A model for chemotaxis with hard-core interactions

Abstract

Group-level behaviour of particles undergoing a velocity-jump process with hard-core interactions is investigated. We look at excluded-volume effects in the context of bacterial or cell chemotaxis. We study the effect that external stimuli can have on particles moving in a crowded environment. Here, the diffusion of finite-sized hard-core interacting particles is considered systematically using the method of matched asymptotic expansions. We will use the Langevin approach to diffusion where stochastic increments are applied to the velocity rather than to the space variable. The result is a nonlinear partial differential equation for the one-particle probability density function taking into account crowding effects. Stochastic simulations are used for a comparison with the analytic/numerical solutions derived. The analytic/numerical solutions compare well with stochastic simulations provided the excluded-volume fraction is small.