Docking Process and Cluster Analysis

After the rigid-body docking process, 29 +/- 28.86 near-native decoys were obtained for 36 out of 44 protein pairs. A near-native decoy is defined as a decoy with interactions similar to the native ones, evaluated using the Tanimoto Coefficient (TCIFP_native) values of more than 0.4, as detailed in the Material and Methods section. There were 8 protein pairs that did not yield any near-native decoys (Table 1) even in their bound-state forms; these protein pairs were composed of 6 ‘Rigid-body’ type, one ‘Medium-Difficulty’ type, and one ‘Difficult’ type. These categories are detailed in the Materials and Method section. In order to circumvent this problem, we used the profile method for analyzing a set of docking decoys. Accordingly, cluster analysis was performed on all 2000 decoys obtained from the initial protein-protein docking process. After hierarchical clustering of decoys by unweighted pair group method with arithmetic mean (UPGMA), decoys were divided into several groups according to different H-threshold values. The average number of clusters obtained for each protein pair was 537.8 +/- 316.8 in H6, 338.0 +/- 303.8 in H5, and 212.4 +/- 295.9 in H4. Formation of large number of clusters suggested that each cluster was composed of fewer decoys.

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Table 1. The number of near-native decoys, near-native core decoys, and near-native profile of interaction fingerprints.

https://doi.org/10.1371/journal.pone.0069365.t001

As summarized in Table 1, out of 88,000 ( = 2,000 x 44) decoys, we found the following number of near-native decoys in each H-threshold group: 242 in H6 (in 35 protein pairs), 144 in H5 (in 31 protein pairs) and 82 in H4 (in 23 protein pairs). In the higher H-threshold groups, clusters containing larger numbers of clusters containing near-native core decoys were obtained. In the H6 group, all protein pairs with near-native decoys, excluding 1KAC, yielded near-native core decoys. Core decoys were chosen from every group after classifying the decoys into groups according to various H-thresholds. In this work, core decoys were defined as the decoys with lowest energy scores, as re-scored by ZRANK, in their respective groups. Naturally, there were no near-native core decoys when there were no near-native decoys, because core decoys were selected from only 2000 decoys. Among all the H-threshold groups, there were cases where protein pairs with near-native decoys did not have any near-native core decoys because lowest energy scoring near-native decoys were not found. We found 12 such cases in H4 and only one case in H6.

We also performed cluster analysis using root mean square deviation (RMSD) for measuring similarities between the decoy interactions. For our analysis, we used L_RMSD, which is the RMSD between the ligand molecules after the receptor molecules are superimposed using C-alpha atoms. In this case, a near-native decoy was defined as the decoy whose L_RMSD was less than 5.0 Å compared to the interacting component of the native complex structure. We found 200 near-native decoys in 41 protein pairs, and on the average 1375.7 +/- 434.7 clusters were found after classifying the decoys into groups using L_RMSD = 5.0 Å, indicating that the number of decoys in each group was smaller than that obtained using the profile method. For example, classification of decoys into groups using L_RMSD = 10.0 Å resulted in 553.0 +/- 284.6 clusters, a number similar to that obtained using H6 (see above). We found 1187 near-native decoys with L_RMSD value<10.0 Å; this number was comparable to the number of near-native decoys (i.e., 1270) with TCIFP_native value ≥ 0.4.

Obtaining P-IFPs Containing High Fraction of Native Interactions by Assembling Clustered Decoys

After obtaining the core decoy, defined as the decoy with the lowest energy score in a cluster, we generated profile of interaction fingerprints (P-IFPs) by assembling decoys at various T-threshold values, as detailed in the Materials and Methods section. Figure 2 illustrates the concept of T-threshold. After classifying the decoys generated from the initial-docking process, core decoys were selected in terms of energy scores after the decoys were re-scored by using ZRANK. Core decoys (indicated using star marks in Figure 2) were considered as the decoys representing each group. However, one core decoy does not contain enough information for performing the re-docking process. Therefore, to perform re-docking, we needed to assemble information of decoys near a core decoy (decoys in shaded large circle of Figure 2) for each group. The process of assembling decoys for generating P-IFPs are described under “Cluster analysis for selecting core decoys and assembled IFPs” in the Materials and Methods section. Assembled decoys were selected on the basis of near to a core decoy in measure of similarity distance using TCIFP. For selecting assembled decoys, some decoys were not used for generating P-IFPs (Figure 2A). For example, largest numbers of decoys used for generating P-IFPs were assembled using H6 and T4 threshold conditions, as the corresponding D_core values were much larger than the D_clust values (Figure 2B). On the other hand, the D_core values were much smaller than the D_clust values when H4 and T6 threshold conditions were used, and thus, only few P-IFP-generating decoys (smallest number) were assembled. Table 2 lists the number of decoys that were assembled for generating P-IFPs at various thresholds. The number of assembled decoys increased as the H-thresholds increased from H4 to H6. Under all H- and T-threshold conditions, each protein pair in the test group generated near-native P-IFPs, defined as TCIFP_native ≥ 0.4.

