Monte Carlo Method for Calculating the Electrostatic Energy of a Molecule

Mascagni, Michael; Simonov, Nikolai A.

doi:10.1007/3-540-44860-8_7

Cited by 8 publications

(3 citation statements)

References 13 publications

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“…We refer to Folgari et al [13] for a survey on applications in structural biology. Monte Carlo (MC) algorithms for the linearized Poisson-Boltzmann equation were proposed first by Mascagni and Simonov in [26,27] and improved or extended in Mascagni et al [31,32,12,23], Bossy et al [7]. These MC algorithms involve double randomization techniques [27], walk on spheres techniques [30] to simulate Brownian motion exit times and positions in Ω out and Ω in , and asymmetric jump methods from the boundary Γ to take into account the discontinuity of ε in the divergence form of the PDE (1.5).…”

Section: Introductionmentioning

confidence: 99%

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

Bossy

Champagnat²,

Leman³

et al. 2015

ESAIM: Proc.

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Abstract. The electrostatic potential in the neighborhood of a biomolecule can be computed thanks to the non-linear divergence-form elliptic Poisson-Boltzmann PDE. Dedicated MonteCarlo methods have been developed to solve its linearized version (see e.g. [7], [27]). These algorithms combine walk on spheres techniques and appropriate replacements at the boundary of the molecule. In the first part of this article we compare recent replacement methods for this linearized equation on real size biomolecules, that also require efficient computational geometry algorithms. We compare our results with the deterministic solver APBS. In the second part, we prove a new probabilistic interpretation of the nonlinear Poisson-Boltzmann PDE. A Monte Carlo algorithm is also derived and tested on a simple test case.Résumé. Le potentielélectrostatique autour d'une biomolécule peutêtre calculé grâceà l'équation de Poisson-Boltzmann, une EDP elliptique non-linéaire sous forme divergence. Des méthodes de Monte-Carlo, dédiéesà sa version linéarisée, combinent la marche sur les sphères avec différents schémas de replacementà la frontière de la molécule (voir [7], [27]). La première partie de cet article est consacréeà l'étude et la comparaison de différentes méthodes de replacement pour l'EDP linéarisée, dans le cas de géométries réalistes de biomolécules. Dans la seconde partie, nous donnons une nouvelle interprétation probabiliste de l'EDP de PoissonBoltzmann non linéaire. Nous en déduisons une méthode de Monte-Carlo originale qui est testée sur un cas test simple.

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Section: Introductionmentioning

confidence: 99%

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

Bossy

Champagnat²,

Leman³

et al. 2015

ESAIM: Proc.

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“…Recently [1,2], we proposed an advanced Monte Carlo technique for calculating different properties of large organic molecules. To use this approach, the problems under consideration have to be treated in the framework of continuous media models.…”

Section: Introductionmentioning

confidence: 99%

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

Fleming¹,

Mascagni²,

Simonov³

2005

Lecture Notes in Computer Science

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“…In spite of its many advantages, the FRW method has not been applied in the numerical solution of NPB equation (and other important nonlinear equations) because analytical expressions for volumetric Green's functions [7] are not available. In particular, previous numerical studies using FRW algorithms [8,9] have examined the linearized Poisson-Boltzmann equation, restricting the applicability of the solution to small values of the potential. Here we present a new technique that eliminates this restriction.…”

Section: Introductionmentioning

confidence: 99%

A Parallelized 3d Floating Random-Walk Algorithm for the Solution of the Nonlinear Poisson-Boltzmann Equation

Chatterjee¹,

Poggie²

2006

PIER

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Abstract-This paper presents a new three-dimensional floating random-walk (FRW) algorithm for the solution of the Nonlinear Poisson-Boltzmann (NPB) equation. The FRW method has not been previously used in the numerical solution of the NPB equation (and other nonlinear equations) because of the non-availability of analytical expressions for volumetric Green's functions. In the past, numerical studies using the FRW method have examined only the linearized Poisson-Boltzmann equation, producing solutions that are only accurate for small values of the potential. No such linearization is required for this algorithm. An approximate expression for a volumetric Green's functions has been calculated with the help of a novel use of perturbation theory, and the resultant integral form has been incorporated within the FRW framework. The algorithm requires no discretization of either the volume or the surface of the problem domains, and hence the memory requirements are expected to be lower than approaches based on spatial discretization, such as finitedifference methods. Another advantage of this algorithm is that each random walk is independent, so that the computational procedure is inherently parallelizable and an almost linear increase in computational speed is expected with increase in the number of processors. We have † Adjunct Scientist at Laboratory for Electromagnetic and Electronic Systems, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA 238Chatterjee and Poggie recently published the preliminary results for benchmark problems in one and two dimensions. In this work, we present our results for benchmark problems in three dimensions and demonstrate excellent agreement between the FRW-and finite-difference based algorithms. We also present the results of parallelization of the newly developed FRW algorithm. The solution of the NPB equation has applications in diverse branches of science and engineering including (but not limited to) the modeling of plasma discharges, semiconductor device modeling and the modeling of biomolecular structures and dynamics.

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Monte Carlo Method for Calculating the Electrostatic Energy of a Molecule

Cited by 8 publications

References 13 publications

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

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

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

A Parallelized 3d Floating Random-Walk Algorithm for the Solution of the Nonlinear Poisson-Boltzmann Equation

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