Spatio-temporal patterns in colonies of rod-shaped bacteria

Abstract

In incubation experiments of bacterial colonies of Proteus Mirabilis, macroscopic spatiotemporal patterns, such as turbulent and unidirectional spiral patterns, appear in colonies. Considering only kinetic propeties of rod-shaped bacteria, we propose a phenomenological model for the directional and positional distributions. As the average density increases, homogeneous states bifurcate sub-critically into nonuniform states exhibiting localized collective motion, and spiral patterns appear for sufficiently large density. These patterns result from interactions between the local bacteria densities and the order parameter representing collective motion. Our model can be described by reduced equations using a perturbative method for large density. The unidirectionality of sprial rotation is also discussed.