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Figure 2. Images of decoys assembled for generating P-IFPs at various H- and T-threshold conditions.

Diagramatic representation of decoys (small circles) in a cluster (large circle) at a given threshold condition: unshaded large circle, H-threshold condition; shaded large circle, T-threshold condition. P-IFPs were generated using the decoys in the shaded large circle. D (distance) values used in the distance matrix for cluster analysis are: D = 1 – TCIFP, no similarities; D_clust = 1 – T-threshold; and D_core = 1 – H-threshold. (A) Some of the decoys assembled in the cluster did not generate any P-IFP. (B) When D_clust<<D_core, all decoys assembled in the cluster generated P-IFPs.

https://doi.org/10.1371/journal.pone.0069365.g002

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Table 2. Number of decoys assembled for generating P-IFPs.

https://doi.org/10.1371/journal.pone.0069365.t002

Results summarized in Table 1 show that all bound-state protein pairs yielded near-native P-IFPs even in cases where there were no near-native decoys generated from the initial docking process. It is notable that near-native P-IFPs were also found even when there were no near-native core decoys. In other words, this procedure yielded more near-native P-IFPs than near-native decoys in 31 protein pairs, suggesting that the P-IFPs might include more native interactions than the individual decoys. For example, Figure 3 shows the changes occurred in the TCIFP_natives during three steps: generation of decoys from the initial docking process, selection of core decoys and generation of P-IFPs from the assembled decoys. Data plotted in Figure 3 illustrate the case of a protein pair having no near-native decoys and least number of divided clusters. In the first step (i.e., docking process for obtaining 2000 decoys) no data point was found in the area where TCIFP_native ≥ 0.4. In the second step, we found that all the core decoys were distributed in the area where TCIFP_native<0.4, which is natural because the core decoys were chosen from the first set of decoys. In the last step, after generating P-IFPs using properly assembled decoys with a certain T-threshold, we found data points in areas where TCIFP_native ≥ 0.4. Some of the P-IFPs, which had TCIFP_native = 0.0, were derived from decoys with TCIFP_native = 0.0. These results suggest that more native interactions can be obtained by assembling decoys after appropriately choosing the core decoys.

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Figure 3. Improvement of TCIFP_native.

Example shown here is for the protein complex between cytochrome c and cytochrome c peroxidase (PDB-id 2PCC). Near-native P-IFPs were obtained for this complex as described in Materials and Methods. This plot shows no near-native decoys in the H6–T6 threshold group. Energy score of P-IFP is defined as the lowest energy of the decoy. Closed circles: 2000 generated decoys, crosses: core decoys, and open circles: P-IFPs.

