title: 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 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.
authors.affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46656, USA. malber@nd.edu
authors.forename: Mark
authors.initials: M
authors.lastname: Alber
authors.forename: Nan
authors.initials: N
authors.lastname: Chen
authors.forename: Tilmann
authors.initials: T
authors.lastname: Glimm
authors.forename: Pavel M
authors.initials: PM
authors.lastname: Lushnikov
mesh_terms: D000818:Animals; D002449:Cell Aggregation / Q000502:physiology*; D002478:Cells, Cultured; D002633:Chemotaxis / Q000502:physiology*; D003198:Computer Simulation; D004023:Dictyostelium / Q000166:cytology* / Q000502:physiology*; D008954:Models, Biological; D015233:Models, Statistical; D013269:Stochastic Processes