Multiple Time Steps: Limits on the Speedup of Molecular Dynamics Simulations of Aqueous Systems

Abstract

We have empirically tested limits of the magnitude of multiple time steps in molecular dynamics simulations of aqueous systems, and the extent to which these offer a means to shorten computation time. Three different steps were employed, δ₀t for calculation of “bonded” forces, δ₁t for calculations of short-range (< 6 Å) non-bonded forces, and δ₂t for long-range (< 10 Å) non-bonded forces. Each longer step was a multiple of the shortest one. The leap-frog integration algorithm was used with SHAKE for restraint of all bond lengths and water molecules. For a system of SPC water molecules, calculation of short-range non-bonded forces could be done with a time step δ₁t = 10 fs, without appreciable change of the average temperature and energy, radial distribution function or diffusion coefficient. These properties were found to be insensitive to the inclusion of long-range non-bonded forces. A multiple-step protocol with δ₀t = 2, δ₁t = 4 and δ₂t = 16 fs has been compared with a single-step procedure with δt 2 fs for small polypeptides in water. The exploration of conformation space, with crossing of low energy barriers, was tested with the glycine dipeptide and was found to proceed at similar rates. Mean, hysteresis and statistical error of the free energy for changing alanine to α-amino butyric acid in the dipeptide, calculated by the slow-growth method, proved independent of the cutoff distance or exact protocol, within 1 kJ/mol. In conclusion, we recommend, instead of use of a single time step of 2 fs at a 10 Å cutoff, use of a time step δ_t = 4 fs for short-range nonbonded forces and a time step δ₂t = 16 fs for long-range nonbonded forces for a 60% reduction of computation time.