A one-dimensional model for chemotaxis with hard-core interactions

TL;DR

This paper develops a nonlinear kinetic model for one-dimensional chemotaxis with hard-core particle interactions, accounting for particle size, and validates it through numerical and stochastic simulations.

Contribution

It introduces two derivation methods for the nonlinear model, one for small particle fractions and one for general cases with constant tumbling rates.

Findings

The nonlinear model accurately captures particle interactions.

The model aligns well with stochastic simulations.

It extends chemotaxis modeling to include particle size effects.

Abstract

In this paper we consider a biased velocity jump process with excluded-volume interactions for chemotaxis, where we account for the size of each particle. Starting with a system of N individual hard rod particles in one dimension, we derive a nonlinear kinetic model using two different approaches. The first approach is a systematic derivation for small occupied fraction of particles based the method of matched asymptotic expansions. The second approach, based on a compression method that exploits the single-file motion of hard core particles, does not have the limitation of a small occupied fraction but requires constant tumbling rates. We validate our nonlinear model with numerical simulations, comparing its solutions with the corresponding noninteracting linear model as well as stochastic simulations of the underlying particle system.