Continuous macroscopic limit of a discrete stochastic model for interaction of living cells

Phys Rev Lett. 2007 Oct 19;99(16):168102. doi: 10.1103/PhysRevLett.99.168102. Epub 2007 Oct 19.

Abstract

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.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Algorithms
  • Bone and Bones / cytology
  • Cell Adhesion / physiology
  • Cell Communication / physiology*
  • Chemotactic Factors / pharmacology
  • Models, Statistical
  • Stochastic Processes

Substances

  • Chemotactic Factors