Commun. Comput. Phys.,
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Volume 3.


Recent Progress in Numerical Methods for the Poisson-Boltzmann Equation in Biophysical Applications

B. Z. Lu 1*, Y. C. Zhou 2, M. J. Holst 3, J. A. McCammon 4

1 Howard Hughes Medical Institute and Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, Dept. 0112, La Jolla, CA 92093-0112, USA.
2 Howard Hughes Medical Institute, Department of Mathematics and Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, Dept. 0112, La Jolla, CA 92093-0112, USA.
3 Department of Mathematics and Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, Dept. 0112, La Jolla, CA 92093-0112, USA.
4 Howard Hughes Medical Institute, Center for Theoretical Biological Physics, Department of Chemistry and Biochemistry and Department of Pharmacology, University of California, San Diego, 9500 Gilman Drive, Dept. 0112, La Jolla, CA 92093-0112, USA.

Received 5 October 2007; Accepted (in revised version) 30 December 2007
Available online 24 January 2008

Abstract

Efficiency and accuracy are two major concerns in numerical solutions of the Poisson-Boltzmann equation for applications in chemistry and biophysics. Recent developments in boundary element methods, interface methods, adaptive methods, finite element methods, and other approaches for the Poisson-Boltzmann equation as well as related mesh generation techniques are reviewed. We also discussed the challenging problems and possible future work, in particular, for the aim of biophysical applications.

AMS subject classifications: 92-08, 65N06, 65N30, 65N38, 65N50, 92C05
PACS: 02.70.-c, 02.60.-x, 07.05.Tp
Key words: Biomolecular electrostatics, Poisson-Boltzmann equation, numerical methods, finite difference methods, finite element methods, boundary element methods, adaptive methods, hybrid methods, mesh generation, electrostatic forces.

*Corresponding author.
Email: blu@mccammon.ucsd.edu (B. Z. Lu), yozhou@math.ucsd.edu (Y. C. Zhou), mholst@math.ucsd.edu (M. Holst), jmccammon@mccammon.ucsd.edu (J. A. McCammon)
 

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