Suggested Running Head : Image Approximations to Electrostatic Potentials in Layered Electrolytes / Dielectrics and an Ion-Channel Corresponding
Suggested Running Head : Image Approximations to Electrostatic Potentials in Layered Electrolytes / Dielectrics and an Ion-Channel Corresponding
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发表时间：
2010
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通讯作者：
Huimin Lin;Zhenli Xu;Huazhong Tang;W. Cai
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作者：
Huimin Lin;Zhenli Xu;Huazhong Tang;W. Cai
图像电荷近似是针对泊松玻尔兹曼理论中由电介质或电解质溶液组成的非均匀介质（例如膜或圆柱形离子通道中的层状结构）中的电势而开发的。通过未知图像电势和精确反应电势（对于层状介质或圆柱区域）之间的最小二乘拟合，或者通过对精确电势（仅层状介质）的傅立叶变换和索末菲式恒等式的 Prony 拟合来获得图像电荷，从而产生图像电荷的位置和强度。接下来，结合两种几何形状的结果，获得由于离子通道内部的电荷而导致的反应电势的图像电荷近似，这解释了离子通道外部区域（由膜和电解质溶液下方和上方组成）的极化。离子通道模型中反应场的这种近似是离子通道建模中静电相互作用的显式/隐式混合处理的关键组成部分。数值测试表明，该方法通过对源电荷和图像电荷之间的成对相互作用进行简单求和，在计算离子通道内源电荷的静电相互作用方面具有有吸引力的性能。
Image charge approximations are developed for electric potentials in the PoissonBoltzmann theory in inhomogeneous media consisting of dielectrics or electrolyte solutions such as the layered structure in a membrane or cylindrical ion-channels. The image charges are obtained either by a least square fitting between the potential of unknown images and the exact reaction potential (for the layered media or cylindrical region) or by a Prony fitting to the Fourier transform of the exact potential (layered media only) and a Sommerfeld-type identity, which yields the locations and strengths of the image charges. Next, combining the results for the two geometries, the image charge approximation for the reaction potential, due to a charge inside the ion-channel, is obtained, which accounts for the polarization of the region outside the ion-channel (consisting of a membrane and electrolyte solutions below and above). Such an approximation to the reaction field in the ion-channel model is the key component for an explicit/implcit hybrid treatment of electrostatics interaction in modeling ion-channels. Numerical tests show that the proposed method has attractive performance in computing electrostatic interactions of source charges inside the ion-channel via a simple summation of pairwise interactions among source and image charges.