The effects of nutrient chemotaxis on bacterial aggregation patterns with non-linear degenerate cross diffusion

TL;DR

This paper develops a reaction-diffusion-chemotaxis model incorporating non-linear degenerate cross diffusion to study bacterial aggregation, revealing how chemotaxis influences colony growth and pattern stability on agar surfaces.

Contribution

It introduces a novel chemotaxis term compatible with degenerate cross diffusion models and demonstrates its effects through high-resolution GPU simulations.

Findings

Chemotaxis increases colony growth velocity.

Chemotaxis stabilizes branch formation in low-nutrient conditions.

Growth velocity depends on nutrient concentration and chemotactic sensitivity.

Abstract

This paper introduces a reaction-diffusion-chemotaxis model for bacterial aggregation patterns on the surface of thin agar plates. It is based on the non-linear degenerate cross diffusion model proposed by Kawasaki et al. (J. of Theor. Biol. 188(2) 1997) and it includes a suitable nutrient chemotactic term compatible with such type of diffusion. High resolution numerical simulations using Graphic Processing Units (GPUs) of the new model are presented, showing that the chemotactic term enhances the velocity of propagation of the colony envelope for dense-branching morphologies. In addition, the chemotaxis seems to stabilize the formation of branches in the soft-agar, low-nutrient regime. An asymptotic estimation predicts the growth velocity of the colony envelope as a function of both the nutrient concentration and the chemotactic sensitivity. For fixed nutrient concentrations, the growth velocity is an increasing function of the chemotactic sensitivity.