Lattice models of nonequilibrium bacterial dynamics

Abstract

We study a model of self-propelled particles exhibiting run-and-tumble dynamics on alattice. This non-Brownian diffusion is characterized by a random walk with a finitepersistence length between changes of direction and is inspired by the motion of bacteriasuch as E. coli. By defining a class of models with multiple species of particles andtransmutation between species we can recreate such dynamics. These models admit exactanalytical results whilst also forming a counterpart to previous continuum models ofrun-and-tumble dynamics. We solve the externally driven non-interacting andzero-range versions of the model exactly and utilize a field-theoretic approach toderive the continuum fluctuating hydrodynamics for more general interactions. Wemake contact with prior approaches to run-and-tumble dynamics off lattice anddetermine the steady state and linear stability for a class of crowding interactions,where the jump rate decreases as density increases. In addition to its interestfrom the perspective of nonequilibrium statistical mechanics, this lattice modelconstitutes an efficient tool to simulate a class of interacting run-and-tumble modelsrelevant to bacterial motion, so long as certain conditions (that we derive) aremet.