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Image Approximations to Electrostatic Potentials in Layered Electrolytes/Dielectrics and an Ion-Channel Model

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Abstract

Image charge approximations are developed for electric potentials in the Poisson-Boltzmann 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 an ion-channel model, 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 can be used for an explicit/implicit hybrid treatment of electrostatics interaction in modeling ion-channels. Numerical tests show that the proposed method has an attractive performance in computing electrostatic interactions of source charges inside the ion-channel model via a simple summation of pairwise interactions among source and image charges.

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Authors and Affiliations

  1. HEDPS, CAPT & LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, P.R. China

    Huimin Lin & Huazhong Tang

  2. Department of Mathematics, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China

    Zhenli Xu

  3. Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC, 28223, USA

    Wei Cai

  4. Beijing International Center for Mathematical Research, Beijing, 100871, China

    Wei Cai

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  1. Huimin Lin
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  2. Zhenli Xu
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  3. Huazhong Tang
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  4. Wei Cai
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Correspondence to Wei Cai.

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Lin, H., Xu, Z., Tang, H. et al. Image Approximations to Electrostatic Potentials in Layered Electrolytes/Dielectrics and an Ion-Channel Model. J Sci Comput 53, 249–267 (2012). https://doi.org/10.1007/s10915-011-9567-2

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  • DOI: https://doi.org/10.1007/s10915-011-9567-2

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