Bacterial aggregation in the presence of directed motion

Abstract

We model directed motion of cells that aggregate into a cluster in the presence of chemotaxis or fluid transport. Starting from a stochastic agent-based model (ABM) of Galante \& Levy (2013), Chavy-Waddy \& Kolokolnikov (2016), we consider two model variants, with (I) directed motion of individuals, or (II) implicit individual bias in one direction. In both cases, we derive fourth order nonlinear PDEs representing the continuum limits of the models as a generalization of Chavy-Waddy \& Kolokolnikov (2016). An exact analytic solution then describes cluster density profile as well as the group velocity, and we identify the regimes where the travelling cluster exists. Excellent agreement is observed between the discrete models and the exact solutions of the PDEs in both models, including the existence and speed of the travelling cluster.