- 學位論文
通過離子通道模擬離子傳輸
Simulation of ion transport through an ion channel
摘要
在本論文中,我們的目的是通過離子通道來模擬離子傳輸。這項研究的動機 主要源於探討在生理過程中離子傳輸的重要性。藉由延伸 Poisson-Nernst-Planck (PNP) 以得到系統控制方程,並使用 Lattice-Boltzmann 方法 (LBM) 對其進行離散 化。本文討論並實現了一些突破 PNP 方程的局限的方法,。浸入式邊界方法 (IBM) 在本論文中被用於更準確地近似系統的邊界條件,同時代碼已在多個圖形處理單元 (GPU) 上並行化。該數值方法首先在經典問題上得到驗證,然後在一系列離子 通道上實施,包括高度理想化的二維離子通道、SARS-CoV-1 和 SARS-CoV-2 E 蛋 白離子通道、TRPV 通道、鉀通道。已經進行了一系列分析以了解不同數學模型 對離子傳輸的作用和影響。 這項工作的新穎之處在於我們通過離子通道來模擬離子傳輸的問題。據我們所知,LBM 尚未廣用於模擬通過離子通道的離子傳輸。此外,我們已經在離子傳輸的背景下實施了 IBM-LBM 方法,這是以前從未被執行的。在這項研究中,我們為 LBM 框架內的離子物質濃度提供了陽性保留標準。我們是最早 使用 SARS-CoV-2 E 蛋白離子通道模擬離子傳輸的研究團隊之一,並進行了與 SARS-CoV-1 的比較。據我們所知,此類的比較尚未被其他學者提出。
並列摘要
In this thesis, our intention is to simulate ion transport through an ion channel within continuum framework. Motivation for this study majorly stems from the importance of ion transport in physiological processes. The governing equations are described through extended Poisson-Nernst-Planck (PNP) equations which are then discretized using lattice Boltzmann method (LBM). Due to the limitations of PNP equations, a few extensions of PNP equations are discussed and implemented in this thesis. Immersed boundary method (IBM) has been used for accurate implementation of boundary condition while the code has been parallelized on multiple graphics processing units (GPU). The numerical methodology has first been verified on classical problems, then it has been implemented on a range of ion channels which includes highly idealized two dimensional ion channel, SARS-CoV-1 and SARS-CoV-2 E protein ion channels, TRPV channel, potassium channel. A series of analysis has been conducted to understand the role and effect of different mathematical models on ion transport. The novelty of the work lies in our approach to solve ion transport through ion channels as to the best of our knowledge LBM has not been used for modeling ion transport through ion channels. Further, we have implemented IBM-LBM in context of ion transport which has not been done before. Additionally, in this work, we have provided the positivity-preserving criteria for the concentration of ionic species within LBM framework. We are one of the first few groups to simulate ion transport through SARS-CoV-2 E protein ion channel. Further, to the best of our knowledge, comparative study between SARS-CoV-1 and SARS-CoV-2 E protein has not been conducted elsewhere.