A hydrodynamic limit for chemotaxis in a given heterogeneous environment

TL;DR

This paper derives a macroscopic chemotaxis equation as a hydrodynamic limit from a stochastic particle system, incorporating environmental heterogeneity and interactions, supported by numerical simulations.

Contribution

It introduces a novel derivation of a chemotaxis PDE from a stochastic lattice model considering heterogeneous environments and cell-chemical interactions.

Findings

Hydrodynamic limit derived for chemotaxis system

Stationary chemical environment with slowly varying mean

Numerical simulations support theoretical results

Abstract

In this paper the first equation within a class of well known chemotaxis systems is derived as a hydrodynamic limit from a stochastic interacting many particle system on the lattice. The cells are assumed to interact with attractive chemical molecules on a finite number of lattice sites, but they only directly interact among themselves on the same lattice site. The chemical environment is assumed to be stationary with a slowly varying mean, which results in a non-trivial macroscopic chemotaxis equation for the cells. Methodologically the limiting procedure and its proofs are based on results by Koukkus [18] and Kipnis/Landim [17]. Numerical simulations extend and illustrate the theoretical findings.