Cellular Automaton Modeling of Biological Pattern Formation

This text explores the use of cellular automata in modeling pattern formation in biological systems. It describes several mathematical modeling approaches utilizing automata that can be used to analyze the dynamics of interacting cell systems and demonstrates how these models are applied beyond mere simulation. New in this edition are chapters covering cell migration, tissue development, and cancer dynamics, as well as updated references and new research topic suggestions that reflect the rapid development of the field. ? The book begins with a historical sketch of the mathematical concepts of static and dynamic space-time, showing how they have influenced the understanding of pattern formation, followed by a brief introduction to pattern-forming principles in biology. Mathematical modeling concepts for analyzing pattern formation are considered next, including PDEs, coupled-map lattices, many particle systems, and cellular automata, with the latter being considered in further detail in a subsequent chapter. Cellular automaton models for different types of cellular processes and interactions are discussed in the chapters that follow, including random movement, cell migration, adhesive cell interaction, alignment and cellular swarming, growth processes, pigment cell pattern formation, tissue development, tumor growth and invasion, and Turing-type patterns and excitable media. In the final chapter, the authors critically discuss possibilities and limitations of the automaton approach in modeling various cell biological applications, along with future directions. Suggestions for research projects are provided throughout the book to encourage additional engagement with the material. Additionally, readers can use the accompanying website to perform their own simulations on some of the models covered in the text. ? With its accessible presentation and interdisciplinary approach, is suitable for graduate and advanced undergraduate students in mathematical biology, biological modeling, and biological computing. It will also be a valuable resource for researchers and practitioners in applied mathematics, mathematical biology, computational physics, bioengineering, and computer science. PRAISE FOR THE FIRST EDITION ? " The book is a good starting point for scientists and students [who] would like to move into the field of studying effects of spatial pattern formation in biology. The introductory chapters are fun reading.... The introduction to the lattice-gas method is thorough and sound, and the array of applications of the method to systems of biological pattern formation is impressive and inspiring. "- Mathematical Biosciences ? " The effort the authors have invested in mathematically describing the CA and its interactions will certainly be very welcome to math students. ...The book remains an ideal guide for someone with a mathematical or physical background to start exploring biological modelling. Importantly, it will also serve as an excellent guide for experienced modellers to innovate and improve their methodologies for analysing simulation results. " - Mathematical Reviews ?