Mathematical Systems Theory in Biology, Communications, Computation, and Finance
Volume 134 of the series The IMA Volumes in Mathematics and its Applications pp 139
On Cellular Automaton Approaches to Modeling Biological Cells
 Mark S. AlberAffiliated withDepartment of Mathematics and Interdisciplinary Center for the Study of Biocomplexity, University of Notre Dame
 , Maria A. KiskowskiAffiliated withDepartment of Mathematics, University of Notre Dame
 , James A. GlazierAffiliated withDepartment of Physics and Biocomplexity Institute, Indiana University
 , Yi JiangAffiliated withTheoretical Division, Los Alamos National Laboratory
Abstract
We discuss two different types of Cellular Automata (CA): latticegasbased cellular automata (LGCA) and the cellular Potts model (CPM), and describe their applications in biological modeling.
LGCA were originally developed for modeling ideal gases and fluids. We describe several extensions of the classical LGCA model to selfdriven biological cells. In particular, we review recent models for rippling in myxobacteria, cell aggregation, swarming, and limb bud formation. These LGCAbased models show the versatility of CA in modeling and their utility in addressing basic biological questions.
The CPM is a more sophisticated CA, which describes individual cells as extended objects of variable shape. We review various extensions to the original Potts model and describe their application to morphogenesis; the development of a complex spatial structure by a collection of cells. We focus on three phenomena: cell sorting in aggregates of embryonic chicken cells, morphological development of the slime mold Dictyostelium discoideum and avascular tumor growth. These models include intercellular and extracellular interactions, as well as cell growth and death.
 Title
 On Cellular Automaton Approaches to Modeling Biological Cells
 Book Title
 Mathematical Systems Theory in Biology, Communications, Computation, and Finance
 Pages
 pp 139
 Copyright
 2003
 DOI
 10.1007/9780387216966_1
 Print ISBN
 9781441923264
 Online ISBN
 9780387216966
 Series Title
 The IMA Volumes in Mathematics and its Applications
 Series Volume
 134
 Series ISSN
 09406573
 Publisher
 Springer New York
 Copyright Holder
 SpringerVerlag New York
 Additional Links
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 eBook Packages
 Editors

 Joachim Rosenthal ^{(2)}
 David S. Gilliam ^{(3)}
 Editor Affiliations

 2. Department of Mathematics, University of Notre Dame
 3. Department of Mathematics and Statistics, Texas Tech University
 Authors

 Mark S. Alber ^{(4)}
 Maria A. Kiskowski ^{(5)}
 James A. Glazier ^{(6)}
 Yi Jiang ^{(7)}
 Author Affiliations

 4. Department of Mathematics and Interdisciplinary Center for the Study of Biocomplexity, University of Notre Dame, 465565670, Notre Dame, IN, USA
 5. Department of Mathematics, University of Notre Dame, 465565670, Notre Dame, IN, USA
 6. Department of Physics and Biocomplexity Institute, Indiana University, 474057105, Bloomington, IN, USA
 7. Theoretical Division, Los Alamos National Laboratory, 87545, Los Alamos, NM, USA
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