Volume 13, Issue 1
A Modified Nonlocal Continuum Electrostatic Model for Protein in Water and Its Analytical Solutions for Ionic Born Models

Dexuan Xie & Hans W. Volkmer

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

Published online: 2013-01

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  • 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 treatedas 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.


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@Article{CiCP-13-174, author = {Dexuan Xie and Hans W. Volkmer}, title = {A Modified Nonlocal Continuum Electrostatic Model for Protein in Water and Its Analytical Solutions for Ionic Born Models}, journal = {Communications in Computational Physics}, year = {2013}, volume = {13}, number = {1}, pages = {174--194}, 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 treatedas 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.


}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.170811.211011s}, url = {http://global-sci.org/intro/article_detail/cicp/7217.html} }
TY - JOUR T1 - A Modified Nonlocal Continuum Electrostatic Model for Protein in Water and Its Analytical Solutions for Ionic Born Models AU - Dexuan Xie & Hans W. Volkmer JO - Communications in Computational Physics VL - 1 SP - 174 EP - 194 PY - 2013 DA - 2013/01 SN - 13 DO - http://dor.org/10.4208/cicp.170811.211011s UR - https://global-sci.org/intro/cicp/7217.html KW - AB -

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 treatedas 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.


Dexuan Xie & Hans W. Volkmer. (1970). A Modified Nonlocal Continuum Electrostatic Model for Protein in Water and Its Analytical Solutions for Ionic Born Models. Communications in Computational Physics. 13 (1). 174-194. doi:10.4208/cicp.170811.211011s
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