Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver

doi:https://doi.org/10.4208/cicp.210711.111111s

Title: Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver

Abstract

This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann (AFMPB) solver. We introduce and discuss the following components in order: the Poisson-Boltzmann model, boundary integral equation reformulation, surface mesh generation, the nodepatch discretization approach, Krylov iterative methods, the new version of fast multipole methods (FMMs), and a dynamic prioritization technique for scheduling parallel operations. For each component, we also remark on feasible approaches for further improvements in efficiency, accuracy and applicability of the AFMPB solver to large-scale long-time molecular dynamics simulations. Lastly, the potential of the solver is demonstrated with preliminary numerical results.

Authors:

Zhang, Bo ^[1]; Lu, Benzhuo ^[2]; Cheng, Xiaolin ^[3]; Huang, Jingfang ^[4]; Pitsianis, Nikos P. ^[5]; Sun, Xiaobai ^[1]; McCammon, J. Andrew ^[6]

Duke Univ., Durham, NC (United States). Dept. of Computer Science
Chinese Academy of Sciences (CAS), Beijing (China). Inst. of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Center for Molecular Biophysics
Univ. of North Carolina, Chapel Hill, NC (United States). Dept. of Mathematics
Duke Univ., Durham, NC (United States). Dept. of Computer Science; Aristotle Univ., Thessaloniki (Greece). Dept. of Electrical and Computer Engineering
Howard Hughes Medical Inst., Chevy Chase, MD (United States). Dept. of Pharmacology; Univ. of California, San Diego, CA (United States)

Publication Date:: 2013-01-01

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE; National Science Foundation (NSF); National Institutes of Health (NIH); Chinese Academy of Sciences

OSTI Identifier:: 1376302

Grant/Contract Number:: AC05-00OR22725

Resource Type:: Journal Article: Accepted Manuscript

Journal Name:: Communications in Computational Physics

Additional Journal Information:: Journal Volume: 13; Journal Issue: 01; Journal ID: ISSN 1815-2406

Publisher:: Global Science Press

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; Biomolecular System; Electrostatics; Poisson-Boltzmann Equation; Fast Multipole Methods; Mesh Generation; Directed Acyclic Graph; Dynamic Prioritization; Parallelization

Citation Formats


                    Zhang, Bo, Lu, Benzhuo, Cheng, Xiaolin, Huang, Jingfang, Pitsianis, Nikos P., Sun, Xiaobai, and McCammon, J. Andrew. Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver.  United States: N. p., 2013. 
        Web.  doi:10.4208/cicp.210711.111111s.

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                    Zhang, Bo, Lu, Benzhuo, Cheng, Xiaolin, Huang, Jingfang, Pitsianis, Nikos P., Sun, Xiaobai, & McCammon, J. Andrew. Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver.  United States.  https://doi.org/10.4208/cicp.210711.111111s

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                    Zhang, Bo, Lu, Benzhuo, Cheng, Xiaolin, Huang, Jingfang, Pitsianis, Nikos P., Sun, Xiaobai, and McCammon, J. Andrew. Tue .  
        "Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver".  United States.  https://doi.org/10.4208/cicp.210711.111111s.  https://www.osti.gov/servlets/purl/1376302.

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@article{osti_1376302,

  title        = {Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver},

  author       = {Zhang, Bo and Lu, Benzhuo and Cheng, Xiaolin and Huang, Jingfang and Pitsianis, Nikos P. and Sun, Xiaobai and McCammon, J. Andrew},

  abstractNote = {This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann (AFMPB) solver. We introduce and discuss the following components in order: the Poisson-Boltzmann model, boundary integral equation reformulation, surface mesh generation, the nodepatch discretization approach, Krylov iterative methods, the new version of fast multipole methods (FMMs), and a dynamic prioritization technique for scheduling parallel operations. For each component, we also remark on feasible approaches for further improvements in efficiency, accuracy and applicability of the AFMPB solver to large-scale long-time molecular dynamics simulations. Lastly, the potential of the solver is demonstrated with preliminary numerical results.},

  doi          = {10.4208/cicp.210711.111111s},

  url          = {https://www.osti.gov/biblio/1376302},
  journal      = {Communications in Computational Physics},

  issn         = {1815-2406},

  number       = 01,

  volume       = 13,

  place        = {United States},

  year         = {2013},

  month        = {1}

}

Copy to clipboard

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Works referencing / citing this record:

