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Mathematical Systems Theory in Biology, Communications, Computation, and Finance

Volume 134 of the series The IMA Volumes in Mathematics and its Applications pp 1-39

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

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Abstract

We discuss two different types of Cellular Automata (CA): lattice-gas-based 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 self-driven biological cells. In particular, we review recent models for rippling in myxobacteria, cell aggregation, swarming, and limb bud formation. These LGCA-based 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.