Scientific Computing Group Seminars - Detail View

Speaker: P. Lushnikov

Affiliation: University of New Mexico

Talk Title: Regularization of collapse in cellular dynamics: connecting microscopic and macroscopic modeling

Invited by: Jan S Hesthaven

Time: April 24 2009 11 a.m.

Location: 182 George Street, Room 110

Abstract:

Biological cells interact through chemotaxis when cells secret diffusing chemical (chemoattractant) and move towards gradient of chemoattractant creating effective nonlocal attraction between cells. Macroscopic description of cellular density dynamics through Keller-Segel model has striking qualitative similarities with nonlinear Schrodinger equation including critical collapse in two dimensions and supercritical in three dimensions. Critical collapse has logarithmic corrections to $(t_0-t)^{1/2}$ scaling law of self-similar solution. Regularization of collapse requires taking into account finite size of cells at microsopic level of cellular dynamics description. Microscopic motion of eucaryotic cells is accompanied by random fluctuations of their shapes which creates serious challenges in microscopic level simulations. We derive a nonlinear diffusion equation coupled with chemoattractant from microscopic cellular dynamics in dimensions one and two using excluded volume approach. Nonlinear diffusion coefficient depends on cellular volume fraction and it provides regularization (prevention) of cellular density collapse. A very good agreement is shown between Monte Carlo simulations of the microscopic Cellular Potts Model and numerical solutions of the derived macroscopic equations for relatively large cellular volume fractions.