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# Free Energy Methods

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## Replica-Exchange Enveloping Distribution Sampling (RE-EDS)

In molecular dynamics (MD) simulations, free-energy differences are often calculated using free energy perturbation (FEP) 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 the calculation of 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 overcome this challenge, we have generalised the replica-exchange EDS (RE-EDS) approach introduced by Lee *et al.* for constant-pH MD simulations [*J. Chem. Theory Comput*., **10**, 2738 (2014)] to arbitrary systems [1]. By exchanging configurations between replicas with different reference-state parameters, the complexity of the parameter-choice problem can be substantially reduced. In a next step, we have developed an efficient algorithm to optimize distribution of the replicas [2]. With this, we could obtain all 36 free-energy differences between nine ligands of a protein from a single simulation.