Comparison of Equilibrium and Nonequilibrium Approaches for Relative Binding Free Energy Predictions

Abstract

Alchemical relative binding free energy calculations have recently found important applications in drug optimization. A series of congeneric compounds are generated from a preidentified lead compound, and their relative binding affinities to a protein are assessed in order to optimize candidate drugs. While methods based on equilibrium thermodynamics have been extensively studied, an approach based on nonequilibrium methods has recently been reported together with claims of its superiority. However, these claims pay insufficient attention to the basis and reliability of both methods. Here we report a comparative study of the two approaches across a large data set, comprising more than 500 ligand transformations spanning in excess of 300 ligands binding to a set of 14 diverse protein targets. Ensemble methods are essential to quantify the uncertainty in these calculations, not only for the reasons already established in the equilibrium approach but also to ensure that the nonequilibrium calculations reside within their domain of validity. If and only if ensemble methods are applied, we find that the nonequilibrium method can achieve accuracy and precision comparable to those of the equilibrium approach. Compared to the equilibrium method, the nonequilibrium approach can reduce computational costs but introduces higher computational complexity and longer wall clock times. There are, however, cases where the standard length of a nonequilibrium transition is not sufficient, necessitating a complete rerun of the entire set of transitions. This significantly increases the computational cost and proves to be highly inconvenient during large-scale applications. Our findings provide a key set of recommendations that should be adopted for the reliable implementation of nonequilibrium approaches to relative binding free energy calculations in ligand-protein systems.

Molecular Insights into the Impact of Mutations on the Binding Affinity of Targeted Covalent Inhibitors of BTK

“…In addition, the EQ and NEQ ABFE approaches yield similar binding free energy estimates for the compounds binding to BTK (Figure ). This result is consistent with published studies on more extensive protein–ligand test sets. ,, We find that error estimates (derived from the standard deviation of three independent repeats) tend to be slightly larger for the NEQ approach than for the EQ approach (Tables and ). The NEQ approach is traditionally more computationally efficient than the EQ approach but requires that several critical parameters be considered for reliable, accurate, and precise free energy estimates. , Overall, the agreement in predicted free energy estimates between the EQ and NEQ ABFE approaches provides an independent check of our results in the absence of comprehensive experimental data.…”

“…The calculations were performed for both wildtype and mutant states of BTK. For details about the EQ and NEQ binding free energy approaches, including challenges and directions for future method development, see recent work by Baumann et al, Coveney and co-workers …”

Multistate Method to Efficiently Account for Tautomerism and Protonation in Alchemical Free-Energy Calculations

“…In recent years, alchemical free-energy calculations have become established as essential tools to support drug discovery projects by helping to prioritize compounds for synthesis. − The groundwork behind these methods dates back to pioneering theoretical work in the 20th century, − followed by subsequent efficiency improvements relying on their combination with various enhanced-sampling algorithms (for examples, see refs – ). While these methods perform well for series of congeneric ligands, , it is typically challenging to estimate relative binding free energies between molecules with different net charges, scaffolds, or binding modes. , In particular, transformations involving ligands with different charges face two main challenges.…”

Ensemble-Based Approaches Ensure Reliability and Reproducibility

“…Studies have reported non-Gaussian behavior for different QoIs in various applications. 3 − 8 In the context of MD simulations, we have reported on numerous occasions the observation of non-Gaussian distributions in binding free energies calculated from both equilibrium 9 − 14 and nonequilibrium 15 approaches. The observation of non-Gaussian distributions from simulations led to the investigation of exceptionally extensive experimental data the results of which we published recently in JCIM.…”