Toward Convergence in Free Energy Calculations for Protein Conformational Changes: A Case Study on the Thin Gate of Mhp1 Transporter.

It has been challenging to obtain reliable free energies for protein conformational changes from all-atom molecular dynamics simulations, despite the availability of many enhanced sampling techniques. To alleviate the difficulties associated with the enormous complexity of the conformational space, here we propose a few practical strategies for such calculations, including (1) a stringent method to examine convergence by comparing independent simulations starting from different initial coordinates, (2) adoption of multistep schemes in which the complete conformational change consists of multiple transition steps, each sampled using a distinct reaction coordinate, and (3) application of boundary restraints to simplify the conformational space. We demonstrate these strategies on the conformational changes between the outward-facing and outward-occluded states of the Mhp1 membrane transporter, obtaining the equilibrium thermodynamics of the relevant metastable states, the kinetic rates between these states, and the reactive trajectories that reveal the atomic details of spontaneous transitions. Our approaches thus promise convergent and reliable calculations to examine intuition-based hypotheses and to eventually elucidate the underlying molecular mechanisms of reversible conformational changes in complex protein systems.