- Research article
- Open Access
HawkRank: a new scoring function for protein–protein docking based on weighted energy terms
© The Author(s) 2017
Received: 19 September 2017
Accepted: 14 December 2017
Published: 28 December 2017
Deciphering the structural determinants of protein–protein interactions (PPIs) is essential to gain a deep understanding of many important biological functions in the living cells. Computational approaches for the structural modeling of PPIs, such as protein–protein docking, are quite needed to complement existing experimental techniques. The reliability of a protein–protein docking method is dependent on the ability of the scoring function to accurately distinguish the near-native binding structures from a huge number of decoys. In this study, we developed HawkRank, a novel scoring function designed for the sampling stage of protein–protein docking by summing the contributions from several energy terms, including van der Waals potentials, electrostatic potentials and desolvation potentials. First, based on the solvation free energies predicted by the Generalized Born model for ~ 800 proteins, a SASA (solvent accessible surface area)-based solvation model was developed, which can give the aqueous solvation free energies for proteins by summing the contributions of 21 atom types. Then, the van der Waals potentials and electrostatic potentials based on the Amber ff14SB force field were computed. Finally, the HawkRank scoring function was derived by determining the most optimal weights for five energy terms based on the training set. Here, MSR (modified success rate), a novel protein–protein scoring quality index, was used to assess the performance of HawkRank and three other popular protein–protein scoring functions, including ZRANK, FireDock and dDFIRE. The results show that HawkRank outperformed the other three scoring functions according to the total number of hits and MSR. HawkRank is available at http://cadd.zju.edu.cn/programs/hawkrank.
Protein–protein interactions (PPIs) are involved in a wide variety of biological processes, such as signal transduction [1, 2], transmembrane transport [3, 4], and antibody-antigen pairing [5, 6]. Deciphering structural and energetic determinants of PPIs is a prerequisite to understanding the PPIs-mediated functions in living cells. Unfortunately, only a tiny fraction of protein–protein complex structures have been characterized by high-resolution experimental techniques, such as X-ray crystallography, solution nuclear magnetic resonance (NMR) spectroscopy and cryo-electron microscopy (cryo-EM), which cannot keep pace with the growing demand in structure-based interactome analysis. Moreover, many weak and/or transient PPIs that play essential roles in regulating dynamic networks in bio-systems cannot be easily captured by experiments due to their unstable nature. On that account, computational approaches, especially protein–protein docking, are expected to provide an alternative and efficient way based on the unbound protein structures for predicting the binding complexes and understanding the recognition mechanisms at the atomic level [7–9].
The ultimate goal of protein–protein docking is the prediction of a near-native structure of the complex from many docking decoys, which generally falls into two stages: sampling and refinement. In the sampling stage, a large number of docking poses are generated and scored by various scoring functions; and in the refinement stage, the top-hit poses (or decoys) given by the first stage are re-scored and re-ranked by more rigorous scoring functions. Apparently, the success of protein–protein docking is, to a large degree, dependent on the ability of the scoring function to score and rank the decoys accurately. So far a large number of scoring functions have been developed, ranging from force field-based scoring functions such as ZRANK and FireDock [10–13], to knowledge-based ones such as dDFIRE and InterEvScore [14–16] and machine-learning scoring functions [17, 18]. However, recognizing near-native structures from a huge pool of alternatives is still quite challenging because the accuracy of most scoring functions needs to be improved. Besides, the ease of use, efficiency and general utility of the scoring functions should also be taken into account. Since the establishment of the Critical Assessment of PRedicted Interactions (CAPRI) campaign  in 2001 offers a community-wide platform that assesses the accuracy of protein–protein docking approaches, all related scoring functions and algorithms can be evaluated by comparing the submitted structures with the unpublished crystal structures from wide range of participants including predictors, servers and scorers. In 2010, Kastritis and Bonvin assessed the performances of 9 commonly used scoring functions and a free energy prediction algorithm on their ability to predict the binding affinities for 81 complexes . They found that all the tested scoring functions could not provide reliable predictions because they all failed to correlate the experimental binding affinities (pK d ) with the scores predicted by the corresponding scoring function, with the highest correlation of only − 0.32. Recently, our group analyzed the prediction results for the 24 targets tested from ROUND14 to ROUND 28 of CAPRI , and we found that, although the scorers perform better than the uploaders and predictors, they could give relatively high success rates (> 50%) for only two targets. Therefore, more approaches should be explored in order to improve the prediction accuracy of scoring functions for more reliable protein–protein docking.
