A NEW MOLECULAR-DYNAMICS METHOD COMBINING THE REFERENCE SYSTEM PROPAGATOR ALGORITHM WITH A FAST MULTIPOLE METHOD FOR SIMULATING PROTEINS AND OTHER COMPLEX-SYSTEMS

An efficient molecular dynamics (MD) algorithm is presented in this pa per for biomolecular systems, which incorporates a novel variation on the fast multipole method (FMM) coupled to the reversible reference sy stem propagator algorithm (r-RESPA). A top-down FMM is proposed which calculates multipoles recursively from the top of the box tree instead of from the bottom in Greengard's original FMM, in an effort to be mo re efficient for noncubic or nonuniform systems. In addition, the use of noncubic box subdivisions of biomolecular systems is used and discu ssed. Reversible RESPA based on a Trotter factorization of the Liouvil le propagator in generating numerical integration schemes is coupled t o the top-down FMM and applied to a MD study of proteins in vacuo, and is shown to be able to use a much larger time-step than the standard velocity Verlet method for a comparable level of accuracy. Furthermore , bq using the FMM it becomes possible to perform MD simulations for v ery large biomolecules, since memory and CPU time requirements are now nearly of order of O(N) instead of O(N-2). For a protein with 9513 at oms (the photosynthetic reaction center), the efficient MD algorithm l eads to 20-fold reduction in CPU time for the Coulomb interaction and approximately 15-fold reduction in total CPU time over the standard ve locity Verlet algorithm with a direct evaluation of Coulomb forces. (C ) 1995 American Institute of Physics.