https://doi.org/10.1371/journal.pone.0069365.g003

In all 44 protein pairs, 96.1% of near-native P-IFPs had more than 40% native interactions. We then observed the interaction sites in one of the protein complexes shown as an example in Figure 1, and compared the interaction sites of the decoys in the native complex (Figure 1A), core decoys (Figures 1B and 1C) and P-IFPs (Figures 1D and 1E) of the receptor molecule. We found that the frequent interacting residues were same in both core decoys and P-IFPs. Other ‘false-positive’ interaction sites, which are not found in the native complex, were however found in the core decoys and also in P-IFPs (Figure 1B – 1E). Occurrence of such frequent ‘false-positive’ sites resulted in lowering the TCIFP_native values of the core decoys (TCIFP_native values 0.14 and 0.17). On the other hand, their TCIFP_natives of P-IFPs were found to be 0.64 and 0.30, which were higher than the TCIFP_natives of the core decoys (Figure 1D and 1E). In all protein pairs, more than 90% of P-IFPs had higher TCIFP_native values than those of the core decoys. Out of 9,345 clusters of H4, percentages of P-IFPs with higher TCIFP_native values than the core decoys were as follows: 93.3% in T6, 93.7% in T5, 94.1% in T4 and 94.3% in T0. The highest percentages of P-IFPs with higher TCIFP_native values were found among the 23,661 clusters in H6, which were 94.6% in T6 and 94.8% in the other T-threshold cases. Similarly, out of 14,871 clusters in H5, 93.8% to 94.5% of P-IFPs showed higher TCIFP_native values than the core decoys. Among all H-threshold cases, the highest percentages (94.3% in H4, 94.5% in H5, and 94.8% in H6) of P-IFPs having higher TCIFP_native values were found in the T0 group. These results suggest that it is possible to use P-IFPs with higher fractions of native interactions in the re-docking process for obtaining more near-native protein complex 3D structures.

Analysis of IFP Similarity with Natives

Because interaction sites of P-IFPs are used for the re-docking process, they are related to the docking search spaces. The number of interaction bits in a P-IFP depends on a set of assembled decoys. After dividing the decoys into clusters, if a set of decoys with much varied interaction sites is used for generating a P-IFP, the number of interaction bits tends to be large. The number of bits is related to the TCIFP_native values, and it depends on the balance between the native complex and P-IFP. When the numbers of bits in two profiles are largely different, TCIFP range is restricted [22]. Next, we analyzed the distributions of TCIFP_native of P-IFPs to determine how the number of interaction bits in P-IFP varies with respect to H-threshold. As shown in Figure 4, the distribution patterns of TCIFP_natives of P-IFPs at various T-thresholds were very similar under the same H-threshold condition (see also Table 1), which suggested that the T-thresholds have little influence on obtaining high TCIFP_native values. We found higher fraction of TCIFP_native in the H6 group than in the H5 and H4 groups. Since P-IFPs with higher TCIFP_natives were obtained under higher H-threshold condition, only the higher H-thresholds generated better size of interaction bits in P-IFPs. Accordingly, when the H-threshold value was set to H7 or H8, most clusters were composed of single decoys, indicating that at these high H-threshold conditions most P-IFPs were same as the IFPs of core decoys. Thus, P-IFPs generated under high H-threshold conditions (such as H7 and H8) are not expected to generate enough docking search spaces. This result suggests that a suitable H-threshold condition, which is H6 in this study, could indeed be obtained. However, this was not the case with the T-thresholds, because in Figure 4 we obtained almost identical plots at all T-thresholds conditions for each H-threshold. Thus, we could not determine any reasonable T-threshold condition from these results. Therefore, we decided to use H6 and T6 conditions in the re-docking process.

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Figure 4. Distribution patterns of TCIFP_natives of P-IFPs at different H- and T-threshold conditions.

TCIFP_natives of P-IFPs for all 44 protein pairs were calculated using the indicated H- and T-threshold conditions. At a given H—threshold condition, all T-threshold conditions produced the same line plot.

https://doi.org/10.1371/journal.pone.0069365.g004

Re-docking Process Generated more Near-native Decoys than the Initial Docking Process

We obtained near-native P-IFPs for all bound-state protein pairs, even in cases where there were no near-native decoys. This result, however, was not enough to solve the rigid-body docking problem since we still could not obtain the 3D-structures of protein complexes because of the abstract nature of P-IFP. Nonetheless, near-native P-IFP provides a very informative profile for selecting the docking space area. This is illustrated in Figure 5, which shows the distributions of TCIFP_natives of decoys. In the bound-state of the protein pair that was used for analysis in this example (i.e., PDB-id 2PCC), there were no near-native decoys, but there were near-native P-IFPs (see Table 1 and Figure 5). We performed three re-docking processes for comparison: first one used near-native P-IFPs with low energy scores, second one used near-native P-IFPs with highest TCIFP_natives, and third one used P-IFPs with most native interactions. In these cases, we obtained more decoys with higher TCIFP_native than those from the initial-docking process, even though each one of these re-docking processes yielded different distribution patterns (Figure 5). Thus, we obtained largest number (i.e., 42) 3D-structures of near-native decoys when near-native P-IFPs with most native interactions were used in the re-docking process. In Figure 1, we showed actual interaction sites for two core decoys. After the re-docking process, we obtained decoys with higher TCIFP_natives than those of the corresponding core decoys and P-IFPs (Figures 1F and 1G). We also found that the resulting decoys with lowest energy scores were almost same TCIFP_natives as the corresponding core decoys.

