Performance of fast multipole methods for calculating electrostatic interactions in biomacromolecular simulations

The fast multipole method proposed by Greengard and Rokhlin (GR) is applied to large biomacromolecular systems. In this method, the system is divided into a hierarchy of cells, and electric field exerted on a particle is decomposed into two parts. The first part is a rapidly varying field due to nearby cells, so that it needs rigorous pairwise calculations. The second part is a slowly varying local field due to distant cells; hence, it allows rapid calculations through a multipole expansion technique. In this work, two additional possibilities for improving the performance are numerically examined. The first is an improvement of the convergence of the expansion by increasing the number of nearby cells, without including higher‐order multipole moments. The second is an acceleration of the calculations by the particle–particle and particle–mesh/multipole expansion (PPPM/MPE) method, which uses fast Fourier transform instead of the hierarchy. For this purpose, the PPPM/MPE method originally developed by the authors for a periodic system is extended to a nonperiodic isolated system. The advantages and disadvantages of the GR and PPPM/MPE methods are discussed for both periodic and isolated systems. It is numerically shown that these methods with reasonable costs can reduce the error in potential felt by each particle to 0.1–1 kcal/mol, much smaller than the 30‐kcal/mol error involved in conventional simple truncations. © 1994 by John Wiley & Sons, Inc.