected]

Paul Bourgine founded the Complex Systems Institute of Paris Ile-de-France. He is director of the CREA at the École Polytechnique. [email protected]

Hugues Chaté is a physicist at CEA-Saclay. He specialises in collective behaviour in non-equilibrium systems. [email protected]

xv xvi About the Authors

Stéphane Douady is CNRS research director at the Complex Matter and Systems Laboratory (UMR 7057 CNRS–Paris-Diderot). His research is focused on dynamic systems, granular media, and morphogenesis, particularly in biology and geology. [email protected]

Florence Elias is a lecturer at the University of Paris 6. Her research is focused on the physical properties of complex fluids: morphologies of systems containing interacting particles, and the macroscopic properties of liquid foams in relation to their internal structure. fl[email protected]

Sara Franceschelli is an epistemologist and historian of science at Ecole Nationale Supérieure de Lyon. Her research is focused on the history of dynamic and complex systems, and on the figure of landscape in these domains. [email protected]

Jean-Louis Giavitto is a computer science researcher at the CNRS and director of the IBISC (Computer Science, Integrative Biology and Complex Systems) Labo- ratory at the University of Évry. His work centres on new computational models (especially those inspired by biological processes): the representation of time and space and the use of concepts of combinatorial topology in programming languages. [email protected]

Guillaume Grégoire is a lecturer at the University of Paris-Diderot. He is a researcher in the Complex Matter and Systems Laboratory (UMR 7057 CNRS– Paris-Diderot), where he uses statistical physics to study non-equilibrium physical systems. [email protected]

Pascal Hersen is a CNRS researcher in the Complex Matter and Systems Labora- tory (UMR 7057 CNRS–Paris-Diderot). His research interests include dune mor- phogenesis, the dynamics of signaling pathways of eukaryotic cells and animal locomotion. [email protected]

François Képès, CNRS research director, co-founder and scientific director of the Epigenomics Project of Genopole (Évry), and former professor of biology at the École Polytechnique, is a cell and systems biologist. [email protected]

Annick Lesne is a CNRS researcher at the Theoretical Physics of Condensed Matter Laboratory (UMR 7600 CNRS-Paris 6) and the Institut des Hautes Études Scien- tifiques. Her research speciality is the mathematical and physical modelling of the regulation mechanisms of living systems. [email protected] About the Authors xvii

Didier Marchand is a paleontologist at the Biogeosciences Laboratory (UMR 5561 CNRS-University of Burgundy). He specialises in the relationship between morphological evolution and embryogenesis and hence in the formation of bauplans. [email protected]

Andras Paldi is a research director at the École Pratique des Hautes Études and a researcher at Généthon. His main field of research is the epigenetic mechanisms regulating gene expression and epigenetic phenomena. [email protected]

Jean Petitot is a research director at the École des Hautes Études en Sciences Sociales and former director of the CREA (École Polytechnique). His research is focused on mathematical models in cognitive neuroscience. [email protected]

Nadine Peyriéras is a CNRS researcher at the DEPSN laboratory of the Institut Alfred Fessard in Gif-sur-Yvette. Her chief interest is the embryogenesis and devel- opment of the Zebrafish. [email protected]

Denise Pumain is a professor at the University of Paris I, member of the Insti- tut Universitaire de France, geographer, founder member of the Géographie-cités laboratory and director of the Cybergeo electronic journal, European Journal of Geography. [email protected]

Caroline Smet-Nocca is an assistant professor at the University of Lille 1. She has worked with Arndt Benecke at the Interdisciplinary Research Institute on the decou- pling of epigenetic signaling and transcriptional regulation in genetic diseases and myeloid leukaemia. Her research interests are focused on the regulation of protein structure and function by posttranslational modifications. [email protected]

Antoine Spicher is a computer science assistant professor at the University of Paris XII – Val de Marne and is a member of the LACL (Laboratory of Algorithmic, Complexity and Logic). His research focuses on the use of concepts of combina- torial topology in programming languages for the modeling and the simulation of dynamical systems. [email protected]

James Tabony is research director at the Commissariat à l’Énergie Atomique, Direction des Sciences du Vivant, Département Réponse et Dynamique Cellulaires, CEA Grenoble, where he is researching the problem of biological self-organisation. [email protected]