Continuous macroscopic limit of a discrete stochastic model for interaction of living cells.
We derive a continuous limit of a two-dimensional stochastic cellular Potts model (CPM) describing cells moving in a medium and reacting to each other through direct contact, cell-cell adhesion, and long-range chemotaxis. All coefficients of the general macroscopic model in the form of a Fokker-Planck equation describing evolution of the cell probability density function are derived from parameters of the CPM. A very good agreement is demonstrated between CPM Monte Carlo simulations and a numerical solution of the macroscopic model. It is also shown that, in the absence of contact cell-cell interactions, the obtained model reduces to the classical macroscopic Keller-Segel model. A general multiscale approach is demonstrated by simulating spongy bone formation, suggesting that self-organizing physical mechanisms can account for this developmental process.
Alber
Mark
M
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46656, USA. malber@nd.edu
Chen
Nan
N
Lushnikov
Pavel M
PM
Newman
Stuart A
SA
D000465:Algorithms; D001842:Bone and Bones / Q000166:cytology; D002448:Cell Adhesion / Q000502:physiology; D002450:Cell Communication / Q000502:physiology*; D002630:Chemotactic Factors / Q000494:pharmacology; D015233:Models, Statistical; D013269:Stochastic Processes
D002630:Chemotactic Factors