Rotational Drift-Diffusion of Proteins in Dynamic Bilayer Lipid Membranes

围绕着活细胞和许多亚细胞隔间的是膜，它允许某些信息和材料通过，但会阻止其他一些信息和材料的通过。在这种选择性运输过程中，膜发生不同程度的变形，有时是剧烈的，这一过程受到各种蛋白质复合体的促进和调节。蛋白质通过在特定位置附着或驻留在膜上来完成调节。了解和量化这些膜蛋白在动态变形的膜上的数量和方向对于开发促进或抑制膜转运的药物和治疗策略至关重要。通过将数学模型和计算模拟相结合，本研究将研究(1)蛋白质的旋转和平移如何导致双层膜的变形；(2)变形如何导致蛋白质停留在特定的位置和方向；(3)这些相互作用如何与蛋白质的结构和膜组成有关。本研究旨在为蛋白质-膜相互作用及其相关的生物医学应用提供可靠的模型和高效的算法。细胞中的双层膜是高度动态的、具有多种关键生物学功能的异质环境，其中许多是由特定蛋白质通过各种蛋白质-膜相互作用来调节的。膜蛋白的旋转和平移定位是膜形态变化的主要驱动机制。然而，在动态双层膜中量化这些局域化仍然是数学和计算上的挑战。这项研究致力于引入主方向和曲率来解释膜中与取向相关的局部化以及由此导致的膜变形。对于低和高蛋白质密度，将推导出整数阶和分数阶的表面漂移扩散方程。通过整合这些方程的数学和计算研究，这项研究将为具有表面蛋白质流的双层膜的动力学生成一个预测模型。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Surrounding living cells and many subcellular compartments are membranes, which allow the passage of certain information and materials but block some others. Membranes deform at different magnitudes, sometimes drastically, during this selective transport, and the processes are facilitated and regulated by various protein complexes. Proteins accomplish regulation through attaching to or residing in membranes at specific locations. Understanding and quantifying the number and orientation of these membrane proteins on dynamically deforming membranes is essential for developing medications and therapeutic strategies to facilitate or suppress membrane transport. By integrating mathematical modeling and computational simulations, this research will examine (1) how the rotation and translation of proteins leads to the deformation of bilayer membranes; (2) how deformation leads proteins to stay at specific positions and orientations; and (3) how these interactions are related to protein structure and membrane composition. This investigation aims to provide reliable models and efficient algorithms for protein-membrane interactions and related biomedical applications.The bilayer membranes in cells are highly dynamic, heterogeneous environments with multiple critical biological functions, many of which are regulated by specific proteins through various protein-membrane interactions. The rotational and translational localizations of membrane proteins are the major driving mechanism of membrane morphological changes. Yet quantification of these localizations in dynamical bilayer membranes remains mathematically and computationally challenging. This research strives to introduce principal directions and curvature to account for orientation-dependent localization in membranes and the resulting membrane deformation. Surface drift-diffusion equations with integer and fractional orders will be derived for low and high protein densities. Through integrating mathematical and computational investigation of these equations, the research will generate a predictive model for the dynamics of bilayer membranes with surface protein flows.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.