Efficient multiple time step method for use with Ewald and particle mesh Ewald for large biomolecular systems

Abstract

The particle–particle particle–mesh (P3M) method for calculating long-range electrostatic forces in molecular simulations is modified and combined with the reversible reference system propagator algorithm (RESPA) for treating the multiple time scale problems in the molecular dynamics of complex systems with multiple time scales and long-range forces. The resulting particle–particle particle–mesh Ewald RESPA (P3ME/RESPA) method provides a fast and accurate representation of the long-range electrostatic interactions for biomolecular systems such as protein solutions. The method presented here uses a different breakup of the electrostatic forces than was used by other authors when they combined the Particle Mesh Ewald method with RESPA. The usual breakup is inefficient because it treats the reciprocal space forces in an outer loop even though they contain a part that changes rapidly in time. This does not allow use of a large time step for the outer loop. Here, we capture the short-range contributions in the reciprocal space forces and include them in the inner loop, thereby allowing for larger outer loop time steps and thus for a much more efficient RESPA implementation. The new approach has been applied to both regular Ewald and P3ME. The timings of Ewald/RESPA and P3ME/RESPA are compared in detail with the previous approach for protein water solutions as a function of number of atoms in the system, and significant speedups are reported.