Modelling of spatio-temporal patterns in bacterial colonies

TL;DR

This paper introduces a nonlinear diffusion-reaction model incorporating hysteresis to simulate bacterial colony patterns, successfully reproducing observed behaviors of Bacillus subtilis based on environmental conditions.

Contribution

It presents a novel mathematical model that captures cooperative bacterial behavior and pattern formation influenced by environmental factors.

Findings

Model reproduces diverse bacterial patterns

Incorporates nonlinear diffusion with hysteresis

Matches experimental observations of Bacillus subtilis

Abstract

A diffusion-reaction model for the growth of bacterial colonies is presented. The often observed cooperative behavior developed by bacteria which increases their motility in adverse growth conditions is here introduced as a nonlinear diffusion term. The presence of this mechanism depends on a response which can present hysteresis. By changing only the concentrations of agar and initial nutrient, numerical integration of the proposed model reproduces the different patterns shown by {\it Bacillus subtilis} OG-01.