In the past few decades, many ingenious efforts have been made in the development of free-energy simulation methods. Because complex systems often undergo nontrivial structural transition during state switching, achieving efficient free-energy calculation can be challenging. As identified earlier, the “Hamiltonian” lagging, which reveals the fact that necessary structural relaxation falls behind the order parameter move, has been a primary problem for generally low free-energy simulation efficiency. Here, we propose an algorithm by achieving a random walk in both the order parameter space and its generalized force space; thereby, the order parameter move and the required conformational relaxation can be efficiently synchronized. As demonstrated in both the alchemical transition and the conformational transition, a leapfrog improvement in free-energy simulation efficiency can be obtained; for instance, ( i ) it allows us to solve a notoriously challenging problem: accurately predicting the pK a value of a buried titratable residue, Asp-66, in the interior of the V66E staphylococcal nuclease mutant, and ( ii ) it allows us to gain superior efficiency over the metadynamics algorithm.

Zheng, L., Chen, M., & Yang, W. (2008). Random walk in orthogonal space to achieve efficient free-energy simulation of complex systems. Proceedings of the National Academy of Sciences, 105(51), 20227–20232.