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 vi llin headpiece subdomain, the native, a compact folding intermediate, and t he random coil. Structures were taken from a 1-mu s molecular dynamics fold ing simulation and a 100-ns control simulation on the native structure. Our approach for each conformation is to first determine the solute internal e nergy from the molecular mechanics potential and then to add the change res ulting from solvation (Delta G(solv)). Explicit water was used to run the s imulation, and a continuum model was used to estimate Delta G(solv) with th e 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 intermed iate, and random coil ensembles. We find the native ensemble to be approxim ate to 26 kcal/mol more stable than the folding intermediate and approximat e to 39 kcal/mol more stable than the random coil ensemble. With an experim ental 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 ex ponential decay of a putative transition state, with an estimate for the t( 1/2) of folding of approximate to 1 mu s. (C) 2000 Wiley-Liss, Inc.