Pattern Formation in Growing Polar Bacteria

We analyze a continuum model of a bacterial suspension that includes motility suppression from steric repulsion, polar alignment, and bacteria reproduction and death. Using a combination of linear stability analysis and numerical solution of the nonlinear equations, we demonstrate that the model exhibits a rich variety of emergent structures, corresponding to generic patterns seen in experiments. Motility suppression in a crowded environment gives rise to a density phase separation, regulated by the growth/death of the bacteria, as demonstrated earlier by Cates et al. [PNAS 107, 11715--11720(2010)], with spherically symmetric patterns similar to those observed in \textit{S. typhimurium}. The addition of polar alignment yields new ring/band and swirl/spiral structures resembling those observed in \textit{E.coli } colonies. The stationary/traveling nature of the patterns and their symmetry is classified and summarized in a phase diagram.