### 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 language | English (US) |
---|---|

Pages (from-to) | 353-367 |

Number of pages | 15 |

Journal | Journal of Computational Chemistry |

Volume | 24 |

Issue number | 3 |

DOIs | |

State | Published - Feb 2003 |

Externally published | Yes |

### Fingerprint

### 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

*Journal of Computational Chemistry*,

*24*(3), 353-367. https://doi.org/10.1002/jcc.10195

**Boundary element solution of the linear Poisson-Boltzmann equation and a multipole method for the rapid calculation of forces on macromolecules in solution.** / Bordner, A. J.; Huber, G. A.

Research output: Contribution to journal › Article

*Journal of Computational Chemistry*, vol. 24, no. 3, pp. 353-367. https://doi.org/10.1002/jcc.10195

}

TY - JOUR

T1 - Boundary element solution of the linear Poisson-Boltzmann equation and a multipole method for the rapid calculation of forces on macromolecules in solution

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

UR - http://www.scopus.com/inward/record.url?scp=0037328258&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037328258&partnerID=8YFLogxK

U2 - 10.1002/jcc.10195

DO - 10.1002/jcc.10195

M3 - Article

VL - 24

SP - 353

EP - 367

JO - Journal of Computational Chemistry

JF - Journal of Computational Chemistry

SN - 0192-8651

IS - 3

ER -