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扮演着重要的角色。一些实验，其中一些是在其中一个COPI的指导下进行的，已经发现了游泳细菌悬浮液中集体运动的几个重要结果：有效扩散率急剧增加，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所在的流体的性质以及单个游泳细菌的性质区分开来。特别是，好氧细菌菌落的集体运动增强了有效的扩散率，从而增加了溶解氧的供应--相对于分离的细菌，这是一种生存优势。集体游泳表现为持续一致的细菌构型，其大小是单一细菌的许多倍。然而，对导致集体运动的机制的描述仍然缺乏。这个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类型的细菌自组织机制的理解。这反过来可以对生物和医学的状态产生深远的影响：从深入了解生物膜的形成和多细胞生物体从单细胞到组织和器官的形成和组织的理解。 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。大多数是基于细菌之间相加的远程流体动力相互作用的中心作用的假设，在动力学理论的背景下，这可以通过平均场近似准确地捕捉到。然而，这个假设在集体运动开始之前普遍存在的无序构型中并不准确，因为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--是显著的，最强烈的相互作用是由于细菌之间的碰撞。这里提出了一个新的动力学模型，它超越了平均场近似，特别是包含了涨落和碰撞。二元非弹性碰撞的影响将用积分算符来模拟。这种波动将采取自猝灭白噪声的形式--这种噪声的强度随着细菌之间的局部比对增加而衰减，反映了这样一个物理事实，即在高度比对的配置中，碰撞是罕见的。这种方法导致了广义福克-普朗克方程(GFPE)--一个控制单个细菌的位置和方向的依赖于时间的积分-微分方程式。将根据适当设计的实验对GFPE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.