scholarly journals Computing Protein pKas Using the TABI Poisson–Boltzmann Solver

2020 ◽  
pp. 2042006
Author(s):  
Jiahui Chen ◽  
Jingzhen Hu ◽  
Yongjia Xu ◽  
Robert Krasny ◽  
Weihua Geng
Keyword(s):  
Boltzmann Distribution ◽  
Dielectric Medium ◽  
Boundary Integral ◽  
Acid Dissociation ◽  
Low Dielectric ◽  
Poisson Boltzmann ◽  
Computing Procedure ◽  
Poisson Boltzmann Equation ◽  
High Dielectric ◽  
Electrostatic Calculations

A common approach to computing protein pKas uses a continuum dielectric model in which the protein is a low dielectric medium with embedded atomic point charges, the solvent is a high dielectric medium with a Boltzmann distribution of ionic charges, and the pKa is related to the electrostatic free energy which is obtained by solving the Poisson–Boltzmann equation. Starting from the model pKa for a titrating residue, the method obtains the intrinsic pKa and then computes the protonation probability for a given pH including site–site interactions. This approach assumes that acid dissociation does not affect protein conformation aside from adding or deleting charges at titratable sites. In this work, we demonstrate our treecode-accelerated boundary integral (TABI) solver for the relevant electrostatic calculations. The pKa computing procedure is enclosed in a convenient Python wrapper which is publicly available at the corresponding author’s website. Predicted results are compared with experimental pKas for several proteins. Among ongoing efforts to improve protein pKa calculations, the advantage of TABI is that it reduces the numerical errors in the electrostatic calculations so that attention can be focused on modeling assumptions.

DelEnsembleElec: Computing Ensemble-Averaged Electrostatics Using DelPhi

2013 ◽  
Vol 13 (1) ◽  
pp. 256-268 ◽  
Author(s):  
Lane W. Votapka ◽  
Luke Czapla ◽  
Maxim Zhenirovskyy ◽  
Rommie E. Amaro
Keyword(s):  
Molecular Dynamics ◽  
Influenza Virus ◽  
Boltzmann Equation ◽  
General Theory ◽  
Electrostatic Interactions ◽  
Biological Interest ◽  
Single Structure ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Electrostatic Calculations

AbstractA new VMD plugin that interfaces with DelPhi to provide ensemble-averaged electrostatic calculations using the Poisson-Boltzmann equation is presented. The general theory and context of this approach are discussed, and examples of the plugin interface and calculations are presented. This new tool is applied to systems of current biological interest, obtaining the ensemble-averaged electrostatic properties of the two major influenza virus glycoproteins, hemagglutinin and neuraminidase, from explicitly solvated all-atom molecular dynamics trajectories. The differences between the ensemble-averaged electrostatics and those obtained from a single structure are examined in detail for these examples, revealing how the plugin can be a powerful tool in facilitating the modeling of electrostatic interactions in biological systems.

scholarly journals Review and Modification of Entropy Modeling for Steric Effects in the Poisson-Boltzmann Equation

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 632
Author(s):  
Tzyy-Leng Horng
Keyword(s):  
Free Energy ◽  
Lattice Gas ◽  
Steric Effect ◽  
Mean Field ◽  
Boltzmann Distribution ◽  
Experimental Conditions ◽  
Ion Concentrations ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Ion Size

The classical Poisson-Boltzmann model can only work when ion concentrations are very dilute, which often does not match the experimental conditions. Researchers have been working on the modification of the model to include the steric effect of ions, which is non-negligible when the ion concentrations are not dilute. Generally the steric effect was modeled to correct the Helmholtz free energy either through its internal energy or entropy, and an overview is given here. The Bikerman model, based on adding solvent entropy to the free energy through the concept of volume exclusion, is a rather popular steric-effect model nowadays. However, ion sizes are treated as identical in the Bikerman model, making an extension of the Bikerman model to include specific ion sizes desirable. Directly replacing the ions of non-specific size by specific ones in the model seems natural and has been accepted by many researchers in this field. However, this straightforward modification does not have a free energy formula to support it. Here modifications of the Bikerman model to include specific ion sizes have been developed iteratively, and such a model is achieved with a guarantee that: (1) it can approach Boltzmann distribution at diluteness; (2) it can reach saturation limit as the reciprocal of specific ion size under extreme electrostatic conditions; (3) its entropy can be derived by mean-field lattice gas model.

