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


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

Notice: Undefined variable: pac in /var/www/html/issue/abstract/readabs.php on line 164
Key words: Nonlocal continuum electrostatic models, Poisson dielectric equations, protein-water interface problem, nonlocal ionic Born models.

*Corresponding author.
Email: (D. Xie), (H. W. Volkmer)

The Global Science Journal