Thermodynamics of protein-peptide interactions in the ribonuclease-S system studied by molecular dynamics and free energy calculations.

Hydrophobic interactions between the S-peptide and S-protein in the ribonuclease-S complex are probed using molecular dynamics simulations and free energy calculations. Three successive mutations at the buried position Met13 are simulated: Met----Leu, Leu----Ile, and Ile----Val, for which X-ray structures and experimental thermodynamic data are available. The calculations give theoretical estimates of the changes in binding free energies associated with these mutations. The calculated free energy differences are small (0-1.6 kcal/mol), in agreement with experiment. However the simulated structures deviate significantly from the experimental ones (mean deviation approximately 1.5-2 A), and a large uncertainty in the calculated free energies (1-2 kcal/mol) arises from the multiple minimum problem. Indeed, multiple conformations are available to the side chains around the mutation site, and the sampling of dihedral rotamer transitions is limited, despite long simulations. Fluctuations within each local minimum give rise to a small statistical error. However the uncertainty due to multiple conformations is much greater than the uncertainty due to random statistical errors. In our work, an artificial cancellation of errors arose because we studied conformations of the RNase complex and of the S-peptide that were very similar. In general, the criterion for a precise simulation is not merely to reduce the random statistical error, as has been suggested, but rather to sample all the important local minima along the mutation pathway, and to reduce the statistical error for each one. Our calculations suggest that the packing changes associated with the mutations are energetically small and localized, and largely cancel when the complex and the S-peptide are compared. Solvation of the methionine side chain partial charges in the S-peptide and the complex appear to be energetically equivalent, so that removing them (as in Met13----Leu, Ile, Val) does not affect binding. Enthalpy and entropy changes could not be estimated reliably.