Multiscale dynamics of biological cells with chemotactic interactions: From a discrete stochastic model to a continuous description
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 onedimensional CPM with the chemotactic interactions between cells in the form of a FokkerPlanck equation for the evolution of the cell probability density function. This equation is then reduced to the classical macroscopic KellerSegel model. In particular, all coefficients of the KellerSegel 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 KellerSegel model.
 Publication:

Physical Review E
 Pub Date:
 May 2006
 DOI:
 10.1103/PhysRevE.73.051901
 arXiv:
 arXiv:physics/0601216
 Bibcode:
 2006PhRvE..73e1901A
 Keywords:

 87.18.Ed;
 05.40.Ca;
 05.65.+b;
 87.18.Hf;
 Aggregation and other collective behavior of motile cells;
 Noise;
 Selforganized systems;
 Spatiotemporal pattern formation in cellular populations;
 Physics  Biological Physics;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 15 pages, 7 figures