Proteins help to copy DNA, transport nutrients and perform many other important roles in cells. To perform these tasks, proteins often interact with other proteins and work together. These interactions can be very complex because each protein has a three-dimensional shape that may change when it binds to other proteins. Also, two proteins may form several connections with each other.

It is possible to carry out experiments to calculate how likely it is that two proteins will physically interact with each other and how strong their connections will be. However, these measurements are time consuming and costly to do. Some researchers have developed computer models to help predict the interactions between proteins, but these models are often incorrect because they leave out some of the chemical or physical properties that influence the ability of proteins to interact.

With the aim of making a better model, Vangone and Bonvin examined 122 different combinations of proteins whose abilities to interact had previously been experimentally measured. Vangone and Bonvin found that the number of connections between each pair of proteins was a strong predictor of how tightly the proteins connect to each other. Particular features of the surface of the proteins—specifically, the region defined as the non-interacting surface—can also influence how strong the interaction is.

Vangone and Bonvin used this information to develop a new model that predicts how tightly proteins interact with each other based on the number of connections between the two proteins and the characteristics of the non-interacting surface. The model is simple, and Vangone and Bonvin show that it is more accurate than previous models. Defects in the interactions between proteins can lead to many diseases in humans, so this model may be useful for the development of new drugs to treat these conditions.

Interactions between proteins play a central role in the processes happening in the cells, from DNA replication to protein degradation (Jones and Thornton, 1996; Alberts, 1998; Nooren and Thornton, 2003; Perkins et al., 2010). Perturbations in those interaction networks can lead to disease (Stites, 1997; Sugiki et al., 2014). Characterizing these protein–protein interactions (PPIs) is therefore crucial for a proper understanding of mechanisms in biological processes for disease research and for drug development, as most common targets of drugs are proteins (such as enzymes, ion channels, and receptors).

Exploring recognition processes at atomic level requires knowledge of the three-dimensional (3D) structure of the associated molecular complexes. It is however the binding affinity (BA) (i.e., the natural inclination of molecules to associate) that defines whether or not complex formation will occur. The BA is therefore the key for understanding and predicting recognition, association and dysfunction phenomena related to protein complexes. It has been shown that changes in BA caused by mutations or post-translational modification errors lead to various diseases (Vidal et al., 2011). Commonly, the affinity of an interaction is described through the equilibrium dissociation constant K_d, or, in thermodynamic terms, the Gibbs free energy ΔG (ΔG = RT ln K_d). Measuring K_d values experimentally is a time-consuming and expensive process. Many computational methods aimed at predicting BA have been developed. Gaining the ability to predict BA is indeed an urgent need as it offers great opportunities not only to control interactions and develop innovative therapeutics (Keskin et al., 2005; Aloy and Russell, 2006; Beltrao et al., 2007; Kiel et al., 2008; Dell'Orco, 2009), but also for other applications such as protein engineering (Kortemme et al., 2004; Sharabi et al., 2011), computational mutagenesis (Ben-Shimon and Eisenstein, 2010), and docking (Halperin et al., 2002).

Different methods aimed at predicting BA have been proposed throughout the years, varying greatly in terms of accuracy and computational cost. Exact methods such as free energy perturbation and thermodynamics integration can be very accurate, but due to their computational costs their application is extremely limited (mostly to low throughput studies and mainly for small drug binding or mutations). Methods based on empirical functions (empirical, force-field-based potentials, statistical potentials, and scoring functions used in docking) are much faster (Jiang et al., 2002; Ma et al., 2002; Zhang et al., 2005; Audie and Scarlata, 2007; Su et al., 2009; Bai et al., 2011; Moal et al., 2011; Qin et al., 2011; Moal and Bates, 2012; Tian et al., 2012; Kastritis et al., 2014; Luo et al., 2014). However, even if some have been very successful on small training sets (Horton and Lewis, 1992; Audie and Scarlata, 2007), most published models still fail to systematically predict BA (Kastritis and Bonvin, 2010) for large datasets or discriminate between binders and non-binders (Sacquin-Mora et al., 2008; Fleishman et al., 2011). The main weaknesses of these methods are that they usually neglect factors such as conformational changes upon binding, allosteric regulation, and solvent and co-factor effects, which may all contribute to the binding strength.

