dataesr/scientific-paragraphs-categorization huggingface dataset:
These complexes mostly belong to Enzyme-Inhibitors and Others (see Figures S10-S16 in Text S1). A protein signature based on the variability of its interaction ranks. The notion of average IR (computed over. The 84 complexes are ordered with respect to their increasing average IR value. For three of the 84 complexes (1BVN, 1BUH, 1N2C), detailed plots show the IR of the complex within each of the 100 random sets and the corresponding AUC value (black dots); green dots correspond to the IR of the complex computed over the Mintseris dataset; orange dots correspond to the IR of the complex computed over complexes in the same functional class. Note that the absence of the green dot on the 1N2C plot corresponds to a too large IR (~79) of the complex. See Table  S2  in Text S1 for the names of complexes ranked on the x-axis.
See Figures S24-S37 and S38-S51 in Text S1 for the analyses on the whole Mintseris dataset. As seen on the 1BUH complex, there is a strong variability of the average IR values associated to the interactions of a protein with different partners. One distinguishes three populations of proteins in the environment that interact with P: 1. those that rank always on the top positions: they strongly compete with the native complex by creating structures of very low energy score and displaying the interaction on the expected binding sites, these latter being either predicted or experimentally validated. They are represented by black dots and lie on the bottom of the plots in Figure  5B. Notice that they are not the same for different P's and do not belong to a particular functional class (see Figures  S56  and S57  in Text S1).
Average IR of true partners. In many cases (41 complexes over 84), true partners display an average IR ƒ10, and on a predictive perspective, one of the major difficulties is to discriminate the true partners from the wrong ones displaying good average IR (black and cyan dots at the bottom of the plots in Figure  5B ). Also, the stability of the average IR gradually decreases with the incrementation of the IR values until rank 20, and then gradually increases (see variation of the colors from black to yellow and from yellow to black in Figure  5B ). This is a pattern observed for all proteins and reveals that extreme IR values are very stable. Based on this observation, some proteins could be eliminated from the list of potential partners with a very high confidence. A. Each partner of the 1BUH complex is coupled with one of the 168 proteins (including the monomer itself) of the dataset forming either a false (167 cases) or the native complex.
Dots are colored in a scale from black, cyan, green to yellow. A color corresponds to the value of the standard deviation s of the distribution of 100 IRs computed for a complex: black if sƒ1, cyan if 1vsƒ2, green if 2vsƒ3 and yellow otherwise (i. e. sw3). The structures of the native complex (red circle) and of four selected false complexes (orange circles) are shown to illustrate the conformations corresponding to the best II value. Notice that the II value is always the same for the 100 random runs while the NII varies with respect to the dataset of proteins used in a run. The receptor 1BUH_r is colored in light blue while the ligand 1BUH_l is colored in dark blue. The four other proteins are colored in grey. All residues with a JET+NIP score §0:2 display interaction propensity and are colored in a color range going from light pink (weak signal) to deep purple (strong signal) for the 6 structures.
See Figure  S54  in Text S1 for a comparative analysis of partners of small proteins when predictions and experimental interfaces are considered. Species representation in the Mintseris Benchmark 2. 0. In the perspective of exploring the competition among potential partners occurring in a crowded environment, we analyzed the distribution of species within the Mintseris dataset. For any pair of protein structures in the dataset, we checked whether given one of the proteins, the other has an homolog at 100%, 80% or 60% of sequence identity coming from the same species (see Methods). Such homologs are expected to display the same structure and functional characteristics of the original structure, and homologs up to 30{40% of sequence identity have been shown to interact the same way  [40, 41].
When proteins are asked to be 100% identical between species, Antibodies and Others are well represented (see Figure  S74  in Text S1). When dropping the sequence identity down to 80% and 60%, the pairs of proteins displaying homologs of the same species considerably increase in number and cover most functional classes (see orange dots in Figures  S75, S76  in Text S1 and Figure  7 ). Notice that most of the represented species are mammalian (112 over 168; Tables S3-S6 in Text S1). This is not the case for Inhibitors which belong to species that are especially under-represented in the Mintseris dataset. To go further in the analysis, we mapped this information on the IR plots in Figures  S38-S51  in Text S1 (see Figures  S60-S73  in Text S1) in order to verify whether there was a particular behavior of the proteins towards partners coming from the same species.
