Predictive Modeling of collective swimming in bacterial supensions

细菌悬浮液中集体游泳的预测模型

• 批准号: 8446640
• 负责人: Leonid Berlyand
• 金额: $ 24.72万
• 依托单位: PENNSYLVANIA STATE UNIVERSITY, THE
• 依托单位国家: 美国
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-07-01 至 2015-04-30
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/8446640
• 关键词: Aerobic; Appearance; Bacteria; Bacterial Typing; Behavior; Biological; Cells; Cooperative Behavior; Disease; Equation; Evolution; Goals; Individual; Kinetics; Knowledge; Life; Life Cycle Stages; Liquid substance; Medical; Microbial Biofilms; Modeling; Motion; Noise; Organ; Organism; Oxygen; Play; Positioning Attribute; Property; Relative (related person); Research; Role; Science; Suspension substance; Suspensions; Swimming; System; Time; Tissues; Viscosity; Work; base; design; human tissue; insight; mathematical model; predictive modeling; research study; self organization; theories

DESCRIPTION (provided by applicant): 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. PUBLIC HEALTH RELEVANCE: 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.

描述（由申请人提供）：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发挥着重要作用。一些实验是在 coPI 的指导下进行的，揭示了游动细菌悬浮液中集体运动的几个重要后果：有效扩散率显着增加，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功。这些现象清楚地将细菌悬浮液的特性与它们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，好氧细菌菌落的集体运动增强了有效扩散性，导致溶解氧供应增加——相对于孤立细菌来说，这是一种生存优势。集体游泳表现为细菌的持久连贯结构的出现，其大小是单个细菌的许多倍。然而，仍然缺乏对导致集体运动的机制的描述。该项目的目标是利用数学模型和精心设计的实验来增进对此类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从单细胞的进化，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特性的影响。大多数都是基于细菌之间加性长程流体动力学相互作用的核心作用的假设，在动力学理论的背景下，可以通过平均场近似准确地捕获这一点。 然而，这种假设在集体运动开始之前普遍存在的无序结构中并不准确，因为来自不同细菌的偶极场在很大程度上相互抵消。 这里的波动——与平均值的偏差——是显着的，最强的相互作用是由于细菌之间的碰撞。这里提出了一种新的动力学模型，该模型超越了平均场近似，特别是包含了波动并捕获了碰撞。 二元非弹性碰撞的影响将使用积分算子进行建模。 这些波动将以自猝灭白噪声的形式出现——当细菌之间的局部排列增加时，这种噪声的强度会衰减，这反映了在高度排列的配置中碰撞很少见的物理事实。这种方法产生了广义福克-普朗克方程（GFPE）——一个控制单个细菌位置和方向的时间相关积分微分方程。 GFPE 将根据适当设计的实验进行推导、分析和验证。 公共健康相关性：单个活细胞如何协调其行为（合作、形成多细胞生物体、器官和组织）的问题是生物和医学科学中的一个基本问题。 借助本研究过程中开发的数学模型，可以更好地理解控制这种合作行为的因素。 这些知识可以通过多种方式发挥作用，例如通过更好地了解甚至控制有害细菌菌落或人体组织和器官的功能。