Prediction of protein–protein binding free energies


  • Thom Vreven,

    1. Program in Bioinformatics and Integrative Biology, University of Massachusetts Medical School, Worcester, Massachusetts 01605
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  • Howook Hwang,

    1. Program in Bioinformatics and Integrative Biology, University of Massachusetts Medical School, Worcester, Massachusetts 01605
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  • Brian G. Pierce,

    1. Program in Bioinformatics and Integrative Biology, University of Massachusetts Medical School, Worcester, Massachusetts 01605
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  • Zhiping Weng

    Corresponding author
    1. Program in Bioinformatics and Integrative Biology, University of Massachusetts Medical School, Worcester, Massachusetts 01605
    • Program in Bioinformatics and Integrative Biology, University of Massachusetts Medical School, Room 1010, Lazare Research Building, 364 Plantation St., Worcester, MA 01605
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We present an energy function for predicting binding free energies of protein–protein complexes, using the three-dimensional structures of the complex and unbound proteins as input. Our function is a linear combination of nine terms and achieves a correlation coefficient of 0.63 with experimental measurements when tested on a benchmark of 144 complexes using leave-one-out cross validation. Although we systematically tested both atomic and residue-based scoring functions, the selected function is dominated by residue-based terms. Our function is stable for subsets of the benchmark stratified by experimental pH and extent of conformational change upon complex formation, with correlation coefficients ranging from 0.61 to 0.66.


The interactions between proteins are one of the most important processes in biology, playing fundamental roles in the immune system, signaling pathways, and enzyme inhibition. The physical processes governing the association of proteins are the van der Waals interactions, electrostatic interactions, hydrogen bonding, exclusion of solvent, and entropic changes. These processes can be modeled with accurate but computationally expensive approaches such as Molecular Dynamics (MD) or Monte Carlo (MC).1 Alternatively, one can use empirical approaches to predict binding free energies from the three-dimensional (3D) structure of the complex.

The computational prediction of binding free energies based on 3D structure alone has a long history. Most approaches use linear regression to obtain a weighted function of physical or knowledge-based terms,2 although machine-learning algorithms have been applied as well.3 Two decades ago, Horton and Lewis obtained a high correlation coefficient of 0.96 with experimental measurements, using only three terms in a linear combination.2 Later works using different methods and datasets also reported high correlation coefficients, ranging from 0.75 to 0.95.4–9 However, as outlined in several recent papers, these high accuracy predictions are due to limitations in the data sets used for training and testing the algorithms.3, 10–12 When a large number of approaches were tested on a larger and more reliable dataset, no correlations higher than 0.53 were observed.12 A community-wide effort on the computational discrimination between binding and non-binding protein pairs highlighted the critical role that the dataset plays for a balanced assessment of the methods.13

In this work, we present the development of a new energy function for the prediction of binding free energies of protein–protein complexes. We express our function as a weighted linear expression, and tested terms from a variety of sources. We use the recently published Affinity Benchmark for training and testing our function.11 This benchmark addresses the shortcomings of previous binding affinity collections: our affinity benchmark is larger than previous collections (144 complexes), is diverse (with 19, 61, and 64 antibody–antigen, enzyme-containing, and “other” complexes respectively), has bound structures as well as unbound structures for each case, and has reliable experimental measurements of binding affinities.

Our final binding free energy function ZAPP (Zlab Affinity for Protein–Protein interaction) has a correlation coefficient of 0.63 with experimental measurements using leave-one-out cross validation, and the root mean square error (RMSE) is 2.25 kcal mol−1. In addition, it correctly predicts the ordering of binding free energies for all nine cognate/noncognate complex pairs that are included in the benchmark.


The energy function

We tested a large collection of terms from various sources, as discussed in Methods, and in Table I we list the nine terms that were retained in ZAPP. Addition of any other term from our collection did not show further improvement. With addition of a constant, the function has 10 free parameters, and has a correlation coefficient of 0.63 with experimental measurements. The benchmark contains nine pairs of cognate/noncognate complexes (see labels in Fig. 1 for the nine pairs). The two complexes of each pair have similar geometry but very different affinities. Our function correctly predicts the high/low-affinity ordering of each pair. However, as shown in Figure 1, the magnitudes of the differences are not predicted well.

Figure 1.

Predicted and experimentally obtained binding free energy differences of cognate/noncognate pairs.

