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

Abstract

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.

Free‐energy calculations of residue mutations in a tripeptide using various methods to overcome inefficient sampling

“…In the tripeptide transformation KXK → KGK with the central residue being alanine, serine, glutamic acid, lysine, phenylalanine, or tyrosine, hysteresis between the forward and backward transformation has been observed previously . The hysteresis could be linked to poor sampling of the φ 2 /ψ 2 dihedral angles.…”

“…As described in the introduction, residue mutations of the tripeptide KXK → KGK were already investigated in previous studies employing either TI or a combination of λ ‐dynamics and local‐elevation umbrella‐sampling ( λ ‐LEUS) . Especially for the KAK → KGK transformation, a significant hysteresis between the forward and backward process was observed and attributed to poor orthogonal sampling of φ 2 /ψ 2 dihedral angle distributions .…”

“…Subsequent switches back to the state with increased barriers mixes in the new conformations into the conformational ensemble with the appropriate weight. The reversible visiting of different states along the transformation is exactly the key aspect of the λ ‐LEUS aproach that was described earlier . There, a single simulation is biased to repeatedly visit all λ values while in the HREMD approach this is naturally enforced for all individual replicas.…”

“…Central residue transformations in the KXK tripeptide of the aforementioned amino acids, but notably not alanine to KGK, have recently been investigated by Bieler and Hünenberger, however, with an eye on their newly developed λ ‐LEUS approach . The λ ‐LEUS approach was developed to overcome sampling shortcomings, for example, in orthogonal φ 2 /ψ 2 dihedral angle distributions of the KXK → KGK transformations during thermodynamic integration (TI).…”

“…In the current study, we revisit the previously investigated KXK → KGK tripeptide transformations in water . On the one hand, we integrate all KXK → KGK tripeptide transformations in water tested so far in the present study. The most interesting transformation, that is, the one with the highest hysteresis in relation to the conducted alchemical transformation, will then be selected to identify the reason for discrepancies in the forward and backward processes.…”