Traveling Pulses for a Two-Species Chemotaxis Model

TL;DR

This paper extends a kinetic-based macroscopic model to analyze the interaction and synchronization of traveling bacterial pulses in a two-species E. coli chemotaxis system, supported by mathematical analysis and numerical simulations.

Contribution

It introduces a novel two-species chemotaxis model capturing pulse interactions and synchronization phenomena, validated through analysis and simulations.

Findings

Synchronization depends on the fraction of the fast population

Model shows qualitative agreement with experimental observations

Traveling pulses exhibit speed synchronization in mixed populations

Abstract

Mathematical models have been widely used to describe the collective movement of bacteria by chemotaxis. In particular, bacterial concentration waves traveling in a narrow channel have been experimentally observed and can be precisely described thanks to a mathematical model at the macroscopic scale. Such model was derived in [1] using a kinetic model based on an accurate description of the mesoscopic run-and-tumble process. We extend this approach to study the behavior of the interaction between two populations of E. Coli. Separately, each population travels with its own speed in the channel. When put together, a synchronization of the speed of the traveling pulses can be observed. We show that this synchronization depends on the fraction of the fast population. Our approach is based on mathematical analysis of a macroscopic model of partial differential equations. Numerical simulations in comparison with experimental observations show qualitative agreement.