Efficient Round-Trip Time Optimization for Replica-Exchange Enveloping Distribution Sampling (RE-EDS).

Replica-exchange enveloping distribution sampling (RE-EDS) allows the efficient estimation of free-energy differences between multiple end-states from a single molecular dynamics (MD) simulation. In EDS, a reference state is sampled, which can be tuned by two types of parameters, i.e., smoothness parameters(s) and energy offsets, such that all end-states are sufficiently sampled. However, the choice of these parameters is not trivial. Replica exchange (RE) or parallel tempering is a widely applied technique to enhance sampling. By combining EDS with the RE technique, the parameter choice problem could be simplified and the challenge shifted toward an optimal distribution of the replicas in the smoothness-parameter space. The choice of a certain replica distribution can alter the sampling efficiency significantly. In this work, global round-trip time optimization (GRTO) algorithms are tested for the use in RE-EDS simulations. In addition, a local round-trip time optimization (LRTO) algorithm is proposed for systems with slowly adapting environments, where a reliable estimate for the round-trip time is challenging to obtain. The optimization algorithms were applied to RE-EDS simulations of a system of nine small-molecule inhibitors of phenylethanolamine N-methyltransferase (PNMT). The energy offsets were determined using our recently proposed parallel energy-offset (PEOE) estimation scheme. While the multistate GRTO algorithm yielded the best replica distribution for the ligands in water, the multistate LRTO algorithm was found to be the method of choice for the ligands in complex with PNMT. With this, the 36 alchemical free-energy differences between the nine ligands were calculated successfully from a single RE-EDS simulation 10 ns in length. Thus, RE-EDS presents an efficient method for the estimation of relative binding free energies.

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