Mathematical Investigations of the Dynamics of Cellular Physiological Processes

该项目将推进使用数学方法来研究各种动力学 细胞生理过程。 特别是，数学建模，动力系统理论，分岔理论，渐近分析，随机过程和数值计算的原则将使用和先进的这项工作。 这项工作的三个生物学主题是心律失常的发生，一维细胞器的构建和调节，以及细菌种群中生化网络的动力学。 一些具体的、有代表性的有待研究的问题是心肌细胞中自发性钙释放事件导致早期后去极化的原因，牵张激活受体对缺氧区域细胞去极化的影响，心肌细胞中缺氧反应控制系统的动力学，沙门氏菌中钩长度调节的机制，有丝分裂期间染色体分离的错误预防机制，以及费氏弧菌群体感应生化网络的结构和功能。虽然要研究的生物学问题相当多样化，但它们通过许多共同的数学特征而统一起来。 因此，这项工作有双重目标，即使用数学建模方法来理解几个特定的复杂细胞过程，并发现在生物学的许多不同领域中运作的共同原则和可转移的概念。 通过这种方式，这项工作将有助于发展一个基本的和统一的理论，生物过程如何工作，并在这样做，将有助于我们了解有关人类健康和医学的许多问题。

This project will advance the use of mathematical methods to study the dynamics of a variety of cellular physiological processes. In particular, principles of mathematical modeling, dynamical systems theory, bifurcation theory, asymptotic analysis, stochastic processes, and numerical computation will be used and advanced by this work. The three biological themes of this work are the onset of cardiac arrhythmias, the construction and regulation of one-dimensional organelles, and the dynamics of biochemical networks in bacterial populations. Some specific, representative, problems to be studied are the cause of spontaneous calcium release events in cardiac cells leading to early afterdepolarizations, the effect of stretch activated receptors on cell depolarization in a region of hypoxia, the dynamics of the hypoxia response control system in cardiac cells, the mechanism of hook length regulation in Salmonella, the error prevention mechanism for chromosomal segregation during mitosis, and the structure and function of the quorum sensing biochemical network in vibrio fischeri.While the biological problems to be studied are quite diverse, they are unified by their many common mathematical features. Thus, this work has the two-fold goal of using mathematical modeling approaches to understand several specific complex cellular processes, and to discover common principles and transferable concepts that are in operation in many different areas of biology. In this way, this work will contribute to the development of a fundamental and unified theory of how biological processes work, and in doing so, will contribute to our understanding of many issues relating to human health and medicine.