Table I. Composition of ZAPP and Performance of Energy Functions with Terms Alone or Left Out
TermTBRos_SolRos_HBElec_LRAElec_LRRBur_C/SLoopHelixMisResConstantComplete function
  • a

    Average of the 144 folds of cross-validation. These weights are for the normalized values of the terms.

  • b

    Number of cognate/noncognate pair orders predicted correctly (out of 9 total).

Standard dev.3.0%2.9%2.5%4.4%3.7%2.6%2.1%4.0%2.3%0.1% 
Term aloner0.−0.19−0.03 0.63
RMSE (kcal mol−1)2.782.852.782.882.882.722.682.832.88 2.25
#C/NC correctb764226611 9
Term left outr0.610.600.600.620.610.590.570.620.55  
RMSE (kcal mol−1)2.292.312.322.262.282.322.372.272.41  
#C/NC correctb988998888  

The highest standard deviation of a weight obtained in all 144-folds of the leave-one-out cross validation is not higher than 4%, thus the 144 functions obtained in the cross validation are highly similar. Of the nine terms, three are physics-based atomic terms and describe interaction between the two proteins: “Ros_HB” is an energy term for hydrogen bonds, and “Elec_LRA” and “Elec_LRR” are long-range electrostatic terms, attractive and repulsive, respectively. The weights for these terms are positive, as expected. Two terms are related to desolvation (replacing solvent–protein interactions with protein–protein interactions). “Ros_Sol” describes the energy loss from removing the solvent upon forming the complex, and the weight is positive as expected. “Bur_C/S” is the number hydrophobic surface atoms buried upon complex formation. The weight is negative, increasing the predicted stability of the complex with increased hydrophobic surface area. “TB” is a residue-based contact potential developed for protein–protein docking and has positive weight. “Loop” and “Helix” are the number of loop and helix residues in the interface, respectively, and “MisRes” is the number of residues in the interface that are present in the bound, but not in the unbound form. MisRes is related to the disorder-to-order transition, which causes an entropic loss that is compensated for by a favorable enthalpic contribution. Disorder-to-order transitions often result in a complexes with relatively low affinity and high specificity.14, 15 Indeed, in the 50% of the complexes with lowest binding affinity, we find 62% (43 of 69) of the complexes with non-zero values for MisRes.

It may seem surprising that some terms are not included in ZAPP, most notably short-range electrostatics. This may be because these are implicit in TB and Ros_HB. There are also no repulsive van der Waals terms in the expression, which is most likely due to using bound structures in the function optimization.

In Table II, we show the correlation coefficients (r) between the terms, as well as with experimentally measured binding free energy. The three largest correlations are: (1) between Ros_Sol and Ros_HB, presumably because both are dominated by hydrophilic residues in the interface; (2) Ros_Sol and Bur_C/S, both are related to solvation; and (3) the two electrostatic terms, which have a correlation close to 1. Surprisingly, combining the two electrostatic terms into one term (with one weight), or leaving either one out, decreases the performance of the function.

Table II. Correlation Coefficients (r) Between the Values of Each Term for the 144 Complexes, as Well as With Experimental Measurement
  1. Entries with absolute values larger than 0.7 are in bold.


We investigated the importance of the nine terms by looking at the performance of each term on its own (energy function optimized with only that term and the constant), and by leaving it out of ZAPP (function optimized with all the terms except the one under investigation). The results are in Table I. Single-term energy functions give a best r with experimental measurement of 0.37, compared with 0.63 for the energy function with all terms included. Because the single-term r in Table I were calculated using cross validation, they are not the same as the r obtained by directly correlating a term with experimental measurement as in Table II. The lowest RMSE for a single term is 2.68 kcal mol−1, compared with 2.25 kcal mol−1 for the full function. When we look at the scoring function with the respective terms removed, we see that terms that perform well on their own do not necessarily decrease performance greatly when removed. For example, removing from the full function the TB term, which gives a r with experiment of 0.27 when used on its own, decreases the r of the full function from 0.63 to 0.61. In contrast, the MisRes term gives a low (negative) r when used on its own (−0.03), but the r of the full function drops from 0.63 to 0.55 when this term is excluded. The reason is that terms such as TB describe physical processes that are also covered by other terms, which is much less so for the entropy term that MisRes adds to the energy function. The RMSE's and correct cognate/noncognate predictions follow mostly the same trends as the correlations discussed above.