Binding between two proteins is mainly defined by their contact region, the interface, and it is indeed the network of contacts between surface residues that holds complexes together, defines their specificity and contributes to their interaction strength. The importance of such inter-residue contacts has already been established in docking. In the Critical Assessment of Prediction of Interactions (CAPRI) experiment (Janin et al., 2003), for instance, assessment of the accuracy of the docked models is based on a combination of positional root mean square deviation (RMSD) criteria and conservation of intermolecular contacts with respect to the native structure (Lensink et al., 2007). In the context of scoring, considering the conservation of contacts at the interface across docking models has been shown to improve the ranking of docked models (Oliva et al., 2013; Chermak et al., 2014). The atom contact frequency in a set of predictions, a similar concept, has also been included in the ZRANK docking pipeline (Hwang et al., 2010). Next to their use in scoring, contacts have been introduced as a way to cluster docking solutions based on the fraction of common inter-residue contacts among a set of decoys (Rodrigues et al., 2012).

However, in addition to properties of the interface, a recent work has also demonstrated an effect of the non-interacting surface (NIS) on BA (Kastritis et al., 2014), a finding that has been corroborated in a recent study by Marillet et al. (Marillet et al., 2015).

Here we show how the network of contacts at the interface of a protein–protein complex can help in describing the BA of the interaction. Based on the number contacts at the interface, we propose an innovative and very simple method to predict BA. To this end we used the protein–protein BA benchmark (Kastritis et al., 2011) consisting of 144 non-redundant protein–protein complexes with experimentally determined K_d (ΔG) and available 3D structures.

Our results show that interfacial contacts, which have so far been neglected in the rationalization and prediction of BA, can be considered the best structural property to describe binding strength. Based on this observation, we describe an extremely simple BA predictor that accounts for different types of contacts and shows the best performance reported so far (to our knowledge) on such a large and diversified dataset of complexes. Its performance is compared to other previously published predictor methods (Moal et al., 2011). Further, we analyze the impact of the experimental method used to characterize BA on the prediction performance.

Considering the critical role of the BA in the study of protein–protein complexes and the still elusive approaches to predict it (Kastritis and Bonvin, 2010; Fleishman et al., 2011), we demonstrate here that the network of inter-residue contacts (ICs) between two interacting proteins is a good descriptor for the BA. Using the structure-based BA benchmark of Kastritis et al. (2011), we correlated ICs with experimentally determined BA data (K_d or ΔG) for protein complexes (bound forms). The diversity of experimental methods used to measure BA in this benchmark allows us to underline their limitations and reliability for use in BA prediction. From the original dataset of 144 complexes, we removed the cases with ambiguity in the exact K_d values and all complexes with missing or unresolved residues (>2) at the interface (data reported in Supplementary file 1). For the remaining 122 complexes, we calculated the number of ICs and evaluated their correlation (expressed through the Pearson's correlation coefficient R) with the experimental ΔGs. We describe the influence of various properties on the results, such as the distance cut-off defining a contact and the experimental method used for BA measurement.

Correlation between ICs and BA

In a protein complex the interactions are usually of relatively short range. Recently, however, Kastritis et al. (2014) revealed the unexpected contribution of NIS residues to BA. We therefore systematically evaluated the effect of the distance on defining the inter-residues network by varying the cut-off distance between 3 Å and 20 Å (see ‘Materials and methods’). For each distance cut-off the number of ICs was correlated with the experimental ΔGs. The results, reported in Figure 1, show that the highest correlation is achieved at a cut-off of 4.0 Å, (R_ICs = −0.50, ρ < 0.0001). This correlation decreases slowly until 8.0 Å (R_ICs = −0.41, ρ < 0.0001) and drops at higher distances. We also evaluated the ranking power of the ICs, expressed through the Spearman's correlation coefficient S, which follows the same trend as R with slightly higher absolute values (Figure 1).

