Practically Efficient and Robust Free Energy Calculations: Double-Integration Orthogonal Space Tempering

The orthogonal space random walk (OSRW) method, which enables synchronous acceleration of the motions of a focused region and its coupled environment, was recently introduced to enhance sampling for free energy simulations. In the present work, the OSRW algorithm is generalized to be the orthogonal space tempering (OST) method via the introduction of the orthogonal space sampling temperature. Moreover, a double-integration recursion method is developed to enable practically efficient and robust OST free energy calculations, and the algorithm is augmented by a novel theta-dynamics approach to realize both the uniform sampling of order parameter spaces and rigorous end point constraints. In the present work, the double-integration OST method is employed to perform alchemical free energy simulations, specifically to calculate the free energy difference between benzyl phosphonate and difluorobenzyl phosphonate in aqueous solution, to estimate the solvation free energy of the octanol molecule, and to predict the nontrivial Bamase Barstar binding affinity change induced by the Bamase N58A mutation. As demonstrated in these model studies, the DI-OST method can robustly enable practically efficient free energy predictions, particularly when strongly coupled slow environmental transitions are involved.