Finally, we look at the weights of the terms, listed in Table I. We normalized the values of each term by subtracting the mean and then dividing by the standard deviation of the values for the 144 complexes. Because the weights listed in Table I are for the normalized values of the terms, it allows the comparison of weights for different terms. Again, the results reflect the correlation between the terms. For example, the electrostatic terms have the largest adjusted weights, but since they are strongly correlated, their effects on the total energy mostly cancel out. We can see that terms related to desolvation have large contributions, as well as Loop. MisRes has a large weight (0.969), despite its having a low correlation with experimental measurement (r = 0.084, Table II, as discussed in the previous paragraph), but consistent with the large drop of r from 0.63 to 0.55 upon leaving this term out. In Supporting Information Table S1 we show the relative change of the weights when the function is optimized with each of the nine terms excluded. We see that removing either one of the electrostatic terms causes a large decrease of the weight of the remaining electrostatic term, which indicates that these terms compensate each other. Also Ros_Sol and Ros_HB show such mutual dependence, and indeed in Table II we see that these terms are strongly correlated (r = −0.763). Removing the Loop term has large effects on the weights of three other terms (Elec_LRA, Bur_C/S, and Helix weights change by more than 50%). As the Loop term performs better on its own than any other term (Table I), it is expected that leaving it out has large effects on the remaining weights.

Performance and comparison with other algorithms

In Table III, we show the correlation coefficients of our predictions with experimental measurement for various subsets of the Affinity Benchmark. We also show the same r calculated with several other algorithms that are discussed in detail in the Methods section. These are the protein–protein docking potentials developed in our group (IRAD,16 ZRANK,17 and ZDOCK18–20), and the three potentials that gave the best results in a previous study using a precursor of the Affinity Benchmark (PyDock,21 Rosetta,22 AffinityScore1.06, 23).10, 12 ZAPP has the highest r with experimental binding free energies, 0.63, with Rosetta second, 0.41, and the other functions between 0.22 and 0.27.

Table III. Correlation Coefficients (r) for Subsets of the Affinity Benchmark
Complex typeaAllAEO
  • a

    A, antibody–antigen; E, enzyme-containing; O, “other” complexes.

I-RMSD cutoffAll<2.0 Å<1.0 Å 
I-RMSD rangeAll>2.0 Å1.0–2.0 Å<1.0 Å
pH dependenceAll7–7.9  
IntersectionAllW/KastritisW/Moal set 

The complexes in the Benchmark are divided into three classes based on protein type: Antibody–antigen complexes (A), complexes containing enzymes (E), and “other” complexes (O). ZAPP predicts enzyme-containing complexes best (r = 0.66), closely followed by the “other” class (r = 0.53). In contrast, the correlation for antibody–antigen complexes is much lower (r = 0.24). This may be due to the lack of atomic contact terms in ZAPP. Previously we observed that atomic contact terms were more accurate in quantifying antibody–antigen interactions than residue-based terms.16, 20 The only atom contact term in ZAPP is Ros_HB, but this only describes a specific type of interaction (hydrogen bonds), and not atom–atom interactions in general. Indeed, we see that the trend is reversed for ZRANK, ZDOCK, and IRAD. These potentials include statistical atom–atom potentials (IFACE20 for ZDOCK, ACE24 for ZRANK, and both IFACE and ACE for IRAD), and for each potential the antibody–antigen binding free energies are predicted more accurately than the enzyme-inhibitor and “other” classes. Since the antibody–antigen complexes are underrepresented in the Benchmark (19 of 144 complexes), our procedure to determine ZAPP could have selected against atom contact terms if they are only relevant for antibody–antigen binding free energy prediction.

It may seem surprising that total correlation is 0.63, while the correlations on the three subsets are similar in one case (r = 0.66 for enzyme-containing) and much lower in the two other cases (r = 0.24 and 0.53 for antibody–antigen and the “other” class, respectively). This can be understood from Figure 2, where we show the predicted against the experimental binding free energies for the different types of complexes. The antibody–antigen predictions only cover a small range, but it is contained within the range of binding free energies of enzyme-containing and “other” complexes. Also, the range of binding free energies for enzyme-containing complexes is shifted with respect to the “other” class, which is favorable for the combined r.

Figure 2.

