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Special Semester on Quantitative Biology analyzed by Mathematical Methods
Linz, October 1, 2007 - January 27, 2008
Continuous macroscopic limit of a discrete stochastic model for interaction of living cells

Workshop on Biomechanics and Chemotaxis, Mon, 10 Dec, 2007

Speaker: Mark Alber

Abstract

In this talk a continuous limit of a two-dimensional Cellular Potts Model (CPM) with excluded volume for cells moving in a medium and reacting to each other through both direct contact and long range chemotaxis will be described in the form of a Fokker-Planck equation for the cell probability density function. All coeffcients of the general macroscopic model are derived from parameters of the CPM and a very good agreement is demonstrated between CPM Monte Carlo simulations and numerical solution of the macroscopic model. It will be also shown that in the absence of contact cell-cell interactions, the obtained model reduces to the classical macroscopic Keller-Segel model. General multiscale approach will be demonstrated by simulating spongy bone formation from loosely packed mesenchyme via the intramembranous route suggesting that self-organizing physical mechanisms can account for this developmental process.

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