Microscale Stochastic Modeling of Biological Mechanics

在本研究项目中，发展了一种通用的数学框架和计算方法，将浸没边界法扩展到考虑热波动。通过在流体方程中加入适当的随机强迫项来考虑热涨落。这些方法随后被应用于研究涉及高尔基体和线粒体这两个细胞器功能的动态膜重排。讨论的主要生物学问题涉及膜的几何形状和生化物种的空间分布在这些细胞器的功能中所起的作用，这些作用是由膜生物化学、渗透胁迫、流体流动和热波动引起的。随着生化分析和电子断层扫描的进步，现在可以获得这些细胞器在健康细胞和疾病细胞中如何发挥作用的数据。虽然全面的理解仍然难以捉摸，但数学建模可能有助于澄清我们目前的理解，并有助于假设这些细胞器发挥作用的基本机制。该项目的详细、大规模的数学建模旨在通过生成和提炼关于细胞器动态结构的可实验验证的假说来阐明其中一些机制。这项工作还可能促进我们对细胞器过程的总体理解，并可能深入了解在疾病状态下分解的细胞机制，从而提出新的医学干预策略。除了对基础科学的贡献外，这项研究中获得的知识将用于培训研究生和博士后研究人员，并用于设计受研究影响的数学生物学课程，其材料将发布在网络上。随着细胞生物学的进步，从主要考虑生化物种之间相互作用的数学模型中获得了关于许多细胞过程的令人信服的信息。此外，如果对这些组成部分的空间组织及其与细胞结构的相互作用进行建模，可能会有更深层次的了解。在这个项目中，研究了细胞结构通过生化物种的空间分布所起的作用，特别强调在粗略水平上模拟高尔基体和线粒体细胞器。许多蜂窝结构的力学可以在粗略水平上视为与流体相互作用的柔性结构。生物系统的这种共同的力学特征给建立模型带来了许多挑战，这些模型既适合于数学分析和计算模拟，又足够现实地捕捉所研究的生物现象的相关特征。浸没边界法是一种同时考虑柔性结构和流体的计算方法，已被用于研究各种生物系统的这些力学特征，包括心脏跳动中瓣膜周围的血液流动，耳蜗波的传播，以及昆虫飞行中的升力产生。在微观尺度上模拟细胞过程提出了进一步的挑战，需要考虑流体和浸没结构的热波动。

In this research project a general mathematical framework and computational method are developed which extend the Immersed Boundary Method to account for thermal fluctuations. The thermal fluctuations are taking into account by including appropriate stochastic forcing terms in the fluid equations. These methods are then applied to study the dynamic membrane rearrangements involved in the functions of two cell organelles, the Golgi Apparatus and Mitochondria. The main biological questions that are addressed concern the role that membrane geometry and spatial distribution of biochemical species play in the functions of these organelles, as induced by the membrane biochemistry, osmotic stresses, fluid flow, and thermal fluctuations. With advances in biochemical assays and electron tomography data is now becoming available which hint at how these cell organelles function both in healthy and in diseased cells. While a comprehensive understanding remains elusive, mathematical modeling may help clarify our present understanding and aid in postulating basic mechanisms by which these cell organelles function. The detailed, large-scale mathematical modeling of this project is intended to shed light on some of these mechanisms, by generating and refining experimentally testable hypothesis about cell organelles' dynamical structures. This work may also advance our understanding of cell organelle processes in general, and possibly give insight into the cellular mechanisms which break down during diseased states suggesting new medical intervention strategies. In addition to contributing to basic science, the knowledge gained in this research will be used in training graduate students and postdoctoral researchers, and in the design of research-influenced mathematical biology courses for which materials will be posted on the web. Software packages will also be made available for the general computational methods developed.With advances in cell biology compelling information has been obtained about many cellular processes from mathematical models which consider primarily the interactions between a collection of biochemical species. An even deeper understanding may become possible if in addition the spatial organization of these components and their interactions with cellular structures are modeled. In this project the role cellular structures play through spatial distribution of biochemical species is studied, with a specific emphasis on modeling at a coarse-level the Golgi Apparatus and Mitochondria cell organelles. The mechanics of many cellular structures can be regarded at a coarse-level as flexible structures which interact with a fluid. This common mechanical feature of biological systems presents many challenges in formulating models which are amenable to mathematical analysis and computational simulation while being realistic enough to capture relevant features of the biological phenomena being studied. The Immersed Boundary Method, a computational method simultaneously accounting for flexible structures and fluid, has been used to perform simulations of these mechanical features in the study of a variety of biological systems, including blood flow around valves in the beating heart, wave propagation in the cochlea, and lift generation in insect flight. Simulating cellular processes at microscopic scales presents further challenges requiring that thermal fluctuations be taking into account for the fluid and immersed structures.