Collaborative Research: Mathematical Studies and Refinements of a Reduced Ion Channel Model and a Nonlocal Dielectric Model

离子通道对生物功能至关重要，也代表着重要的独立电子器件。它们促进和调节带电离子进出细胞的流动，它们这样做的精确行为尚不完全清楚。更精确的模型和更高效的数值算法将极大地推进离子通道和其他重要蛋白质的研究。在本项目中，pi计划研究两种离子通道（钠通道和钙通道）的模型，以了解介电模型在预测离子通道机制中的作用。特别是，pi将建立在一个现有的模型上，该模型使用一个非常简单，几乎幼稚，但非常有效的电介质模型。然后，他们将对该模型进行数学分析，以进一步揭示其特性和适用范围。此外，他们将研究一个更复杂的介电体模型，通常被称为非局部模型。此外，该项目将为研究生和本科生提供多学科的培训机会。离子通道模型（包括非局部连续介质溶剂模型）数值解的快速计算对于定量理解关键生理过程和细胞代谢和能量学至关重要，这对提高我们对健康和疾病的理解至关重要。本项目开发的新的离子通道模型、非局部连续溶剂模型和高效的数值算法将对数学生物学、计算生理学和计算数学做出重大贡献。它们将在研究各种离子通道、计算溶质-溶质系统的连续静电以及模拟大规模蛋白质系统等方面发挥重要作用。

Ion channels are critical for biological function and also represent remarkable electronic devices of independent interest. They facilitate and regulate the flow of charged ions in and out of cells, and they do so with precise behaviors that are not fully understood. The more accurate models and more efficient numerical algorithms will significantly advance the research on ion channels and other important proteins. In this project, the PIs plan to study models for two ion channels (sodium and calcium channels) to understand the role of dielectric models in predicting the mechanism of ion channels. In particular, the PIs will build upon an existing model that uses a very simple, almost naive, yet remarkably effective, model of dielectrics. They then will analyze this model mathematically to further reveal its properties and range of applicability. Moreover, they will study a more sophisticated model of dielectrics, commonly known as a non-local model. In addition, this project will provide multi-disciplinary training opportunities to both graduate and undergraduate students. Fast computation of numerical solutions of ion channel models including nonlocal continuum solvent models is essential for quantitative understanding of critical physiological processes and cellular metabolism and energetics, which is central to improving our understanding of health and diseases. The new ion channel models, nonlocal continuum solvent models, and efficient numerical algorithms developed in this project will be a considerable contribution to mathematical biology, computational physiology, and computational mathematics. They will play important roles in studying various ion channels, computing continuum electrostatics for solvent-solute systems, and simulating large scale protein systems.