On the stabilizing effect of chemotaxis on bacterial aggregation patterns

We consider a chemotaxis-reaction-diffusion system that models the dynamics of colonies of Bacillus subtilis on thin agar plates. The system of equations was proposed by Leyva et al. [14], based on a previous non-chemotactic model by Kawasaki and collaborators [9], which reproduces the dense branching patterns observed experimentally in the semi-solid agar, low-nutrient regime. Numerical simulations show that, when the chemotactic sensitivity toward nutrients is increased, the morphology of the colony changes from a dense branched pattern to a uniform envelope that propagates outward. Here, we provide a quantitative argument that explains this change in morphology. This result is based on energy estimates on the spectral equations for perturbations around the envelope front, suggesting the suppression of colony branching as a result of the stabilizing effect of the increasing chemotactic signal.