All-atom calculation of protein free-energy profiles

The Bias Functional (BF) approach is a variational method which enables one to efficiently generate ensembles of reactive trajectories for complex biomolecular transitions, using ordinary computer clusters. For example, this scheme was applied to simulate in atomistic detail the folding of proteins consisting of several hundreds of amino acids and with experimental folding time of several minutes. A drawback of the BF approach is that it produces trajectories which do not satisfy microscopic reversibility. Consequently, this method cannot be used to directly compute equilibrium observables, such as free energy landscapes or equilibrium constants. In this work, we develop a statistical analysis which permits us to compute the potential of mean-force (PMF) along an arbitrary collective coordinate, by exploiting the information contained in the reactive trajectories calculated with the BF approach. We assess the accuracy and computational efficiency of this scheme by comparing its results with the PMF obtained for a small protein by means of plain molecular dynamics.