Boundary element solution of the linear Poisson-Boltzmann equation and a multipole method for the rapid calculation of forces on macromolecules in solution

A. J. Bordner, G. A. Huber

Research output: Contribution to journalArticle

58 Citations (Scopus)

Abstract

The Poisson-Boltzmann equation is widely used to describe the electrostatic potential of molecules in an ionic solution that is treated as a continuous dielectric medium. The linearized form of this equation, applicable to many biologic macromolecules, may be solved using the boundary element method. A single-layer formulation of the boundary element method, which yields simpler integral equations than the direct formulations previously discussed in the literature, is given. It is shown that the electrostatic force and torque on a molecule may be calculated using its boundary element representation and also the polarization charge for two rigid molecules may be rapidly calculated using a noniterative scheme. An algorithm based on a fast adaptive multipole method is introduced to further increase the speed of the calculation. This method is particularly suited for Brownian dynamics or molecular dynamics simulations of large molecules, in which the electrostatic forces must be calculated for many different relative positions and orientations of the molecules. It has been implemented as a set of programs in C++, which are used to study the accuracy and speed of this method for two actin monomers.

Original languageEnglish (US)
Pages (from-to)353-367
Number of pages15
JournalJournal of Computational Chemistry
Volume24
Issue number3
DOIs
StatePublished - Feb 2003
Externally publishedYes

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Insulator Elements
Poisson-Boltzmann Equation
Boltzmann equation
Macromolecules
Boundary Elements
Linear equation
Molecules
Electrostatic Force
Electrostatic force
Boundary element method
Brownian Dynamics
Formulation
Actin
C++
Electrostatics
Molecular Dynamics Simulation
Integral equations
Torque
Molecular dynamics
Actins

Keywords

  • Boundary element method
  • Brownian dynamics
  • Cell multipole method
  • Molecular dynamics
  • Poisson-Boltzmann equation

ASJC Scopus subject areas

  • Chemistry(all)
  • Safety, Risk, Reliability and Quality

Cite this

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abstract = "The Poisson-Boltzmann equation is widely used to describe the electrostatic potential of molecules in an ionic solution that is treated as a continuous dielectric medium. The linearized form of this equation, applicable to many biologic macromolecules, may be solved using the boundary element method. A single-layer formulation of the boundary element method, which yields simpler integral equations than the direct formulations previously discussed in the literature, is given. It is shown that the electrostatic force and torque on a molecule may be calculated using its boundary element representation and also the polarization charge for two rigid molecules may be rapidly calculated using a noniterative scheme. An algorithm based on a fast adaptive multipole method is introduced to further increase the speed of the calculation. This method is particularly suited for Brownian dynamics or molecular dynamics simulations of large molecules, in which the electrostatic forces must be calculated for many different relative positions and orientations of the molecules. It has been implemented as a set of programs in C++, which are used to study the accuracy and speed of this method for two actin monomers.",
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AU - Bordner, A. J.

AU - Huber, G. A.

PY - 2003/2

Y1 - 2003/2

N2 - The Poisson-Boltzmann equation is widely used to describe the electrostatic potential of molecules in an ionic solution that is treated as a continuous dielectric medium. The linearized form of this equation, applicable to many biologic macromolecules, may be solved using the boundary element method. A single-layer formulation of the boundary element method, which yields simpler integral equations than the direct formulations previously discussed in the literature, is given. It is shown that the electrostatic force and torque on a molecule may be calculated using its boundary element representation and also the polarization charge for two rigid molecules may be rapidly calculated using a noniterative scheme. An algorithm based on a fast adaptive multipole method is introduced to further increase the speed of the calculation. This method is particularly suited for Brownian dynamics or molecular dynamics simulations of large molecules, in which the electrostatic forces must be calculated for many different relative positions and orientations of the molecules. It has been implemented as a set of programs in C++, which are used to study the accuracy and speed of this method for two actin monomers.

AB - The Poisson-Boltzmann equation is widely used to describe the electrostatic potential of molecules in an ionic solution that is treated as a continuous dielectric medium. The linearized form of this equation, applicable to many biologic macromolecules, may be solved using the boundary element method. A single-layer formulation of the boundary element method, which yields simpler integral equations than the direct formulations previously discussed in the literature, is given. It is shown that the electrostatic force and torque on a molecule may be calculated using its boundary element representation and also the polarization charge for two rigid molecules may be rapidly calculated using a noniterative scheme. An algorithm based on a fast adaptive multipole method is introduced to further increase the speed of the calculation. This method is particularly suited for Brownian dynamics or molecular dynamics simulations of large molecules, in which the electrostatic forces must be calculated for many different relative positions and orientations of the molecules. It has been implemented as a set of programs in C++, which are used to study the accuracy and speed of this method for two actin monomers.

KW - Boundary element method

KW - Brownian dynamics

KW - Cell multipole method

KW - Molecular dynamics

KW - Poisson-Boltzmann equation

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