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

TL;DR

This study reveals that the integration time-step in molecular dynamics simulations critically affects the accuracy of volume, dielectric, and hydration free energy predictions for water and proteins, emphasizing the need for small time-steps.

Contribution

It extends previous work on equipartition failure to NpT conditions and proteins, demonstrating the importance of small time-steps for reliable simulation results.

Findings

Larger time-steps lead to inaccurate volume and dielectric constant predictions.

Hydration free energy components are sensitive to the integration time-step.

Small time-steps are necessary for consistent and accurate simulation outcomes.

Abstract

Earlier we showed that in the molecular dynamics simulation of a rigid model of water it is necessary to use an integration time-step $\delta t \leq 0.5$ 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 $\delta t$ 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 $\delta t$. 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 $\delta t$. In going from $\delta t = 2$ fs to $\delta t = 0.5$ 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.