Use of MM-PB/SA in estimating the free energies of proteins: application to native, intermediates, and unfolded villin headpiece.

We investigated the stability of three different ensembles of the 36-mer villin headpiece subdomain, the native, a compact folding intermediate, and the random coil. Structures were taken from a 1-micros molecular dynamics folding simulation and a 100-ns control simulation on the native structure. Our approach for each conformation is to first determine the solute internal energy from the molecular mechanics potential and then to add the change resulting from solvation (DeltaG(solv)). Explicit water was used to run the simulation, and a continuum model was used to estimate DeltaG(solv) with the finite difference Poisson-Boltzmann model accounting for the polarization part and a linearly surface area-dependent term for the non-polar part. We leave out the solute vibrational entropy from these values but demonstrate that there is no statistical difference among the native, folding intermediate, and random coil ensembles. We find the native ensemble to be approximately 26 kcal/mol more stable than the folding intermediate and approximately 39 kcal/mol more stable than the random coil ensemble. With an experimental estimate for the free energy of denaturation equal to 3 kcal/mol, we approximate the non-native degeneracy to lie between 10(16) and 10.(25) We also present a possible scheme for the mechanism of folding, first-order exponential decay of a putative transition state, with an estimate for the t(1/2) of folding of approximately 1 micros.