Extremely precise free energy calculations of amino acid side chain analogs: Comparison of common molecular mechanics force fields for proteins

Quantitative free energy computation involves both using a model that is sufficiently faithful to the experimental system under study (accuracy) and establishing statistically meaningful measures of the uncertainties resulting from finite sampling (precision). We use large-scale distributed computing to access sufficient computational resources to extensively sample molecular systems and thus reduce statistical uncertainty of measured free energies. In order to examine the accuracy of a range of common models used for protein simulation, we calculate the free energy of hydration of 15 amino acid side chain analogs derived from recent versions of the OPLS-AA, CHARMM, and AMBER parameter sets in TIP3P water using thermodynamic integration. We achieve a high degree of statistical precision in our simulations, obtaining uncertainties for the free energy of hydration of 0.02–0.05 kcal/mol, which are in general an order of magnitude smaller than those found in other studies. Notably, this level of precision is comparable to that obtained in experimental hydration free energy measurements of the same molecules. Root mean square differences from experiment over the set of molecules examined using AMBER-, CHARMM-, and OPLS-AA-derived parameters were 1.35 kcal/mol, 1.31 kcal/mol, and 0.85 kcal/mol, respectively. Under the simulation conditions used, these force fields tend to uniformly underestimate solubility of all the side chain analogs. The relative free energies of hydration between amino acid side chain analogs were closer to experiment but still exhibited significant deviations. Although extensive computational resources may be needed for large numbers of molecules, sufficient computational resources to calculate precise free energy calculations for small molecules are accessible to most researchers.