Applying physics-based scoring to calculate free energies of binding for single amino acid mutations in protein-protein complexes

Abstract

Predicting changes in protein binding affinity due to single amino acid mutations helps us better understand the driving forces underlying protein-protein interactions and design improved biotherapeutics. Here, we use the MM-GBSA approach with the OPLS2005 force field and the VSGB2.0 solvent model to calculate differences in binding free energy between wild type and mutant proteins. Crucially, we made no changes to the scoring model as part of this work on protein-protein binding affinity--the energy model has been developed for structure prediction and has previously been validated only for calculating the energetics of small molecule binding. Here, we compare predictions to experimental data for a set of 418 single residue mutations in 21 targets and find that the MM-GBSA model, on average, performs well at scoring these single protein residue mutations. Correlation between the predicted and experimental change in binding affinity is statistically significant and the model performs well at picking "hotspots," or mutations that change binding affinity by more than 1 kcal/mol. The promising performance of this physics-based method with no tuned parameters for predicting binding energies suggests that it can be transferred to other protein engineering problems.

Figure 1. Results summary for predicted change in protein-protein binding affinity for 19 protein-protein interaction targets [13].

Each R² is the correlation between the predicted change in binding affinity and the experimental change in binding affinity. Three different refinement methods were used, as described in Materials and Methods. Accuracy is an overall measure of the ability to categorize residues as “neutral” or “hot spot” (see Results and Discussion). “Hotspot precision” indicates the ability of the model to select mutations that make binding affinity worse by more than 1 kcal/mol. The experimental standard deviation is computed after removing qualifiers from qualified values (i.e. >2.0 is treated as 2.0) and has units of kcal/mol.

Figure 2. Plots of observed versus predicted affinity using the “minimization” refinement method, for four targets: 1JCK, 1VFB, 1DFJ, and 3HFM.

The R² correlation, accuracy, and hotspot precision are shown for each target.

Figure 3. Mutations in where repacking residues nearby the mutation improves the prediction compared to minimization alone.

In each case the mutant structure refined by minimization is shown in cyan and the mutant structure where a 5A radius was refined by side-chain prediction is shown in brown. The mutation residue is shown in ball-and-stick. Panel A shows the C:Thr170Ala mutation in 1AHW along with nearby residues. Panels B and C show the C:Trp43Ala mutation in 1FCC.

Figure 4. Comparison of the Accuracy metric for the minimization MM-GBSA refinement method to two different null hypotheses: the null hypothesis that all mutations are neutral, and the null hypothesis that all mutations make binding affinity worse by more than 1 kcal/mol.

Figure 5. Plots of predicted versus experimental change in protein-protein binding affinity for two additional targets: 1C4Z and 2OM2.

For 2OM2 the results shown are for the minimization refinement method (with only the mutated residue minimized) and for 1C4Z the results shown are for side chain refinement, with a 0 Å radius (i.e. only the mutated residue refined).

Figure 6. Thermodynamic cycle for calculating the net ΔΔG free energy difference between binding the wild-type protein P and the mutant protein P’.

In the associated equation for ΔΔG_bind, E is the calculated energy of each protein or complex after refinement.