An Adaptive, Finite Difference Solver for the Nonlinear Poisson-Boltzmann Equation with Applications to Biomolecular Computations

An Adaptive, Finite Difference Solver for the Nonlinear Poisson-Boltzmann Equation with Applications to Biomolecular Computations

Year:    2013

Communications in Computational Physics, Vol. 13 (2013), Iss. 1 : pp. 150–173

Abstract

We present a solver for the Poisson-Boltzmann equation and demonstrate its applicability for biomolecular electrostatics computation. The solver uses a level set framework to represent sharp, complex interfaces in a simple and robust manner. It also uses non-graded, adaptive octree grids which, in comparison to uniform grids, drastically decrease memory usage and runtime without sacrificing accuracy. The basic solver was introduced in earlier works [16, 27], and here is extended to address biomolecular systems. First, a novel approach of calculating the solvent excluded and the solvent accessible surfaces is explained; this allows to accurately represent the location of the molecule's surface. Next, a hybrid finite difference/finite volume approach is presented for discretizing the nonlinear Poisson-Boltzmann equation and enforcing the jump boundary conditions at the interface. Since the interface is implicitly represented by a level set function, imposing the jump boundary conditions is straightforward and efficient.

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.290711.181011s

Communications in Computational Physics, Vol. 13 (2013), Iss. 1 : pp. 150–173

Published online:    2013-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:   

  1. Conservative finite volume method on deforming geometries: The case of protein aggregation in dividing yeast cells

    Heydari, A. Ali | Sindi, Suzanne S. | Theillard, Maxime

    Journal of Computational Physics, Vol. 448 (2022), Iss. P.110755

    https://doi.org/10.1016/j.jcp.2021.110755 [Citations: 3]
  2. A conservative discretization of the Poisson–Nernst–Planck equations on adaptive Cartesian grids

    Mirzadeh, Mohammad | Gibou, Frédéric

    Journal of Computational Physics, Vol. 274 (2014), Iss. P.633

    https://doi.org/10.1016/j.jcp.2014.06.039 [Citations: 40]
  3. TABI-PB 2.0: An Improved Version of the Treecode-Accelerated Boundary Integral Poisson-Boltzmann Solver

    Wilson, Leighton | Geng, Weihua | Krasny, Robert

    The Journal of Physical Chemistry B, Vol. 126 (2022), Iss. 37 P.7104

    https://doi.org/10.1021/acs.jpcb.2c04604 [Citations: 12]
  4. A review of level-set methods and some recent applications

    Gibou, Frederic | Fedkiw, Ronald | Osher, Stanley

    Journal of Computational Physics, Vol. 353 (2018), Iss. P.82

    https://doi.org/10.1016/j.jcp.2017.10.006 [Citations: 290]
  5. A kernel-free boundary integral method for the nonlinear Poisson-Boltzmann equation

    Zhou, Han | Yang, Jiahe | Ying, Wenjun

    Journal of Computational Physics, Vol. 493 (2023), Iss. P.112423

    https://doi.org/10.1016/j.jcp.2023.112423 [Citations: 1]
  6. Efficient calculation of fully resolved electrostatics around large biomolecules

    Chowdhury, Rochishnu | Egan, Raphael | Bochkov, Daniil | Gibou, Frederic

    Journal of Computational Physics, Vol. 448 (2022), Iss. P.110718

    https://doi.org/10.1016/j.jcp.2021.110718 [Citations: 6]
  7. A Cartesian FMM-accelerated Galerkin boundary integral Poisson-Boltzmann solver

    Chen, Jiahui | Tausch, Johannes | Geng, Weihua

    Journal of Computational Physics, Vol. 478 (2023), Iss. P.111981

    https://doi.org/10.1016/j.jcp.2023.111981 [Citations: 3]
  8. An implicit boundary integral method for computing electric potential of macromolecules in solvent

    Zhong, Yimin | Ren, Kui | Tsai, Richard

    Journal of Computational Physics, Vol. 359 (2018), Iss. P.199

    https://doi.org/10.1016/j.jcp.2018.01.021 [Citations: 15]
  9. Regularization methods for the Poisson-Boltzmann equation: Comparison and accuracy recovery

    Lee, Arum | Geng, Weihua | Zhao, Shan

    Journal of Computational Physics, Vol. 426 (2021), Iss. P.109958

    https://doi.org/10.1016/j.jcp.2020.109958 [Citations: 9]
  10. Calculation of electrostatic free energy for the nonlinear Poisson-Boltzmann model based on the dimensionless potential

