Collaborative Proposal: Mathematical and experimental study of lipid bilayer shape and dynamics mediated by surfactants and proteins

本项目的目的是研究基础数学和生物物理学，这些基础数学和生物物理学是脂质双分子层与表面活性剂和蛋白质相互作用的平衡形状和动力学的基础。脂质双分子层是由不同种类的脂质组成的弹性生物膜的主要结构成分，含有多种蛋白质，以及胆固醇、表面活性剂等多种分子。此外，生物膜是不对称的双小叶，连接到细胞骨架，这是细胞适应不同形状和运动的关键。现在我们知道，脂质成分可能会限制可能的形状和变形，而细胞膜的实际形状取决于力（例如来自细胞骨架）和使膜变形的蛋白质。在揭示和破译蛋白质感知和/或诱导膜曲率的机制方面已经取得了很大进展。然而，最近的实验表明，脂质膜与两亲分子（如表面活性剂和两亲肽）之间的相互作用也会导致膜的总面积、曲率和刚度的变化。目前还没有关于这些效应的数学模型来帮助阐明由于表面活性剂和蛋白质导致的脂质双分子层的不对称性，或者细胞如何利用这些机制来执行各种生物功能。本项目旨在建立表面活性剂和蛋白质在引起脂质双小叶的不对称及其随后的形状和动力学中的作用的数学理解。特别关注的是(1)表面活性剂诱导的膜面积调节和形状变化，以及(2)跨膜蛋白的运输、组装和组织对膜形状和动力学的影响。此外，实验（由Stone）将验证和完善建模方法（由Young），这将反过来促进弹性脂质双分子层与表面活性剂和蛋白质相互作用的数值模拟（由Veerapaneni）。结果将有助于揭示细胞膜中蛋白质和脂质结构域之间的复杂组织和相互作用。该项目的主题是在大空间（微米）和长时间（秒到分钟）尺度上开发和分析脂质膜与表面活性剂或蛋白质之间相互作用的数学模型，这是使用最先进的粗粒度分子动力学模拟难以实现的。将对实验、数学建模和数值模拟进行定量比较。这项研究的广泛影响包括开发新的数学模型、数值方法和补充分析和实验，这将有利于研究筏动力学的科学家和工程师，以及在药物输送、细胞粘附、运动性和机械传感方面的新兴应用。这里描述的概念和方法超越了由活性物种介导的移动边界动力学的背景，并扩展到以化学物质的反应扩散为特征的其他问题。这种方法有可能适用于更复杂的生物膜，从数学的角度来看，它们是相似的。参与该项目的学生将在广泛的数学，生物物理学和计算机科学方面接受有价值的跨学科培训。

The objective of this project is to investigate the fundamental mathematics and biophysics that underlie the equilibrium shape and dynamics of a lipid bilayer interacting with surfactants and proteins. The lipid bilayer is the main structural component of the elastic biological membranes that consist of different lipid species, and contain many kinds of proteins, and many other molecules such as cholesterols and surfactants. In addition, the biomembranes are asymmetric double leaflets coupled to a cytoskeleton that is crucial for cellular adaptation of different shapes and motility. It is now known that lipid composition may set limits to the possible shapes and deformations, while the actual shape of the cellular membrane depends on both the force (from the cytoskeleton, for example) and membrane-deforming proteins. Much progress has been made to uncover and decipher the mechanisms by which proteins can sense and/or induce membrane curvature. However, recent experiments have shown that interaction between lipid membranes and amphipathic molecules, such as surfactant and amphipathic peptides, also leads to changes in total membrane area, curvature and rigidity. No mathematical modeling of these effects have yet been obtained to help elucidate the asymmetry in the lipid bilayer due to surfactants and proteins, or how cells may utilize these mechanisms to perform diverse biological functions. This project aims to establish mathematical understanding of the roles of surfactants and proteins in causing the asymmetries in lipid double leaflets and their subsequent shape and dynamics. The particular focuses are on (1) surfactant-induced membrane area regulation and shape change, and (2) effects of transport, assembly, and organization of trans-membrane proteins on membrane shape and dynamics. In addition, the experiments (by Stone) will validate and refine the modeling approach (by Young), which will in turn facilitate the numerical simulation (by Veerapaneni) of the elastic lipid bilayer interacting with surfactant and protein. Results will help uncover the complex organization and interplay between proteins and lipid domains in cellular membranes. The theme of this project is the development and analysis of mathematical models of the interaction between lipid membranes and surfactant or protein over large spatial (microns) and long time (seconds to minutes) scales, which is difficult to achieve using state-of-the-art coarse-grained molecular dynamics simulations. Quantitative comparison between experiments, mathematical modeling, and numerical simulations will be conducted. Broader impacts of the research include the development of new mathematical models, numerical methods and complementary analysis and experiments that will be of benefit to scientists and engineers studying rafts dynamics as well as emerging applications in drug delivery, cellular adhesion, motility and mechanosensing. The concepts and methods described here go beyond the context of moving boundary dynamics mediated by an active species, and extend to other problems featuring reaction-diffusion of chemicals. The approach has the potential to be adapted to more complicated biological membranes that are similar from a mathematical point of view. The students involved in this project will receive valuable interdisciplinary training in a wide range of mathematics, biophysics and computer science.