On Growth and Form Spatio-temporal Pattern Formation in Biology

, by Chaplain, M. A. J.; Singh, G. D.; McLachlan, J. C.

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ISBN: 9780471984511 | 0471984515
Cover: Hardcover
Copyright: 1/4/2000

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Spatio-temporal pattern formation is a major area of research within the subject of mathematical biology. The topic involves the use of mathematical modelling to analyse how patterns in biology are created and develop. For example, the growth, over time, of the intricate and beautiful patterns on certain sea-shells or the striped markings on a tiger can be modelled and their development predicted in terms of nonlinear mathematical processes. The current volume captures the breadth of recent research into various aspects of spatio-temporal pattern and form, such as development biology, reaction-diffusion systems and morphometrics. Brings the ideas of the classic On Growth and Form by D'Arcy Thompson, the founding classic of mathematical biology, fully up to date and looks to future developments in the subject. * Foreword provided by Professor John Tyler Bonner, Princeton University. * World class collection of internationally renowned contributors from both experimental and theoretical backgrounds Taking its inspiration from D'Arcy Thompson's classic and still influential volume On Growth and Form, this new volume presents a collection of 21 articles from the Plenary Speakers of the recent D'Arcy Thompson Conference, held at the University of Dundee, 20-24 September 1998. The topics covered include pattern formation in development biology, reaction-diffusion systems, intercellular systems and morphometrics, offering the reader a stimulating blend of theory and experiment. This book will be of particular interest to bio-mathematicians and development biologists. Paediatric clinicians, evolutionary biologists, orthodontists, anatomists, physiologists and many other members of the biology community will also benefit greatly from it.

Foreword

xvii

Series Preface

xix

Editors' Preface

xxi

Problems of Development: The Microcosm and the Macrocosm

(12)

Introduction: The Problem of Regional Specification Is Largely Solved

(1)

Morphogenetic Movements

(1)

The French Flag Problem

(1)

Regeneration

(1)

Size and Proportion

(3)

Stochastic Character of Cell Differentiation

(5)

References

(2)

Development of the Vertebrate Limb: A Model for Growth and Patterning

(18)

Introduction

(1)

Chick Wing Development

(1)

Growth and Shaping of the Limb Bud

(4)

Tissue Patterning

(6)

Anteroposterior patterning

(3)

Proximodistal patterning

(1)

Dorsoventral patterning

(2)

Coordination of Signalling and Responses

(1)

Other signalling interactions

(1)

Tissue Arrangements Including Musculature

(6)

References

(5)

Pattern Formation on Butterfly Wings

(16)

Introduction

(1)

The Diversity of Colour Patterns

(2)

The Development of Pattern Elements: Surgical Manipulation

(3)

Eyespots: Foci, Gradients and Gene Expression

(3)

The Development of Wing Patterns: Mechanisms and Models

(3)

Conclusion

(4)

References

(3)

Pattern Formation in Cancer

(28)

Introduction

(1)

Tumour Encapsulation

(9)

Formulation of the model

(1)

Connective tissue waves

(6)

Extension to model transcapsular spread

(1)

Macrophage Induction of Tumour Heterogeneity

(18)

Model development

(3)

Spatially independent solutions

(1)

Wave front solutions and spatial patterns

(5)

Numerical simulations in two dimensions

(1)

Summary of model predictions

(1)

References

(5)

Turing Structures of the Second Kind

(14)

Introduction

(1)

Pattern Formation in Reaction-Diffusion Systems

(3)

Slowing Down the Effective Diffusion of the Self-activator

(1)

Turing Patterns of the Second Kind

(1)

Size Regulation of Pattern Forming Processes

(1)

Pair-rule Patterns in Drosophila

(2)

Clocks and Patterns from the Same Mechanism

(2)

Conclusion

(1)

Numerical Treatment of 3D Pattern Formation

(4)

References

(2)

Pattern Formation Mechanisms in Skin and Hair: Some Experimental Tests

(22)

Introduction

(2)

Follicles Initiation and Development

(7)

Equidistant follicles

(1)

Increasing density of follicles

(1)

Spatial patterns in follicle location

(1)

Spatial patterns produced by an RD system

(4)

Experiments on Follicle Initiation

(4)

Skin stretching

(2)

Follicle density and follicle diameter

100

(1)

The sweat gland and the trio group

100

(1)

Patterns of mitotic activity

101

(1)

Fibre Formation

102

(3)

Concentric patterns of cell type

102

(1)

Non-concentric patterns

102

(3)

Experiments on Fibre Formation

105

(3)

The relationship between pattern and follicle bulb size

105

(2)