    Zhao, Shan | Ijaodoro, Idowu E. | McGowan, Mark | Alexov, Emil

    Journal of Computational Physics, Vol. 497 (2024), Iss. P.112634

    https://doi.org/10.1016/j.jcp.2023.112634 [Citations: 0]
  11. A regularization approach for solving the super-Gaussian Poisson-Boltzmann model with heterogeneous dielectric functions

    Wang, Siwen | Shao, Yuanzhen | Alexov, Emil | Zhao, Shan

    Journal of Computational Physics, Vol. 464 (2022), Iss. P.111340

    https://doi.org/10.1016/j.jcp.2022.111340 [Citations: 5]
  12. Reduced basis method for the nonlinear Poisson–Boltzmann equation regularized by the range-separated canonical tensor format

    Kweyu, Cleophas | Feng, Lihong | Stein, Matthias | Benner, Peter

    International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 24 (2024), Iss. 8 P.2915

    https://doi.org/10.1515/ijnsns-2021-0103 [Citations: 1]
  13. PDE-Based Multidimensional Extrapolation of Scalar Fields over Interfaces with Kinks and High Curvatures

    Bochkov, Daniil | Gibou, Frederic

    SIAM Journal on Scientific Computing, Vol. 42 (2020), Iss. 4 P.A2344

    https://doi.org/10.1137/19M1307883 [Citations: 6]
  14. A sharp numerical method for the simulation of Stefan problems with convective effects

    Bayat, Elyce | Egan, Raphael | Bochkov, Daniil | Sauret, Alban | Gibou, Frederic

    Journal of Computational Physics, Vol. 471 (2022), Iss. P.111627

    https://doi.org/10.1016/j.jcp.2022.111627 [Citations: 6]
  15. Computational mean-field modeling of confined active fluids

    Theillard, Maxime | Saintillan, David

    Journal of Computational Physics, Vol. 397 (2019), Iss. P.108841

    https://doi.org/10.1016/j.jcp.2019.07.040 [Citations: 20]
  16. Bridging Eulerian and Lagrangian Poisson–Boltzmann solvers by ESES

    Ullah, Sheik Ahmed | Yang, Xin | Jones, Ben | Zhao, Shan | Geng, Weihua | Wei, Guo‐Wei

    Journal of Computational Chemistry, Vol. 45 (2024), Iss. 6 P.306

    https://doi.org/10.1002/jcc.27239 [Citations: 0]
  17. Sharp numerical simulation of incompressible two-phase flows

    Theillard, Maxime | Gibou, Frédéric | Saintillan, David

    Journal of Computational Physics, Vol. 391 (2019), Iss. P.91

    https://doi.org/10.1016/j.jcp.2019.04.024 [Citations: 22]
  18. 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]
  19. An energy minimization strategy based on an improved nonlinear conjugate gradient method for accelerating the charged polymer dynamics simulation

    Lin, Hao | Shi, Yiwei | Shang, Enlong | Dai, Shuyang

    Physical Chemistry Chemical Physics, Vol. 25 (2023), Iss. 17 P.12290

    https://doi.org/10.1039/D2CP05839A [Citations: 1]
  20. Fast and scalable algorithms for constructing Solvent-Excluded Surfaces of large biomolecules

    Egan, Raphael | Gibou, Frédéric

    Journal of Computational Physics, Vol. 374 (2018), Iss. P.91

    https://doi.org/10.1016/j.jcp.2018.07.035 [Citations: 13]
  21. Regularization of Poisson--Boltzmann Type Equations with Singular Source Terms Using the Range-Separated Tensor Format

    Benner, Peter | Khoromskaia, Venera | Khoromskij, Boris | Kweyu, Cleophas | Stein, Matthias

    SIAM Journal on Scientific Computing, Vol. 43 (2021), Iss. 1 P.A415

    https://doi.org/10.1137/19M1281435 [Citations: 6]
  22. Computational modeling of protein conformational changes - Application to the opening SARS-CoV-2 spike

    Kucherova, Anna | Strango, Selma | Sukenik, Shahar | Theillard, Maxime

    Journal of Computational Physics, Vol. 444 (2021), Iss. P.110591

    https://doi.org/10.1016/j.jcp.2021.110591 [Citations: 7]
  23. Solving elliptic interface problems with jump conditions on Cartesian grids

    Bochkov, Daniil | Gibou, Frederic

    Journal of Computational Physics, Vol. 407 (2020), Iss. P.109269

    https://doi.org/10.1016/j.jcp.2020.109269 [Citations: 27]
  24. A Sharp Computational Method for the Simulation of the Solidification of Binary Alloys

    Theillard, Maxime | Gibou, Frédéric | Pollock, Tresa

    Journal of Scientific Computing, Vol. 63 (2015), Iss. 2 P.330

    https://doi.org/10.1007/s10915-014-9895-0 [Citations: 33]