Document Type
Article
Publication Date
5-1-2006
Keywords
Cellular Potts model, CPM, Fokker-Planck equation, Keller-Segel model
Abstract
The cellular Potts model (CPM) has been used for simulating various biological phenomena such as differential adhesion, fruiting body formation of the slime mold Dictyostelium discoideum, angiogenesis, cancer invasion, chondrogenesis in embryonic vertebrate limbs, and many others. We derive a continuous limit of a discrete one-dimensional CPM with the chemotactic interactions between cells in the form of a Fokker-Planck equation for the evolution of the cell probability density function. This equation is then reduced to the classical macroscopic Keller-Segel model. In particular, all coefficients of the Keller-Segel model are obtained from parameters of the CPM. Theoretical results are verified numerically by comparing Monte Carlo simulations for the CPM with numerics for the Keller-Segel model.
Publication Title
Physical Review E
Volume
73
Issue
5
DOI
http://dx.doi.org/10.1103/PhysRevE.73.051901
Required Publisher's Statement
Published by the American Physical Society
DOI link: http://dx.doi.org/10.1103/PhysRevE.73.051901
Recommended Citation
Alber, Mark; Chen, Nan; Glimm, Tilmann; and Lushnikov, Pavel M., "Multiscale Dynamics of Biological Cells with Chemotactic Interactions: From a Discrete Stochastic Model to a Continuous Description" (2006). Mathematics Faculty Publications. 54.
https://cedar.wwu.edu/math_facpubs/54
Subjects - Topical (LCSH)
Cell physiology--Mathematical models; Stochastic models
Genre/Form
articles
Type
Text
Rights
Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.
Language
English
Format
application/pdf
