Large Scale Study of Ligand–Protein Relative Binding Free Energy Calculations: Actionable Predictions from Statistically Robust Protocols

Abstract

The accurate and reliable prediction of protein–ligand binding affinities can play a central role in the drug discovery process as well as in personalized medicine. Of considerable importance during lead optimization are the alchemical free energy methods that furnish an estimation of relative binding free energies (RBFE) of similar molecules. Recent advances in these methods have increased their speed, accuracy, and precision. This is evident from the increasing number of retrospective as well as prospective studies employing them. However, such methods still have limited applicability in real-world scenarios due to a number of important yet unresolved issues. Here, we report the findings from a large data set comprising over 500 ligand transformations spanning over 300 ligands binding to a diverse set of 14 different protein targets which furnish statistically robust results on the accuracy, precision, and reproducibility of RBFE calculations. We use ensemble-based methods which are the only way to provide reliable uncertainty quantification given that the underlying molecular dynamics is chaotic. These are implemented using TIES (Thermodynamic Integration with Enhanced Sampling). Results achieve chemical accuracy in all cases. Ensemble simulations also furnish information on the statistical distributions of the free energy calculations which exhibit non-normal behavior. We find that the “enhanced sampling” method known as replica exchange with solute tempering degrades RBFE predictions. We also report definitively on numerous associated alchemical factors including the choice of ligand charge method, flexibility in ligand structure, and the size of the alchemical region including the number of atoms involved in transforming one ligand into another. Our findings provide a key set of recommendations that should be adopted for the reliable application of RBFE methods.

Ensemble Simulations and Experimental Free Energy Distributions: Evaluation and Characterization of Isoxazole Amides as SMYD3 Inhibitors

“…Only by large scale ensemble sampling can the nature of statistical distributions of free energies be assessed; we have previously shown that they exhibit non-normal behavior. 8 , 16 , 18 , 19 Binding free energies obtained from independent replica simulations of the same molecular system can vary by a wide range, while their distributions deviates from the Gaussian behavior usually assumed as we have reported. 16 Such properties are important for the proper use of many statistical methods (discussed further in Section 3.5 ).…”

“… 8 , 16 , 18 , 19 Binding free energies obtained from independent replica simulations of the same molecular system can vary by a wide range, while their distributions deviates from the Gaussian behavior usually assumed as we have reported. 16 Such properties are important for the proper use of many statistical methods (discussed further in Section 3.5 ). ESMACS and TIES are performed using a binding affinity calculator (BAC), 20 which is a computational pipeline to automate the processes of building, running, and marshaling the molecular dynamics simulations, as well as collecting and analyzing data.…”

“…The assertion that the calculated binding free energies Δ G cal or binding free energy differences ΔΔ G cal follow a normal distribution conflicts with our observation that such data are not in general normally distributed. 8 , 16 , 18 , 19 Newtonian molecular dynamics is inherently nonlinear, and this is the underlying reason why the dynamics is chaotic in the technical sense. Not only are individual trajectories extremely sensitive to initial conditions, they become increasingly inaccurate as the duration of such a simulation unfolds.…”

“…Although the protocols are built around the standard MMPBSA and TI methodologies, the names and abbreviations of these protocols are used to emphasize the central importance of the ensemble-based nature of the protocols employed. 8 , 10 , 13 − 16 The term “ensemble” here refers to a set of individual (often called “replica”) simulations conducted for the same physical system, starting from different initial conformations 13 (and possibly also with varying model parameters 14 ). Advances in high-end computing capabilities offer the opportunity to run all of the replicas concurrently, ensuring that the results can be delivered rapidly, exactly as has been done in climate and weather forecasting for the past 20 years.…”

“…It is notable that until now virtually no other groups have been using or reporting results based on ensemble calculations which hitherto remain anything but routine methods within the entire field of classical molecular dynamics. 8 , 16 , 18 …”