Viscoelastic Cytoskeletal-Membrane Mechanics: Hybrid Discrete-Continuum Stochastic Approaches

细胞是生命的基本单位。在细胞生物学中，许多生物功能需要复杂的机械事件的产生和协调，这些事件分布在细胞的各个个体或群体中。这包括细胞运动的产生和控制，以响应毒素或营养物质的环境信号，在细胞分裂过程中产生作用力，以及调节组织内的生长。对疾病发生的条件、治疗和疫苗的发展、生物反应器的工程以及新材料的开发的理解要求采用先进的定量方法来研究细胞力学。细胞力学中的一个中心挑战是理解较小尺度的分子水平事件所产生的较大尺度力学的原理。这个项目开发了新的数学建模范例和模拟软件工具，用于在多个尺度上研究细胞力学。这包括细胞膜和细胞骨架的贡献，它们是提供维持细胞形状和内部组织的机械支持的结构。这些方法包括几何、弹性结构、流体力学和涨落的作用。计划开展外联活动，使加州大学圣巴巴拉分校和当地社区的不同学生和代表性不足的学生参与进来。这包括与当地K-12学校和大学合作，让学生参与到科学、数学和计算的主题中来。还计划开展教育活动，为下一代研究人员和学生提供独特的机会，使他们了解数学和生物相结合的新出现的定量方法。该项目通过提供新的理论和计算随机方法来处理跨越一系列尺度的分子水平的相互作用和动力学，从而解决了细胞力学中的挑战。这包括对蛋白质-莱登脂质双层膜的粘弹性机制的调节，由交联马达蛋白质驱动的细胞骨架细丝重排，以及细胞骨架-膜的相互作用。该项目开发了新的随机计算方法，以获取来自弹性力学、流体动力耦合、几何和涨落的连续和离散贡献。发展了用于处理曲面和一般体域的几何的随机数值方法和高效的求解器和采样器。该方法借鉴了微分几何的结果，并建立在有限元方法和无网格方法的基础上的非结构离散。这些方法将用于研究细胞骨架-膜相互作用的机制，以及由重组细胞骨架元素组成的体外活性软材料。这包括在细胞运动的启动和细胞骨架力量的产生过程中发挥重要作用的气泡过程。对于引入的建模方法和计算方法，还将开发和发布带有C++/Python接口的软件工具，允许对细胞力学、复杂流体和软材料中的现象进行一般模拟和分析。该项目由数学科学部门的数学生物学和计算数学项目和物理部门的生命系统物理项目共同资助。该奖项反映了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。

Cells are the fundamental units of life. In cell biology, many biological functions require the generation and coordination of complex mechanical events distributed throughout individual or populations of cells. This includes the generation and control of cellular motions in response to environmental signals of toxins or nutrients, generation of forces during cell division, and regulation of growth within tissues. Understanding of the roles of conditions arising in diseases, development of therapeutics and vaccines, engineering of bioreactors, and development of novel materials calls for advanced quantitative methods for studying cell mechanics. A central challenge in cell mechanics is to understand the principles by which larger scale mechanics arise from the smaller scale molecular-level events. This project develops new mathematical modeling paradigms and simulation software tools for investigating cell mechanics over multiple scales. This includes contributions from cell membranes and the cytoskeleton, which are structures providing the mechanical support maintaining the cell shape and internal organization. The methods capture contributions including the roles of the geometry, elastic structures, fluid mechanics, and fluctuations. Outreach activities are planned for engaging diverse and under-represented students at the University of California Santa Barbara and in the local community. This includes working with local area K-12 schools and colleges on programs to engage students on topics in the sciences, mathematics, and computation. Educational activities are also planned providing unique opportunities to train the next generation of researchers and students on recent emerging quantitative methods at the interface of mathematics and biology. The project addresses challenges in cell mechanics by providing new theoretical and computational stochastic approaches for handling molecular-level interactions and kinetics spanning over a hierarchy of scales. This includes regulation of the viscoelastic mechanics of protein-laiden lipid bilayer membranes, cytoskeletal filament rearrangements driven by cross-linked motor proteins, and cytoskeleton-membrane interactions. The project develops new stochastic computational methods for capturing both continuum and discrete contributions from the elastic mechanics, hydrodynamic coupling, geometry, and fluctuations. Stochastic numerical methods and efficient solvers and samplers are developed for handling the geometry of curved surfaces and general bulk domains. The methods draw on results from differential geometry and formulate unstructured discretizations building on finite element methods and meshless approaches. The methods will be used to study mechanisms underlying the mechanics of cytoskeleton-membrane interactions and in vitro active soft materials consisting of reconstituted cytoskeletal elements. This includes processes playing important roles in blebbing during initiation of cell motility and the generation of cytoskeletal forces. For the introduced modeling approaches and computational methods, software tools also will be developed and released with C++/python interfaces allowing for performing general simulations and analysis of phenomena in cell mechanics, complex fluids, and soft materials.This project is jointly funded by the Mathematical Biology and Computational Mathematics Programs at the Division of Mathematical Sciences and the Physics of Living Systems Program at the Division of Physics.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.