Predicted and experimentally obtained binding free energies separated by complex type, and the x = y line.

In Figure 2, we see one outlier, the 1DE4 complex. A possible reason for errors in our predicted binding free energies is that we neglect the unbound-to-bound conformational changes of the monomers. Conformational changes can weaken the binding free energy when the bound structure is in a higher energy state than the free structure. Therefore, our method will be less accurate in predicting the binding free energies that have a larger contribution from the unbound-to-bound conformational change. However, the predicted binding free energy for 1DE4 is less negative than the experimentally measured values, which indicates that the error is not due to the neglect of the unbound-to-bound contribution in our energy model. Further investigation shows that the monomers in 1DE4 interact mostly through helical residues. The ratio of Helix to Loop residues in this interface is 8.6, whereas the ratio for all other complexes is below four. Since the secondary structure information is an important component of ZAPP, the unusually high helix content of this complex causes the prediction to show a large error. It must be noted that error in the prediction for 1DE4 of 5.7 kcal mol−1 is not exceptionally large; four other complexes also show absolute errors larger than 5 kcal mol−1.

We also investigated the performance for subsets of complexes classified based on the interface root mean square deviation between bound and unbound structures (I-RMSD). The argument is that conformational changes upon binding imply breaking favorable interactions in the unbound structures, which lowers the binding free energy. Using a simple energy function, based on the change in accessible surface area upon binding, Kastritis et al.11 showed that correlation vanished when only complexes with I-RMSD > 1.5 were considered. In Table III, we show the correlation of the potentials with either I-RMSD cutoffs or ranges, for including complexes below the I-RMSD cutoff or within the I-RMSD range. The performance of ZAPP is stable for the various I-RMSD based subsets, with correlations ranging from 0.61 to 0.66. Also pyDock does not show the best performance for the complexes with lowest I-RMSD, and the remaining algorithms show behavior similar to that observed by Kastritis, with best predictions for the tightest I-RMSD cutoff.

Furthermore, we calculated the correlations for subsets based on experimental pH. Protonation states depends on pH, which in turn affects binding affinity. Recently, several groups have developed computational models to predict the pH dependence of binding affinities.25–27 It is however not clear how accurate these models are, as large deviations between the predicted and observed pH dependence were observed.27 Therefore, we did neither attempt to include pH dependence in ZAPP nor has it been included in the other algorithms we compare our predictions with. In Table III, we show the results on the complexes for which the affinities were measured in the pH range of 7–7.9, excluding the more extreme pH cases. The accuracy of our predictions as well as most other algorithms does not depend much on the pH. Only pyDock and ZDOCK show better correlation when the pH is restricted.

Finally, we restrict our Benchmark to the intersection with test cases also used in other work. Kastritis et al. reported higher correlations than the current work. Indeed, when we compute correlations for the intersect of the Kastritis set with our set (42 of 46 cases in the Kastritis set), we see that in all cases the correlations improve, and in most cases more than double. Only pyDock and Rosetta show less improvement, and ZAPP shows only slight improvement. Thus the composition of a Benchmark can affect the results dramatically (as discussed in earlier work11), but our energy function remains stable.

Most recently, Moal et al.3 used machine learning approaches to predict binding free energies, using the dataset as in this work excluding seven complexes. They used four different machine learning methods, of which Multivariate Adaptive Regression Splines (MARS) yielded the best r of 0.52. Combining the four methods using a consensus approach yielded r with experimental measurements of 0.55. In Table III, we show the correlation coefficients computed for several scoring functions using Moal's subset of complexes, and ZAPP obtained an r of 0.64, which is nearly identical to the correlations computed with our full set (r = 0.63) .

Discussion and Conclusions

Using a linear expression of nine terms, we obtained a correlation coefficient of 0.63 with experimentally measured binding free energies of 144 protein–protein complexes upon cross validation. Although others have reported higher correlations for protein–protein binding free energy prediction, the earlier results were obtained using less diverse or less reliable data sets. We also tested the performance on several other algorithms that were shown to be promising in previous work, but the highest r we observed for those methods was 0.41. On a dataset very similar to ours, recent work by Moal et al.3 achieved r = 0.55 using machine learning approaches. In addition, Moal tested the performance of other algorithms, and did not observe r higher than 0.37. Using these comparisons, we believe our energy function is the best predictor of protein–protein binding free energies using 3D structures to date.

