Commun. Comput. Phys., 13 (2013), pp. 174-194.


A Modified Nonlocal Continuum Electrostatic Model for Protein in Water and Its Analytical Solutions for Ionic Born Models

Dexuan Xie 1*, Hans W. Volkmer 1

1 Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201-0413, USA.

Received 17 August 2011; Accepted (in revised version) 21 October 2011
Available online 12 June 2012
doi:10.4208/cicp.170811.211011s

Abstract

A nonlocal continuum electrostatic model, defined as integro-differential equations, can significantly improve the classic Poisson dielectric model, but is too costly to be applied to large protein simulations. To sharply reduce the model's complexity, a modified nonlocal continuum electrostatic model is presented in this paper for a protein immersed in water solvent, and then transformed equivalently as a system of partial differential equations. By using this new differential equation system, analytical solutions are derived for three different nonlocal ionic Born models, where a monoatomic ion is treated as a dielectric continuum ball with point charge either in the center or uniformly distributed on the surface of the ball. These solutions are analytically verified to satisfy the original integro-differential equations, thereby, validating the new differential equation system.

AMS subject classifications: 92-08, 65N30

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Key words: Nonlocal continuum electrostatic models, Poisson dielectric equations, protein-water interface problem, nonlocal ionic Born models.

*Corresponding author.
Email: dxie@uwm.edu (D. Xie), volkmer@uwm.edu (H. W. Volkmer)
 

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