Efficient calculations of coulombic interactions in biomolecular simulations with periodic boundary conditions

Abstract

To make improved treatments of electrostatic interactions in biomacromolecular simulations, two possibilities are considered. The f i s t is the famous particle-particle and particle-mesh (PPPM) method developed by Hockney and Eastwood, and the second is a new one developed here in their spirit but by the use of the multipole expansion technique suggested by Ladd. It is then numerically found that the new PPPM method gives more accurate results for a two-particle system at small separation of particles. Preliminary numerical examination of the various computational methods for a single configuration of a model BPTI-water system containing about 24,000 particles indicates that both of the PPPM methods give far more accurate values with reasonable computational cost than do the conventional truncation methods. It is concluded the two PPPM methods are nearly comparable in overall performance for the many-particle systems, although the fist method has the drawback that the accuracy in the total electrostatic energy is not high for configurations of charged particles randomly generated. 0 1993 by John Wiley & Sons. Inc.

A fast algorithm for three-dimensional potential fields calculation: fast Fourier transform on multipoles

“…The present FFTM is similar to the approach implemented by Shimada et al [24,25] for the biomolecular simulations. They called it the particle-particle and particle-mesh/multipole expansion (PPPM/ MPE) method.…”

An image-based reaction field method for electrostatic interactions in molecular dynamics simulations of aqueous solutions

“…There are a number of ways to compute interactions among charges in explicit solvents, including simple cutoff methods, 35 a variety of lattice-sum methods such as Ewald summation, 36,37 particle-mesh Ewald ͑PME͒ 38,39 or particle-particle particle-mesh, 40,41 and fast multipole methods ͑FMM͒. 42,43 Of these, the lattice-sum methods are considered to be most accurate.…”

Simple recursive implementation of fast multipole method

“…''Fast multipole'' methods [1] (FMMs) grew out of the fast Fourier transform method and have been used for about 15 years [2], to speed up large scale simulations involving long ranged forces. The advantage of this method is that the required time is of order N, where N is the number of objects (atoms, computational cells, etc.)…”