A Fast Solver for a Nonlocal Dielectric Continuum Model

Xie, Dexuan; Jiang, Yi; Brune, Peter; Scott, L. Ridgway

doi:10.1137/110839254

Cited by 20 publications

(33 citation statements)

References 21 publications

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“…Since Hildebrandt et al 's PDE system is an approximation to the Lorentz nonlocal model, the ana- * dxie@uwm.edu † Corresponding author: Dexuan Xie (dxie@uwm.edu) lytical solution of the Lorentz nonlocal model with D p containing multiple charges was still unknown so far. Motivated by Hildebrandt et al 's novel work, a fast finite element algorithm for solving a Lorentz nonlocal model for water was developed in [15]. This Lorentz nonlocal model was then extended into a nonlocal Poisson dielectric model for a protein in an ionic solvent [16].…”

Section: Introductionmentioning

confidence: 99%

Analytical solutions of nonlocal Poisson dielectric models with multiple point charges inside a dielectric sphere

2016

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The nonlocal dielectric approach has led to new models and solvers for predicting electrostatics of proteins (or other biomolecules), but how to validate and compare them remains a challenge. To promote such a study, in this paper, two typical nonlocal dielectric models are revisited. Their analytical solutions are then found in the expressions of simple series for a dielectric sphere containing any number of point charges. As a special case, the analytical solution of the corresponding Poisson dielectric model is also derived in simple series, which significantly improves the well known Kirkwood's double series expansion. Furthermore, a convolution of one nonlocal dielectric solution with a commonly-used nonlocal kernel function is obtained, along with the reaction parts of these local and nonlocal solutions. To turn these new series solutions into a valuable research tool, they are programmed as a free Fortran software package, which can input point charge data directly from a protein data bank file. Consequently, different validation tests can be quickly done on different proteins. Finally, a test example for a protein with 488 atomic charges is reported to demonstrate the differences between the local and nonlocal models as well as the importance of using the reaction parts to develop local and nonlocal dielectric solvers.

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Section: Introductionmentioning

confidence: 99%

Analytical solutions of nonlocal Poisson dielectric models with multiple point charges inside a dielectric sphere

2016

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“…Furthermore, SDPBS is an ongoing software development project. It will be frequently updated to improve its performance, and will be expanded to include our new nonlocal continuum dielectric software packages reported in [29,60,61]. By way of the SDPBS web server, the end users always has access to the most up-to-date version of SDPBS for their calculations.…”

Section: Introductionmentioning

confidence: 99%

SDPBS Web Server for Calculation of Electrostatics of Ionic Solvated Biomolecules

Jiang

Xie

Ying

et al. 2015

Computational and Mathematical Biophysics

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Abstract: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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“…Implicit solvent models that treat the solvent as a dielectric continuum, and describe the solute molecule as a static atomistic charge distribution 3,49,76,85,131,138,160,169 have become popular recently, due to their simplicity and efficiency. Generalized Born, 7,25,51,66,70,97,114,118,150,152,182 polarizable continuum, 6,18,38,45,82,113,147,151 Poisson-Boltzmann (PB) models 49,62,101,138 and nonlocal dielectric methods 171 are commonly used. Among them, the PB models are the most popular and can be formally derived from Maxwell's theories.…”

Section: Introductionmentioning

confidence: 99%

Multiscale, Multiphysics and Multidomain Models I: Basic Theory

Guo

2013

J. Theor. Comput. Chem.

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This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e., electrostatic) solvation, nonpolar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace-Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson-Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst-Planck (NP) equations for the dynamics of charged solvent species, generalized Navier-Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent-solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent-solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field.

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A Fast Solver for a Nonlocal Dielectric Continuum Model

Cited by 20 publications

References 21 publications

Analytical solutions of nonlocal Poisson dielectric models with multiple point charges inside a dielectric sphere

Analytical solutions of nonlocal Poisson dielectric models with multiple point charges inside a dielectric sphere

SDPBS Web Server for Calculation of Electrostatics of Ionic Solvated Biomolecules

Multiscale, Multiphysics and Multidomain Models I: Basic Theory

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