ISBN: 3540418881
TITLE: Les Houches, Volume 14
AUTHOR: Fleury et al. (Eds.)
TOC:

Preface V
INTRODUCTION
Patterns with Open Branches or Closed Networks: Growth in Scalar or Tensorial Fields
by Y. Couder
1. Growth in a diffusive scalar field 2
1.1 The basic Phenomenon 2
1.2 The length scales of the patterns 4
1.3 The branching process 5
1.4 Speculations on isotropic or tip dominated growth in plants 11
2. Growth in a tensorial field 13
2.1 The formation of a network of fractures in a 2D stressed material 13
2.2 The network of the plant leaves venation 16
2.3 How can the venation patterns be similar to the crack patterns? 17
2.4 Discussion 20
3. Conclusion 20
PLANTS
CHAPTER I
Branching in Plants
by F. Hall
Introduction 23
1. Growth and branching 24
2. Why are there meristems in plants? 25
3. Branching and architecture 28
4. Unbranched trees 28
5. Apical vs. lateral branching 28
6. Exogenous vs endogenous branching 29
7. Continuous vs. rhythmic branching 30
8. Immediate vs. delayed branching 32
9. Homogeneous vs. differentiated branching 33
10. Spontaneous vs. traumatic branching 34
11. The architectural models 35
12. Unitarian trees vs. colonies 36
13. Crown-shyness 38
14. Branching in trees and corals 38
CHAPTER II
Inside the Buds: The Meristems
by P. Laufs and J. Traas
1. Introduction 41
2. The internode: The basic unit of plant architecture 42
3. Meristem identity and branching patterns 44
3.1 Modified meristem identity can affect branching patterns 44
3.2 Regulation of meristem identity 46
4. The shoot apical meristem -SAM-: A major actor in the establishment of architecture 47
4.1 Organization of the SAM: Cells and domains 47
4.2 Distribution of meristem functions between the zones 48
4.3 Self-organization of the meristem 49
4.4 The meristem as a functional unit 50
4.5 Genetic regulation of meristem development and molecular markers 51
4.6 Forming a primordium, what makes a meristem bulge? 52
4.7 Conclusion 53
5. Mechanisms and regulation of branch formation 53
5.1 Hypothetical mechanisms of branch formation 53
5.2 Some examples of branching mechanisms 55
5.3 Conclusions 61
6. Regulation of meristem outgrowth 61
7. Branching in leaves 62
7.1 Different leaf morphologies 62
7.2 The compound tomato leaf 62
8. Final remarks 66
CONTRIBUTED PAPER 1
Two Symmetries Linking Biological and Physical Branching Morphogenesis
by V. Fleury
1. Introduction 73
2. Dendritic growth, botany and in-out symmetry 74
2.1 General principles of vegetal growth 74
2.2 A possible relationship between vegetal and crystal morphogenesis 75
2.3 A numerical simulation showing the growth patterns 77
3. Viscous fingers, organ function and time reversal 83
3.1 Reversibility of the dendritic growth process 83
3.2 Transposition to organ morphogenesis and function 83
CHAPTER III
Establishing a Growth Axis in Fucoid Algae
by D.L. Kropf, S.R. Bisgrove and W.E. Hable
1. Embryonic morphogenesis 87
2. Axis selection 89
2.1 Sperm entry 89
2.2 Adhesion and vector perception 90
3. Axis amplification 93
4. Transmembrane domains and morphogenesis 95
CONTRIBUTED PAPER 2
Shape Stability during Osmotic Growth
by M. Lonetti
1. Introduction 99
2. Osmotic growth 100
2.1 Osmosis 100
2.2 Osmotic growth 101
3. Stability during osmotic growth 102
3.1 Formulation of the problem 102
3.2 The planar stationary solution 103
3.3 Linear stability analysis 104
4. Conclusion 105
CONTRIBUTED PAPER 3
On Transcellular Ionic Currents
by M. Lonetti and E. Dubois-Violette
1. Introduction 107
2. The theoretical approach 108
3. Ionic currents resulting from Turing instability 110
4. Ionic currents by self-organization of membrane proteins 111
5. Ionic currents by negative differential conductance 115
6. Conclusion 117
RIVERS
CHAPTER IV
Branched Patterns in Geology: Rivers and Other Systems
by P. Meakin, T. Sun and T. Jssang
1. Introduction 119
2. Quantitative analysis of branched patterns 122