Modified Poisson–Boltzmann equations for characterizing biomolecular solvation

2014 ◽  
Vol 13 (03) ◽  
pp. 1440001 ◽  
Author(s):  
Patrice Koehl ◽  
Frederic Poitevin ◽  
Henri Orland ◽  
Marc Delarue
Keyword(s):  
Electrostatic Interactions ◽  
Degrees Of Freedom ◽  
Lattice Gas ◽  
Homogeneous Medium ◽  
Variable Density ◽  
Solvent Density ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
High Dielectric ◽  
Solvation Free Energies

Methods for computing electrostatic interactions often account implicitly for the solvent, due to the much smaller number of degrees of freedom involved. In the Poisson–Boltzmann (PB) approach the electrostatic potential is obtained by solving the Poisson–Boltzmann equation (PBE), where the solvent region is modeled as a homogeneous medium with a high dielectric constant. PB however is not exempt of problems. It does not take into account for example the sizes of the ions in the atmosphere surrounding the solute, nor does it take into account the inhomogeneous dielectric response of water due to the presence of a highly charged surface. In this paper we review two major modifications of PB that circumvent these problems, namely the size-modified PB (SMPB) equation and the Dipolar Poisson–Boltzmann Langevin (DPBL) model. In SMPB, steric effects between ions are accounted for with a lattice gas model. In DPBL, the solvent region is no longer modeled as a homogeneous dielectric media but rather as an assembly of self-orienting interacting dipoles of variable density. This model results in a dielectric profile that transits smoothly from the solute to the solvent region as well as in a variable solvent density that depends on the charges of the solute. We show successful applications of the DPBL formalism to computing the solvation free energies of isolated ions in water. Further developments of more accurately modified PB models are discussed.

scholarly journals Poisson-Boltzmann Calculations: van der Waals or Molecular Surface?

2013 ◽  
Vol 13 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Xiaodong Pang ◽  
Huan-Xiang Zhou
Keyword(s):  
Hydrogen Exchange ◽  
High Dielectric Constant ◽  
Van Der Waals ◽  
Molecular Surface ◽  
Explicit Solvent ◽  
Calculation Results ◽  
Van Der Waals Surface ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
High Dielectric

AbstractThe Poisson-Boltzmann equation is widely used for modeling the electro-statics of biomolecules, but the calculation results are sensitive to the choice of the boundary between the low solute dielectric and the high solvent dielectric. The default choice for the dielectric boundary has been the molecular surface, but the use of the van der Waals surface has also been advocated. Here we review recent studies in which the two choices are tested against experimental results and explicit-solvent calculations. The assignment of the solvent high dielectric constant to interstitial voids in the solute is often used as a criticism against the van der Waals surface. However, this assignment may not be as unrealistic as previously thought, since hydrogen exchange and other NMR experiments have firmly established that all interior parts of proteins are transiently accessible to the solvent.

scholarly journals Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Jaydeep P. Bardhan ◽  
Matthew G. Knepley ◽  
Peter Brune
Keyword(s):  
Boundary Integral Equations ◽  
Pure Water ◽  
Boundary Integral ◽  
Dielectric Constants ◽  
Computationally Efficient ◽  
Nonlocal Models ◽  
Surface Spherical Harmonics ◽  
Poisson Boltzmann Equation ◽  
High Dielectric ◽  
Key Steps

AbstractIn this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundaryintegral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood’s classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson–Boltzmann equation. The eigenfunctionexpansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pHdependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online.

scholarly journals A boundary integral Poisson-Boltzmann solvers package for solvated bimolecular simulations

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Weihua Geng
Keyword(s):  
Boltzmann Equation ◽  
High Performance ◽  
Numerical Algorithms ◽  
Boundary Integral ◽  
Partial Charges ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
High Performance Computers ◽  
Energy Computation ◽  
A Current

