Mathematical Modelling of the Dynamics of Cellular Processes

该项目开发并使用数学工具来研究各种细胞生理过程的动力学。 具体项目包括一项研究，以更好地了解协调心脏活动的电信号如何在细胞之间传递，包括突触耦合的影响;离子通道的随机波动如何导致神经中的自发电活动;分裂细胞如何协调其复制染色体的分离;蛋白质是如何制造的，如何被分类成囊泡，如何被运输和加工，（回收或销毁），以及细菌如何按照明确的规格构建鞭毛马达。 所有这些项目都采用非线性偏微分方程和/或随机微分方程，而数学建模，动力系统理论，分歧理论，渐近分析，随机过程和数值模拟的工具都在这项工作中使用。虽然要研究的生物学问题是相当多样化的，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 develops and uses mathematical tools to study the dynamics of a variety of cellular physiological processes. The specific projects include a study to better understand how the electrical signal that coordinates cardiac activity is transmitted from cell to cell, including the effects of ephaptic coupling; how random fluctuations of ion channels can lead to spontaneous electrical activity in nerves; how dividing cells coordinate the separation of their duplicated chromosomes; how proteins are made, sorted into vesicles, transported and processed, (recycled or destroyed) in a well-controlled manner, and how bacteria build their flagellar motors to well-defined specifications. All of these projects employ nonlinear partial differential equations and/or stochastic differential equations while the tools of mathematical modeling, dynamical systems theory, bifurcation theory, asymptotic analysis, stochastic processes, and numerical simulation are all used in this work. 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 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 contributes 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.