An Effective MM/GBSA Protocol for Absolute Binding Free Energy Calculations: A Case Study on SARS-CoV-2 Spike Protein and the Human ACE2 Receptor

Abstract

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.

Keywords: SARS-CoV-2; binding free energy; entropy; implicit solvent.

Figure 1

Binding scheme of the SARS-CoV-2 spike protein to the human ACE2 receptor.

Figure 2

Binding a ligand (shown in red) to a protein receptor (shown in grey) in a box of solvent (shown in blue) releases free energy of $\Delta G_{bind}$. A negative value of $\Delta G_{bind}$ indicates that spontaneous binding occurs, and the magnitude of $\Delta G_{bind}$ characterizes the binding strength (affinity).

Figure 3

The thermodynamic cycle used to estimate the binding free energy of a protein–ligand complex in the solvent.

Figure 4

MM/PB(GB)SA flowchart. The initial structure of the complex is solvated using a water model. An MD simulation is run, from which a relatively large number of snapshots are extracted. After removing solvent molecules, the average binding free energy of the snapshots is assigned as the $\Delta G_{bind}$ of the system. The mean and standard deviation of each component of the $\Delta G_{bind}$ are supplemented by MM/PB(GB)SA.

Figure 5

Truncated structures of the Ras–Raf complex. The protein, Ras, is shown in orange and the ligand, Raf, is shown in green. The untruncated complex (full structure) is on the left, followed by the 10% truncated structure (17 residues of Ras eliminated) in the middle, and the 50% truncated structure (83 residues of Ras eliminated) on the right. The image on the left shows two pairs of residues in the binding interface that are less than 8 Å apart.

Figure 6

Truncation of SARS-CoV-2 S RBD used in the entropy estimate. The spike protein is in cyan, and the ACE2 receptor is in green. Left: original complex. Right: truncated complex. A pair of atoms on the binding interface that are 8.8 Å apart is shown in a solid red segment to illustrate the length scale.

Figure 7

Backbone RMSD of the truncated SARS-CoV-2 S RBD and ACE2 complex relative to the truncated part of the experimental crystal structure of the full complex, along the 50 ns production trajectory.

Figure 8

Entropy convergence of the truncated SARS-CoV-2 S RBD and ACE2 complex. Means and standard error of the means are shown. Increasing the number of equidistant sample points from 15 to 150 shows the stability of the entropy around 52 kcal/mol.

Figure 9

MM/GBSA results for Ras-Raf. The experimental value is from isothermal titration calorimetry [72]. An offset of 1.79 kcal/mol has been subtracted from the $\Delta H$ component of MGB-based estimate [28] for consistency with the author’s recommendation.