title: Approximating the dynamics of communicating cells in a diffusive medium by ODEs-homogenization with localization.
abstract: Bacteria may change their behavior depending on the population density. Here we study a dynamical model in which cells of radius [R] within a diffusive medium communicate with each other via diffusion of a signalling substance produced by the cells. The model consists of an initial boundary value problem for a parabolic PDE describing the exterior concentration [u] of the signalling substance, coupled with [N] ODEs for the masses [ai] of the substance within each cell. We show that for small [R] the model can be approximated by a hierarchy of models, namely first a system of [N] coupled delay ODEs, and in a second step by [N] coupled ODEs. We give some illustrations of the dynamics of the approximate model.
authors.affiliation: Zentrum Mathematik, TU München, Boltzmannstraße 3, 85758 , Garching, Germany, johannes.mueller@mytum.de.
authors.forename: Johannes
authors.initials: J
authors.lastname: Müller
authors.forename: Hannes
authors.initials: H
authors.lastname: Uecker
mesh_terms: D001419:Bacteria / Q000254:growth & development*; D003198:Computer Simulation; D008954:Models, Biological; D053038:Quorum Sensing / Q000502:physiology*; D015398:Signal Transduction / Q000502:physiology*