Commun. Comput. Phys., 6 (2009), pp. 955-977.


Image Charge Methods for a Three-Dielectric-Layer Hybrid Solvation Model of Biomolecules

Peihua Qin 1*, Zhenli Xu 2, Wei Cai 2, Donald Jacobs 3

1 Institute of Computational Mathematics, Chinese Academy of Sciences; Graduate University of Chinese Academy of Sciences, Beijing 100190, China.
2 Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223-0001, USA.
3 Department of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, NC 28223-0001, USA.

Received 28 October 2008; Accepted (in revised version) 2 April 2009
Available online 5 May 2009

Abstract

This paper introduces a three dielectric layer hybrid solvation model for treating electrostatic interactions of biomolecules in solvents using the Poisson-Boltzmann equation. In this model, an interior spherical cavity will contain the solute and some explicit solvent molecules, and an intermediate buffer layer and an exterior layer contain the bulk solvent. A special dielectric permittivity profile is used to achieve a continuous dielectric transition from the interior cavity to the exterior layer. The selection of this special profile using a harmonic interpolation allows an analytical solution of the model by generalizing the classical Kirkwood series expansion. Discrete image charges are used to speed up calculations for the electrostatic potential within the interior and buffer layer regions. Semi-analytical and least squares methods are used to construct an accurate discrete image approximation for the reaction field due to solvent with or without salt effects. In particular, the image charges obtained by the least squares method provide accurate approximations to the reaction field independent of the ionic concentration of the solvent. Numerical results are presented to validate the accuracy and effectiveness of the image charge methods.


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PACS: 41.20.Cv, 02.60.-x, 34.20.Cf, 87.10.Ca
Key words: Image charge methods, distance-dependent dielectric permittivity, hybrid implicit/explicit model, reaction field, Poisson-Boltzmann equation, protein.

*Corresponding author.
Email: phqin@lsec.cc.ac.cn (P. Qin), zxu7@uncc.edu (Z. Xu), wcai@uncc.edu (W. Cai), djacobs1@uncc.edu (D. Jacobs)
 

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