Commun. Comput. Phys., 9 (2011), pp. 1056-1070.

Image Charge Method for Reaction Fields in a Hybrid Ion-Channel Model

Zhenli Xu 1*, Wei Cai 2, Xiaolin Cheng 3

1 Department of Mathematics and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China.
2 Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA; and Beijing International Center for Mathematical Research, Beijing 100871, China.
3 Center for Molecular Biophysics, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA.

Received 16 April 2010; Accepted (in revised version) 20 September 2010
Available online 10 November 2010


A multiple-image method is proposed to approximate the reaction-field potential of a source charge inside a finite length cylinder due to the electric polarization of the surrounding membrane and bulk water. When applied to a hybrid ion-channel model, this method allows a fast and accurate treatment of the electrostatic interactions of protein with membrane and solvent. To treat the channel/membrane interface boundary conditions of the electric potential, an optimization approach is used to derive image charges by fitting the reaction-field potential expressed in terms of cylindric harmonics. Meanwhile, additional image charges are introduced to satisfy the boundary conditions at the planar membrane interfaces. In the end, we convert the electrostatic interaction problem in a complex inhomogeneous system of ion channel/membrane/water into one in a homogeneous free space embedded with discrete charges (the source charge and image charges). The accuracy of this method is then validated numerically in calculating the solvation self-energy of a point charge.

AMS subject classifications: 31B05, 92C05, 65Z05

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Key words: Ion channels, image charges, cylindrical harmonics, electrostatic interactions.

*Corresponding author.
Email: (Z. Xu), (W. Cai), (X. Cheng)

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