Interfacial Mechanics of Cell Membranes: Stochastic Exterior Calculus Approaches for Curved Fluid Lipid-Protein Bilayers

细胞膜的界面力学：弯曲流体脂质-蛋白质双层的随机外微积分方法

• 批准号: 1616353
• 负责人: Paul Atzberger
• 金额: $ 33.17万
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2021-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1616353&HistoricalAwards=false
• 关键词: Interfacial; Mechanics; Cell; Membranes; Stochastic

Mathematical approaches are playing an increasingly important role in the biological sciences. This ranges from the development of new models and theories that provide insights into biological processes, to the development of new analytic tools and software that are useful in experimental design and in the analysis of experimental data. In cell biology, lipid bilayer membranes can be thought of as effectively two-dimensional materials comprising of a heterogeneous mixture of lipids, proteins, and other small molecules. The individual and collective dynamics of these molecules are fine-tuned to carry out complex cellular processes ranging from signaling to synaptic transmission to the regulation of shapes of organelles. The effective two-dimensional fluid-elastic nature of cell membranes yields interfacial phenomena and complicated geometric shapes effecting both molecular interactions and dynamics that can be very distinct from their bulk three dimensional counterparts. To gain a deeper understanding of cellular processes in curved protein-lipid bilayers, there is a need for new approaches for incorporating the important roles played by geometry. This research develops new mathematical approaches and software for handling complicated geometries in investigations conducted through laboratory experiments and computational simulations of membrane-protein systems. The educational activities of the project will further enhance the training of both undergraduate and graduate students in new quantitative approaches to the biological sciences. The research of this project will develop new mathematical approaches to capture diffusive transport of proteins within curved membranes arising from both active collective motions and passive thermal fluctuations, hydrodynamics and viscoelastic deformations of curved surfaces, and discrete heterogeneous interactions between inclusions incorporating stochastic kinetics. Mathematical approaches will be extended for both continuum mechanics and coarse-grained molecular descriptions so as to provide insights into the emergent mechanics and dynamics of inclusions within bilayer membranes. To perform computational simulations, a general class of numerical methods based on exterior calculus will be designed to address the challenges associated with solving differential equations on curved manifolds. The research of this project advances the next generation of theoretical models and analysis tools for investigating membrane-protein systems. Societal impacts of the work derive from fundamental contributions to the understanding of membrane-protein systems in cell biology, which may give insights into processes relevant to membrane-related technologies such as drug delivery through permeation or design of antimicrobials such as membrane disruptors.

数学方法在生物科学中发挥着越来越重要的作用。这包括从新模型和理论的发展，提供对生物过程的见解，到新的分析工具和软件的开发，这些工具和软件在实验设计和实验数据分析中非常有用。在细胞生物学中，脂质双层膜可以被认为是由脂质、蛋白质和其他小分子的异质混合物组成的有效二维材料。这些分子的个体和集体动力学被微调以进行复杂的细胞过程，从信号传导到突触传递再到调节细胞器的形状。细胞膜的有效二维流体弹性性质产生界面现象和影响分子相互作用和动力学的复杂几何形状，其可以与它们的大体积三维对应物非常不同。为了更深入地了解弯曲的蛋白质-脂质双层中的细胞过程，需要新的方法来结合几何形状所起的重要作用。这项研究开发了新的数学方法和软件，用于处理通过实验室实验和膜蛋白质系统的计算模拟进行的调查中的复杂几何形状。该项目的教育活动将进一步加强对本科生和研究生进行生物科学新的定量方法方面的培训。该项目的研究将开发新的数学方法来捕捉蛋白质在弯曲膜内的扩散运输，这些扩散运输来自主动集体运动和被动热波动、流体动力学和弯曲表面的粘弹性变形以及包含随机动力学的夹杂物之间的离散异质相互作用。数学方法将被扩展为连续介质力学和粗粒度的分子描述，以便提供深入了解双层膜内的夹杂物的新兴力学和动力学。为了进行计算模拟，将设计基于外部微积分的一般类数值方法来解决与求解弯曲流形上的微分方程相关的挑战。该项目的研究推进了下一代研究膜蛋白系统的理论模型和分析工具。这项工作的社会影响来自于对细胞生物学中膜蛋白系统的理解的基本贡献，这可能会使人们深入了解与膜相关技术相关的过程，例如通过渗透或设计抗菌剂（如膜破坏剂）进行药物递送。