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
-
Conservative finite volume method on deforming geometries: The case of protein aggregation in dividing yeast cells
Heydari, A. Ali | Sindi, Suzanne S. | Theillard, MaximeJournal of Computational Physics, Vol. 448 (2022), Iss. P.110755
https://doi.org/10.1016/j.jcp.2021.110755 [Citations: 3] -
A conservative discretization of the Poisson–Nernst–Planck equations on adaptive Cartesian grids
Mirzadeh, Mohammad | Gibou, FrédéricJournal of Computational Physics, Vol. 274 (2014), Iss. P.633
https://doi.org/10.1016/j.jcp.2014.06.039 [Citations: 40] -
TABI-PB 2.0: An Improved Version of the Treecode-Accelerated Boundary Integral Poisson-Boltzmann Solver
Wilson, Leighton | Geng, Weihua | Krasny, RobertThe Journal of Physical Chemistry B, Vol. 126 (2022), Iss. 37 P.7104
https://doi.org/10.1021/acs.jpcb.2c04604 [Citations: 12] -
A review of level-set methods and some recent applications
Gibou, Frederic | Fedkiw, Ronald | Osher, StanleyJournal of Computational Physics, Vol. 353 (2018), Iss. P.82
https://doi.org/10.1016/j.jcp.2017.10.006 [Citations: 290] -
A kernel-free boundary integral method for the nonlinear Poisson-Boltzmann equation
Zhou, Han | Yang, Jiahe | Ying, WenjunJournal of Computational Physics, Vol. 493 (2023), Iss. P.112423
https://doi.org/10.1016/j.jcp.2023.112423 [Citations: 1] -
Efficient calculation of fully resolved electrostatics around large biomolecules
Chowdhury, Rochishnu | Egan, Raphael | Bochkov, Daniil | Gibou, FredericJournal of Computational Physics, Vol. 448 (2022), Iss. P.110718
https://doi.org/10.1016/j.jcp.2021.110718 [Citations: 6] -
A Cartesian FMM-accelerated Galerkin boundary integral Poisson-Boltzmann solver
Chen, Jiahui | Tausch, Johannes | Geng, WeihuaJournal of Computational Physics, Vol. 478 (2023), Iss. P.111981
https://doi.org/10.1016/j.jcp.2023.111981 [Citations: 3] -
An implicit boundary integral method for computing electric potential of macromolecules in solvent
Zhong, Yimin | Ren, Kui | Tsai, RichardJournal of Computational Physics, Vol. 359 (2018), Iss. P.199
https://doi.org/10.1016/j.jcp.2018.01.021 [Citations: 15] -
Regularization methods for the Poisson-Boltzmann equation: Comparison and accuracy recovery
Lee, Arum | Geng, Weihua | Zhao, ShanJournal of Computational Physics, Vol. 426 (2021), Iss. P.109958
https://doi.org/10.1016/j.jcp.2020.109958 [Citations: 9] -
Calculation of electrostatic free energy for the nonlinear Poisson-Boltzmann model based on the dimensionless potential
Zhao, Shan | Ijaodoro, Idowu E. | McGowan, Mark | Alexov, EmilJournal of Computational Physics, Vol. 497 (2024), Iss. P.112634
https://doi.org/10.1016/j.jcp.2023.112634 [Citations: 0] -
A regularization approach for solving the super-Gaussian Poisson-Boltzmann model with heterogeneous dielectric functions
Wang, Siwen | Shao, Yuanzhen | Alexov, Emil | Zhao, ShanJournal of Computational Physics, Vol. 464 (2022), Iss. P.111340
https://doi.org/10.1016/j.jcp.2022.111340 [Citations: 5] -
Reduced basis method for the nonlinear Poisson–Boltzmann equation regularized by the range-separated canonical tensor format
Kweyu, Cleophas | Feng, Lihong | Stein, Matthias | Benner, PeterInternational Journal of Nonlinear Sciences and Numerical Simulation, Vol. 24 (2024), Iss. 8 P.2915
https://doi.org/10.1515/ijnsns-2021-0103 [Citations: 1] -
PDE-Based Multidimensional Extrapolation of Scalar Fields over Interfaces with Kinks and High Curvatures
Bochkov, Daniil | Gibou, FredericSIAM Journal on Scientific Computing, Vol. 42 (2020), Iss. 4 P.A2344
https://doi.org/10.1137/19M1307883 [Citations: 6] -
A sharp numerical method for the simulation of Stefan problems with convective effects
Bayat, Elyce | Egan, Raphael | Bochkov, Daniil | Sauret, Alban | Gibou, FredericJournal of Computational Physics, Vol. 471 (2022), Iss. P.111627
https://doi.org/10.1016/j.jcp.2022.111627 [Citations: 6] -
Computational mean-field modeling of confined active fluids
Theillard, Maxime | Saintillan, DavidJournal of Computational Physics, Vol. 397 (2019), Iss. P.108841
https://doi.org/10.1016/j.jcp.2019.07.040 [Citations: 20] -
Bridging Eulerian and Lagrangian Poisson–Boltzmann solvers by ESES
Ullah, Sheik Ahmed | Yang, Xin | Jones, Ben | Zhao, Shan | Geng, Weihua | Wei, Guo‐WeiJournal of Computational Chemistry, Vol. 45 (2024), Iss. 6 P.306
https://doi.org/10.1002/jcc.27239 [Citations: 0] -
Sharp numerical simulation of incompressible two-phase flows
Theillard, Maxime | Gibou, Frédéric | Saintillan, DavidJournal of Computational Physics, Vol. 391 (2019), Iss. P.91
https://doi.org/10.1016/j.jcp.2019.04.024 [Citations: 22] -
Progress in developing Poisson-Boltzmann equation solvers
Li, Chuan | Li, Lin | Petukh, Marharyta | Alexov, EmilComputational and Mathematical Biophysics, Vol. 1 (2013), Iss. 2013 P.42
https://doi.org/10.2478/mlbmb-2013-0002 [Citations: 24] -
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, ShuyangPhysical Chemistry Chemical Physics, Vol. 25 (2023), Iss. 17 P.12290
https://doi.org/10.1039/D2CP05839A [Citations: 1] -
Fast and scalable algorithms for constructing Solvent-Excluded Surfaces of large biomolecules
Egan, Raphael | Gibou, FrédéricJournal of Computational Physics, Vol. 374 (2018), Iss. P.91
https://doi.org/10.1016/j.jcp.2018.07.035 [Citations: 13] -
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, MatthiasSIAM Journal on Scientific Computing, Vol. 43 (2021), Iss. 1 P.A415
https://doi.org/10.1137/19M1281435 [Citations: 6] -
Computational modeling of protein conformational changes - Application to the opening SARS-CoV-2 spike
Kucherova, Anna | Strango, Selma | Sukenik, Shahar | Theillard, MaximeJournal of Computational Physics, Vol. 444 (2021), Iss. P.110591
https://doi.org/10.1016/j.jcp.2021.110591 [Citations: 7] -
Solving elliptic interface problems with jump conditions on Cartesian grids
Bochkov, Daniil | Gibou, FredericJournal of Computational Physics, Vol. 407 (2020), Iss. P.109269
https://doi.org/10.1016/j.jcp.2020.109269 [Citations: 27] -
A Sharp Computational Method for the Simulation of the Solidification of Binary Alloys
Theillard, Maxime | Gibou, Frédéric | Pollock, TresaJournal of Scientific Computing, Vol. 63 (2015), Iss. 2 P.330
https://doi.org/10.1007/s10915-014-9895-0 [Citations: 33]