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Figure 5. Distributions of TCIFP_natives of decoys.

A bound-state protein pair, PDB-id 2PCC, was used for this analysis. TCIFP_native values were determined as described in the Materials and Methods. Thin solid line, 2000 decoys generated by the initial-docking process; dotted line, 2000 decoys generated by the re-docking process using the near-native P-IFP with highest TCIFP_native (0.84); thick solid line, 2000 decoys generated by the re-docking process using the near-native P-IFP with lowest energy score; dash-dot line, 2000 decoys generated by the re-docking process using the P-IFP with most (41.7%) native interactions. We found 42 near-native decoys in the last case.

https://doi.org/10.1371/journal.pone.0069365.g005

Next, to determine which P-IFPs generated more near-native decoys by re-docking, we randomly selected 12 protein pairs (1ACB, 1AK4, 1ATN, 1AY7, 1B6C, 1BVN, 1D6R, 1GCQ, 1GHQ, 1GRN, 2PCC, and 7CEI) and subjected them to the re-docking process. Results summarized in Table 3 (columns 2–4) show that we were able to obtain near-native decoys after the re-docking process even when no near-native decoys were found by the initial-docking process. In the initial-docking process, only 2000 decoys were generated. However, as the re-docking process uses multiple input data (P-IFPs) generated from several groups of decoys, we could explore the docking space more efficiently by the re-docking process than by the intial docking process. Therefore, it is possible to solve the sampling problem of rigid-body docking by performing re-docking using P-IFPs. Even when no near-native decoys were found in the initial-docking process (1GHQ and 2PCC), which could be considered as a case of most difficult situation, we were able to obtain near-native decoys by using the re-docking method outlined here. Therefore, the re-docking method is a powerful tool in conditioning non-near-native decoys derived from the decoy sampling that resulted from a rigid-body docking. These results suggested that better decoy sampling was achieved by the re-docking process than the initial docking process, simply because the P-IFPs used in the re-docking process restricted the docking surfaces of protein molecules. Accordingly, when P-IFPs with more native interactions are used in the re-docking process, we expect to obtain more near-native decoys. We next identified the most number of near-native decoy-generating P-IFPs by assessing three P-IFP properties in terms of native interactions: TCIFPnative and two types of ratio of native interaction bits used for the re-docking process – one involving native interaction surface (“nat/nat” in Table 3) and the other involing P-IFP surface (“nat/P-IFP” in Table 3, same as “F_nat”). For each property, we then ranked the P-IFPs with most number of near-native decoys and the results are summarized in Table 3. In 9 out of 12 cases (1ACB, 1AK4, 1AY7, 1B6C, 1GCQ, 1GHQ, 1GRN, 2PCC, and 7CEI) assessed in terms of F_nat, we found that the P-IFPs ranked in the top 10 (“nat/P-IFP” column in Table 3, top 10 are underlined), indicating that the P-IFPs with most number of near-native decoys are profiles involving more native interactions (i.e., high F_nat). It is natural that the P-IFP with more native interactions could generate more near-native decoys. However, F_nat values were among the highest for some of them, suggesting that the generation of more near-native decoys not only depended on the high value of F_nat, but also depended on which of the interacting components of P-IFP (e.g., ‘key residues’ involved in protein interaction) were included in the analysis [23], [24]. In the case of 2PCC, for example, the highest F_nat value was actually same as the second highest F_nat value. Thus, when selecting appropriate P-IFPs, one could use information on the ‘key residues’.

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Table 3. Comparison of fractions of near-native decoys and rankings of 12 P-IFPs generating most number of near-native decoys in the re-docking process.

https://doi.org/10.1371/journal.pone.0069365.t003

There is another approach for obtaining near-native decoys in which residues involved in the native interactions are first searched and then the docking is carried out using the interacting residues as the interface. Generally, such ‘key residues’ do not include all the neighbouring residues that are present in the native interacting surface. Therefore, in this approach, it is necessary to specify that the docking search surface include the neighbouring residues. Our method using IFPs, however, can easily assemble protein surfaces necessary for obtaining near-native decoys.

