title: Macroscopic dynamics of biological cells interacting via chemotaxis and direct contact.
abstract: A connection is established between discrete stochastic model describing microscopic motion of fluctuating cells, and macroscopic equations describing dynamics of cellular density. Cells move towards chemical gradient (process called chemotaxis) with their shapes randomly fluctuating. Nonlinear diffusion equation is derived from microscopic dynamics in dimensions one and two using excluded volume approach. Nonlinear diffusion coefficient depends on cellular volume fraction and it is demonstrated to prevent collapse of cellular density. A very good agreement is shown between Monte Carlo simulations of the microscopic cellular Potts model and numerical solutions of the macroscopic equations for relatively large cellular volume fractions. Combination of microscopic and macroscopic models were used to simulate growth of structures similar to early vascular networks.
authors.affiliation: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131, USA. plushnik@math.unm.edu
authors.forename: Pavel M
authors.initials: PM
authors.lastname: Lushnikov
authors.forename: Nan
authors.initials: N
authors.lastname: Chen
authors.forename: Mark
authors.initials: M
authors.lastname: Alber
mesh_terms: D055592:Biophysical Phenomena; D002450:Cell Communication / Q000502:physiology*; D002452:Cell Count; D002465:Cell Movement / Q000502:physiology; D048430:Cell Shape; D002633:Chemotaxis / Q000502:physiology*; D008954:Models, Biological; D009010:Monte Carlo Method; D018919:Neovascularization, Physiologic; D013269:Stochastic Processes