Progress in developing Poisson-Boltzmann equation solvers
journal, January 2013

Li, Chuan; Li, Lin; Petukh, Marharyta
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Title: Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver

Abstract

Citation Formats

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Continuum solvation model: Computation of electrostatic forces from numerical solutions to the Poisson-Boltzmann equation journal, June 1998

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A fast algorithm for particle simulations journal, December 1987

A Fast Adaptive Multipole Algorithm in Three Dimensions journal, November 1999

The interpretation of protein structures: Estimation of static accessibility journal, February 1971

Load Balancing and Data Locality in Adaptive Hierarchical N-Body Methods: Barnes-Hut, Fast Multipole, and Radiosity journal, June 1995

van der Waals Volumes and Radii journal, March 1964

Coupling Hydrophobicity, Dispersion, and Electrostatics in Continuum Solvent Models journal, March 2006

An Efficient Program for Many-Body Simulation journal, January 1985

AFMPB: An adaptive fast multipole Poisson–Boltzmann solver for calculating electrostatics in biomolecular systems journal, June 2010

Minimal molecular surfaces and their applications journal, January 2007

Computation of molecular electrostatics with boundary element methods journal, October 1997

Implicit solvent models journal, April 1999

Ion Selectivity Mechanism in a Bacterial Pentameric Ligand-Gated Ion Channel journal, January 2011

A smooth permittivity function for Poisson-Boltzmann solvation methods journal, January 2001

A hierarchical O(N log N) force-calculation algorithm journal, December 1986

PBEQ-Solver for online visualization of electrostatic potential of biomolecules journal, May 2008

FMM-Yukawa: An adaptive fast multipole method for screened Coulomb interactions journal, November 2009

TMSmesh: A Robust Method for Molecular Surface Mesh Generation Using a Trace Technique journal, November 2010

Physical scoring function based on AMBER force field and Poisson-Boltzmann implicit solvent for protein structure prediction journal, April 2004

Fast Boundary Element Method for the Linear Poisson−Boltzmann Equation journal, March 2002

Optimization of Gaussian surface calculations and extension to solvent-accessible surface areas journal, May 1999

Areas, Volumes, Packing, and Protein Structure journal, June 1977

Electrostatics and diffusion of molecules in solution: simulations with the University of Houston Brownian Dynamics program journal, September 1995

The Poisson-Boltzmann equation for biomolecular electrostatics: a tool for structural biology journal, January 2002

Theoretical Methods for the Description of the Solvent Effect in Biomolecular Systems journal, November 2000

A precorrected-FFT method for electrostatic analysis of complicated 3-D structures journal, January 1997

A parallel adaptive fast multipole method conference, January 1993

A Matrix Version of the Fast Multipole Method journal, January 2001

Provably Good Partitioning and Load Balancing Algorithms for Parallel Adaptive N-Body Simulation journal, March 1998

NP-complete scheduling problems journal, June 1975

A parallel hashed Oct-Tree N-body algorithm conference, January 1993

Highly accurate biomolecular electrostatics in continuum dielectric environments journal, January 2007

Quality meshing of implicit solvation models of biomolecular structures journal, August 2006

Particle mesh Ewald: An N ⋅log( N ) method for Ewald sums in large systems journal, June 1993

Solution of acoustic scattering problems by means of second kind integral equations journal, June 1983

The electric potential of a macromolecule in a solvent: A fundamental approach journal, November 1991

Parallel Sequencing and Assembly Line Problems journal, December 1961

Protein folding and association: Insights from the interfacial and thermodynamic properties of hydrocarbons journal, December 1991

Progress in developing Poisson-Boltzmann equation solvers journal, January 2013

Progress in developing Poisson-Boltzmann equation solvers journal, January 2013

Electrodiffusion: A continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution
journal, October 2007

Improved Boundary Element Methods for Poisson−Boltzmann Electrostatic Potential and Force Calculations
journal, March 2007

