Collective swimming -- a highly correlated motion of bacteria -- plays an important role in the life cycle of many bacterial species. Experiments, some conducted under the direction of one of the coPIs, have uncovered several important consequences of collective motion in suspensions of swimming bacteria: a dramatic increase in the effective diffusivity, a lowering of the effective viscosity by an order of magnitude, and the extraction of useful work from the correlated motion of bacteria. These phenomena clearly distinguish the properties of bacterial suspensions both from the properties of the fluid they swim in, and from the properties of individual swimming bacteria. In particular, an effective diffusivity enhanced by the collective motion of an aerobic bacterial colony leads to an increased supply of dissolved oxygen -- a survival advantage relative to an isolated bacterium. Collective swimming manifests in the appearance of persistent coherent configurations of bacteria many times the size of a single bacterium. However, a description of the mechanism leading to collective motion remains lacking. The goal of this project is to use mathematical modeling and carefully designed experiments to advance the understanding of the mechanisms of this type of bacterial self-organization. This can in turn have a profound effect on the state of biological an medical sciences: from to insight into the formation of biofilms and evolution of multicellular organisms from unicellular, to the understanding of the formation and organization of tissues and organs. There are many theoretical works trying to explain the appearance of collective motion and its impact on the macroscopic properties of the system. Most are based on the assumption of the central role of the additive long-range hydrodynamic interactions between the bacteria, which in the context of kinetic theory can be accurately captured by the mean field approximation. This assumption, however, is not accurate in the disordered configurations prevalent before the onset of collective motion, were the dipolar fields from different bacteria largely cancel each other. Here fluctuations -- deviations from the mean -- are significant, and the strongest interactions are due to collisions between the bacteria. Here a new kinetic model is proposed that goes beyond the mean field approximation and, in particular, incorporates fluctuations and captures collisions. The effect of binary inelastic collisions will be modeled using an integral operator. The fluctuations will take the form of a self-quenching white noise - a noise whose strength decays when the local alignment between the bacteria increases, reflecting the physical fact that in a highly-aligned configuration collisions are rare. This approach leads to a generalized Fokker-Plank equation (GFPE) - a time-dependent integro-differential equation governing the position and orientation of a single bacterium. GFPE will be derived, analyzed and validated against suitably-designed experiments.
The question of how individual living cells coordinate their behavior -- cooperate, form multicellular organisms, organs and tissues -- is a fundamental question in biological and medical sciences. What governs this cooperative behavior can be better understood with the help of the mathematical models developed in the course of this research. This knowledge can be useful in various way, such as through a better understanding or even control of the functioning of colonies of harmful bacteria or of human tissues and organs.
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