Figure 1

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How experimental BA methods affect the correlations

Many different experimental methods can be used to determine the ΔG of a protein–protein complex. Each presents different characteristics so that the measured ΔG values depend on the method used, its sensitivity and the strength of the interactions that are being measured. For the set of 122 complexes used in this work, ten different experimental methods have been used to detect the ΔGs: stopped-flow fluorimetry (8 cases), surface plasmon resonance (SPR) (40 cases), high performance liquid chromatography (HPLC)/UV absorption spectroscopy (14 cases), sedimentation (1 case), radioligand binding (competitive binding experiments) (2 cases), potentiometry (1 case), reduction assay (1 case), isothermal titration calorimetry (ITC) (19 cases), inhibition assay (17 cases), fluorescence spectrophotometric assays (19 cases).

We analyzed separately the BAs from the various experimental methods with enough data points (≥8) and compared the prediction performance with the full data set. As reported in Table 1, the correlations between ICs and experimental ΔGs increased to R_ICs = −0.70 (ρ = 0.03), R_ICs = −0.53 (ρ = 0.0003), R_ICs = −0.65 (ρ = 0.006) and R_ICs = −0.55 (ρ = 0.006) in the case of ΔGs determined by stopped-flow fluorimetry, SPR, spectroscopic methods and ITC, respectively. For the 17 cases measured by inhibition assays and the 19 by fluorescence spectrophotometry techniques the correlations were meaningless (R_ICs = 0.04 with ρ = 0.9 and R_ICs = 0.05 with ρ = 0.8, respectively). These are indirect methods useful in calculating relative binding strengths (known as IC50s), but these have limitations when used to calculate absolute BA values (Lazareno and Birdsall, 1993; Wilkinson, 2004; Masi et al., 2010).

Table 1

Class	#Complexes	RICs		RBSA
All	122	−0.50	(ρ < 0.0001)	−0.32	(ρ = 0.002)
Stopped-flow	8	−0.70	(ρ = 0.03)	−0.55	(ρ = 0.08)
SPR	39	−0.53	(ρ = 0.0003)	−0.44	(ρ = 0.002)
Spectroscopy	14	−0.65	(ρ = 0.006)	−0.27	(ρ = 0.2)
ITC	20	−0.55	(ρ = 0.006)	−0.64	(ρ = 0.001)
Inhibition assay	17	0.05	(ρ = 0.4)	−0.08	(ρ = 0.4)
Fluorescence	19	0.04	(ρ = 0.4)	0.34	(ρ = 0.1)

1. The ICs were calculated for a 4.0 Å cut-off.

Removing the cases from inhibition assays and fluorescence spectrophotometry methods, and all others for which only a few data points were reported (potentiometry, radioligand, reduction assay, and sedimentation), we end up with a reliable dataset of 81 structures (a ‘cleaned’ dataset) showing an increased correlation of R_ICs = −0.59 (ρ < 0.0001) at the re-optimized distance threshold of 5.5 Å to define a contact (Figure 2). All further results will therefore refer to the 5.5 Å cut-off to define ICs.

Figure 2

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Structural properties contributing to BA

In order to assess which structural property might be the best descriptor for the binding strength, we calculated on the ‘cleaned’ dataset values for the widely used buried surface area (BSA), the NIS characteristics (recently shown to contribute in the BA) (Kastritis et al., 2014), and our ICs. We further classified these properties based on the amino acid type—polar/apolar—for BSA and NIS, and contact types—polar/polar, polar/charged, polar/apolar, charged/charged, charged/apolar, apolar/apolar—for the ICs. For the latter we also considered the hydrophobic/hydrophilic classification. For all these, we evaluated whether this finer classification (resulting, of course, in more parameters in our model) improves the correlations. It is clear from the results summarized in Table 2 that the number of ICs is a better descriptor than the BSA, with R_{ICs_total} = −0.59 (ρ < 0.0001) vs R_{BSA_total} = −0.46 (ρ < 0.0001). When distinguishing between the amino acid properties, the factors that contribute the most to BA are the number of ICs between polar and apolar residues (R = −0.56, ρ < 0.0001) and between hydrophilic residues (R = −0.53, ρ < 0.0001). However, none of these individual classes shows better correlation than the total ICs and BSA. All the calculated data are provided in Supplementary file 2.

