Computational Models for the Study of Various Immunological and Electrophysiological Systems

免疫学和内分泌学中的许多生理过程是极其复杂的，至今仍未完全了解。这些高度非线性的生物系统仍在继续使用实验方法进行研究，但随着计算生物学领域的出现，现在可以使用数学方法和计算工具从理论上对它们进行检验。我们在这个研究计划中的目标是使用这些替代的和强大的理论方法来解决在各种免疫学和电生理系统中出现的无法通过实验回答的基本问题。更具体地说，我们的目标是使用计算生物学和非线性动力学(稳态和稳定性分析、分叉方法和数值计算)的方法来构建确定性和随机微分方程模型，这些模型描述这些系统的(空间)时间动力学，并提供关于它们行为的预测和有洞察力的结论。具体地说，我们计划：(1)使用基因网络和种群模型来检查控制免疫细胞招募和相互作用的过程，并确定潜在的操纵免疫反应的靶点；(2)分析神经元同步性/节律性和激素分泌的动态调节背后的分子机制(涉及几个受体和离子通道)，这些机制最终可能被用来确定异常的主要原因。这项工作将与几个国际知名的实验实验室密切合作进行。除了它们与生理学有价值的相关性外，这些模型还将产生有趣的数学问题，这些问题可以用非线性稳定性分析从数值或理论上解决。

Many physiological processes in immunology and endocrinology are extremely complex and remain incompletely understood. These highly nonlinear biological systems continue to be investigated using experimental methods, but with the emergence of the field of computational biology, they can now be examined theoretically using mathematical methods and computational tools. Our goal in this research program is to use these alternative and powerful theoretical approaches to tackle fundamental questions arising in various immunological and electrophysiological systems that cannot be answered experimentally. More specifically, we aim to use methods from computational biology and nonlinear dynamics (steady states and stability analysis, bifurcation methods, and numerical computations) to construct deterministic and stochastic differential-equation models that describe the (spatio)temporal dynamics of these systems and provide predictions and insightful conclusions about their behavior. Particularly, we plan to: (1) examine the processes controlling immune-cell recruitment and interaction, using both gene-network and population models, and identify potential targets for manipulating the immune response; (2) analyze the molecular mechanisms (involving several receptors and ion channels) underlying the dynamic regulation of neuronal synchrony/rhythmicity and hormone secretion, that could eventually be used to determine the main causes of abnormalities. This work will be conducted in close collaboration with several, internationally renowned, experimental laboratories. Beside their valuable relevance to physiology, these models will also generate intriguing mathematical problems that are either solved numerically or theoretically using nonlinear stability analysis.