Change of pattern within a fibre

107

(1)

Conclusion

108

(3)

References

109

(2)

Some Mathematical Models for Biological Pattern Formation

111

(18)

Introduction

111

(1)

Simple Models

112

(4)

Chemical prepattern models

112

(2)

Cell movement models

114

(1)

Applications

115

(1)

Coupled Models

116

(4)

Feather germ formation

116

(1)

Cell aggregation in slime mould

117

(3)

The Role of Domain Growth

120

(3)

Alligator tooth primordia

120

(2)

Pigmentation patterning in fishes

122

(1)

Discussion and Future Directions

123

(6)

References

125

(4)

On Pattern and Growth

129

(20)

Introduction

129

(1)

The Generation of Organizing Regions by Local Self-enhancement and Long-Range Inhibition

130

(5)

Regular and Irregular Periodic Patterns

135

(1)

The Wavelength Problem: Stabilization of a Monotonic Gradient by a Feedback on the Source Density

135

(2)

Space-dependent Activation of Genes by a Morphogen

137

(3)

Somite Formation: Sequential Conversion of a Periodic Pattern in Time into a Periodic Pattern in Space

140

(2)

Patterns on Shells of Tropical Molluscs

142

(2)

Formation of crossings by an additional diffusible inhibitor

143

(1)

Arrangement of Leaves and Staggered Dots on Shells: Two Corresponding Patterns

144

(2)

Conclusion

146

(3)

References

146

(3)

Diversity in Pattern and Form of Biological Systems and Evolution: A Theoretical Approach

149

(8)

Introduction

149

(1)

Possible Factors in Determining Pattern and Form

150

(2)

Gene activity

150

(1)

Physico-chemical aspect

150

(1)

Ecological aspect

151

(1)

Biological function

151

(1)

Pioneering Work

152

(1)

Shell shape

152

(1)

Plant evolution

152

(1)

Animal skin and insect wing

153

(1)

Summary and Conclusion

153

(4)

References

154

(3)

Developmental Morphologies Not Directly Specified by the Genome of the Individual

157

(16)

Introduction

157

(2)

Physical and Mathematical Constraints

159

(1)

Morphologies Arising from Non-genetic Mechanisms of Inheritance

160

(1)

Environmental Specification

161

(1)

Self-establishing Interactive Mechanisms

162

(2)

Parental Specification

164

(1)

Tissue Self-assembly

164

(1)

Tissue Interaction

165

(1)

Specification by Use

166

(1)

Conclusions

167

(6)

References

169

(4)

The Role of Chemotactic Cell Movement in Dictyostelium Morphogenesis

173

(28)

Introduction

173

(2)

Cell Type Differentiation

175

(1)

Aggregation

176

(4)

Formation of Aggregation Streams

180

(1)

Mounds

180

(2)

Cell Movement in Slugs

182

(3)

Is cAMP the Signal That Controls Cell Movement in the Slug?

185

(1)

Other Possible Mechanisms Controlling Cell Movement in Slugs

185

(1)

How Do the Cells in the Multicellular Stages of Development Get Their Traction?

186

(1)

The Mechanism of Cell Sorting

187

(1)

Culmination

188

(1)

Modelling Morphogenesis

188

(6)

Aggregation

189

(2)

Mound formation

191

(1)

Cell sorting and slug formation

191

(3)

Slug migration

194

(1)

Conclusion and Outlook

194

(7)

References

195

(6)

Angiogenesis: Experimental Data Relevant to Theoretical Analysis

201

(24)

Introduction

201

(1)

Vascular and Perivascular Cells Involved in Angiogenesis

202

(2)

Phenotypic Heterogeneity and Lineage Relationships Amongst Vascular Cells

204

(2)

Angiogenesis: A Morphogenetic process

206

(3)

In Vitro Models to Study Angiogenesis: Interactions between Cytokines and Extracellular Matrix Macromolecules

209

(9)

Conclusions

218

(7)

References

220

(5)

Modelling the Growth and Form of Capillary Networks

225

(26)

Introduction

225

(1)

Tumour-Induced Angiogenesis

226

(2)

Mathematical Modelling of Tumour-Induced Angiogenesis

228

(1)

The Continuous Mathematical Model

229

(4)

Model Results

233

(3)

The Discrete Mathematical Model

236

(5)

Branching and anastomosis

238

(1)

Cell proliferation

239

(1)

Simulation process for the discrete model

239

(1)

Discrete model simulation results

240

(1)

Three-Dimensional Simulations

241

(3)

3D Simulation Results

243

(1)

Discussion and Conclusions

244

(7)

References

246

(5)

