Run-and-tumble dynamics in a crowded environment: Persistent exclusion process for swimmers

The effect of crowding on the run-and-tumble dynamics of swimmers such as bacteria is studied using a discrete lattice model of mutually excluding particles that move with constant velocity along a direction that is randomized at a rate α. In stationary state, the system is found to break into dense clusters in which particles are trapped or stopped from moving. The characteristic size of these clusters predominantly scales as α(-0.5) in both one and two dimensions. For a range of densities, due to cooperative effects, the stopping time scales as T(1d)(0.85) and as T(2d)(0.8), where T(d) is the diffusive time associated with the motion of cluster boundaries. Our findings might be helpful in understanding the early stages of biofilm formation.