2.1 Stream order and Horton/Strahler ratios 123
2.2 Crossovers 126
3. The diffusion-limited aggregation model 131
3.1 Examples of DLA-like patterns 136
4. Branched rivers 144
4.1 Optimization models 148
5. Discussion 156
NEURONS
CHAPTER V
Neuronal Arborization
by J.-P. Ternaux
1. Introduction 161
1.1 Historical orientation 163
2. Biological events involved in the growth of neuronal arborizations 165
2.1 Neuronal morphogenesis 165
2.2 Cytoskeleton and neuronal development 166
2.3 Transport of materials in the neuron 169
2.4 The growth cone 170
2.5 Formation of dendritic trees 180
2.6 Mechanisms of neurite initiation and branching. Biophysical considerations 182
3. Morphological properties of neuronal cells and neuronal information processing 193
CONTRIBUTED PAPER 4
Chemical Waves and Dendrites Navigation during Self-Wiring of Neural Nets
by R. Segev and E. Ben-Jacob
1. Introduction. 203
2. Neurite as amoeba with a tail 204
3. A need for additional mechanism 205
4. The excitable media mechanism 205
5. Conclusions 208
BRANCHING ORGANS
CHAPTER VI
The Mouse Embryonic Lung: A Biological Example of Branching Morphogenesis
by S. Bellusci, A. Mailleux, D. Ndiaye and J.-P. Thiery
1. Introduction 211
2. Embryonic lung development 211
3. Bud formation is a multistep process 213
4. Interactions between epithelial and mesenchymal compartments are essential for the branching process 213
5. Several classes of genes are expressed in the embryonic lung 214
6. Bone morphogenetic protein 4 inhibits proliferation of the epithelial compartment 215
7. Sonic hedgehog induces mesenchymal cell proliferation 216
8. Fibroblast growth factor 10 is associated with directional growth of the epithelial buds 217
9. Two vertebrate homologs of the drosophila gene sprouty are expressed in the developing lung 219
10. Toward an integrated model of budding 220
CHAPTER VII
Branched Structures, Acinus Morphology and Optimal Design of Mammalian Lungs
by B. Sapoval, M. Filoche and E.R. Weibel
1. Introduction 225
2. Structure and geometry of pulmonary acinus 229
3. Physical parameters determining the acinus efficiency 230
4. A better geometrical model: The "Hilbert" acinus 234
5. Smaller is better: An optimized acinus 236
6. Comparison with anatomical data 238
7. Conclusions 240
CONTRIBUTED PAPER 5
Quantitative Studies of Branching Morphogenesis in the Developing Kidney
by I.S. Harper, L.A. Cullen and J.F. Bertram
1. Introduction 243
1.1 Epithelial - mesenchymal interaction 243
1.2 Pattern of ureteric branching morphogenesis in humans 244
1.3 In vitro models of branching morphogenesis 245
2. A quantitative approach to 3D branching 245
3. Comments on the methodology 246
4. Concluding remarks 248
CONTRIBUTED PAPER 6
Morphogenic Responses of Mammary Epithelial Cells Grown in Biological Semi-Solid Substrates
by V. Fafeur, A. Delannoy-Courdent, J.C. Bout and B. Vandenbunder
1. Introduction 251
2. Experiments and methods 252
3. Results 254
4. Summary 255
VESSELS
CHAPTER VIII
Vascular Development: Design Principles and Morphometric Analysis of a Branched Vascular Tree
by F. le Noble, W. Hacking, D. Slaaf and H. Struijker-Boudier
1. General introduction 257
2. The circulation 258
3. Formation of the vascular tree 260
4. Growth factors 263
4.1 Chemical mediators 264
4.2 Mechanical mediators 265
5. Hemodynamics, metabolic demand and vascular network adaptation 266
5.1 Flow 267
5.2 Pressure 268
5.3 Metabolic demand 269
6. Analysis of vascular structure 272
7. Conclusion 277
CHAPTER IX
Mechanics of the Large Artery Vascular Wall
by B. Levy and A. Tedgui
1. Introduction 281
2. Parameters in vessel wall mechanics 281
2.1 Forces and stresses 281
2.2 Compliance 283
3. Determination of mechanical properties of blood vessels 284
3.1 In vitro measurements 284
3.2 In vivo measurements 287
CONTRIBUTED PAPER 7
A Link Between Dendritic Growth and Remodeling of Blood Vessels
by V. Fleury and L. Schwartz
1. Introduction 293