No tendency has been observed and the uniform distribution of orange dots across the IR interval in Figures  S60-S73  in Text S1 supports our hypothesis of the existence of three populations of proteins in cells (see ''A protein signature based on the variability of its interaction ranks''). As an example, the enzyme 1MAH_r, coming from Mus musculus, shows an homogeneous repartition of the orange dots versus the blue ones (Figure  7 ). This holds true for all mammalian proteins (see Tables S3-S6 in Text S1) which are highly represented in the dataset. Notice that a number of proteins in the dataset are poorly represented such as the inhibitor 1MAH_l in Figure  7 , a toxin protein coming from the venomous snake Dendroaspis angusticeps, for which all partners in the dataset come from remote species (see blue dots in Figure  7 ).
Comparison with other docking large-scale studies A few large-scale studies that wish to identify true interacting partners among a set of potential ones, have been recently proposed. They are computationally demanding and they remain, for this reason, rare. All large-scale studies we compared to have been based on shape complementarity to quickly scan through several thousand ligands in a matter of seconds. These approaches do not include any electrostatic component in their energy model, while electrostatic forces are known to play an important role in PPI. Notice that, given a protein P, no other docking studies besides this one tries to quantify the effect of binding promiscuity of a large and variate dataset of protein structures interacting with P. Comparison with Wass et al. [33]. Docking by shape complementarity between 56 monomers (carefully) chosen from the Docking Benchmark 2.
0 and a background of 922 potential interactors (excluding all partners in the Mintseris dataset) has been analyzed in  [33]. A precise quantitative comparison of this computational experiment with our has been impossible because the set of protein partners of the Mintseris dataset considered in  [33]  is smaller and constituted only by a selected subset of receptors (with no ligand), ligands (with no receptor) and complexes (receptor and ligand) extracted from the classes Enzyme-Inhibitors and Others. A qualitative comparison with our predictions based on JET+NIP scores could have been made on the set of 10 complexes discussed in the SI of  [33] , but these results are not reproducible with more recent versions of HEX  [42]  (see Figure  S58  in Text S1), the docking program used in  [33].
Therefore, we decided to realize a CC-D with a more recent version of HEX (v6. 3) on the Mintseris' Enzyme-Inhibitors dataset and to analyze HEX behavior either by assuming knowledge of the experimental interfaces or by considering predicted binding sites based on JET+NIP scores. In this latter case, NIP scores come from docking calculations using HEX. The distribution of interaction ranks for both our docking algorithm MAXDo (see Methods) and HEX are shown in Table  3 , where we report how many proteins among the 46 enzymes and inhibitors are identified by each method within increasing sets of best partners, with respect to an environment of 46 proteins. From Table  3 , MAXDo and HEX behave similarly on experimental interfaces while on predicted binding sites, MAXDo performance is definitely superior to the one of HEX.
Notice that a perfect binding sites identification allows for the detection of native complexes for 36 out of 56 proteins within the top 17 predictions. Notice that true partners for 36 proteins are obtained in  [33]  by considering 184 best predictions out of 922, a set that is far too large to be experimentally tested. The second observation concerns the composition of the set of proteins analyzed in  [33]. Antibody-Antigens complexes are absent from the CC-D experiment in  [33] , are intrinsically difficult for interface prediction and they could constitute good test cases where both methods might highlight their respective weaknesses. Also, all 922 proteins (except 3) coming from the Mintseris or the background dataset in  [33]  are monomeric with two third of the background dataset having only one domain.
