### Abstract

This article presents a fast adaptive method for the computation of long-range electrostatic interactions in computer simulations of polyelectrolyte DNA. Classically, the computation of electrostatic energy involves a direct summation of all pairwise interactions due to the charged phosphate groups in the molecule. This results in an N-body interaction problem with an asymptotic time complexity of O(N^{2}) which is computationally very expensive and limits the number of phosphate groups that can be used in computer simulations of polyelectrolyte DNA to at most several hundred. We describe an effort to speed up computer simulations of polyelectrolyte DNA with the use of a fast adaptive hierarchical algorithm for the computation of electrostatic energy (i.e., modified Debye-Hückel energy). The asymptotic time complexity is reduced to O(N) with the implementation of the fast hierarchical algorithm on serial computers. This is achieved by grouping phosphate groups into an adaptive hierarchical data structure and computing the interactions between groups using low order multipole and Taylor series expansions expressed in Cartesian coordinates. We first examine the accuracy and speed enhancements of the fast hierarchical method in the computation of the electrostatic energy of circular DNA at zero and high salt concentrations. The fast hierarchical method is further tested in a one-step Monte Carlo (MC) simulated annealing algorithm for closed circular supercoiled DNA. In all cases, we observe order of magnitude reductions in the computation time with negligible loss of numerical accuracy in the electrostatic energy computation.

Original language | English (US) |
---|---|

Pages (from-to) | 976-991 |

Number of pages | 16 |

Journal | Journal of Computational Chemistry |

Volume | 17 |

Issue number | 8 |

DOIs | |

State | Published - Jun 1996 |

### All Science Journal Classification (ASJC) codes

- Chemistry(all)
- Computational Mathematics

## Fingerprint Dive into the research topics of 'Fast adaptive multipole method for computation of electrostatic energy in simulations of polyelectrolyte DNA'. Together they form a unique fingerprint.

## Cite this

*Journal of Computational Chemistry*,

*17*(8), 976-991. https://doi.org/10.1002/(SICI)1096-987X(199606)17:8<976::AID-JCC7>3.0.CO;2-O