Generalized Poisson Nernst-Planck equations for ion channel transport: Numerical schemes and modified models
Qiong Zheng, Department of Mathematics, Michigan State University (April 27, 2011)
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As a mean-field continuum model, Poisson Nernst-Planck (PNP) theory is an efficient computational tool for the study of ion transport phenomenon in the biological systems such as ion channels, which are important in the cell survival and the regulation of cellular activity. The present talk reports advanced numerical schemes and modified PNP models for ion channels. Based on our matched interface and boundary (MIB) method, we constructs second order convergent numerical scheme to efficiently solve the PNP equations in the presence of realistic macromolecular geometries and singular charges. Numerical applications are carried out to the Gramicidin A (GA) channel protein. Good agreement between our theoretical prediction and experimental measurements is found over a wide range of external voltages and concentrations. We also develop two modified PNP models to achieve either better computational efficiency or better prediction accuracy. One of our models serves as a simplified description of a multiple ion species system at the presence of external voltages, and the other incorporates the anisotropic property of certain biomolecular systems in inhomogeneous media.