2. Description of the model 294
3. 2D numerical simulation 296
4. A model of 3D growth, and its numerical simulation 297
5. Comment on existing work 300
6. Reasonable modifications of the model 301
BACTERIA
CHAPTER X
Adaptive Branching During Colonial Development of Lubricating Bacteria
by I. Golding, I. Cohen, I.G. Ron and E. Ben-Jacob
1. Introduction 305
2. Basic branching patterns 308
2.1 Observations and biological background 308
2.2 Experimental observations: Branching growth of bacterial colonies 312
2.3 The communicating walkers model: A hybrid model 318
2.4 The lubricating bacteria model 320
2.5 The non-linear diffusion model 323
3. Chiral branching patterns 324
3.1 Observations 324
3.2 The communicating spinors model 326
4. Chemotaxis and chemotactic signaling 331
4.1 Biological background - chemotaxis in swimming bacteria 331
4.2 Modeling the effect of chemotaxis on branching growth 334
4.3 Modeling the effect of chemotaxis on chiral branching 336
4.4 Weak chirality in P. dendritiformis 339
5. Branching patterns of swarming bacteria 342
5.1 Observation of bacterial vortices 342
5.2 Modeling the collective migration 344
5.3 Rotational chemotaxis and vortex formation 345
5.4 Modeling the cooperative organization of colonies 345
6. Sector formation in branching colonies 347
6.1 Observations 347
7. The effect of antibiotics on bacterial branching growth 349
8. Conclusions 354
CONTRIBUTED PAPER 8
Pattern Formation Modeling of Bacterial Colonies
by I.R. Cantalapiedra, A.M. Lacasta, C.E. Auguet, A. Pearanda and L. Ramrez-Piscina
1. Introduction 359
2. Description of the model 360
3. Numerical results 361
CRYSTALS
CHAPTER XI
Dendritic Growth
by A. Karma
1. Introduction and outline 365
2. Basic physics 369
2.1 Surface tension 370
2.2 Diffusion 372
2.3 Noise 374
3. Morphogenesis 375
3.1 Planar Growth 375
3.2 Instability 376
4. Needle dynamics 377
4.1 Tip growth conditions 379
4.2 Applications 381
4.3 Extension to three dimensions 384
5. Branching 388
5.1 Sidebranching 388
5.2 Tip splitting 392
6. Morphological classification 392
6.1 Doublons and multiplets 393
6.2 Compact and fractal structures 394
7. Summary and future prospects 396
CONTRIBUTED PAPER 9
Sidebranching in Solutal Dendritic Growth
by R. Gonzlez-Cinca, L. Ramrez-Piscina, J. Casademunt and A. Hernndez-Machado
1. Introduction 403
2. Sidebranching in solutal solidification 404
3. Sidebranching characteristics 406
4. Conclusions 406
CONTRIBUTED PAPER 10
Experimental Study of Sidebranching in Directional Solidification
by M. Georgelin and A. Pocheau
1. Introduction 409
2. Secondary cell instabilities 409
3. Sidebranching 410
3.1 Critical curve 410
3.2 Noise-amplification theory 411
3.3 Questioning theory 413
4 Conclusion 414
FLUIDS
CHAPTER XII
Branching during Dewetting and Wetting
by C. Misbah
1. Introduction 417
2. Definition of the contact angle and spreading pressure 418
3. What determines wetting properties? 419
3.1 Coexistence film/film 420
4. Experimental facts 421
5. Mapping of front dewetting dynamics onto crystal growth 422
5.1 The Stokes equation 422
5.2 The lubrication approximation 423
5.3 Mass conservation 425
5.4 A constitutive law 426
6. Observed patterns 427
7. The stable enveloppe of a wetting or dewetting front moves as (t)^1/2 428
8. Branching of a front 430
9. Discussion 430
CONTRIBUTED PAPER 11
Viscous Fingering in a Gel
by A. Lindner, P. Coussot and D. Bonn
1. Introduction 433
2. Experiment 434
3. Discussion and conclusion 437
CONTRIBUTED PAPER 12
Branching Transition in Viscous Fingering with a Liquid Crystal
by R. Folch, J. Casademunt and A. Hernndez-Machado
1. Introduction 439
2. Model 440
3. Results 441
MATHEMATICS
CONTRIBUTED PAPER 13
Mathematical Meristems: The Singularities of Laplacian Growth
by M.A. Peterson
1. Introduction 445
2. Singular model 446
3. Mathematical meristems 449
Glossary 451
List of Participants 463
Color Plates 467
END
