Consequences of the failure of equipartition for the p-V behavior of liquid water and the hydration free energy components of a small protein

Earlier we showed that in the molecular dynamics simulation of a rigid model of water it is necessary to use an integration time-step δ_t ≤ 0.5 fs to ensure equipartition between translational and rotational modes. Here we extend that study in the NVT ensemble to NpT conditions and to an aqueous protein. We study neat liquid water with the rigid, SPC/E model and the protein BBA (PDB ID: 1FME) solvated in the rigid, TIP3P model. We examine integration time-steps ranging from 0.5 fs to 4.0 fs for various thermostat plus barostat combinations. We find that a small δ_t is necessary to ensure consistent prediction of the simulation volume. Hydrogen mass repartitioning alleviates the problem somewhat, but is ineffective for the typical time-step used with this approach. The compressibility, a measure of volume fluctuations, and the dielectric constant, a measure of dipole moment fluctuations, are also seen to be sensitive to δ_t. Using the mean volume estimated from the NpT simulation, we examine the electrostatic and van der Waals contribution to the hydration free energy of the protein in the NVT ensemble. These contributions are also sensitive to δ_t. In going from δ_t = 2 fs to δ_t = 0.5 fs, the change in the net electrostatic plus van der Waals contribution to the hydration of BBA is already in excess of the folding free energy reported for this protein.