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Analysis on Some Basic Ion Channel Modeling Problems

Mr. Zhen Chao
University of Wisconsin-Milwaukee
PhD Graduate Student – Fellow

The modeling and simulation of ion channel proteins are essential to the study of many vital physiological processes within a biological cell because most ion channel properties are very difficult to address experimentally in biochemistry. They also generate a lot of new numerical issues to be addressed in applied and computational mathematics. In this dissertation, we mainly deal with some numerical issues that are arisen from the numerical solution of one important ion channel dielectric continuum model, Poisson-Nernst-Planck (PNP) ion channel model, based on the finite element approximation approach under different boundary conditions and unstructured tetrahedral meshes. To solve this PNP ion channel model numerically, we develop a fast finite element iterative method and program it as a software package by using effective numerical techniques.

To solve a PNP ion channel model by the finite element method, one important task is to generate an interface fitted unstructured tetrahedral mesh but is very challenging to complete since the PNP ion channel model involves three physical regions — a protein region, a membrane region, and a solvent region, and the interfaces between these three regions are very complex. To address this mesh challenge, in this dissertation, we develop a new algorithm for generating a triangular surface mesh of a simulation box domain and a new algorithm for constructing a tetrahedral mesh of the membrane region.

With our PNP ion channel program package, we study the impacts of boundary value conditions, membrane surface changes, and simulation box sizes on the quality of a PNP ion channel model.

Committee Members:
Profs. Peter Hinow, Hans Volkmer, Lei Wang, Dexuan Xie and Chao Zhu.