Role of non-exponential reversal times in aggregation models of bacterial populations

Individual bacteria typically follow somewhat simple rules of motion, but collective behavior can exhibit complex behavioral patterns. For instance, the formation and dispersal of aggregates of reversing bacteria in biofilms are primarily driven by coordinated motion among cells. Many mathematical models of aggregation assume that cells have no memory, e.g., the time between their behavior changes, such as direction reversals, is exponentially distributed. However, in practice, the distribution is quite distinct from exponential. Therefore, in this paper, we analyze numerically the importance of non-exponential reversal times in 1D agent-based and kinetic models of aggregation. In particular, we consider these models in a practical parameter regime by fitting a Gamma distribution to represent the run times of myxobacteria and study their collective behavior with exponential and non-exponential reversal times. We demonstrate that non-exponential reversal times aid aggregation and result in tighter aggregates. We compare and contrast the behavior of agent-based and kinetic models that consider aggregation driven by chemotaxis. Thus, incorporating non-exponential reversal times into models of aggregation can be particularly important for reproducing experimental data, such as aggregate persistence and dispersal. These results provide a simple example of how the existence of memory helps bacteria coordinate their behaviors.