在動物細胞體內有數以萬計的離子通道，其中每個通道會允許特定離子通過，並控制細胞膜電壓差。觀察此現象需要大量的時間和昂貴的特定儀器設備來獲取生物離子通道實驗數據。由於離子通道太小，生物學家必須使用特殊的顯微鏡觀察TRPV1通道結構。在本文中，我們使用泊松-能斯特-普朗克-費米(PNPF)模型模擬陽離子通過此通道時的情形，其中PNPF 模型是考慮離子間的孔隙關係、通道內均佈滿水分子在孔隙之情形和許多不同價態離子的相關效應。我們結合古典的Scharfetter-Gummel(SG)方法與Simplified matched interface and boundary(SMIB)方法使之成為一種新方法(SMIB-SG)。該方法能分析通道蛋白質的分子表面、奇異電荷而且可展現出模擬離子流動情形上的重要特徵，如最佳集中、有效率的非線性迭代和物理特性，且此方法允許水通過此通道。PNPF模型模擬TRPV1 通道在不同濃度、電壓下所產生的電流與實驗的電流-電壓、電流-濃度數據一致。

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. It requires a lot of time and uses expensive
equipment to get the channel data in biological experiments. Since the channel is too small, biologists must use the special microscopy to observe the structure of TRPV1 channel. In this thesis, we simulate the cation transport through TRPV1 by using the Poisson-Nernst-Planck-Fermi (PNPF) model. The PNPF solvers for simulating biological ion channels and nanofluids include the steric effect of ions and water molecules with interstitial voids and the correlation effect of many ions with different valences. We combine the classical Scharfetter-Gummel (SG) method with simplified matched interface and boundary (SMIB) method so that it become 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 I-V (current-voltage) data and I-C (current-concentration) data of the TRPV1 channel with various calcium concentrations.

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