Simple physics-based analytical formulas for the potentials of mean force for the interaction of amino acid side chains in water. IV. Pairs of different hydrophobic side chains.

The potentials of mean force of 21 heterodimers of the molecules modeling hydrophobic amino acid side chains: ethane (for alanine), propane (for proline), isobutane (for valine), isopentane (for leucine and isoleucine), ethylbenzene (for phenylalanine), methyl propyl sulfide (for methionine), and indole (for tryptophane) were determined by umbrella-sampling molecular dynamics simulations in explicit water as functions of distance and orientation. Analytical expressions consisting of the Gay-Berne term to represent effective van der Waals interactions and the cavity term proposed in our earlier work were fitted to the potentials of mean force. The positions and depths of the contact minima and the positions and heights of the desolvation maxima, including their dependence on the orientation of the molecules, are well represented by the analytical expressions for all systems; large deviations between the MD-determined PMF and the analytical approximations are observed for pairs involving the least spheroidal solutes: ethylbenzene, indole, and methyl propyl sulfide at short distances at which the PMF is high and, consequently, these regions are rarely visited. When data from the PMF within only 10 kcal/mol above the global minimum are considered, the standard deviation between the MD-determined and the fitted PMF is from 0.25 to 0.55 kcal/mol (the relative standard deviation being from 4% to 8%); it is larger for pairs involving nonspherical solute molecules. The free energies of contact computed from the PMF surfaces are well correlated with those determined from protein-crystal data with a slope close to that relating the free energies of transfer of amino acids (from water to n-octanol) to the average contact free energies determined from protein-crystal data. These observations justify future use of the determined potentials in coarse-grained protein-folding simulations.