In molecular dynamics (MD) simulations, free-energy differences are often calculated using free energy perturbation or thermodynamic integration (TI) methods. However, both techniques are only suited to calculate free-energy differences between two end states. Enveloping distribution sampling (EDS) presents an attractive alternative that allows to calculate multiple free-energy differences in a single simulation. In EDS, a reference state is simulated which “envelopes” the end states. The challenge of this methodology is the determination of optimal reference-state parameters to ensure equal sampling of all end states. Currently, the automatic determination of the reference-state parameters for multiple end states is an unsolved issue that limits the application of the methodology. To resolve this, we have generalised the replica-exchange EDS (RE-EDS) approach, introduced by Lee et al. [J. Chem. Theory Comput. 10, 2738 (2014)] for constant-pH MD simulations. By exchanging configurations between replicas with different reference-state parameters, the complexity of the parameter-choice problem can be substantially reduced. A new robust scheme to estimate the reference-state parameters from a short initial RE-EDS simulation with default parameters was developed, which allowed the calculation of 36 free-energy differences between nine small-molecule inhibitors of phenylethanolamine N-methyltransferase from a single simulation. The resulting free-energy differences were in excellent agreement with values obtained previously by TI and two-state EDS simulations.

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