Predictive Modeling of collective swimming in bacterial supensions

集体游泳--细菌的一种高度相关的运动--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，它们揭示了游泳细菌悬浮液中集体运动的几个重要后果：有效扩散率的急剧增加，有效粘度降低一个数量级，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性质与它们在其中游动的流体的性质以及单个游动细菌的性质区分开来。特别是，通过好氧细菌菌落的集体运动增强的有效扩散率导致溶解氧的供应增加-相对于孤立细菌的生存优势。集体游泳表现在细菌的持久连贯配置的外观是单个细菌大小的许多倍。然而，仍然缺乏对导致集体运动的机制的描述。该项目的目标是使用数学建模和精心设计的实验来促进对这种细菌自组织机制的理解。这反过来又会对生物学和医学产生深远的影响：从洞察生物膜的形成和多细胞生物从单细胞生物的进化，到理解组织和器官的形成和组织。 有许多理论著作试图解释集体运动的出现及其对系统宏观性质的影响。大多数是基于假设的核心作用的添加剂之间的远程流体动力学相互作用的细菌，这在动力学理论的背景下，可以准确地捕获的平均场近似。然而，这种假设在集体运动开始之前普遍存在的无序配置中是不准确的，来自不同细菌的偶极场在很大程度上相互抵消。在这里波动-偏离平均值-是显着的，最强的相互作用是由于细菌之间的碰撞。在这里，提出了一个新的动力学模型，超越了平均场近似，特别是，采用波动和捕获碰撞。二元非弹性碰撞的影响将使用积分算子来模拟。这种波动将以自猝灭白色噪声的形式出现--当细菌之间的局部排列增加时，这种噪声的强度就会衰减，这反映了一个物理事实，即在高度排列的构型中，碰撞是罕见的。这种方法导致一个广义的福克-普朗克方程（GFPE）-时间依赖的积分微分方程的位置和方向的一个单一的细菌。GFPE将根据适当设计的实验进行推导、分析和验证。

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.