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

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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.