Cellular Automaton Modeling of Biological Pattern Formation,9780817642815

Cellular Automaton Modeling of Biological Pattern Formation

by ; ;
ISBN13: 9780817642815
ISBN10: 0817642811
Format: Hardcover
Pub. Date: 2004-11-01
Publisher(s): Birkhauser
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Summary

This book focuses on a challenging application field of cellular automata: pattern formation in biological systems, such as the growth of microorganisms, dynamics of cellular tissue and tumors, and formation of pigment cell patterns. These phenomena, resulting from complex cellular interactions, cannot be deduced solely from experimental analysis, but can be more easily examined using mathematical models, in particular, cellular automaton models.While there are various books treating cellular automaton modeling, this interdisciplinary work is the first one covering biological applications. The book is divided into three parts: Part I deals with general principles, theories, and models of pattern formation; Part II examines cellular automaton modeling; and Part III explains various applications. The models and analytic techniques described may be extended to other exciting applications in biology, medicine, and immunology.Key topics and features:* Provides an introduction and historical account of the principles of biological pattern formation (morphogenesis)* Gives an overview of mathematical modeling approaches to morphogenesis, and an introduction to cellular automata and analytic techniques* A supplementary web-based Java applet---"Cellular Automaton Simulator"---enables interactive simulation of various cellular automaton applications described in the book; available on the internet at www.biomodeling.info* Self-contained presentation is accessible to a broad audience; only basic calculus and linear algebra are required* Careful balance of theory, models, and applications useful to both experimentalists and theoreticians* Includes suggestions for further research topicsThe book is aimed at researchers, practitioners, and students in applied mathematics, mathematical biology, computational physics, bioengineering, and computer science interested in a cellular automaton approach to biological modeling. The book's accessible presentation and interdisciplinary approach make it suitable for graduate and advanced undergraduate courses and seminars in mathematical biology, biomodeling, and biocomputing.

