Mathematical models of membrane biophysics and microbial locomotion

描述(申请人提供)：在这项资助期间进行的研究分为两大类(I)膜生物物理学和(Ii)细菌推进。这 将与从事特定生物体研究的实验实验室合作和/或通信开展工作。这些模型将主要针对理解和解释他们的实验观察结果。然而，以前的经验确保，针对特定生物系统的模型经常导致适用于更广泛现象的一般原则。该项目的具体目标是对以下系统进行建模。1.膜动力学。我们将使用脂倾斜模型来解决内质网(ER)中脂滴的形成问题。我们认为这一自由度对于解释囊泡融合和破裂至关重要，囊泡融合和破裂涉及膜几何结构的拓扑变化。利用脂类倾斜的连续体模型，我们将重点研究芽的启动和生长以及随后的分裂。我们的模型还允许我们对膜中的脂质流动进行建模。这在细胞内细胞器从立方到片层的转变等显著的膜形状变化中是重要的。这项工作将与加州大学伯克利分校的D.Steigmann教授合作进行。2.细菌推进。我们将解决以前没有建模过的新的推进机制，实验观察为它们的工作方式提供了线索。我们的注意力将集中在(I)黄色粘球菌和相关细菌(如黄杆菌)的滑动A-运动系统，以及(Ii)蓝藻、聚球藻的游动。这项工作将与D.Zusman教授(加州大学伯克利分校)和B.Brahamsha博士(斯克里普斯)的实验实验室合作进行。数学建模将与J.Neu教授(加州大学伯克利分校)合作进行。 与公共卫生相关：这些项目中的每一个都调查了数学模型，这些模型的结构和性质到目前为止还没有得到充分的探索。膜模型探索了在很大程度上被忽视的脂倾斜自由度，但我们确信它在推动生物膜结构的拓扑变化方面是关键的。我们提出的细菌滑动的机制是全新的，数学结构是新的，一些将要开发的分析它们的数值和微扰方法也是新的。

DESCRIPTION (provided by applicant): The research undertaken during the period of this grant falls into two general categories (i) membrane biophysics and (ii) bacterial propulsion. This work will be performed in collaboration and/or correspondence with experimental laboratories engaged in studies on specific organisms. The models will be primarily directed towards understanding and explaining their experimental observations. However, previous experience assures that models directed at particular biological systems frequently lead to general principles that apply to a wider range of phenomena. The specific goals of this project are to model the following systems. 1. Membrane dynamics. We will address the formation of lipid droplets from the endoplasmic reticulum (ER) using models of lipid tilt. We consider this degree of freedom essential to explain vesicle fusion and scission that involve topological changes in membrane geometry. Using continuum models of lipid tilt, we will focus on the initiation and growth of the bud and its subsequent scission. Our model also allows us to model the flow of lipid in the membrane. This is important in dramatic membrane shape changes such as that in the cubic-to-lamellar transition in intracellular organelles. This work will be carried out in collaboration with Prof. D. Steigmann (UC Berkeley). 2. Bacterial propulsion. We will address novel propulsive mechanisms that have not been previously modeled, and for which experimental observations provide clues to their modus operandi. Our attention will be directed at (i) the gliding A-motility system of Myxococcus xanthus and related bacteria (e.g. Flavobacteria), and (ii) the swimming of the cyanobacterium, Synechococcus. This work will be carried out in collaboration with the experimental laboratories of Professor D. Zusman (UC Berkeley) and Dr. B. Brahamsha (Scripps). The mathematical modeling will be carried out in collaboration with Professor J. Neu (UC Berkeley). PUBLIC HEALTH RELEVANCE: Each of these projects investigates mathematical models whose structure and properties have not been fully explored heretofore. The membrane model explores the lipid tilt degree of freedom that has been largely ignored, but which we are convinced is critical in driving topological changes in biomembrane structure. The mechanism that we propose for gliding bacteria is entirely new, the mathematical structures are novel as are some of the numerical and perturbation methods to be developed to analyze them.