On the Mechanochemical Theory of Biological Pattern Formation with Applications to Wound Healing and Angiogenesis

251

(36)

Introduction and Biological Background

251

(4)

Theories of morphogenesis

252

(3)

Mechanochemical Theory Framework

255

(6)

Cell density conservation

256

(2)

Conservation of matrix density

258

(1)

Mechanical interaction of cell and matrix

258

(3)

Model analysis

261

(1)

Wound Healing

261

(9)

Biological background and motivation

262

(2)

Mechanochemical modeling of wound healing

264

(6)

Vascular Network Formation: Angiogenesis

270

(9)

Biological background and motivation

270

(1)

Cell-extracellular matrix interactions for vasculogenesis

271

(1)

Mechanical theory of in vitro vascular network formation

271

(1)

Mathematical model

272

(3)

Parameter values

275

(1)

Results from the model analysis

276

(2)

Results from the model mechanism

278

(1)

Discussion

279

(8)

References

281

(6)

Statistics and Dynamics of Cellular Shape Changes

287

(22)

Introduction

287

(1)

Examples of Cellular Shape Changes

288

(5)

Tip growth of hyphae

288

(1)

Deformations of red blood cells

289

(1)

Cleavage of a sand dollar egg

289

(1)

Amoeboid motion

290

(3)

Descriptors of Form in 2D

293

(11)

Geometric shape factors

294

(1)

Invariant 2D moments

295

(3)

Fourier and Kahunen--Loeve expansions

298

(2)

Angular-temporal autocorrelations

300

(3)

Protrusion-retraction dynamics

303

(1)

Discussion: Current and Future Tasks

304

(5)

References

305

(4)

Shape Asymmetry and Developmental Stability

309

(16)

Introduction

309

(1)

Nature of Asymmetries

310

(1)

Nature of Characters

311

(1)

Developmental Stability and Canalisation

312

(2)

Shape Asymmetry

314

(6)

Towards the Form Asymmetry

320

(5)

References

322

(3)

Invariance and Morphometrics: A Critical Appraisal of Statistical Techniques for Landmark Data

325

(12)

Introduction

325

(1)

Limiting Factors: Three Major Classes

326

(1)

Comparison of Related Forms

327

(6)

Superimposition approaches

328

(1)

Transformation grid or deformation approach

329

(2)

Orbits of equivalent forms

331

(1)

Euclidean distance matrix analysis (EDMA)

332

(1)

Non-Invariant Descriptors and Scientific Consequences

333

(2)

Conclusions and Future Directions

335

(2)

References

335

(2)

Statistical Shape Analysis and its Applications

337

(20)

Introduction

337

(1)

Examples

338

(1)

Bookstein Shape Coordinates

338

(3)

Kendall's Shape Space and Procrustes Coordinates

341

(4)

Shape Change and Deformations

345

(2)

Models and Concentrated Data

347

(2)

Different Approaches

349

(3)

Future Perspectives

352

(5)

References

353

(4)

Sphenothemoidal Growth, Malgrowth, and Midfacial Profile

357

(16)

Introduction

357

(2)

Computerized Reconstruction of the Murine Cranial Base

359

(3)

Thompsonian Grid Transformation Analysis Using Finite Element Methods

362

(1)

Localizing Anatomical Form Change in the Cranial Base of Normal and Br mice

363

(2)

Regionalization of Cellular Growth Activity in the Br Cranial Base

365

(2)

Discussion

367

(6)

References

370

(3)

Ontogeny and Phylogeny: Some Morphometric Approaches to Skeletal Growth and Evolution

373

(22)

Introduction

373

(2)

What Can We Learn of Form Variations Using the Morphometric Toolkit?

375

(3)

Motivation

375

(3)

Localisation and Characterisation of Form Differences

378

(1)

Shape Spaces for Registered Landmarks

378

(2)

Shape Space for Interlandmark Distances

380

(1)

Deformations

381

(1)

Morphometrics: Models, Assumptions and Biology

382

(1)

Example Studies

382

(8)

Growth of the face in Cercocebus torquatus

383

(4)

Comparative growth; Cercocebus torquatus vs Cebus apella

387

(3)

Concluding Remarks

390

(5)

References

391

(4)

D'Arcy Thompson and the Problem of Biological Form

395

(8)

Introduction

395

(1)

Historical Narratives and Scientific Explanations

395

(3)

A Generative Biology: Morphogenetic Fields

398

(1)

Genetic Networks, Morphogenesis and Evolution

399

(4)

References

401

(2)

Index

403

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On Growth and Form Spatio-temporal Pattern Formation in Biology

Summary

Author Biography

Table of Contents

Supplemental Materials