The Geometry Behind Numerical Solvers of the Poisson-Boltzmann Equation  

作　　者：Xinwei Shi Patrice Koehl 

机构地区：[1]Genome Center,University of California,Davis,CA 95616,USA. [2]Department of Computer Science and Genome Center,University of California,Davis,CA 95616,USA.

出　　处：《Communications in Computational Physics》2008年第5期1032-1050,共19页计算物理通讯（英文）

基　　金：the National Institute of Health under contract GM080399.

摘　　要：Electrostatics interactions play a major role in the stabilization of biomolecules:as such,they remain a major focus of theoretical and computational studies in biophysics.Electrostatics in solution is strongly dependent on the nature of the solvent and on the ions it contains.While methods that treat the solvent and ions explicitly provide an accurate estimate of these interactions,they are usually computationally too demanding to study large macromolecular systems.Implicit solvent methods provide a viable alternative,especially those based on Poisson theory.The Poisson-Boltzmann equation(PBE)treats the system in a mean field approximation,providing reasonable estimates of electrostatics interactions in a solvent treated as continuum.In the first part of this paper,we review the theory behind the PBE,including recent improvement in which ions size and dipolar features of solvent molecules are taken into account explicitly.The PBE is a non linear second order differential equation with discontinuous coefficients,for which no analytical solution is available for large molecular systems.Many numerical solvers have been developed that solve a discretized version of the PBE on a mesh,either using finite difference,finite element,or boundary element methods.The accuracy of the solutions provided by these solvers highly depend on the geometry of their underlying meshes,as well as on the method used to embed the physical system on the mesh.In the second part of the paper,we describe a new geometric approach for generating unstructured tetrahedral meshes as well as simplifications of these meshes that are well fitted for solving the PBE equation using multigrid approaches.

关 键 词：Poisson-Boltzmann equation biomolecular modeling mesh generation finite difference methods finite element methods 

分 类 号：O17[理学—数学]