Table 2

Property	R	p-value
ICs_total	−0.59	<0.0001
ICs_charged/charged	−0.17	=0.06
ICs_charged/polar	−0.26	=0.009
ICs_charged/apolar	−0.45	<0.0001
ICs_polar/polar	−0.13	=0.1
ICs_polar/apolar	−0.56	<0.0001
ICs_apolar/apolar	−0.34	=0.001
ICs_hydrophilic/hydrophilic	−0.53	<0.0001
ICs_hydrophilic/hydrophobic	−0.34	=0.001
ICs_hydrophobic/hydrophilic	−0.05	=0.3
BSA_total	−0.46	<0.0001
BSA_polar	−0.36	=0.0005
BSA_apolar	−0.47	<0.0001
%NIS_polar	0.07	=0.06
%NIS_apolar	−0.33	=0.001
%NIS_charged	0.28	=0.006

1. A fine classification of those properties based on the polar/apolar/charged and hydrophobic/hydrophilic nature of the amino acids is also reported. The property with the highest R value is highlighted in bold. The corresponding data are provided in Supplementary file 2.

In order to assess the predictor power of the above-described structural properties, we built different predictor models (contacts-based, BSA-based, NIS-based and combinations of these), optimizing the following model:

(1) $\text{Model\hspace{0.17em}N:\hspace{0.17em}}\Delta {\text{G}}_{\text{calc}}={\text{w}}_1{\text{P}}_1+{\text{w}}_2{\text{P}}_2+....+\text{Q},$

where P_N values are the properties used to train Model N, w_N values are the weight and Q is a shift value. To avoid the problem of over-fitting when many variables are used (>3), we applied the Akaike's Information Criterion (AIC) stepwise selection method implemented in R (R Development Core Team, 2014) in order to identify (and consider only) the significant variables among the training ones. Each derived model, with associated weights w_N and performance, is reported in Table 3.

Table 3

Properties (PN)	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6
ICs_total	0.07782	-	-	-	-	-
ICs_charged/charged	-	-	/	-	-	0.09420
ICs_charged/polar	-	-	/	-	-	/
ICs_charged/apolar	-	-	0.11627	-	-	0.10038
ICs_polar/polar	-	-	−0.12655	-	-	−0.19522
ICs_polar/apolar	-	-	0.23595	-	-	0.22609
ICs_apolar/apolar	-	-	/	-	-	/
ICs_hydrophil/hydrophil	-	-	-	0.09055	-	-
ICs_hydrophil/hydrophob	-	-	-	0.05726	-	-
ICs_hydrophob/hydrophil	-	-	-	0.06037	-	-
BSA_total	-	0.00278	-	-	-	-
BSA_polar	-	-	-	-	0.00131	-
BSA_apolar	-	-	-	-	0.00400	-
%NIS_polar	-	-	-	-	-	/
%NIS_apolar	-	-	-	-	-	−0.18786
%NIS_charged	-	-	-	-	-	−0.13872
Intercept (Q)	4.78839	5.66032	5.13766	4.90452	5.44809	15.9433
R	−0.59	−0.46	−0.67	−0.60	−0.48	−0.73
p-value	<0.0001	<0.0001	<0.0001	<0.0001	<0.0001	<0.0001
RMSE (kcal mol−1)	2.25	2.46	2.08	2.22	2.45	1.89

1. The weights w_N are reported for each properties P_N used to train Model N. Properties that have not been used for training the Model or have been evaluated as not relevant from the Akaike's An Information Criterion (AIC) evaluation are reported as ‘-’ and ‘/’, respectively. At the bottom of the table, the correlation coefficient and prediction error (expressed as R and RMSE) are reported.

