Fast and accurate calculation of solvation free energies is central to many applications, such as rational drug design. In this study, we present a grid-based molecular surface implementation of "R6" flavor of the generalized Born (GB) implicit solvent model, named GBNSR6. The speed, accuracy relative to numerical Poisson-Boltzmann treatment, and sensitivity to grid surface parameters are tested on a set of 15 small protein-ligand complexes and a set of biomolecules in the range of 268 to 25099 atoms. Our results demonstrate that the proposed model provides a relatively successful compromise between the speed and accuracy of computing polar components of the solvation free energies (ΔG) and binding free energies (ΔΔG). The model tolerates a relatively coarse grid size h = 0.5 Å, where the grid artifact error in computing ΔΔG remains in the range of kT ∼ 0.6 kcal/mol. The estimated ΔΔGs are well correlated (r = 0.97) with the numerical Poisson-Boltzmann reference, while showing virtually no systematic bias and RMSE = 1.43 kcal/mol. The grid-based GBNSR6 model is available in Amber (AmberTools) package of molecular simulation programs.

The binding free energy calculation of protein–ligand complexes is necessary for research into virus–host interactions and the relevant applications in drug discovery. However, many current computational methods of such calculations are either inefficient or inaccurate in practice. Utilizing implicit solvent models in the molecular mechanics generalized Born surface area (MM/GBSA) framework allows for efficient calculations without significant loss of accuracy. Here, GBNSR6, a new flavor of the generalized Born model, is employed in the MM/GBSA framework for measuring the binding affinity between SARS-CoV-2 spike protein and the human ACE2 receptor. A computational protocol is developed based on the widely studied Ras–Raf complex, which has similar binding free energy to SARS-CoV-2/ACE2. Two options for representing the dielectric boundary of the complexes are evaluated: one based on the standard Bondi radii and the other based on a newly developed set of atomic radii (OPT1), optimized specifically for protein–ligand binding. Predictions based on the two radii sets provide upper and lower bounds on the experimental references: −14.7(ΔGbindBondi)<−10.6(ΔGbindExp.)<−4.1(ΔGbindOPT1) kcal/mol. The consensus estimates of the two bounds show quantitative agreement with the experiment values. This work also presents a novel truncation method and computational strategies for efficient entropy calculations with normal mode analysis. Interestingly, it is observed that a significant decrease in the number of snapshots does not affect the accuracy of entropy calculation, while it does lower computation time appreciably. The proposed MM/GBSA protocol can be used to study the binding mechanism of new variants of SARS-CoV-2, as well as other relevant structures.

The ability to estimate protein-protein binding free energy in a computationally efficient via a physics-based approach is beneficial to research focused on the mechanism of viruses binding to their target proteins. Implicit solvation methodology may be particularly useful in the early stages of such research, as it can offer valuable insights into the binding process, quickly. Here we evaluate the potential of the related molecular mechanics generalized Born surface area (MMGB/SA) approach to estimate the binding free energy ΔGbind between the SARS-CoV-2 spike receptor-binding domain and the human ACE2 receptor. The calculations are based on a recent flavor of the generalized Born model, GBNSR6. Two estimates of ΔGbind are performed: one based on standard bondi radii, and the other based on a newly developed set of atomic radii (OPT1), optimized specifically for protein-ligand binding. We take the average of the resulting two ΔGbind values as the consensus estimate. For the well-studied Ras-Raf protein-protein complex, which has similar binding free energy to that of the SARS-CoV-2/ACE2 complex, the consensus ΔGbind = −11.8 ± 1 kcal/mol, vs. experimental −9.7 ± 0.2 kcal/mol.The consensus estimates for the SARS-CoV-2/ACE2 complex is ΔGbind = −9.4 ± 1.5 kcal/mol, which is in near quantitative agreement with experiment (−10.6 kcal/mol). The availability of a conceptually simple MMGB/SA-based protocol for analysis of the SARS-CoV-2 /ACE2 binding may be beneficial in light of the need to move forward fast.

Accuracy of protein–ligand binding free energy calculations utilizing implicit solvent models is critically affected by parameters of the underlying dielectric boundary, specifically, the atomic and water probe radii. Here, a global multidimensional optimization pipeline is developed to find optimal atomic radii specifically for protein–ligand binding calculations in implicit solvent. The computational pipeline has these three key components: (1) a massively parallel implementation of a deterministic global optimization algorithm (VTDIRECT95), (2) an accurate yet reasonably fast generalized Born implicit solvent model (GBNSR6), and (3) a novel robustness metric that helps distinguish between nearly degenerate local minima via a postprocessing step of the optimization. A graph-based “kT-connectivity” approach to explore and visualize the multidimensional energy landscape is proposed: local minima that can be reached from the global minimum without exceeding a given energy threshold (kT) are considered to be connected. As an illustration of the capabilities of the optimization pipeline, we apply it to find a global optimum in the space of just five radii: four atomic (O, H, N, and C) radii and water probe radius. The optimized radii, ρW = 1.37 Å, ρC = 1.40 Å, ρH = 1.55 Å, ρN = 2.35 Å, and ρO = 1.28 Å, lead to a closer agreement of electrostatic binding free energies with the explicit solvent reference than two commonly used sets of radii previously optimized for small molecules. At the same time, the ability of the optimizer to find the global optimum reveals fundamental limits of the common two-dielectric implicit solvation model: the computed electrostatic binding free energies are still almost 4 kcal/mol away from the explicit solvent reference. The proposed computational approach opens the possibility to further improve the accuracy of practical computational protocols for binding free energy calculations.

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Calculation of protein–ligand binding affinity is a cornerstone of drug discovery. Classic implicit solvent models, which have been widely used to accomplish this task, lack accuracy compared to experimental references. Emerging data-driven models, on the other hand, are often accurate yet not fully interpretable and also likely to be overfitted. In this research, we explore the application of Theory-Guided Data Science in studying protein–ligand binding. A hybrid model is introduced by integrating Graph Convolutional Network (data-driven model) with the GBNSR6 implicit solvent (physics-based model). The proposed physics-data model is tested on a dataset of 368 complexes from the PDBbind refined set and 72 host–guest systems. Results demonstrate that the proposed Physics-Guided Neural Network can successfully improve the “accuracy” of the pure data-driven model. In addition, the “interpretability” and “transferability” of our model have boosted compared to the purely data-driven model. Further analyses include evaluating model robustness and understanding relationships between the physical features.

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