Lattice Models of Nonequilibrium Bacterial Dynamics

We study a model of self propelled particles exhibiting run-and-tumble dynamics on lattice. This non-Brownian diffusion is characterised by a random walk with a finite persistence length between changes of direction, and is inspired by the motion of bacteria such as E. coli. By defining a class of models with multiple species of particle and transmutation between species we can recreate such dynamics. These models admit exact analytical results whilst also forming a counterpart to previous continuum models of run-and-tumble dynamics. We solve the externally driven non-interacting and zero-range versions of the model exactly and utilise a field theoretic approach to derive the continuum fluctuating hydrodynamics for more general interactions. We make contact with prior approaches to run-and-tumble dynamics off lattice and determine the steady state and linear stability for a class of crowding interactions, where the jump rate decreases as density increases. In addition to its interest from the perspective of nonequilibrium statistical mechanics, this lattice model constitutes and efficient tool to simulate a class of interacting run-and-tumble models relevant to bacterial motion, so long as certain conditions (that we derive) are met. ar X iv :1 01 2. 07 86 v2 [ co nd -m at .s ta tm ec h] 2 3 Fe b 20 11 Lattice Models of Nonequilibrium Bacterial Dynamics 2