With the rapid development of computational techniques and hardware, more rigorous and precise theoretical models have been used to predict the binding affinities of a large number of small molecules to biomolecules. By employing continuum solvation models, the MM/GBSA and MM/PBSA methodologies achieve a good balance between low computational cost and reasonable prediction accuracy. In this study, we have thoroughly investigated the effects of interior dielectric constant, molecular dynamics (MD) simulations, and the number of top-scored docking poses on the performance of the MM/GBSA and MM/PBSA rescoring of docking poses for three tyrosine kinases, including ABL, ALK, and BRAF. Overall, the MM/PBSA and MM/GBSA rescoring achieved comparative accuracies based on a relatively higher solute (or interior) dielectric constant (i.e. ε = 2, or 4), and could markedly improve the 'screening power' and 'ranking power' given by Autodock. Moreover, with a relatively higher solute dielectric constant, the MM/PBSA or MM/GBSA rescoring based on the best scored docking poses and the multiple top-scored docking poses gave similar predictions, implying that much computational cost can be saved by considering the best scored docking poses only. Besides, compared with the rescoring based on the minimized structures, the rescoring based on the MD simulations might not be completely necessary due to its negligible impact on the docking performance. Considering the much higher computational demand of MM/PBSA, MM/GBSA with a high solute dielectric constant (ε = 2 or 4) is recommended for the virtual screening of tyrosine kinases.

Understanding protein-protein interactions (PPIs) is quite important to elucidate crucial biological processes and even design compounds that interfere with PPIs with pharmaceutical significance. Protein-protein docking can afford the atomic structural details of protein-protein complexes, but the accurate prediction of the three-dimensional structures for protein-protein systems is still notoriously difficult due in part to the lack of an ideal scoring function for protein-protein docking. Compared with most scoring functions used in protein-protein docking, the Molecular Mechanics/Generalized Born Surface Area (MM/GBSA) and Molecular Mechanics/Poisson Boltzmann Surface Area (MM/PBSA) methodologies are more theoretically rigorous, but their overall performance for the predictions of binding affinities and binding poses for protein-protein systems has not been systematically evaluated. In this study, we first evaluated the performance of MM/PBSA and MM/GBSA to predict the binding affinities for 46 protein-protein complexes. On the whole, different force fields, solvation models, and interior dielectric constants have obvious impacts on the prediction accuracy of MM/GBSA and MM/PBSA. The MM/GBSA calculations based on the ff02 force field, the GB model developed by Onufriev et al. and a low interior dielectric constant (εin = 1) yield the best correlation between the predicted binding affinities and the experimental data (rp = -0.647), which is better than MM/PBSA (rp = -0.523) and a number of empirical scoring functions used in protein-protein docking (rp = -0.141 to -0.529). Then, we examined the capability of MM/GBSA to identify the possible near-native binding structures from the decoys generated by ZDOCK for 43 protein-protein systems. The results illustrate that the MM/GBSA rescoring has better capability to distinguish the correct binding structures from the decoys than the ZDOCK scoring. Besides, the optimal interior dielectric constant of MM/GBSA for re-ranking docking poses may be determined by analyzing the characteristics of protein-protein binding interfaces. Considering the relatively high prediction accuracy and low computational cost, MM/GBSA may be a good choice for predicting the binding affinities and identifying correct binding structures for protein-protein systems.

Entropy effects play an important role in drug-target interactions, but the entropic contribution to ligand-binding affinity is often neglected by end-point binding free energy calculation methods, such as MM/GBSA and MM/PBSA, due to the expensive computational cost of normal mode analysis (NMA). Here, we systematically investigated entropy effects on the prediction power of MM/GBSA and MM/PBSA using >1500 protein-ligand systems and six representative AMBER force fields. Two computationally efficient methods, including NMA based on truncated structures and the interaction entropy approach, were used to estimate the entropic contributions to ligand-target binding free energies. In terms of the overall accuracy, we found that, for the minimized structures, in most cases the inclusion of the conformational entropies predicted by truncated NMA (enthalpynmode_min_9Å) compromises the overall accuracy of MM/GBSA and MM/PBSA compared with the enthalpies calculated based on the minimized structures (enthalpymin). However, for the MD trajectories, the binding free energies can be improved by the inclusion of the conformation entropies predicted by either truncated-NMA for a relatively high dielectric constant (εin = 4) or the interaction entropy method for εin = 1-4. In terms of reproducing the absolute binding free energies, the binding free energies estimated by including the truncated-NMA entropies based on the MD trajectories (ΔGnmode_md_9Å) give the lowest average absolute deviations against the experimental data among all the tested strategies for both MM/GBSA and MM/PBSA. Although the inclusion of the truncated NMA based on the MD trajectories (ΔGnmode_md_9Å) for a relatively high dielectric constant gave the overall best result and the lowest average absolute deviations against the experimental data (for the ff03 force field), it needs too much computational time. Alternatively, considering that the interaction entropy method does not incur any additional computational cost and can give comparable (at high dielectric constant, εin = 4) or even better (at low dielectric constant, εin = 1-2) results than the truncated-NMA entropy (ΔGnmode_md_9Å), the interaction entropy approach is recommended to estimate the entropic component for MM/GBSA and MM/PBSA based on MD trajectories, especially for a diverse dataset. Furthermore, we compared the predictions of MM/GBSA with six different AMBER force fields. The results show that the ff03 force field (ff03 for proteins and gaff with AM1-BCC charges for ligands) performs the best, but the predictions given by the tested force fields are comparable, implying that the MM/GBSA predictions are not very sensitive to force fields.

The past few years have witnessed enormous progress toward applying machine learning approaches to the development of protein–ligand scoring functions. However, the robust performance and wide applicability of scoring functions remain a big challenge for increasing the success rate of docking-based virtual screening. Herein, a novel scoring function named RTMScore was developed by introducing a tailored residue-based graph representation strategy and several graph transformer layers for the learning of protein and ligand representations, followed by a mixture density network to obtain residue–atom distance likelihood potential. Our approach was resolutely validated on the CASF-2016 benchmark, and the results indicate that RTMScore can outperform almost all of the other state-of-the-art methods in terms of both the docking and screening powers. Further evaluation confirms the robustness of our approach that can not only retain its docking power on cross-docked poses but also achieve improved performance as a rescoring tool in larger-scale virtual screening.