Table of Contents

Foreword vii
Philip K. Maini
List of Figures
xv
List of Notation
xxi
Part I General Principles, Theories, and Models of Pattern Formation
Introduction and Outline
3(10)
On the Origin of Patterns
13(32)
Space, Time, and the Mathematics of Pattern Formation: A Brief Historical Excursion
13(18)
Greek Antiquity: Static and Dynamic World Conceptions
13(6)
The Prescientific Age
19(1)
The Deterministic World of Classical Mechanics
19(5)
Discovering the History of Time
24(3)
From Equilibrium to Self-Organizing Systems
27(4)
Principles of Biological Pattern Formation
31(14)
Preformation and Epigenesis
31(3)
Ontogeny and Phylogeny
34(1)
On Organizers and Embryonic Regulation
35(2)
Molecular and Genetic Analysis
37(1)
Self-Assembly
38(1)
Physical Analogues
39(2)
On Gradients and Chemical Morphogens
41(1)
Self-Organization and Morphogenesis
42(1)
Cell-Cell Interactions
42(3)
Mathematical Modeling of Biological Pattern Formation
45(14)
The Art of Modeling
45(1)
How to Choose the Appropriate Model
46(13)
Model Perspectives
51(2)
From Individual Behavior to Population Dynamics
53(6)
Part II Cellular Automaton Modeling
Cellular Automata
59(46)
Biological Roots
60(3)
Cellular Automaton Models of Pattern Formation in Interacting Cell Systems
63(4)
Definition of Deterministic, Probabilistic and Lattice-Gas Cellular Automata
67(12)
Lattice Geometry and Boundary Conditions
67(3)
Neighborhood of Interaction
70(1)
States
71(2)
System Dynamics
73(6)
Analysis and Characterization
79(18)
Chapman-Kolmogorov Equation
81(2)
Cellular Automaton Mean-Field Equations
83(7)
Linear Stability Analysis
90(7)
From Cellular Automata to Partial Differential Equations
97(3)
Further Research Projects
100(5)
Part III Applications
Random Movement
105(24)
Brownian Motion
106(1)
Discrete Random Walk and Diffusion
107(4)
Random Movement in Probabilistic Cellular Automaton Models
111(4)
Random Walk Rule According to Toffoli and Margolus
111(3)
Random Walk in Probabilistic Cellular Automata with Asynchronous Updating
114(1)
Random Movement in Lattice-Gas Cellular Automation Models
115(11)
Stability Analysis for the One-Dimensional Random Walk Model with One Rest Channel
119(3)
Checkerboard Artefact
122(4)
Growth by Diffusion-Limited Aggregation
126(2)
Further Research Projects
128(1)
Growth Processes
129(14)
Classical Growth Models
129(2)
Growth Processes in Cellular Automata
131(5)
Growth Processes in Lattice-Gas Cellular Automata
136(6)
Further Research Projects
142(1)
Adhesive Cell Interaction
143(18)
Cellular Patterns Originating from Adhesive Interaction
144(2)
Adhesive Lattice-Gas Cellular Automaton
146(2)
Analysis of Aggregation Dynamics in the Single-Cell-Type Adhesion Model
148(7)
Linear Stability Analysis
149(4)
Spatial Pattern Formation
153(2)
Phase Separation and Engulfment in a Two-Cell-Type Adhesion Model
155(4)
Further Research Projects
159(2)
Alignment and Cellular Swarming
161(12)
Orientation-Induced Pattern Formation
161(3)
A Swarm Lattice-Gas Cellular Automation
164(8)
Linear Stability Analysis
166(2)
The Swarming Instability
168(4)
Further Research Projects
172(1)
Pigment Cell Pattern Formation
173(12)
Principles of Pigment Cell Pattern Formation
173(2)
Automaton Model with Adhesive/Orientational Interaction
175(3)
Simulation of Stripe Pattern Formation
178(2)
Development and Evolutionary Change
180(2)
Further Research Projects
182(3)
Tissue and Tumor Development
185(22)
Modeling Contact Inhibition of Movement in Lattice-Gas Cellular Automata
186(1)
Tissue Growth
187(4)
A Cellular Automaton Model for Chemotaxis
191(4)
Avascular Tumor Growth
195(11)
A Hybrid Lattice-Gas Cellular Automaton Model for Tumor Growth
197(5)
Simulations
202(4)
Further Research Projects
206(1)
Turing Patterns and Excitable Media
207(50)
Turing Patterns
207(36)
Turing Pattern Formation in Macroscopic Reaction-Diffusion Systems
208(3)
A Lattice-Gas Cellular Automaton Model for Activator-Inhibitor Interaction
211(8)
Pattern Formation in One Dimension: Analysis and Simulations
219(10)
Pattern Formation in Two Dimensions
229(9)
Derivation and Analysis of a Macroscopic Description of the Lattice-Gas Cellular Automaton
238(5)
Excitable Media
243(12)
Introduction
243(3)
Definition of the Automaton Rules
246(2)
Lattice-Boltzmann Equation and Its Uniform Steady States
248(3)
Stability Analysis of the Lattice-Boltzmann Equation
251(4)
Further Research Projects
255(2)
Discussion and Outlook
257(22)
Cellular Automaton Characterization
258(3)
Cell-Based Instabilities and Cellular Self-Organization
258(1)
Discreteness and Finite Size Effects
259(2)
Cellular Automata as a Modeling Tool
261(1)
Diffusive Behavior and Growth Patterns
262(1)
Adhesive Interactions and Cell Sorting
263(5)
Collective Motion and Aggregation
268(4)
Pigment Pattern Formation
272(1)
Tumor Growth
272(1)
Turing Patterns and Excitable Media
273(1)
Outlook
274(5)
Further Applications
275(1)
Further Analysis
276(3)
Appendices
279(14)
A. Growth Processes: A Mean-Field Equation
279(2)
B. Turing Patterns
281(4)
B.1 Complete Interaction Rule
281(1)
B.2 Linear Stability Analysis
282(3)
C. Excitable Media: Complete Interaction Rule
285(2)
D. Isotropy, Lattices, and Tensors
287(6)
D.1 Isotropic Media and Lattices
287(2)
D.2 Introduction to Tensors
289(1)
D.3 LGCA Dynamics and the Influence of the Lattice
290(3)
References 293(26)
Index 319

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