使用經平行化後的PNP-NS數學與數值模型模擬細胞膜上多離子通道之傳輸行為

Abstract

本論文改善及平行化一有限差分的高階數值方法來求解非正交座標複雜外型的PNP-NS方程組，此方程組包含了描述外加電場電位勢的Laplace方程、描述壁面電位勢的Poisson方程、描述離子濃度分布的Nernst-Planck方程以及由庫倫力驅動的不可壓縮Navier-Stokes方程組。論文內容主要描述因電位差開啟的各種不同邊界外型離子通道，其內部流體經由通道留出至外部的物理行為，以及模擬完整細胞膜上多離子通道的傳輸行為。

Abstract In this study, a high-order numerical method of finite difference is improved and parallelized to solve the PNP-NS equations of complex external shape with non-orthogonal coordinates. The equations under investigation includes the Laplace equation for potential of the applied electric field and the Poisson equation describing the potential of the wall potential. The Nernst-Planck equation describing the ion concentration distribution and the incompressible Navier-Stokes equations for the Coulomb force. The content of the paper mainly describes the various boundary-shaped ion channels opened by the potential difference, the physical behavior of the internal fluid leaving the channel through the channel, and the transmission behavior of the multi-ion channel on the intact cell membrane.