Orthogonal sampling in free-energy calculations of residue mutations in a tripeptide: TI versus λ-LEUS

In a recent article (Bieler et al., J. Chem. Theory Comput. 2014, 10, 3006), we introduced a combination of λ-dynamics and local-elevation umbrella-sampling termed λ-LEUS to calculate free-energy changes associated with alchemical processes using molecular dynamics simulations. This method was suggested to be more efficient than thermodynamic integration (TI), because the dynamical variation of the alchemical variable λ opens up pathways to circumvent barriers in the orthogonal space (defined by the N - 1 degrees of freedom that are not subjected to the sampling enhancement), a feature λ-LEUS shares with Hamiltonian replica-exchange (HR) approaches. However, the mutation considered, hydroquinone to benzene in water, was no real challenge in terms of orthogonal-space properties, which were restricted to solvent-relaxation processes. In the present article, we revisit the comparison between TI and λ-LEUS considering non-trivial mutations of the central residue X of a KXK tripeptide in water (with X = G, E, K, S, F, or Y). Side-chain interactions that may include salt bridges, hydrogen bonds or steric clashes lead to slow relaxation in the orthogonal space, mainly in the two-dimensional subspace spanned by the central φ and ψ dihedral angles of the peptide. The efficiency enhancement afforded by λ-LEUS is confirmed in this more complex test system and can be attributed explicitly to the improved sampling of the orthogonal space. The sensitivity of the results to the nontrivial choices of a mass parameter and of a thermostat coupling time for the alchemical variable is also investigated, resulting in recommended ranges of 50 to 100 u nm(2) and 0.2 to 0.5 ps, respectively.