Mathematical Modeling of the Dynamics of Cellular Processes

该项目的目标是利用数学工具，对生物有机体功能的基本过程进行改进的理论和定量理解。本研究将探讨细胞行为的机制，包括运动、定向、蛋白质含量的调节、复杂亚结构的构建、细胞间的通信、信息处理和决策。本研究的策略是构建基于潜在物理和化学机制的这些过程的数学模型，目的是演示和理解单个组件如何配合并一起工作以提供协调的、更高层次的行为。该项目的一个主要组成部分是培养研究生进行合作，跨学科的研究和教学。这些努力的综合效果将是向更广泛的科学界传达数学对理解生物学的重要性和力量，帮助数学家和生物学家之间建立合作的桥梁，并将新的研究人员引入数学生物学领域。该提案的研究部分是使用数学方法来研究各种生物问题，这些问题被广泛地确定为细胞生理过程的动力学。具体项目包括心脏细胞的外缘偶联、鞭毛旋转马达的构建及其旋转方向的调控、蛋白质运输、细胞分裂过程中微管解聚产生的力以及纤毛的跳动运动。虽然每个项目的生物学细节都有很大的不同，但它们的数学描述包含了许多共同的特征，并依赖于共同的原则和可转移的概念，正是数学的共性将这项工作统一起来。特别是，数学建模原理、动力系统理论、分岔理论、渐近分析、均匀化和多尺度分析、随机过程和数值模拟都将在这项工作中使用。因此，这项工作带来了现代应用数学的工具承担生物学的挑战性和复杂的问题，同时推动了应用数学的前沿。不同的生物学问题和复杂的数学工具的结合，预计将导致对细胞功能的新颖和意想不到的见解。

The goal of this project is to bring to bear the tools of mathematics to gain an improved theoretical and quantitative understanding of the fundamental processes underlying the function of biological organisms. This research will examine the mechanisms underlying cell behavior including processes such as movement, direction finding, regulation of protein content, construction of complex substructures, communication between cells, information processing, and decision making. The strategy for this investigation is to construct mathematical models of these processes that are based on the underlying physical and chemical mechanisms, with the intent of demonstrating and understanding how the individual components fit and work together to give coordinated, higher level behavior. A major component of this project is the training of graduate students to do collaborative, interdisciplinary research and teaching. The combined effect of these efforts will be to communicate to the broader scientific community the importance and power of mathematics to understanding biology, to help build bridges of collaboration between mathematicians and biologists, and to bring new researchers into the field of mathematical biology. The research component of this proposal is to use mathematical methods to study a variety of biological problems broadly identified as the dynamics of cellular physiological processes. Specific projects include study of ephaptic coupling of cardiac cells, regulation of the construction of flagellar rotary motors and control of their rotation direction, protein trafficking, force generation by depolymerization of microtubules during cell division, and the beating motion of cilia. While the details of the biology of each of the projects are quite different, their mathematical descriptions contain many common features and rely on common principles and transferable concepts, and it is the commonality of mathematics that unifies this work. In particular, principles of mathematical modeling, dynamical systems theory, bifurcation theory, asymptotic analysis, homogenization and multi-scale analysis, stochastic processes, and numerical simulation will all be used in this work. Thus, this work brings the tools of modern applied mathematics to bear on challenging and complex problems of biology while pushing forward the frontiers of applied mathematics. The combination of diverse biological problems and sophisticated mathematical tools is expected to result in novel and unexpected insights into the way cells function.