Models 1 and 2 were trained on ICs_total and BSA_total, respectively, with a better performance of the ICs-based model (as already reported in Table 2) (root mean square errors [RMSEs] of 2.25 and 2.46 kcal/mol, for ICs and BSA, respectively). Models 3 and 4 have been trained using the ICs classified by residue type (polarity in Model 3, hydrophobicity in Model 4). While single amino-acid-type ICs properties do not improve the correlations, their linear combination results in a significant improvement from R = −0.59 (ρ < 0.0001) for Model 1 to R = −0.67 (ρ < 0.0001) for Model 3 and R = −-0.60 for Model 4 (ρ < 0.0001). Model 5 has been trained on the polar/apolar classification of the Horton and Lewis BSA model, (Horton and Lewis, 1992), with a slightly improved performance compared with Model 2 based on the total BSA, but it is still worse than any of the contact-based models (i.e., Model 1, Model 3, and Model 4).

Among the models that are based on properties of the interface of the binding site, the one based on polarity-classification of ICs (i.e., Model 3) shows the best performance. We therefore added to it the NIS properties in order to obtain a full description of the structural properties of the complex, resulting in Model 6. After AIC evaluation, we obtained the following linear equation:

(2) $\Delta {\text{G}}_{\text{calc}}=0.09459{\text{\hspace{0.17em}ICs}}_{\text{charged}/\text{charged}}+0.10007{\text{\hspace{0.17em}ICs}}_{\text{charged\_apolar}}-0.19577{\text{\hspace{0.17em}ICs}}_{\text{polar}/\text{polar}}+0.22671{\text{\hspace{0.17em}ICs}}_{\text{polar/apolar}}-0.18681{\text{\%NIS}}_{\text{apola}}\text{r}-0.13810{\text{\%NIS}}_{\text{charged}}+15.9433.$

Fourfold cross-validation results for this model (repeated 10 times) are reported in Supplementary file 3, showing consistency in terms of coefficient and prediction accuracy. A scatter plot of predicted vs experimental affinities is reported in Figure 3. The most relevant contributions to BA are the number of ICs made by charged and polar residues (ICs__{charged/charged} and ICs__polar/polar in Equation 2), while the apolar residues are only counted when interacting with charged and polar ones (ICs__{charged/apolar} and ICs__polar/apolar in Equation 2). This ICs/NIS-based model show the best performance of any model developed so far, with R = −0.73 and RMSE = 1.89 kcal mol⁻¹.

Figure 3

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The effect of conformational changes on BA-prediction accuracy

In many assemblies, the structure of free monomers differs from their structure in the oligomeric state (the ‘bound’ form) due to the association process. The affinity benchmark also reports the interface RMSD (i_rmsd) between the unbound and bound structures. This is a measure of how much conformational change takes place upon association. We investigated if our model would have a higher predictive power when classifying the complexes according to their amplitude of conformational change upon binding. Predictions made with our combined contacts and NIS model (Model 6, Equation 2) are much less sensitive to conformational changes than all previous models (Figure 3 and Figure 4), with only minor differences in performance between rigid (i_rmsd ≤ 1.0 Å, R = −0.75 and RMSE = 1.88 kcal mol⁻¹) and flexible cases (i_rmsd > 1.0 Å, R = −0.73 and RMSE = 1.89 kcal mol⁻¹). This indicates that, in contrast to previous predictors, the number of interface residue contacts is a rather robust predictor that is less sensitive to conformational changes.

Figure 4

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In order to perform a fair comparison with other previously published methods, we calculated their performance on the complexes that are in common between our clean dataset, the one reported by Moal et al. (2011), and the pre-calculated data on the Computational Characterisation of Protein–Protein Interactions (CCHarPPI) web server, ending up in 79 protein–protein complexes (Figure 4). The considered models include the ‘global surface model’ of Kastritis et al. (2014), the BSA-based model of Horton and Lewis (1992), the top three best performing methods reported by Moal et al. (2011) (their consensus model, DFIRE [Liu et al., 2004] and PMF[Su et al., 2009]) and the composite scoring functions reported by the CCHarPPI webserver [Moal et al., 2015a, b], such as ZRANK [Pierce and Weng, 2007], ZRANK2 [Pierce and Weng, 2008], RosettaDock [Chaudhury et al., 2010], PyDock [Cheng et al., 2007], FireDock [Andrusier et al., 2007], PISA [Viswanath et al., 2013], PIE [Ravikant and Elber, 2010], and SIPPER [Pons et al., 2011]. As shown in Figure 4, our ICs/NIS-based model (Model 6) outperforms all other methods tested. It is also less sensitive to conformational changes. All associated data are provided in Supplementary file 4. In addition to the composite scoring function of CCharPPI, none of the other 99 intermolecular parameters reported by CCharPPI outperformed our model, even if some show correlations above −0.50.