Docking Process & Dataset

We selected 44 protein complexes from the commonly used protein-protein docking benchmark 2.0 dataset [25], [26] and used the available data (Table 4) in our study. As each selected protein complex is composed of two monomers, each complex is, therefore, suitable for use in the typical docking process. These 44 protein complexes were categorized as follows: 34 rigid, 6 medium-difficult and 4 difficult protein complexes, each complex consisted of a pair of monomer proteins. These categories are based on the structural differences between the bound and unbound states of these protein complexes [25], [26]. The benchmark dataset was constructed by dividing the protein complex coordinates into single constituent protein coordinates. In this case, data for one complex structure was divided into data from two monomer structures (namely, receptor and ligand). Definitions of receptor and ligand were followed as in the ZDOCK benchmark dataset. 3D-Structural data of the receptor and ligand pairs were fed into the ZDOCK ver.2.3.1 program as the input data [27]. ZDOCK was used with the option for high rotational sampling density of 6 degree (option “-D”). We used 2,000 decoys in this work. We used the same ZDOCK options for the re-docking process. Details of the re-docking process are described under “Re-docking process” (see below).

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Table 4. List of PDB-ids of 44 protein complex structures selected for this study.

https://doi.org/10.1371/journal.pone.0069365.t004

Definition of IFP and Similarity between Decoys

As suggested previously, it is sufficient to compare the interacting fragments rather than the whole structures to obtain information on near-native molecular interactions [9], [10]. Accordingly, profiles of interacting amino acid pairs were obtained using the dimplot command of the LIGPLOT program [28]. For this purpose, we used a LIGPLOT default cut-off distance of 3.9 Å between the non-hydrogen atoms [28]. After the dimplot analysis, IFP was introduced for profiling protein-protein interactions [21]. We used IFPs for comparing decoys. Information on residue pairs was entered into a bit sequence, in which one bit corresponded to a residue pair. If a pair was found, the bit was assigned a numerical value based on the number of interacting atoms; in the case where there was no interacting pair, the bit was assigned a numerical value of zero. At first, we tested a basic concept of similarity between IFPs consisting of only 0 and 1 bit values. After generating an interaction profile of the molecular complex, cluster analysis was performed. Similarity between the decoys and native molecular complexes was determined by calculating the Tversky similarity [29] as follows:where a and b are the number of bits including queries P_a and P_b, which are sequences consisting of a and b numbers of non-zero bits, respectively, and c is the common bit-number between a and b. Parameters α and β varied independently from 1 to 0. When α = 1 and β = 1, the similarity between the queries P_a and P_b could be calculated as follows:

where S_Tanimoto is known as the Tanimoto coefficient (TCIFP). We used TCIFP when comparing decoys to native interactions. IFPs were subsequently used in cluster analysis to compare decoy interactions, which are independent of the method used for the superposition of the 3D-structural data. The TCIFP index was used to quickly calculate whole pairs of decoys. For example in the bit sequence{s}, TCIFP between “0100”( = sequnce A) and “0110”( = sequence B) {is} was calculated {as} to be 0.5 using a = 1, b = 2, and c = 1. When sequence C {is} was “0001”, TCIFP { = } was calculated to be 0 using a = 1, b = 1, and c = 0. When identical sequences are compared, TCIFP = 1.0 using a = b = c. In this study, each element in IFP describes the number of atoms involved in the interaction between a pair of amino acid residues. The following equation was used for calculating TCIFPs:

We used the TCIFP_native value as the similarity index of the native interaction profile. We paid special attention in calculating the TCIFPs of the receptor proteins, making sure that only the number of atoms in each interacting residue of the receptor protein was used for describing an IFP. Near-native decoys were defined as decoys with TCIFP_native values more than 0.4. In this study, decoys were first divided into clusters, and then the corresponding elements were added for generating the representative IFPs for each cluster. Similarity between the IFPs was calculated after normalizing all elements whose values ranged from 0.0 to 1.0. When calculating TCIFP using P-IFPs after assembling the decoys, values of elements in the P-IFPs were normalized.