In contrast to other work, ZAPP contains only a few terms that describe interactions at the atomic level. Explicitly only hydrogen bonding falls in this category, while implicitly the TB potential includes atomic terms that describe the interaction among backbone atoms. The remaining terms are either at the residue level, or they are not pairwise. We speculate that residue-based terms introduce less noise than atom-based terms. Although atom–atom interactions have the potential to be more precise than residue-based terms, the reduction of noise is more important for the overall performance, and thus residue-based terms are preferred. This may mean that our energy function may not perform as well on predicting changes in binding free energies from mutations without additional atomic terms, where the specific interactions are more important than global effects. Eventually, effective potentials for protein engineering will likely be hybrids of residue-based potentials to describe large-scale binding, and atom-based terms to describe the effects of mutations or other modifications.

We tested our function for various subsets of the Affinity Benchmark. Whereas other algorithms show strong dependence on data set reduction based on experimental pH, conformational change between bound and unbound structures, or intersections with datasets used in other work, our function yielded correlation with experiment ranges from 0.61 to 0.66, and is always higher than any of the other methods tested. Thus, ZAPP does not suffer from overfitting and may retain its accuracy for new test cases. In comparison, for the same subsets, the correlation obtained with Rosetta (the algorithm that achieved the best overall r among the algorithms we tested) ranges from 0.24 to 0.61. When we test the ZAPP function for different complex types, we see a large drop in performance for the antibody–antigen complexes (correlation is 0.24, lower than several other algorithms tested). This is likely due to the dominance of residue-based terms in our function. The performance for enzyme-containing and “other” complexes remains high.

The accuracy of our function brings the prediction of binding free energies closer to the area of practical applicability. Examples are the prediction of protein–protein interaction networks, multimeric complexes, and design of specific enzyme inhibitors.

Our work suggests several areas where the binding free energy prediction may be improved further. First, we observe a large drop in performance for the antibody–antigen complexes, and other tested methods perform better. Thus determination of complex-type specific terms and weights may improve overall performance. Second, the 1DE4 case is an outlier because it has an unusual secondary structure composition in the interface. Nonlinear regression methods or machine learning approaches may be able to predict such cases better than the linear weighted function we have used. Finally, there are several physical phenomena that we do not include in our model. Examples are the small-scale conformational changes between the unbound and bound forms of the monomers, bound solvent molecules, and explicit protonation states of the titratable residues. Our current work demonstrates the value of the large and reliable benchmark for the development of binding free energy models, and we expect the benchmark to be equally valuable for the further investigation of protein–protein binding mechanisms.


Form of the function

We expressed our function as a linear combination of terms:

equation image

where C denotes a complex, wi the weight for term i, and vC,i the normalized value of term i for complex C. The normalization was performed so that each term would have zero mean and standard deviation of 1 for the 144 complexes in the benchmark. Except for the MisRes term discussed below, all the terms were calculated using only the bound structures, which implies that the conformational changes between the bound and unbound forms are ignored. Hence, we only computed the interactions between the (bound) monomers, discarding the energy differences between the bound and unbound forms of the monomers. To obtain the weights, we used a downhill simplex optimizer,28 with the correlation with experimental values as target function. Unless stated, all the results presented here are obtained using leave-one-out cross validation. To avoid overtraining and make the downhill simplex optimization feasible, we limited the number of terms we considered. We tested various combinations of the terms listed below, until we found a function of nine terms that did not improve further by inclusion of any other term. In Supporting Information Tables S2 (as from the original sources) and S3 (normalized), we give the values of the terms that are in our function for the individual complexes. In Supporting Information Tables S4 and S5, we give the weights obtained for each fold in the cross validation, specified for the non-normalized and normalized terms. In Supporting Information Table S6 we give the experimental measurements and predicted binding free energies.


For training and testing our functions, we used the Affinity Benchmark that was based on our protein–protein docking benchmark and recently published by us and other groups.11, 29 All the hetero-atoms were removed from the structures, so that we did not bias potentials that are parameterized for non-amino acid atom over potentials that are not. Some of the terms need hydrogen atoms present, which were added using Rosetta.22 We did not refine the structures; the positions of the non-hydrogen atoms were kept the same as in the X-ray structures. The Benchmark is non-redundant at the SCOP family level,30 and has nine cognate/noncognate pairs. Each pair consists of complexes that have similar geometry, but very different affinity. Robust prediction algorithms should be able to predict the correct order of affinities for the cognate/noncognate pairs.

