Cellular Automaton Modeling of Biological Pattern Formation

1. Front Matter

   Pages i-xxv

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2. General Principles, Theories, and Models of Pattern Formation

   1. Front Matter

      Pages 1-1

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   2. Introduction and Outline

      Pages 3-11

   3. On the Origin of Patterns

      Pages 13-43

   4. Mathematical Modeling of Biological Pattern Formation

      Pages 45-56

3. Cellular Automaton Modeling

   1. Front Matter

      Pages 57-57

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   2. Cellular Automata

      Pages 59-101

4. Applications

   1. Front Matter

      Pages 103-103

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   2. Random Movement

      Pages 105-128

   3. Growth Processes

      Pages 129-142

   4. Adhesive Cell Interaction

      Pages 143-159

   5. Alignment and Cellular Swarming

      Pages 161-172

   6. Pigment Cell Pattern Formation

      Pages 173-183

   7. Tissue and Tumor Development

      Pages 185-206

   8. Turing Patterns and Excitable Media

      Pages 207-256

   9. Discussion and Outlook

      Pages 257-278

5. Back Matter

   Pages 279-331

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The recent dramatic advances inbiotechnology have led to an explosion of data in the life sciences at the molecular level as well as more detailed observation and ch- acterization at the cellular and tissue levels. Itis now absolutely clear that one needs a theoretical framework inwhich to place this data to gain from it as much information as possible. Mathematical and computational modelling approaches are the obvious waytodothis. Heeding lessons from the physical sciences, one might expect that all areas in the life sciences would be actively pursuing quantitative methods to c- solidate the vast bodies of data that exist and to integrate rapidly accumulating new information. Remarkably, with a few notable exceptions, quite the contrary situation exists. However, things are now beginning to change and there is the sense that we are at the beginning of an exciting new era of research inwhich the novel problems posed by biologists will challenge the mathematicians and computer scientists, who, in turn, will use their tools to inform the experimentalists, who will verify model predictions. Only through such a tight interaction among disciplines will we have the opportunity to solve many of the major problems in the life sciences. One such problem, central to developmental biology, is the understanding of how various processes interact to produce spatio-temporal patterns in the embryo.

• Biocomputing
• Java
• Pattern Recognition
• Simulation
• Simulation and Modeling
• development
• modeling

From the reviews:

"Due to its ample usage, and for being a paradigm of how basic rules can indeed bring forth complex forms, the [Cellular Automaton (CA)] has undoubtedly established itself as a symbol of ‘creation by the simplest.’

…How can it be that two so very different methods, Partial Differential Equations…and CAs, which are essentially based on discretized space, time, and variables, can be utilised to approach the same topics, and furthermore, with the same underlying motivations? …Andreas Deutsch and Sabine Dormann address this question, by beautifully bridging the traditional gap between CAs and the more classic PDE description of the same biological problems. They construct this bridge by cementing the CA in a formalised mathematical language, while also delivering a broad overview on some of [the] applications of CAs and inserting it in an ontological context on developmental processes. …After reading Deutsch and Dormann’s work, one should be able to start using mathematical techniques in CA modelling.

…The authors offer a succinct, comprehensive history on the general concepts of the origin of patterns… In fact, chapter two is a true ‘history of pattern formation in 90 minutes,’ and, as such, astonishingly captures the basic breakthroughs in scientific and philosophical thought, charmingly offering a setting, both scientific as well as cultural, for those readers naïve in the field of development. …The authors lead the reader elegantly from the basic random walk to more elaborate applications involving cellular interactions…

Taken as a whole, the book under review fills a rather significant gap in the spatial modelling literature. It presents a unifying framework for mathematicians, physicists, and theoretical biologists. It is clear that Deutsch and Dormann’s book possesses great pedagogical value. Chapters end with proposed topics for further projects,rendering the book a good source of inspiration for courses on pattern formation in which computer simulations and methods are utilised. 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.

…Deutsch and Dormann strive to go beyond [an eye-balling] approach, and propose more quantifiable methods of analysis. This by itself is already of great importance to the field of biological modelling." —Mathematical Reviews

"This book focuses on [the] application of so-called lattice-gas cellular automaton models to the field of biological pattern formation.... In the book, the authors describe an interesting number of applications of the method in the field of biological pattern formation. The examples include tumor development, population growth, swarming behavior, and cell sorting.... 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.... I particularly like the format of suggesting potential further projects at the end of each chapter, which shows that the field is only starting and many research questions still have to be explored."—Mathematical Biosciences

"This is a very well written book on how to use cellular automaton, and especially Lattice-Gas-based Cellular Automaton (LGCA), to modelvarious biological phenomena such as schools of fish, pigment distribution in salamanders, and tumor growth. It is suitable for researchers interested in modeling pattern formation, in general, and CA, or Turing patterns, in particular. It is also well adapted for graduate (and advanced undergraduate) students.... There are lists of highly interesting possible future research projects. Such lists are very valuable and show both that the field itself has potential for further research and that the authors are generous in sharing such problems. The book is well suited for a graduate course. Indeed parts of it might even be used in an undergraduate course.... I especially like the way Deutsch and Dormann give the historical background [of the field].... The authors show that [cellular automaton modeling] is a useful concept with great potential in many areas, and that CAs are more than preliminary toy models compared to "real" partial differential equation (PDE) models."—Genetic Programming and Evolvable Machines

"This monograph is a volume in the series Modeling and Simulation in Science, Engineering and Technology edited by the prestigious Birkhäuser Publishing House. It is aimed to undergraduates and graduates students as well as experienced researchers in mathematical biology." (Alexandru Carausu, Iasi Polytechnic Magazine, Vol. 28 (1/4), 2006)

• Center for High Performance Computing, Dresden University of Technology, Dresden, Germany

  Andreas Deutsch

• Department of Mathematics, University of Osnabrück, Osnabrück, Germany

  Sabine Dormann

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