Predictive Modeling of collective swimming in bacterial supensions

集体游泳——一种高度相关的细菌运动——在许多细菌物种的生命周期中起着重要作用。一些实验是在copi的指导下进行的，发现了游泳细菌悬浮液集体运动的几个重要结果：有效扩散率的显著增加，有效粘度的一个数量级的降低，以及从细菌的相关运动中提取有用的功。这些现象清楚地将细菌悬浮液的特性与它们所游动的液体的特性以及单个游动细菌的特性区分开来。特别是，好氧细菌集落的集体运动增强了有效的扩散率，导致溶解氧供应增加，这是相对于孤立细菌的生存优势。集体游泳表现为细菌的持久一致的结构，其大小是单个细菌的许多倍。然而，对导致集体运动的机制的描述仍然缺乏。该项目的目标是利用数学建模和精心设计的实验来推进对这种细菌自组织机制的理解。这反过来又会对生物和医学科学的现状产生深远的影响：从洞察生物膜的形成和多细胞生物从单细胞的进化，到了解组织和器官的形成和组织。

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.