The Poisson-Boltzmann equation (PBE) is one important implicit solvent continuum model for calculating electrostatics of protein in ionic solvent. Several numerical algorithms and program packages have been developed but verification and comparison between them remains an interesting topic. In this paper, a PBE test model is presented for a protein in a spherical solute region, along with its analytical solution. It is then used to verify a PBE finite element solver and applied to a numerical comparison study between a finite element solver and a finite difference solver. Such a study demonstrates the importance of retaining the interface conditions in the development of PBE solvers.
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We present a nonlocal electrostatic formulation of nonuniform ions and water molecules with interstitial voids that uses a Fermi-like distribution to account for steric and correlation efects in electrolyte solutions. The formulation is based on the volume exclusion of hard spheres leading to a steric potential and Maxwell’s displacement field with Yukawa-type interactions resulting in a nonlocal electric potential. The classical Poisson-Boltzmann model fails to describe steric and correlation effects important in a variety of chemical and biological systems, especially in high field or large concentration conditions found in and near binding sites, ion channels, and electrodes. Steric effects and correlations are apparent when we compare nonlocal Poisson-Fermi results to Poisson-Boltzmann calculations in electric double layer and to experimental measurements on the selectivity of potassium channels for K+ over Na+.
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The Poisson-Boltzmann equation (PBE) is one important implicit solvent continuum model for calculating electrostatics of protein in ionic solvent. We recently developed a PBE solver library, called SDPBS, that incorporates the finite element, finite difference, solution decomposition, domain decomposition, and multigrid methods. To make SDPBS more accessible to the scientific community, we present an SDPBS web server in this paper that allows clients to visualize and manipulate the molecular structure of a biomolecule, and to calculate PBE solutions in a remote and user friendly fashion. The web server is available on the website https://lsextrnprod.uwm.edu/electrostatics/.
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