Electrostatic interactions in micellar solutions. A comparison between Monte Carlo simulations and solutions of the Poisson-Boltzmann equation

1982 ◽  
Vol 86 (3) ◽  
pp. 413-421 ◽  
Author(s):  
Per Linse ◽  
Gudmundur Gunnarsson ◽  
Bo Joensson
Keyword(s):  
Monte Carlo ◽  
Boltzmann Equation ◽  
Monte Carlo Simulations ◽  
Electrostatic Interactions ◽  
Micellar Solutions ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

scholarly journals Monte Carlo methods for linear and non-linear Poisson-Boltzmann equation

2015 ◽  
Vol 48 ◽  
pp. 420-446 ◽  
Author(s):  
Mireille Bossy ◽  
Nicolas Champagnat ◽  
Hélène Leman ◽  
Sylvain Maire ◽  
Laurent Violeau ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Boltzmann Equation ◽  
Monte Carlo Methods ◽  
Non Linear ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

Geometry entrapment in Walk-on-Subdomains

2019 ◽  
Vol 25 (4) ◽  
pp. 329-340 ◽  
Author(s):  
Preston Hamlin ◽  
W. John Thrasher ◽  
Walid Keyrouz ◽  
Michael Mascagni
Keyword(s):  
Monte Carlo ◽  
Boltzmann Equation ◽  
Monte Carlo Method ◽  
Electrostatic Energy ◽  
Potential Solution ◽  
Long Time ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Monte Carlo Implementation

Abstract One method of computing the electrostatic energy of a biomolecule in a solution uses a continuum representation of the solution via the Poisson–Boltzmann equation. This can be solved in many ways, and we consider a Monte Carlo method of our design that combines the Walk-on-Spheres and Walk-on-Subdomains algorithms. In the course of examining the Monte Carlo implementation of this method, an issue was discovered in the Walk-on-Subdomains portion of the algorithm which caused the algorithm to sometimes take an abnormally long time to complete. As the problem occurs when a walker repeatedly oscillates between two subdomains, it is something that could cause a large increase in runtime for any method that used a similar algorithm. This issue is described in detail and a potential solution is examined.

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.

Numerical Optimization of a Walk-on-Spheres Solver for the Linear Poisson-Boltzmann Equation

2013 ◽  
Vol 13 (1) ◽  
pp. 195-206 ◽  
Author(s):  
Travis Mackoy ◽  
Robert C. Harris ◽  
Jesse Johnson ◽  
Michael Mascagni ◽  
Marcia O. Fenley
Keyword(s):  
Monte Carlo ◽  
Boltzmann Equation ◽  
Nearest Neighbor ◽  
Optimization Techniques ◽  
Nearest Neighbor Search ◽  
Computational Time ◽  
Neighbor Search ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Exact Nearest Neighbor

AbstractStochastic walk-on-spheres (WOS) algorithms for solving the linearized Poisson-Boltzmann equation (LPBE) provide several attractive features not available in traditional deterministic solvers: Gaussian error bars can be computed easily, the algorithm is readily parallelized and requires minimal memory and multiple solvent environments can be accounted for by reweighting trajectories. However, previously-reported computational times of these Monte Carlo methods were not competitive with existing deterministic numerical methods. The present paper demonstrates a series of numerical optimizations that collectively make the computational time of these Monte Carlo LPBE solvers competitive with deterministic methods. The optimization techniques used are to ensure that each atom’s contribution to the variance of the electrostatic solvation free energy is the same, to optimize the bias-generating parameters in the algorithm and to use an epsilon-approximate rather than exact nearest-neighbor search when determining the size of the next step in the Brownian motion when outside the molecule.

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