Interactions of solitary pulses of E. coli in a one-dimensional nutrient gradient

Abstract

Abstract We study the interaction of two bacterial pulses in a one-dimensional nutrient gradient. Simulations of the Keller–Segel chemotaxis model reveal two qualitatively distinct behaviors. As the two pulses approach one another, they either combine and move as a single pulse or, surprisingly, change direction and begin moving away from each other in the direction from which they originated. To study this phenomenon, we introduce a heuristic approximation to the spatial profiles of the pulses in the Keller–Segel model and derive a system of ordinary differential equations approximating the dynamics of the pulse centers of mass and widths. This approximation simplifies analysis of the global dynamics of the bacterial system and allows us to efficiently explore qualitative behavior changes under a range of parameter variations. We end by presenting experimental data showing that populations of E. coli display behavior that qualitatively agrees with our theoretical results.