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Type: Journal article
Title: Exclusion processes on a growing domain
Author: Binder, B.
Landman, K.
Citation: Journal of Theoretical Biology, 2009; 259(3):541-551
Publisher: Academic Press Ltd
Issue Date: 2009
ISSN: 0022-5193
Statement of
Benjamin J. Binder and Kerry A. Landman
Abstract: A discrete model provides a useful framework for experimentalists to understand the interactions between growing tissues and other biological mechanisms. A cellular automata (CA) model with domain growth, cell motility and cell proliferation, based on cellular exclusion processes, is developed here. Average densities can be defined from the CA model and a continuum representation can be determined. The domain growth mechanism in the CA model gives rise to a Fokker-Planck equation in the corresponding continuum model, with a diffusive and a convective term. Deterministic continuum models derived from conservation laws do not include this diffusive term. The new diffusive term arises because of the stochasticity inherited from the CA mechanism for domain growth. We extend the models to multiple species and investigate the influence of the flux terms arising from the exclusion processes. The averaged CA agent densities are well approximated by the solution of nonlinear advection-diffusion equations, provided that the relative size of the proliferation processes to the diffusion processes is sufficiently small. This dual approach provides an understanding of the microscopic and macroscopic scales in a developmental process.
Keywords: Discrete model; Cellular automata; Continuum model; Exclusion processes; Growing domain
Rights: Copyright 2009 Elsevier Ltd. All rights reserved.
RMID: 0020114371
DOI: 10.1016/j.jtbi.2009.04.025
Appears in Collections:Mathematical Sciences publications

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