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Microscopically Computing Free-energy Profiles and Transition Path Time of Rare Macromolecular Transitions

We introduce a rigorous method to microscopically compute the observables which characterize the thermodynamics and kinetics of rare macromolecular transitions for which it is possible to identify a priori a slow reaction coordinate. In order to sample the ensemble of statistically significant reaction pathways, we define a biased molecular dynamics (MD) in which barrier-crossing transitions are accelerated without introducing any unphysical external force. In contrast to other biased MD methods, in the present approach the systematic errors which are generated in order to accelerate the transition can be analytically calculated and therefore can be corrected for. This allows for a computationally efficient reconstruction of the free-energy profile as a function of the reaction coordinate and for the calculation of the corresponding diffusion coefficient. The transition path time can then be readily evaluated within the Dominant Reaction Pathways (DRP) approach. We illustrate and test this method by characterizing a thermally activated transition on a two-dimensional energy surface and the folding of a small protein fragment within a coarse-grained model.