An Efficient Monte Carlo Approach for Solving Linear Problems in Biomolecular Electrostatics

Fleming, Charles B.; Mascagni, Michael; Simonov, Nikolai A.

doi:10.1007/11428862_103

Cited by 4 publications

(1 citation statement)

References 3 publications

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“…67 This usually requires setting up a new computation with many more unknowns and thus leads to an increase in the memory and CPU requirements for computing the solution. In this Article, we use a Monte Carlo method (MCM) [68][69][70][71][72][73][74] to solve this same system, eqs 1, 3, 4, and 5. Monte Carlo methods (MCMs) are fundamentally different from deterministic methods.…”

Section: Methodsmentioning

confidence: 99%

Using Correlated Monte Carlo Sampling for Efficiently Solving the Linearized Poisson−Boltzmann Equation Over a Broad Range of Salt Concentration

Fenley

Mascagni

McClain

et al. 2009

J. Chem. Theory Comput.

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Dielectric continuum or implicit solvent models provide a significant reduction in computational cost when accounting for the salt-mediated electrostatic interactions of biomolecules immersed in an ionic environment. These models, in which the solvent and ions are replaced by a dielectric continuum, seek to capture the average statistical effects of the ionic solvent, while the solute is treated at the atomic level of detail. For decades, the solution of the three-dimensional Poisson-Boltzmann equation (PBE), which has become a standard implicit-solvent tool for assessing electrostatic effects in biomolecular systems, has been based on various deterministic numerical methods. Some deterministic PBE algorithms have drawbacks, which include a lack of properly assessing their accuracy, geometrical difficulties caused by discretization, and for some problems their cost in both memory and computation time. Our original stochastic method resolves some of these difficulties by solving the PBE using the Monte Carlo method (MCM). This new approach to the PBE is capable of efficiently solving complex, multi-domain and salt-dependent problems in biomolecular continuum electrostatics to high precision. Here we improve upon our novel stochastic approach by simultaneouly computating of electrostatic potential and solvation free energies at different ionic concentrations through correlated Monte Carlo (MC) sampling. By using carefully constructed correlated random walks in our algorithm, we can actually compute the solution to a standard system including the linearized PBE (LPBE) at all salt concentrations of interest, simultaneously. This approach not only accelerates our MCPBE algorithm, but seems to have cost and accuracy advantages over deterministic methods as well. We verify the effectiveness of this technique by applying it to two common electrostatic computations: the electrostatic potential and polar solvation free energy for calcium binding proteins that are compared with similar results obtained using mature deterministic PBE methods.

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Section: Methodsmentioning

confidence: 99%

Using Correlated Monte Carlo Sampling for Efficiently Solving the Linearized Poisson−Boltzmann Equation Over a Broad Range of Salt Concentration

Fenley

Mascagni

McClain

et al. 2009

J. Chem. Theory Comput.

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Random walk on spheres method for solving anisotropic drift-diffusion problems

Shalimova

Sabelfeld

2018

Monte Carlo Methods and Applications

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We suggest a random walk on spheres based stochastic simulation algorithm for solving drift-diffusion-reaction problems with anisotropic diffusion. The diffusion coefficients and the velocity vector vary in space, and the size of the walking spheres is adapted to the local variation of these functions. The method is mesh free and extremely efficient for calculation of fluxes to boundaries and the concentration of the absorbed particles inside the domain. Applications to cathodoluminescence (CL) and electron beam induced current (EBIC) methods for the analysis of dislocations and other defects in semiconductors are discussed.

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A random walk on small spheres method for solving transient anisotropic diffusion problems

Shalimova

Sabelfeld

2019

Monte Carlo Methods and Applications

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A meshless stochastic algorithm for solving anisotropic transient diffusion problems based on an extension of the classical Random Walk on Spheres method is developed. Direct generalization of the Random Walk on Spheres method to anisotropic diffusion equations is not possible, therefore, we have derived approximations of the probability densities for the first passage time and the exit point on a small sphere. The method can be conveniently applied to solve diffusion problems with spatially varying diffusion coefficients and is simply implemented for complicated three-dimensional domains. Particle tracking algorithm is highly efficient for calculation of fluxes to boundaries. We present some simulation results in the case of cathodoluminescence and electron beam induced current in the vicinity of a dislocation in a semiconductor material.

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An Efficient Monte Carlo Approach for Solving Linear Problems in Biomolecular Electrostatics

Cited by 4 publications

References 3 publications

Using Correlated Monte Carlo Sampling for Efficiently Solving the Linearized Poisson−Boltzmann Equation Over a Broad Range of Salt Concentration

Using Correlated Monte Carlo Sampling for Efficiently Solving the Linearized Poisson−Boltzmann Equation Over a Broad Range of Salt Concentration

Random walk on spheres method for solving anisotropic drift-diffusion problems

A random walk on small spheres method for solving transient anisotropic diffusion problems

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