Electrostatic binding energy calculation using the finite difference solution to the linearized Poisson-Boltzmann equation: Assessment of its accuracy

1996 ◽  
Vol 17 (3) ◽  
pp. 350-357 ◽  
Author(s):  
Jian Shen ◽  
John Wendoloski
Keyword(s):  
Boltzmann Equation ◽  
Binding Energy ◽  
Finite Difference ◽  
Energy Calculation ◽  
Electrostatic Binding ◽  
Binding Energy Calculation ◽  
Poisson Boltzmann ◽  
Finite Difference Solution ◽  
Poisson Boltzmann Equation ◽  
Difference Solution

Accurate estimation of electrostatic binding energy with Poisson-Boltzmann equation solver DelPhi program

2016 ◽  
Vol 15 (08) ◽  
pp. 1650071
Author(s):  
Anbang Li ◽  
Kaifu Gao
Keyword(s):  
Boltzmann Equation ◽  
Binding Energy ◽  
Binding Free Energy ◽  
Molecular Surface ◽  
Accurate Estimation ◽  
Free Energies ◽  
Grid Spacing ◽  
Electrostatic Binding ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

Poisson–Boltzmann (PB) model is a widely used implicit solvent approximation in biophysical modeling because of its ability to provide accurate and reliable PB electrostatic salvation free energies ([Formula: see text] as well as electrostatic binding free energy ([Formula: see text] estimations. However, a recent study has warned that the 0.5[Formula: see text]Å grid spacing which is normally adopted can produce unacceptable errors in [Formula: see text] estimation with the solvent excluded surface (SES) (Harris RC, Boschitsch AH and Fenley MO, Influence of grid spacing in Poisson–Boltzmann equation binding energy estimation, J Chem Theory Comput 19: 3677–3685, 2013). In this work, we investigate the grid dependence of the widely used PB solver DelPhi v6.2 with molecular surface (MS) for estimating both electrostatic solvation free energies and electrostatic binding free energies. Our results indicate that, for the molecular complex and components the absolute errors of [Formula: see text] are smaller than that of [Formula: see text], and grid spacing of 0.8[Formula: see text]Å with DelPhi program ensures the accuracy and reliability of [Formula: see text]; however, the accuracy of [Formula: see text] largely relies on the order of magnitude of [Formula: see text] itself rather than that of [Formula: see text] or [Formula: see text]. Our findings suggest that grid spacing of 0.5[Formula: see text]Å is enough to produce accurate [Formula: see text] for molecules whose [Formula: see text] are large, but finer grids are needed when [Formula: see text] is very small.

Solving the finite-difference non-linear Poisson-Boltzmann equation

1992 ◽  
Vol 13 (9) ◽  
pp. 1114-1118 ◽  
Author(s):  
Brock A. Luty ◽  
Malcolm E. Davis ◽  
J. Andrew McCammon
Keyword(s):  
Boltzmann Equation ◽  
Finite Difference ◽  
Non Linear ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

An Adaptive, Finite Difference Solver for the Nonlinear Poisson-Boltzmann Equation with Applications to Biomolecular Computations

2013 ◽  
Vol 13 (1) ◽  
pp. 150-173 ◽  
Author(s):  
Mohammad Mirzadeh ◽  
Maxime Theillard ◽  
Asdís Helgadöttir ◽  
David Boy ◽  
Frédéric Gibou
Keyword(s):  
Boltzmann Equation ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Level Set ◽  
Level Set Function ◽  
Novel Approach ◽  
Uniform Grids ◽  
Poisson Boltzmann ◽  
Finite Volume Approach ◽  
Poisson Boltzmann Equation

AbstractWe present a solver for the Poisson-Boltzmann equation and demonstrate its applicability for biomolecular electrostatics computation. The solver uses a level set framework to represent sharp, complex interfaces in a simple and robust manner. It also uses non-graded, adaptive octree grids which, in comparison to uniform grids, drastically decrease memory usage and runtime without sacrificing accuracy. The basic solver was introduced in earlier works [16,27], and here is extended to address biomolecular systems. First, a novel approach of calculating the solvent excluded and the solvent accessible surfaces is explained; this allows to accurately represent the location of the molecule’s surface. Next, a hybrid finite difference/finite volume approach is presented for discretizing the nonlinear Poisson-Boltzmann equation and enforcing the jump boundary conditions at the interface. Since the interface is implicitly represented by a level set function, imposing the jump boundary conditions is straightforward and efficient.

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