In the past decade, more theoretically rigorous free energy calculation methods, such as Molecular Mechanics/Poisson Boltzmann Surface Area (MM/PBSA) and Molecular Mechanics/Generalized Born Surface Area (MM/GBSA), have been employed to predict binding affinities and identify correct binding structures for protein–protein systems [22–29]. For example, in our previous study , we evaluated the performances of MM/PBSA and MM/GBSA to predict the binding affinities and recognize the near-native binding structures for more than forty protein–protein complexes. The results show that, compared with most scoring functions used in protein–protein docking, MM/GBSA achieved better accuracy to predict the correct binding modes and binding affinities for the studied protein–protein systems. Therefore, the desolvation energy, which is related to the leading role of solvent exclusion during the protein inter-molecular assembly, is critical to identify these correct binding poses.
Although MM/GBSA is of more computational efficiency than other end-state free-energy calculation methods like thermodynamic integration (TI) and free energy perturbation (FEP), it is still much more time-consuming than the commonly used scoring functions in protein–protein docking, such as ZRANK, which treats the desolvation energy term with Atomic Contact Energy (ACE) model . The computational cost in MM/GBSA is mainly attributed to the calculation of the polar desolvation energy term based on the GB model. In that regard, we developed HawkRank, a force field-based scoring function in which the energy terms are similar to those in MM/GBSA. Besides the frequently used van der Waals and electrostatic potentials, a simplified aqueous solvation model based on SASA (solvent accessible surface areas) was implemented into our scoring function. HawkRank is designed for the sampling stage of protein–protein docking and it can score a huge number of docked structures with low computational cost and high efficiency. We developed and benchmarked the present scoring function based on 176 high-resolution protein–protein complexes that are nonredundant at the family–family pair level. Compared with ZRANK, FireDock and dDFIRE, HawkRank performs consistently best on both the total number of hits and the (modified) success rate.
HawkRank was developed by combining the weighted van der Waals potentials, electrostatic potentials and desolvation potentials. The workflow of the development of HawkRank is discussed below in details.
Preparation of the protein–protein decoy dataset
More and more protein–protein complexes have been discovered, researchers classify protein–protein complexes based on various angles. The most common is that classify protein–protein complexes by protein family. The other researchers classify complexes as homo- and hetero-oligomeric complexes, non-obligate and obligate complexes and transient and permanent complexes, by the type of protein–protein interaction . Besides, some researchers also excavate many effective statistical knowledge from the interface of the protein–protein interaction, such as the reported by Ref  and Ref . Therefore, collecting a protein–protein complex database is a challenging task, by reason that, comprehensive consideration including protein family, the type of protein–protein interaction or characteristics of interface is need. However, there are still some databases pick out protein–protein complexes for theoretical research, such as protein–protein complexes in PDBbind , 2P2I-DB [35, 36], ZDOCK benchmark  and etc. The protein–protein complexes in ZDOCK benchmark 4.0  were chose to develop the HawkRank scoring function in our study. ZDOCK benchmark 4.0 provides 176 nonredundant protein–protein complexes with high-resolution X-ray or NMR structures in bound and unbound states at the family–family pair level, including 124 complexes in the previous version 3.0 plus 52 newly-added ones. Besides, the protein–protein complex dataset used in training ZARNK and FireDock is the same ZDOCK benchmark series. More than that, the structured files of predictions docked by the unbound receptor and ligand from the ZDCOK benchmark are available from Zlab official website (https://zlab.umassmed.edu/zdock/benchmark.shtml), which is convenience for the training of scoring function. Therefore, we choose ZDOCK benchmark 4.0 for its convenience and the rationality of comparing HawkRank with ZRANK and FireDock. In this study, the 124 complexes were used as the training set to develop HawkRank and the other 52 ones as the test set to validate the actual performance of HawkRank. It should be noted that the benchmark 4.0 only contains binary interactions, so HawkRank is not suitable for the interactions between more than two proteins. Besides, HawkRank is also not suitable for the interactions between protein and peptide.
