Consequences of the failure of equipartition for the <i>p</i> – <i>V</i> 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 <i>δ</i> _t ≤ 0.5 fs to ensure equipartition between translational and rotational modes. Here we extend that study in the <i>NVT</i> ensemble to <i>NpT</i> 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 <i>δ</i> _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 <i>δ</i> _t. Using the mean volume estimated from the <i>NpT</i> simulation, we examine the electrostatic and van der Waals contribution to the hydration free energy of the protein in the <i>NVT</i> ensemble. These contributions are also sensitive to <i>δ</i> _t. In going from <i>δ</i> _t = 2 fs to <i>δ</i> _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.