A Fast and Robust Poisson–Boltzmann Solver Based on Adaptive Cartesian Grids

Boschitsch, Alexander H.; Fenley, Márcia O.

doi:10.1021/ct1006983

Cited by 56 publications

(66 citation statements)

References 75 publications

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“…In order to demonstrate application of the non-uniform ion size model to a realistic biomolecular configuration the model has been incorporated into the adaptive Cartesian grid (ACG)-based Poisson-Boltzmann solver described in 36 . This solver utilizes an octree data structure to represent the potential solution and provide the variable length scales needed to accommodate large complex structures.…”

Section: Resultsmentioning

confidence: 99%

“…This solver utilizes an octree data structure to represent the potential solution and provide the variable length scales needed to accommodate large complex structures. Here this solver is used to revisit the deformed and nonlinear DNA structure in association with the Tc3 transposase protein (PDBid: 1tc3 with net charge −37e) previously considered on the basis of the standard PBE in 36 (specifically, Figure 8 of that article). Charges and radii are assigned using the AMBER force field 37 and the solute boundary is represented using the solvent excluded molecular surface.…”

Section: Resultsmentioning

confidence: 99%

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Formulation of a new and simple nonuniform size‐modified poisson–boltzmann description

Boschitsch

Danilov

2012

J Comput Chem

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The nonlinear Poisson-Boltzmann equation (PBE) governing biomolecular electrostatics neglects ion size and ion correlation effects and recent research activity has focused on accounting for these effects to achieve better physical modeling realism. Here attention is focused on the comparatively simpler challenge of addressing ion size effects within a continuum-based solvent modeling framework. Prior works by Borukhov 1, 2 have examined the case of uniform ion size in considerable detail. Generalizations to accommodate different species ion sizes have been carried out by Li3, 4 and Zhou5 using a variational principle, Chu6 using a lattice gas model and Tresset7 using a generalized Poisson-Fermi distribution. The current work provides an alternative derivation using simple statistical mechanics principles that place the ion size effects and energy distributions on a consistent statistical footing. The resulting expressions differ from the prior non-uniform ion-size developments. However, all treatments reduce to the same form in the cases of uniform ion-size and zero ion size (the PBE). Because of their importance to molecular modeling and salt-dependent behavior, expressions for the salt sensitivities and ionic forces are also derived using the non-uniform ion size description. Emphasis in this article is on formulation and numerically robust evaluation; results are presented for a simple sphere and a previously considered DNA structure for comparison and validation. More extensive application to biomolecular systems is deferred to a subsequent article.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Formulation of a new and simple nonuniform size‐modified poisson–boltzmann description

Boschitsch

Danilov

2012

J Comput Chem

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“…All results were obtained with the adaptive Cartesian grid (ACG) finite difference Poisson-Boltzmann equation solver described elsewhere 3 . This software solves the PB equation and determines the electrostatic potential on an octree structure consisting of hierarchically nested cubes, as shown in Figure 1.…”

Section: Methodsmentioning

confidence: 99%

Influence of Grid Spacing in Poisson–Boltzmann Equation Binding Energy Estimation

Harris¹,

Boschitsch

Fenley³

2013

J. Chem. Theory Comput.

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Grid-based solvers of the Poisson-Boltzmann, PB, equation are routinely used to estimate electrostatic binding, ΔΔGel, and solvation, ΔGel, free energies. The accuracies of such estimates are subject to grid discretization errors from the finite difference approximation to the PB equation. Here, we show that the grid discretization errors in ΔΔGel are more significant than those in ΔGel, and can be divided into two parts: (i) errors associated with the relative positioning of the grid and (ii) systematic errors associated with grid spacing. The systematic error in particular is significant for methods, such as the molecular mechanics PB surface area, MM-PBSA, approach that predict electrostatic binding free energies by averaging over an ensemble of molecular conformations. Although averaging over multiple conformations can control for the error associated with grid placement, it will not eliminate the systematic error, which can only be controlled by reducing grid spacing. The present study indicates that the widely-used grid spacing of 0.5 Å produces unacceptable errors in ΔΔGel, even though its predictions of ΔGel are adequate for the cases considered here. Although both grid discretization errors generally increase with grid spacing, the relative sizes of these errors differ according to the solute-solvent dielectric boundary definition. The grid discretization errors are generally smaller on the Gaussian surface used in the present study than on either the solvent-excluded or van der Waals surfaces, which both contain more surface discontinuities (e.g., sharp edges and cusps). Additionally, all three molecular surfaces converge to very different estimates of ΔΔGel.

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“…Further, they developed a nonlinear PBE solver that combines boundary element and finite difference to solve the nonlinear PBE[28, 31]. Special attention was paid on the boundary formulation [29, 30] . These methods were applied to solve various problems in molecular biology [76, 95, 176, 177] .…”

Section: Mathematical and Computational Developmentsmentioning

confidence: 99%

Progress in developing Poisson-Boltzmann equation solvers

Li¹,

Li²,

Petukh³

et al. 2013

Computational and Mathematical Biophysics

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This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nano-objects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided the specific definition of the system to be modeled and as a physical problem aiming to better capture the phenomena occurring in the real experiments. In addition, specific attention is paid to methods to extend the capabilities of the existing solvers to model large systems toward applications of calculations of the electrostatic potential and energies in molecular motors, mitochondria complex, photosynthetic machinery and systems involving large nano-objects.

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A Fast and Robust Poisson–Boltzmann Solver Based on Adaptive Cartesian Grids

Cited by 56 publications

References 75 publications

Formulation of a new and simple nonuniform size‐modified poisson–boltzmann description

Formulation of a new and simple nonuniform size‐modified poisson–boltzmann description

Influence of Grid Spacing in Poisson–Boltzmann Equation Binding Energy Estimation

Progress in developing Poisson-Boltzmann equation solvers

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