ZDOCK (version 3.0) was used to generate the decoys for each complex. ZDOCK systematically evaluates a huge number of docked conformations on a grid by using a combination of shape complementarity, electrostatics and statistical potential terms for scoring , and the search process is accelerated by the Fast Fourier Transformation (FFT) algorithm . Depending on the sampling density in the rotational space (15° or 6°), ZDOCK can output 3600 or 54,000 predictions for each system. Benchmark 4.0 was downloaded from Zlab official website. For each system, the unbound RCSB Protein Data Bank (PDB) files of the receptor and ligand are provided in Benchmark 4.0. Cases in Benchmark 4.0 have been docked using ZDOCK3.0 and the results depending on the sampling density in the 6° rotational space are deposited in decoys_bm4_zd3.0_6 deg package file which can be download from Zlab official website. The missing hydrogen atoms in the unbound structures were added by using the reduce program (version 3.24) . The decoys for each complex were generated by the Perl script in decoys_bm4_zd3.0_6 deg offered by ZDOCK, and a total of 54,000 decoys sorted by the ZDOCK scores were generated for each system. It should be noted that for each system only the top scored 10,000 decoys were used in our analysis.
Criteria to evaluate the performance of protein–protein docking
Generally, in a protein–protein complex, the smaller protein is defined as the ligand protein and the larger one as the receptor protein. In our study, two types of root mean square deviations (RMSDs) between the predicted structure and the corresponding crystal structure, including ligand RMSD (L_RMSD) and interface RMSD (I_RMSD), were used as the criteria to evaluate the performance of protein–protein docking. L_RMSD, which is calculated over the C α atoms of the ligand proteins when the receptors are superposed, was used to assess the global geometric fit between the predicted and native conformations . I_RMSD, calculated over the C α atoms of the interfacial residues when the predefined interfacial residues are superposed, was used to measure the geometric fit of the interface regions . The interfacial residues in a protein–protein complex are defined as the residues within 10 Å of any atom in another protein . The L_RMSDs and I_RMSDs were calculated by using the ProFit program , which employs the McLachlan algorithm in fitting. The structures of the protein–protein complexes were predicted from the unbound proteins, and therefore the structures of the proteins in the crystal complexes and the predicted complexes may have obvious difference.
The criteria to evaluate the performance of protein–protein docking for Target 107 in Round 35 of the CAPRI campaign are summarized in Additional file 1: Table S1. Based on these criteria, the predictions can be classified into several categories: incorrect, acceptable, medium, and high quality predictions. In this study, the hits are the predictions with L_RMSD less than 10 Å or I_RMSD less than 4 Å, which follows the criteria used in CAPRI.
Parameterization of the SASA-based solvation model
Generation of the protein dataset for the GB calculation
A protein dataset was established for the GB calculations (referred to as the GB dataset). The 1640 proteins in this dataset were selected from PDB based on the following criteria: (1). the structures are obtained by X-ray experiment, (2). the resolution should be lower than 2 Å, (3) the proteins do not contain any small molecule ligands, (4). the proteins are asymmetric, and (5) the proteins do not contain any modified residue.
Besides, for multiple structures whose sequences have at least 30% sequence identity, only a single structure is included in the dataset. Moreover, the protein structures with multiple conformations were eliminated.