Insights on the difference between ICs and BSA

The ICs introduced in this work to describe BA seem to be a ‘higher level definition’ structural parameter than the BSA since they express not only the contact surface but also the pairwise non-bonded interactions that the two proteins make, which is related to the packing of the interface. Indeed, a weak complex is expected to be less tightly packed than a strong one, a difference that should be better reflected in the ICs than in the BSA. In particular, the origin of this difference might reside in the fact that the contribution of each residue to the BSA will greatly depend on the solvent-accessible surface area of the residue in the free form, whereas this does not affect ICs. To illustrate this point we checked the main differences between ICs and BSA for the complex between Fab D3H44 and Tissue factor (PDB code: 1JPS [Faelber et al., 2001]; ΔG_exp = −13.6 kcal mol⁻¹). This complex has a BSA of 1852 Ų and 83 ICs at 5.5 Å, resulting in a ICs-based affinity prediction of −12.8 kcal mol⁻¹ and a BSA-based one of −10.3 kcal mol⁻¹. The relative contribution of each interfacial Fab residue to the total BSA and number of ICs is shown in Figure 5A—figure supplement 1A: The contributions of the various residues to the ICs are more equally distributed than for the BSA. The latter shows high contributions for some residues, which is closely related to their solvent-accessible surface area (ASA) in the free form (defined here as the conformation extracted from the complex, that is, without any conformational changes—see ‘Materials and methods’) (see Figure 5B—figure supplement 1) and the surface representation in Figure 5. Indeed, because BSA_Fab = ASA_{Fab_free} −ASA_{Fab_complex}, when a residue is at the core of the binding interface (in other words totally shielded by Tissue factor) the ASA_{Fab_complex} will be close to 0, resulting in BSA_Fab ∼ASA_{Fab_free}. In contrast, residues already almost fully buried in the free form will not contribute to the BSA, whereas they might be able to form contacts in our ICs model.

Figure 5 with 1 supplement see all

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To report an example of this, the three residues GLU_H31, TYR_H32, and TYR_H33 located at the core of binding site (see Figure 5) contribute equally to the ICs calculation (6%), while they account for 10.5%, 5.6%, and 8.1% of the BSA_Fab, respectively. On the other hand, residues such as ILE_H29, TYR_H53 and ASP_H99, which are already highly buried in the free form and therefore contribute less than 0.1% to the BSA_Fab, are still making contacts, contributing between 1.2% and 2.4% in the calculation of ICs. In general, it seems that our ICs-based model is accounting more evenly than the BSA model for the contributions of highly solvent-accessible and buried residues, which leads to a higher prediction accuracy.

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Author details

1. Anna Vangone

   Computational Structural Biology Group, Bijvoet Center for Biomolecular Research, Faculty of Science—Chemistry, Utrecht University, Utrecht, Netherlands

   Contribution

   AV, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article

   Competing interests

   The authors declare that no competing interests exist.

2. Alexandre MJJ Bonvin

   Computational Structural Biology Group, Bijvoet Center for Biomolecular Research, Faculty of Science—Chemistry, Utrecht University, Utrecht, Netherlands

   Contribution

   AMJJB, Conception and design, Analysis and interpretation of data, Drafting or revising the article

   For correspondence

   a.m.j.j.bonvin@uu.nl

   Competing interests

   The authors declare that no competing interests exist.

   "This ORCID iD identifies the author of this article:" 0000-0001-7369-1322

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