Expanded Ensemble Methods Can be Used to Accurately Predict Protein-Ligand Relative Binding Free Energies

Abstract

Alchemical free energy methods have become indispensable in computational drug discovery for their ability to calculate highly accurate estimates of protein-ligand affinities. Expanded ensemble (EE) methods, which involve single simulations visiting all of the alchemical intermediates, have some key advantages for alchemical free energy calculation. However, there have been relatively few examples published in the literature of using expanded ensemble simulations for free energies of protein-ligand binding. In this paper, as a test of expanded ensemble methods, we compute relative binding free energies using the Open Force Field Initiative force field (codename “Parsley”) for 24 pairs of Tyk2 inhibitors derived from a congeneric series of 16 compounds. The EE predictions agree well with the experimental values (root-mean-square error (RMSE) of 0.94 ± 0.13 kcal mol–1 and mean unsigned error (MUE) of 0.75 ± 0.12 kcal mol–1). We find that while increasing the number of alchemical intermediates can improve the phase space overlap, faster convergence can be obtained with fewer intermediates, as long as acceptance rates are sufficient. We also find that convergence can be improved using more aggressive updating of biases, and that estimates can be improved by performing multiple independent EE calculations. This work demonstrates that EE is a viable option for alchemical free energy calculation. We discuss the implications of these findings for rational drug design, as well as future directions for improvement.

MELD-Bracket Ranks Binding Affinities of Diverse Sets of Ligands

“…It is to be noted that FEP+ employs a different force field as compared to MELD-Bracket. Comparison, though not exactly apple-to-apple, is still advisable because of its wide acceptability and use for benchmark study. − …”

Expanded ensemble predictions of absolute binding free energies in the SAMPL9 host–guest challenge

“…Absolute binding free energies computed using expanded-ensemble (EE) methods have been used previously in SAMPL challenges, 16,22 and our methods closely follow these efforts, with some innovations inspired by recent work. 42…”

“…Using this improved strategy, Zhang et al recently showed that EE methods can predict relative binding free energies of Tyk2 inhibitors to within a mean unsigned error (MUE) of 0.75 AE 0.12 kcal mol À1 . 42 The current SAMPL9 host-guest challenge represents the first time these improved protocols have been tested for predicting absolute binding free energies.…”

“…Absolute binding free energies computed using expandedensemble (EE) methods have been used previously in SAMPL challenges, 16,22 and our methods closely follow these efforts, with some innovations inspired by recent work. 42 The free energy DG L of decoupling the guest from solvent in a ligand-only (L) simulation was calculated using 101 alchemical intermediates in which Coulomb (coul) interactions are turned off, and then van der Waals (vdW) interactions. The free energy DG RL of decoupling the guest from a receptor-ligand (RL) simulation was calculated using 101 alchemical intermediates in which a restraint potential is turned on, then Coulomb interactions are turned off, and then vdW interactions.…”

Enhanced Sampling of Buried Charges in Free Energy Calculations Using Replica Exchange with Charge Tempering

“…Many enhanced sampling methods have been developed and applied to free energy simulations, such as different variants of replica exchange methods including replica exchange with solute tempering, − grand canonical Monte Carlo, − Gaussian accelerated molecular dynamics, − weighted ensemble, − metadynamics, − orthogonal space tempering, − and expanded ensemble. − For more complete reviews, we refer the reader to refs – . Despite significant advancements in enhanced sampling methods, sufficient sampling of systems with buried charges in many cases remains challenging.…”