AbstractNumerically solving the Poisson-Boltzmann equation is a challenging task due to the existence of the dielectric interface, singular partial charges representing the biomolecule, discontinuity of the electrostatic field, infinite simulation domains, etc. Boundary integral formulation of the Poisson-Boltzmann equation can circumvent these numerical challenges and meanwhile conveniently use the fast numerical algorithms and the latest high performance computers to achieve combined improvement on both efficiency and accuracy. In the past a few years, we developed several boundary integral Poisson-Boltzmann solvers in pursuing accuracy, efficiency, and the combination of both. In this paper, we summarize the features and functions of these solvers, and give instructions and references for potential users. Meanwhile, we quantitatively report the solvation free energy computation of these boundary integral PB solvers benchmarked with Matched Interface Boundary Poisson-Boltzmann solver (MIBPB), a current 2nd order accurate finite difference Poisson-Boltzmann solver.

scholarly journals Finite electric boundary-layer solutions of a generalized Poisson–Boltzmann equation

2015 ◽  
Vol 471 (2178) ◽  
pp. 20150024
Author(s):  
Bon M. N. Clarke ◽  
Peter J. Stiles
Keyword(s):  
Boundary Layer ◽  
Surface Charge ◽  
Mean Field ◽  
Boltzmann Distribution ◽  
Uniform Density ◽  
Nonlinear Phenomenon ◽  
Parallel Plates ◽  
Generalized Poisson ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

We solve the nonlinear Poisson–Boltzmann (P–B) equation of statistical thermodynamics for the external electrostatic potential of a uniformly charged flat plate immersed in an unbounded strong aqueous electrolyte. Our rather general variational formulation yields new solutions for the external potential derived from both the classical Boltzmann distribution and its heuristic Eigen–Wicke modification for concentrated symmetric electrolytes. Electrostatic potentials of these mean-field solutions satisfy a homogeneous condition at a free boundary plane parallel to the electrically conducting plate. The preferred position of this plane, characterizing the outer limit of the charged electrolyte, is determined by minimizing electrostatic free energy of the electrolyte. For a given uniform density of surface charge exceeding a well-defined and experimentally accessible threshold, we show that the generalized nonlinear P–B equation predicts a unique sharp interface separating a charged boundary layer or double layer from electroneutral bulk electrolyte. Sharp electric boundary layers are shown to be an essentially nonlinear phenomenon. In the super-threshold regime, the diffuse Gouy–Chapman solution is inapplicable and thus the Derjaguin–Landau–Verwey–Overbeek analysis, predicting electrostatic repulsion between two sufficiently separated and identically charged parallel plates must be rejected. Similar limitations restrict the applicability of the Grahame equation relating surface charge density to surface potential.

scholarly journals Modeling the Opening SARS-CoV-2 Spike: an Investigation of its Dynamic Electro-Geometric Properties

2020 ◽  
Author(s):  
Anna Kucherova ◽  
Selma Strango ◽  
Shahar Sukenik ◽  
Maxime Theillard
Keyword(s):  
High Fidelity ◽  
Geometric Properties ◽  
New Class ◽  
Multiple Length Scales ◽  
Pharmacological Studies ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Numerical Solver ◽  
Dynamics Simulations ◽  
Electrostatic Calculations

AbstractThe recent COVID-19 pandemic has brought about a surge of crowd-sourced initiatives aimed at simulating the proteins of the SARS-CoV-2 virus. A bottleneck currently exists in translating these simulations into tangible predictions that can be leveraged for pharmacological studies. Here we report on extensive electrostatic calculations done on an exascale simulation of the opening of the SARS-CoV-2 spike protein, performed by the Folding@home initiative. We compute the electric potential as the solution of the non-linear Poisson-Boltzmann equation using a parallel sharp numerical solver. The inherent multiple length scales present in the geometry and solution are reproduced using highly adaptive Octree grids. We analyze our results focusing on the electro-geometric properties of the receptor-binding domain and its vicinity. This work paves the way for a new class of hybrid computational and data-enabled approaches, where molecular dynamics simulations are combined with continuum modeling to produce high-fidelity computational measurements serving as a basis for protein bio-mechanism investigations.

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