在典型的動物細胞內有成千上萬個通道，其中每個通道允許特定離子通過並控制細胞膜電壓差異。由於這些通道太小，生物學家必須通過像特殊顯微鏡這樣昂貴的設備觀察通道結構，而且在生物實驗中也需要花費大量的時間來獲取通道數據。在本文中，我們使用泊松-能斯特-普朗克-費米模型來模擬通過TRPV1離子傳輸的情況。我們將古典的Scharfetter-Gummel方法與simplified matched interface and boundary方法相結合，成為一種新的方法（SMIB-SG）。該方法可以分析通道蛋白的分子表面和電荷，並模擬出離子流動的重要特徵，如最佳收斂，有效的非線性迭代和物理守恆。該方法還允許水通過通道。PNPF模型模擬出TRPV1通道在不同濃度、電壓下所產生的Ca電流與實驗數據中的I-V、I-C數據一致。在本論文中，我們根據以前的模型，使用新的對齊方式，來與實驗數據更好地匹配。

There are tens of thousands of channels within a typical animal cell in which each channel allows specific ions to pass through and control cellular membrane voltage difference. Since these channels are too small, biologists must observe the channel structure by expensive equipment like special microscope, and it takes a lot of time to get the channel data in biological experiments too. In this paper, we use the Poisson-Nernst-Planck-Fermi model to simulate the case where ions transport through TRPV1. We combine the classical Scharfetter-Gummel method with the simplified matched interface and boundary method so that it becomes a new method (SMIB-SG). The method can analyze molecular surfaces and singular charges of channel proteins and exhibit important features in flow simulations such as optimal convergence, efficient nonlinear iterations, and physical conservation. This method also allows water to pass through the channel. The PNPF currents are in accord with the experimental current-voltage data and current-concentration data of the TRPV1 channel with various calcium concentrations. In this thesis, we propose a mobility model that is based on a previous work and achieve better match to experimental data.

1. Introduction ....1
2. Structures of TRPV1 ....2
3. Poisson-Nernst-Planck-Fermi model ....6
4. Numerical results ...13
4.1 TRPV1 channel ...13
5. Summary ...21

References ...22

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