Energy terms

We tested a large number of terms for our energy function. These are the terms from our ZDOCK3.0 algorithm for protein–protein docking,18, 19, 31 ZRANK for refining protein–protein docking solutions,17 and all the terms we tested in the development of the IRAD potential for reranking and described in detail in reference.16 We also tested a modified version of the electrostatic terms from ZRANK/IRAD, where the cutoff for long-range/short-range interaction was determined at the residue level instead of the atomic level: If any pair of atomic interactions between two residues is below the cutoff, all electrostatic interactions between those residues will be considered short-range. In addition, we tested the individual terms from the three potentials that performed best using a preliminary version of the Affinity Benchmark:10, 12 pyDock,21 Rosetta22 (high resolution mode only), and AffinityScore1.0,*,6,23 where the latter uses the programs NACCESS,32 SURFNET,33 and Libproteingeometry34, 35 for the calculation of solvent accessible surface area, interface gap, and hydrogen bonds, respectively. Throughout this work we use Rosetta version 2.3, since initial calculations showed that it performs better for the current Benchmark than Rosetta 3.2.

Further, we tested several entropy-related terms. First, we tested the rigid body complexation entropy change (separated for translational and rotational entropy).36 We also constructed a term that counts the residues that are present in the bound structure (within a given distance from the binding partner), but not in the unbound structure. We argue that this quantity represents a loss in entropy. We did not consider further terms based on the unbound structures, as exploratory calculations showed poor performance.

Finally, we identified additional terms that were shown to be relevant in other work. We included a modified version of the “hydrophilic bridges,”37, 38 which was an important term according to Ma et al.5 For the latter we used a simple distance cutoff, and counted the number of contacts between hydrophilic atoms. Bai showed that secondary structure information can be effective for the prediction of binding free energies.9 We included variations: The total number of helical, beta sheet, or loop residues, the relative numbers, and the same quantities restricted to residues in the interface.

Using the approach outlined above, the following nine terms were retained in our energy function:

TB: Residue-based pair potential from Tobi and Bahar,39 optimized for discriminating hits from non-hits in a protein–protein docking decoy set. Residues are represented by three interaction sites: the side-chain centroid, the backbone amide nitrogen, and the carbonyl oxygen. Only the side-chain centroids are residue specific, yielding a total number of 253 independent parameters. The cutoffs for contacts are 4.0 Å, 6.8 Å, and 5.6 Å between backbone sites, side-chain sites, and backbone/side-chain sites, respectively.

Ros_Sol and Ros_HB: Ros_Sol and Ros_HB40 are the solvation and hydrogen bonding terms calculated in Rosetta.22 The solvation term is computed using the algorithm by Lazaridis and Karplus.41 See the footnote in Supporting Information Table S2 for details on how these terms were obtained from the Rosetta output files.

Elec_LRA and Elec_LRR: We used modified versions of the long-range electrostatic terms from ZRANK/IRAD, where Elec_LRA and Elec_LRR denote the attractive and repulsive interactions, respectively. Only charged residues are used, with charges located on the charged atoms only. The interaction between two residues is included only when all pairs of atomic distances between those residues is above 6.5 Å.

Bur_C/S: This term was presented by Audie and Scarlata,6 and counts the number of hydrophobic (carbon and sulfur) atoms that exposed in the monomers but buried in the complex. Atoms are considered exposed when the solvent accessible surface, calculated using NACCESS,32 is larger than 1 Å2.

Loop and Helix: Loop and Helix count the number of loop and helical residues in the interface. Residues are in the interface when at least one atom is within 6 Å of any atom of the binding partner, and secondary structure is assigned using the S2C database.42

MisRes: MisRes is the number of interface residues that are present in the bound, but not in the unbound form. Only Cα atoms are used in this assignment, and are considered missing when they are not present in the X-ray crystallography structure, or have B-factor of zero. Cα atoms within 11 Å of any Cα atom of the binding partner are considered in the interface.

  1. 1

    AffinityScore1.0 was kindly provided by CMD Bioscience. Because the program could not parse some of the files from our Benchmark, we modified the code for it to handle all the complexes. The results presented here were obtained with the modified version of AffinityScore1.0.