We also defined the fraction of native interactions in a decoy (F_nat) as F_nat = c/b, which is used in Critical Assessment of Predicted Interactions (CAPRI). In this work, bit number c indicates the number of native interactions in a P-IFP with bit number b. When a P-IFP is identical to the native interaction surface, F_nat = 1. This measure is used for calculating the similarity of P-IFPs after assembling the IFPs of decoys, because the P-IFPs were generated by accumulating interactions found in the corresponding bits of a set of decoys. For the re-docking process, it is important to know how many bits of native interactions are in a P-IFP.

Cluster Analysis for Selecting Core Decoys and Assembled IFPs (P-IFPs)

Cluster analysis of the post-docking data was carried out to search for core decoys. Similarities among IFPs (TCIFPs) of decoys ranged from 0.0 to 1.0, which corresponded to completely different and virtually same, respectively. This TCIFP was then converted into the D value, used in the distance matrix of cluster analysis, by using the relationship D = 1-TCIFP. We used unweighted pair group method with arithmetic mean (UPGMA) algorithm for the cluster analysis, which is categorized according to a hierarchical algorithm and one of the pair group methods, and is often used for generating phylogenetic tree of life. We used the statistical computing R software ver.2.8.0 for the cluster analysis. To compare results, we divided the decoys using three threshold values of TCIFP: namely, 0.4, 0.5, and 0.6. These parameters, called H-thresholds, were respectively termed as H4, H5, and H6. For example, the parameter H4 implies that each cluster in this group is composed of decoys with TCIFP similarity index of more than 0.4. Similarly, decoys with higher similarities were assembled into clusters in H5 and H6 groups.

To obtain the core decoys in each cluster, we used energy scores, which was calculated as a linear weighted sum of electrostatic, desolvation, and van der Waals energies by using the ZRANK program [30]. In this study, the decoy with the lowest energy score among a group of decoys, after re-scoring using ZRANK, was defined as a core decoy, which seems to be the most stable decoy. Therefore, for each protein pair, the number of core decoys was same as the number of divided groups. If any protein pair did not have any near-native decoys, we could not obtain near-native core decoys for that pair because the core decoys were selected from only 2000 decoys that were generated by the initial-docking process. We generated the interaction profile by assembling decoys that are expected to have native interactions.

Assembled decoys were chosen as decoys similar to a core decoy in a threshold, called a T-threshold (illustrated in Figure 2). The T-threshold conditions T0, T4, T5 and T6 corresponded to TCIFP values 0.0, 0.4, 0.5, and 0.6, respectively. Decoys with higher similarity to the core decoy were assembled for generating IFPs at higher T-threshold conditions. When T0 condition was used, all decoys in a cluster were used for creating the assembly of decoys for generating IFPs, because TCIFP = 0.0 means that the decoys are completely different. As Table 2, not all decoys were used for assembling to generate a P-IFP, excepting for the case of T0. Multiple P-IFPs were generated from one protein pair because cluster analysis using a value of H-threshold produced multiple clusters (groups). For example, in the case of 2PCC, we obtained 280 clusters after cluster analysis using the initial-docking decoys, which in turn generaing 280 P-IFPs. For each cluster, the selected IFPs of decoys were assembled by adding up each and every bit of the corresponding interaction residue pairs. Thus, each bit of a P-IFP indicates an interaction residue pair of the assembled decoy. We expected that when P-IFPs contained more native interactions, more near-native decoys were obtained through the re-docking process.

Re-docking Process

We performed the re-docking process using P-IFPs. To restrict the surface of the receptor molecule, we used the block function, “block.pl” script, included in the ZDOCK package, which blocked the molecular surface before the start of the docking process [28]. In the re-docking scheme, residues of interacting bit in P-IFPs were used for the as the docking surface, indicating that interaction of other residues were not considered in the re-docking process. Consequently, we obtained decoy sets, which interacted with the restricted surface in terms of bits of P-IFP. We used ZDOCK for obtaining the re-docking decoy sets with the option for high rotational sampling density of 6 degree (option “-D”) and generated 2000 decoys for each protein pair with restricted surface. Because of multiple P-IFPs, when the full re-docking process was carried out for a protein pair, we obtained more than 2000 decoys; for example, in the case of 2PCC, we obtained 560,000 ( = 280 x 2000) decoys.