Evaluation of Machine Learning/Molecular Mechanics End-State Corrections with Mechanical Embedding to Calculate Relative Protein–Ligand Binding Free Energies

The development of machine-learning (ML) potentials offers significant accuracy improvements compared to molecular mechanics (MM) because of the inclusion of quantum-mechanical effects in molecular interactions. However, ML simulations are several times more computationally demanding than MM simulations, so there is a trade-off between speed and accuracy. One possible compromise are hybrid machine learning/molecular mechanics (ML/MM) approaches with mechanical embedding that treat the intramolecular interactions of the ligand at the ML level and the protein–ligand interactions at the MM level. Recent studies have reported improved protein–ligand binding free energy results based on ML/MM using ANI-2x with mechanical embedding, arguing that intramolecular interactions like torsion potentials of the ligand are often the limiting factor for accuracy. This claim is evaluated based on 108 relative binding free energy calculations for four different benchmark systems. As an alternative strategy, we also tested a tool that fits the MM dihedral potentials to the ML level of theory. Fitting was performed with the ML potentials ANI-2x and AIMNet2, and, for the benchmark system TYK2, also with quantum-mechanical calculations using ωB97M-D3(BJ)/def2-TZVPPD. Overall, the relative binding free energy results from MM with Open Force Field 2.2.0, MM with ML-fitted torsion potentials, and the corresponding ML/MM end-state corrected simulations show no statistically significant differences in the mean absolute errors (between 0.8 and 0.9 kcal mol–1). This can probably be explained by the usage of the same MM parameters to calculate the protein–ligand interactions. Therefore, a well-parametrized force field is on a par with simple mechanical embedding ML/MM simulations for protein–ligand binding. In terms of computational costs, the reparametrization of poor torsional potentials is preferable over employing computationally intensive ML/MM simulations of protein–ligand complexes with mechanical embedding. Also, the refitting strategy leads to lower variances of the protein–ligand binding free energy results than the ML/MM end-state corrections. For free energy corrections with ML/MM, the results indicate that better convergence and more advanced ML/MM schemes will be required for applications in computer-guided drug discovery.