“New-version-fast-multipole-method” accelerated electrostatic calculations in biomolecular systems
journal, October 2007

A New Version of the Fast Multipole Method for Screened Coulomb Interactions in Three Dimensions
journal, August 2002

The Amber biomolecular simulation programs
journal, January 2005

A new version of the Fast Multipole Method for the Laplace equation in three dimensions
journal, January 1997

Continuum solvation model: Computation of electrostatic forces from numerical solutions to the Poisson-Boltzmann equation
journal, June 1998

A parallel version of the fast multipole method
journal, January 1990

Hybrid boundary element and finite difference method for solving the nonlinear Poisson-Boltzmann equation
journal, January 2004

A fast algorithm for particle simulations
journal, December 1987

A Fast Adaptive Multipole Algorithm in Three Dimensions
journal, November 1999

The interpretation of protein structures: Estimation of static accessibility
journal, February 1971

Load Balancing and Data Locality in Adaptive Hierarchical N-Body Methods: Barnes-Hut, Fast Multipole, and Radiosity
journal, June 1995

van der Waals Volumes and Radii
journal, March 1964

Coupling Hydrophobicity, Dispersion, and Electrostatics in Continuum Solvent Models
journal, March 2006

An Efficient Program for Many-Body Simulation
journal, January 1985

AFMPB: An adaptive fast multipole Poisson–Boltzmann solver for calculating electrostatics in biomolecular systems
journal, June 2010

Minimal molecular surfaces and their applications
journal, January 2007

Computation of molecular electrostatics with boundary element methods
journal, October 1997

Implicit solvent models
journal, April 1999

Ion Selectivity Mechanism in a Bacterial Pentameric Ligand-Gated Ion Channel
journal, January 2011

A smooth permittivity function for Poisson-Boltzmann solvation methods
journal, January 2001

A hierarchical O(N log N) force-calculation algorithm
journal, December 1986

PBEQ-Solver for online visualization of electrostatic potential of biomolecules
journal, May 2008

FMM-Yukawa: An adaptive fast multipole method for screened Coulomb interactions
journal, November 2009

TMSmesh: A Robust Method for Molecular Surface Mesh Generation Using a Trace Technique
journal, November 2010

Physical scoring function based on AMBER force field and Poisson-Boltzmann implicit solvent for protein structure prediction
journal, April 2004

Fast Boundary Element Method for the Linear Poisson−Boltzmann Equation
journal, March 2002

Optimization of Gaussian surface calculations and extension to solvent-accessible surface areas
journal, May 1999

Areas, Volumes, Packing, and Protein Structure
journal, June 1977

Electrostatics and diffusion of molecules in solution: simulations with the University of Houston Brownian Dynamics program
journal, September 1995

The Poisson-Boltzmann equation for biomolecular electrostatics: a tool for structural biology
journal, January 2002

Theoretical Methods for the Description of the Solvent Effect in Biomolecular Systems
journal, November 2000

A precorrected-FFT method for electrostatic analysis of complicated 3-D structures
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A parallel adaptive fast multipole method
conference, January 1993

A Matrix Version of the Fast Multipole Method
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Provably Good Partitioning and Load Balancing Algorithms for Parallel Adaptive N-Body Simulation
journal, March 1998

NP-complete scheduling problems
journal, June 1975

A parallel hashed Oct-Tree N-body algorithm
conference, January 1993

Highly accurate biomolecular electrostatics in continuum dielectric environments
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Quality meshing of implicit solvation models of biomolecular structures
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Particle mesh Ewald: An N ⋅log( N ) method for Ewald sums in large systems
journal, June 1993

Solution of acoustic scattering problems by means of second kind integral equations
journal, June 1983

The electric potential of a macromolecule in a solvent: A fundamental approach
journal, November 1991

Parallel Sequencing and Assembly Line Problems
journal, December 1961

Protein folding and association: Insights from the interfacial and thermodynamic properties of hydrocarbons
journal, December 1991

Progress in developing Poisson-Boltzmann equation solvers
journal, January 2013

Progress in developing Poisson-Boltzmann equation solvers
journal, January 2013