Multiscale dynamics of biological cells with chemotactic interactions: From a discrete stochastic model to a continuous description

Mark Alber, Nan Chen, Tilmann Glimm, and Pavel M. Lushnikov

Phys. Rev. E 73, 051901 – Published 1 May 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. 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.

Received 30 January 2006

DOI:https://doi.org/10.1103/PhysRevE.73.051901

Authors & Affiliations

Mark Alber^1,*, Nan Chen¹, Tilmann Glimm², and Pavel M. Lushnikov^1,3

¹Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46656, USA
²Department of Mathematics, Western Washington University, Bellingham, Washington 98225-9063, USA
³Landau Institute for Theoretical Physics, Kosygin Street 2, Moscow, 119334, Russia

^*Corresponding author. Electronic address: malber@nd.edu

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Vol. 73, Iss. 5 — May 2006

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Physical Review E

covering statistical, nonlinear, biological, and soft matter physics