Traveling Pulses for a Two-Species Chemotaxis Model
Provides a mathematical framework for understanding collective bacterial behavior in two-species systems, but results are incremental and qualitative.
The authors extend a chemotaxis model to two interacting E. coli populations, showing that traveling pulse speeds synchronize depending on the fraction of the fast population, with qualitative agreement to experiments.
Mathematical models have been widely used to describe the collective movement of bacteria by chemotaxis. In particular, bacterial concentration waves traveling in a narrow channel have been experimentally observed and can be precisely described thanks to a mathematical model at the macroscopic scale. Such model was derived in [1] using a kinetic model based on an accurate description of the mesoscopic run-and-tumble process. We extend this approach to study the behavior of the interaction between two populations of E. Coli. Separately, each population travels with its own speed in the channel. When put together, a synchronization of the speed of the traveling pulses can be observed. We show that this synchronization depends on the fraction of the fast population. Our approach is based on mathematical analysis of a macroscopic model of partial differential equations. Numerical simulations in comparison with experimental observations show qualitative agreement.