Document Type

Article

Publication Date

5-2006

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. In this paper, we derive continuous limit of 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

Required Publisher's Statement

Copyright 2006 American Physical Society. The original published version of this article may be found at http://dx.doi.org/10.1103/PhysRevE.73.051901.

Included in

Mathematics Commons

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