We introduce a powerful iterative algorithm to compute protein folding pathways, with realistic all-atom force fields. Using the path integral formalism, we explicitly derive a modified Langevin equation which samples directly the ensemble of reactive pathways, exponentially reducing the cost of simulating thermally activated transitions. The algorithm also yields a rigorous stochastic estimate of the reaction coordinate. After illustrating this approach on a simple toy model, we successfully validate it against the results of ultra-long plain MD protein folding simulations for a fast folding protein (Fip35), which were performed on the Anton supercomputer. Using our algorithm, computing a folding trajectory for this protein requires only 1000 core hours, a computational load which could be even carried out on a desktop workstation.
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