Efficient Multiple Timestep Integrators with Distance-Based Force Splitting for Particle-Mesh-Ewald Molecular Dynamics Simulations

We develop an efficient multiple timestep (MTS) force splitting scheme for Particle Mesh Ewald (PME) molecular dynamics simulations in the AMBER program. Our method exploits smooth switch functions effectively to regulate direct and reciprocal space terms for the electrostatic interactions. The reciprocal term with the near field contributions removed is assigned to the slow class; the van der Waals and regulated-PME direct-space terms, each associated with a tailored switch function, are assigned to the medium class. All other bonded terms are assigned to the fast class.

This protocol yields better stability and larger outer timesteps for Newtonian algorithms, with temperature and pressure coupling, as well as for Langevin dynamics. Performance of the algorithms is optimized and tested on water, solvated DNA, and solvated protein systems over 400 ps or longer simulations. With a 6~fs outer timestep, we find CPU speedup ratios of over 6.5 for Newtonian dynamics, compared with 0.5 fs single-timestep simulations. With modest Langevin damping, an outer timestep of up to 16 fs can be used with a speedup ratio of 7.5. Theoretical analyses in our appendices produce guidelines for choosing the Langevin damping constant and show the close relationship among the Leapfrog Verlet, Velocity Verlet, and Position Verlet variants.

Our careful stability tests also emphasize the need to test MTS/PME algorithms over long times, since instabilities can evolve slowly and be evident only after several hundred picoseconds or more. We also suggest that further improvements in MTS/PME integrators can only be achieved with alternative core functions (to Gaussians) or by other variants of fast electrostatics methods that allow better separation of near-field from far-field terms.

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