Calculation of Relative Binding Free Energy in the Water-Filled Active Site of Oligopeptide-Binding Protein A

Abstract

Abstract:The periplasmic oligopeptide binding protein A (OppA) represents a well-known example of water-mediated protein-ligand interactions. Here, we perform free-energy calculations for three different ligands binding to OppA, using a thermodynamic integration approach. The tripeptide ligands share a high structural similarity (all have the sequence KXK), but their experimentally-determined binding free energies differ remarkably. Thermodynamic cycles were constructed for the ligands, and simulations conducted in the bound and (freely solvated) unbound states. In the unbound state, it was observed that the difference in conformational freedom between alanine and glycine leads to a surprisingly slow convergence, despite their chemical similarity. This could be overcome by increasing the softness parameter during alchemical transformations. Discrepancies remained in the bound state however, when comparing independent simulations of the three ligands. These difficulties could be traced to a slow relaxation of the water network within the active site. Fluctuations in the number of water molecules residing in the binding cavity occur mostly on a timescale larger than the simulation time along the alchemical path. After extensive simulations, relative binding free energies that were converged to within thermal noise could be obtained, which agree well with available experimental data.

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

“…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 .…”

“…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 . The sampling problem was tackled with the λ ‐LEUS approach, in which the coupling parameter λ is treated as a dynamic variable, which is subsequently biased to cycle repeatedly between states A and B, with a prolonged residence time at the end‐states.…”

“…High energy barriers that are difficult to cross during MD simulations caused surprisingly high hysteresis for the initial TI of the KAK → KGK transformation. To overcome these barriers, different approaches were used (see the results section for details): Extending the production runs to 10 ns per λ value; Overcoming barriers by (A) Increasing the softness parameter α VdW from 0.5 to 1.0 nm 2 to lower repulsive energies from overlapping atoms; (B) Excluding specific intramolecular interactions, with coordinate trajectories written out every 0.1 ps for post‐MD analysis; (C) Changing the mass and/or size of the alanine side chain to change its momentum; Mixing conformations during Hamiltonian replica exchange simulations (see below); Using a single unphysical reference state and the one‐step perturbation (OSP) (see below). …”

“…The free‐energy changes of the tripeptide transformations calculated according to λ ‐LEUS or TI showed significant differences in mean absolute deviations with respect to the average free energy difference ( n = 10) between different transformations but also for single transformations calculated according to both methods . 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.…”

“…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.…”