Calculation of polar solvation free energies based on the GB model
The electrostatic/polar solvation free energies for the proteins in the GB dataset were computed by using the GB model implemented in Amber14. First, all missing heavy atoms and hydrogens of the proteins were added by using the tleap program in Amber14, and then the partial charges and force field parameters of the ff14SB force field were assigned. Subsequently, all proteins were optimized by 5000 cycles of minimization (2500 cycles of steepest descent and 2500 cycles of conjugate gradient). At last, the electrostatic solvation free energy for each protein was computed by using the modified GB model developed by Onufriev and colleagues (referred to as GB OBC1 ) . A value of 80 was used for the exterior dielectric constant, and 1 was used for the solute dielectric constant.
Definition of atom types
Parameterization of the SASA-based solvation model
Development of the HawkRank scoring function
The details about the energy terms used in the scoring function are described below. The workflow of the development of HawkRank is shown in Fig. 1b.
Calculation of the van der Waals potentials
Calculation of the electrostatic potentials
Calculation of desolvation potentials
Training the scoring function
For each case in ZDOCK benchmark 4.0, the I_RMSDs and L_RMSDs for the top 10,000 decoys were calculated. After eliminating those cases whose hits could not be found in the top 10,000 decoys, 151 cases out of 176 were included in the whole dataset. The 105 cases out of the 124 found in ZDOCK benchmark 3.0 were put into the training set and the remaining 46 cases into the test set. Then, based on the training set, genetic algorithm (GA) implemented in the R package (genalg) was used to determine the optimal set of the weights for the energy terms used in HawkRank. We set the maximum (3.0) and minimum (0.0) value for the weight of the van der Waals attractive potentials, electrostatic attractive potentials, electrostatic repulsive potentials and the polar desolvation potentials. However, we set the maximum (0.001) and minimum (0.0) value for the weight of the van der Waals repulsive potentials, on account of inherent defect in the equation function to calculate the van der Waals repulsive potentials and we want to reduce the impact of the van der Waals repulsive potentials on the whole scoring function. Besides, the population size was set as 200, the number of iterations was set as 1500 and the number of chromosomes that are kept into the next generation was about 20% of the population size.
Evaluation of the performance of HawkRank
The capability of HawkRank to recognize the near-native poses from the decoys was compared with those of two popular force field-based scoring functions used in protein–protein docking, ZRANK  and FireDock , and a knowledge-based scoring function named dDFIRE .
ZRANK is a force field-based scoring function that is a linear combination of atom-based potentials, including electrostatics, van der Waals, and desolvation potentials. Pairwise Atomic Contact Energy (ACE) model  is used to calculate the desolvation energy. Parameters used to calculate the van der Waals and desolvation potentials in the ZRANK scoring function are derived from the CHARMM 19 polar hydrogen force field.
FireDock is a method for the refinement and rescoring of rigid-body docking solutions. The function of FireDock includes ACE, softened van der Waals interactions, electrostatic interactions and internal energy. Moreover, hydrogen and disulfide bonds, π-stacking and aliphatic interactions are also considered . Compared with ZRANK and HawkRank, FireDock includes more energy terms.
dDFIRE is an all-atom statistical and knowledge-based energy function. Each polar atom is treated as a dipole with a direction. The orientation of the dipole is defined by the bond vectors that connect the polar atoms with other heavy atoms, and the function of dDFIRE is extracted from protein structures based on the distance between two atoms and the three angles involved in dipole–dipole interactions . Besides, the hydrogen bonding interactions are considered in dDFIRE via the physical dipole–dipole interactions.
It is well known that how to quantitatively evaluate the performance of a scoring function is quite essential. Traditionally, success rate (SR), the proportion of total cases with at least one hit in the top N predictions, has been widely used to evaluate the performance of a given scoring function . However, SR has its own intrinsic deficiency. For example, for two different protein–protein complexes, one has nine hits in the top 100 predictions while the other has only one hit in the top 100 predictions. However, when we calculate SR for these two systems, the contributions of the predictions for these two complexes to SR are identical, but nonetheless, the capacity of the scoring function to correctly rank the predictions for these two complexes is quite different. Moreover, SR ignores the rank for each hit. The “top-ranking” method is also a popular way to evaluate the performance of a given scoring function by identifying the first hit in the ranked predictions and comparing their ranks. The two evaluation strategies mentioned above are relatively intuitional, but not quite reasonable.
