Simulation of the solvation free energies for methane, ethane, and propane and corresponding amino acid dipeptides: a critical test of the bond-PMF correction, a new set of hydrocarbon parameters, and the gas phase-water hydrophobicity scale

We have carried out free energy perturbation calculations to determine the relative free energies of solvation in water for methane, ethane, and propane. Experimentally, the relative solvation free energy of methane and ethane is -0.16 +/- 0.01 kcal/mol, and the relative solvation free energy of ethane and propane is 0.17 +/- 0.04 kcal/mol. Using the recently described bond-PMF correction and a new set of hydrocarbon parameters, we calculate the relative free energy of solvation of methane and ethane to be 0.03 kcal/mol with Mulliken charges and 0.16 kcal/mol for electrostatic potential derived charges and the relative solvation free energies of ethane and propane to be 0.17 and 0.20 kcal/mol for the two sets of charges. The rather good agreement with experiment for these difficult to calculate quantities is encouraging, in that the methane to ethane free energy is within approximately 0.3 kcal/mol of experiment and the ethane to propane value is in near-quantitative agreement with experiment. To examine amino acid side chain effects, a simulation was also carried out to mutate N-acetylalanine N-methylamide to the corresponding valine dipeptide. The free energy difference is 1.1 +/- 0.1 kcal/mol, larger than the 0.4 +/- 0.1 kcal/mol calculated free energy difference between methane and propane. We show that this difference is due to indirect contributions from backbone atoms. An analysis of these results shows that the use of side chain analogs (e.g. methane --> propane to represent alanine to valine) to describe free energy differences is likely to be an excellent approximation only when the presence/absence of the beta-carbon and the presence/absence of beta-branching do not change upon mutation.