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

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

Year:    2013

Communications in Computational Physics, Vol. 13 (2013), Iss. 1 : pp. 195–206

Abstract

Stochastic 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, previouslyreported 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. 

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.220711.041011s

Communications in Computational Physics, Vol. 13 (2013), Iss. 1 : pp. 195–206

Published online:    2013-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:   

  1. Examining sharp restart in a Monte Carlo method for the linearized Poisson–Boltzmann equation

    Thrasher, W. John | Mascagni, Michael

    Monte Carlo Methods and Applications, Vol. 26 (2020), Iss. 3 P.223

    https://doi.org/10.1515/mcma-2020-2069 [Citations: 3]
  2. Monte Carlo Methods for Partial Differential Equations With Applications to Electronic Design Automation

    Introduction

    Yu, Wenjian | Mascagni, Michael

    2023

    https://doi.org/10.1007/978-981-19-3250-2_1 [Citations: 0]
  3. Reference Module in Life Sciences

    A Review of Mathematical Modeling, Simulation and Analysis of Membrane Channel Charge Transport ☆

    Chen, Duan | Wei, Guo-Wei

    2017

    https://doi.org/10.1016/B978-0-12-809633-8.12044-8 [Citations: 3]
  4. Influence of Grid Spacing in Poisson–Boltzmann Equation Binding Energy Estimation

    Harris, Robert C. | Boschitsch, Alexander H. | Fenley, Marcia O.

    Journal of Chemical Theory and Computation, Vol. 9 (2013), Iss. 8 P.3677

    https://doi.org/10.1021/ct300765w [Citations: 26]
  5. Progress in developing Poisson-Boltzmann equation solvers

    Li, Chuan | Li, Lin | Petukh, Marharyta | Alexov, Emil

    Computational and Mathematical Biophysics, Vol. 1 (2013), Iss. 2013 P.42

    https://doi.org/10.2478/mlbmb-2013-0002 [Citations: 24]
  6. A Stochastic Solver of the Generalized Born Model

    Harris, Robert C. | Mackoy, Travis | Fenley, Marcia O.

    Computational and Mathematical Biophysics, Vol. 1 (2013), Iss. 2013 P.63

    https://doi.org/10.2478/mlbmb-2013-0003 [Citations: 5]
  7. Unbiased ‘walk-on-spheres’ Monte Carlo methods for the fractional Laplacian

    Kyprianou, Andreas E | Osojnik, Ana | Shardlow, Tony

    IMA Journal of Numerical Analysis, Vol. 38 (2018), Iss. 3 P.1550

    https://doi.org/10.1093/imanum/drx042 [Citations: 25]
  8. Advanced Potential Energy Surfaces for Condensed Phase Simulation

    Demerdash, Omar | Yap, Eng-Hui | Head-Gordon, Teresa

    Annual Review of Physical Chemistry, Vol. 65 (2014), Iss. 1 P.149

    https://doi.org/10.1146/annurev-physchem-040412-110040 [Citations: 59]
  9. Fractional Poisson–Nernst–Planck Model for Ion Channels I: Basic Formulations and Algorithms

    Chen, Duan

    Bulletin of Mathematical Biology, Vol. 79 (2017), Iss. 11 P.2696

    https://doi.org/10.1007/s11538-017-0349-3 [Citations: 2]
  10. Geometry entrapment in Walk-on-Subdomains

    Hamlin, Preston | Thrasher, W. John | Keyrouz, Walid | Mascagni, Michael

    Monte Carlo Methods and Applications, Vol. 25 (2019), Iss. 4 P.329

    https://doi.org/10.1515/mcma-2019-2052 [Citations: 10]
  11. Accuracy Comparison of Generalized Born Models in the Calculation of Electrostatic Binding Free Energies

    Izadi, Saeed | Harris, Robert C. | Fenley, Marcia O. | Onufriev, Alexey V.

    Journal of Chemical Theory and Computation, Vol. 14 (2018), Iss. 3 P.1656

    https://doi.org/10.1021/acs.jctc.7b00886 [Citations: 25]