Results and discussion
Performance of the SASA-based solvation model
Performance of HawkRank
Next, we analyzed the performance of each individual energy term used in HawkRank from the view of MSR. The Y values of the five energy terms are shown in Additional file 1: Figure S1. The performances of the two repulsive potentials are not satisfactory, but the attractive ones perform much better, especially the electrostatic attractive potentials. When N ≤ 200, the polar desolvation potentials show good performance, and its performance decreases gradually with the increase of N.
Comparison of Pearson correlations between RMSDs and scores
Number of the cases for each scoring function in different intervals of r a
Training set (124 cases)
0.6 < r ≤ 0.8
0.4 < r ≤ 0.8
0.2 < r ≤ 0.8
0.0 < r ≤ 0.8
Test set (52 cases)
0.6 < r ≤ 0.8
0.4 < r ≤ 0.8
0.2 < r ≤ 0.8
0.0 < r ≤ 0.8
Limitations of HawkRank
Although HawkRank has better ranking capability than ZRANK, FireDock and dDFIRE, it still has some limitations. The F (N = 500) values for the 46 tested cases with the hits found in the top 10,000 decoys are listed in Additional file 1: Table S3. The 46 cases are ranked by the HawkRank’s F values in ascending order. F = 0 means that the scoring function does not find any hit in the top 500 predictions. For dDFIRE, ZRANK, FireDock and HawkRank, the numbers of the cases with F = 0 are 16, 8, 12 and 10, respectively. For 1XU1, 1ZHH, 2B4 J and 2OOR, the four scoring functions cannot find any hit in their top 500 predictions. For 1GXD, 1JZD, 1US7 and 2FJU, more than 60 hits docked by ZDOCK, but HawkRank performs poorly on them.
Comparative analysis of the interface areas for 1GXD, 1JZD, 1US7 and 2FJU
Native percentage (%)a
Spurious percentage (%)b
Computational cost of HawkRank
The arithmetic speed of HawkRank is closely related to the size of the protein–protein complex. The speed of HawkRank is fast enough to meet the requirements for scoring a large number of decoys in the sampling stage of protein–protein docking. The scoring of a complex with 500 residues needs less than 0.3 s on a core (Intel Xeon CPU E5-2692 v2 @2.20 GHz) with Linux operating system.
In this study, we developed a new scoring function named HawkRank by combining polar desolvation potentials, van der Waal potentials and electrostatic potentials. HawkRank introduces a fast and effective way to calculate the desolvation potentials based on a SASA-based solvation model. Compared with ZRANK, FireDock and dDFIRE, HawkRank shows better ranking capabilities to the 46 cases in test set. Besides, the scores predicted by HawkRank have higher correlations with L/I_RMSDs than those predicted by ZRANK, FireDock and dDFIRE, suggesting that the HawkRank scoring gives a better funnel-shaped energy landscape than the other three scoring functions. Although its prediction accuracy still needs to be improved for some protein–protein complexes with small interface areas, HawkRank is efficient to meet current requirements for scoring a large number of decoys in the sampling stage of protein–protein docking. In the light of the above assessment and the conclusion in our previous study that MM/GBSA rescoring has good capability to distinguish the correct protein–protein binding structures from the decoys, it would suggest to be an efficient protocol of using HawkRank followed by the MM/GBSA rescoring to improve the predictions of protein–protein docking.
TF and TH designed and implement the algorithm. TF, FC and YK performed the simulations. TF, HS, HL, DL and FZ analyzed the data. TF and TH wrote the manuscript. All authors read and approved the final manuscript.
We thank the National Supercomputer Center in Guangzhou (NSCC-GZ) for providing the computing resources.
The authors declare that they have no competing interests.
Consent for publication
Ethics approval and consent to participate
This study was supported by the National Key R&D Program of China (2016YFA0501701), the National Science Foundation of China (81773632, 21575128, 81302679), and the Fundamental Research Funds for the Central Universities (2017QNA7032, 2017QNA7033, 2017QNA7034).
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