The use of monomeric structures (especially when they are constituted by a single domain) renders the prediction easier as it is generally associated with a decrease of the number of potential interactions. Notice that our experiment is run on the full Mintseris database for which about a half of the complexes (41 over 84) involve a multimeric structure (spanning from 2 up to 4 chains), hence enhancing the difficulty of the prediction. We observe an AUC~86 for monomeric complex predictions based on experimental interfaces, that decreases to 81 for multimeric complexes, as detailed in Table  2  and in Table  S8  in Text S1. This performance on multimeric complexes is affected even more when interface predictions are considered, since sensitivity and precision of interface predictions decrease for multimeric proteins as shown in Table  S11  in Text S1.
In both cases, we report the results obtained on the restricted (by evolutionary information) conformational space. On three complexes (1ML0, 1GCQ, 1DFJ), JET provided too small interaction sites (leading to a FIR~0 because of no common residue between the small predicted interface and the docked one); hence, we cleaned the original Mintseris dataset of these three complexes and marked the affected subsets with the * symbol. Performance of protein prediction is evaluated through AUC values computed on the Mintseris dataset and its different subsets. Sensitivity (Sen) and specificity (Spe) are also given at a threshold cutoff of 0. 5 for predictions based on experimental interfaces, and at a threshold cutoff of 0. 25 for predicted interfaces. Calculations based on JET predicted interfaces use weights a~0:4, b~0:6 (see Methods), with the exception of the analysis run for Antibody-Antigen and Antigen-Bound Antibody where a~0:6, b~0:4.
Discussion We have addressed the problem of predicting protein interactions using high-throughput CC-D calculations on a dataset of 168 proteins. We have shown that a simple docking algorithm combined with evolutionary information, can be used to discriminate interacting from non-interacting proteins. The purpose of the method is the in silico large-scale screening of protein structures to find a small set of potential protein partners that could be tested experimentally. The approach reminds the one of drug design aiming to screen large sets of small molecules in order to identify a small set of potential drugs that becomes experimentally testable. These approaches do not pretend to exactly identify a unique solution but rather a set of reasonable candidates, and reduce, in this manner, the amount of experimental time and costs.
to decouple true PPI signal from noise and identify PPI properties that are not consequences of accumulated errors due to predictive algorithms. This second reason allowed us to be confident, for instance, on the promiscuity observed in Figure  5B  (bottom black dots) by ensuring that it is not generated by noise in predictions (see Figure  5A ). A few large-scale analyses, that are similar in spirit, have been performed  [32, 33]. A comparison of our results with  [33] , based on the ten protein complexes discussed in detail in  [33] , reveals a similar performance of the two methods. However, a full comparison with  [33]  is impossible since they treat only a subset of the Mintseris dataset, use a large background set and do not provide a detailed measure of the performance of their method.
On the contrary, our method is tested on all complexes of the Mintseris dataset, a good testing platform for methods dedicated to protein partner prediction due to its numerous structural differences. The global analysis of the two methods (over the subset of 56 proteins; see Table  1  and  [33] ) highlights that we can reasonably search for protein partners within sets of a few hundred monomers. We demonstrated that improving current predictive methods is possible through a better prediction of binding sites, and we precisely estimated the effect of such predictions. We could only partially compare to  [32]  since they do not perform a CC-D of the Mintseris dataset but only cross the 84 receptors against the 84 ligands, that is a fourth of the interactions explored in our analysis. Performances of our method and the one reported in  [32]  are comparable on the common subset, but notice that contrary to  [32] , we use unbound structures and we make no use of the non-naive split of the dataset (that is, receptors versus ligands).
The predictive performance of the method is encouraging for the whole Mintseris Benchmark 2. 0 and very satisfactory for the enzyme-inhibitor subset (Table  2 ). For this latter, the AUC reaches a very high value of 77% while the AUC for the whole Mintseris dataset is 61%. Notice that the way we computed the AUC is very strict, since we asked the true partner to be ranked first over the tested dataset. A more relaxed evaluation is reported in Table  1  where we show that a fourth of the 168 proteins in the Mintseris dataset are recognized by looking at the top 17 predictions over the 168 tested partners. If the binding site of the proteins is correctly predicted, the half of the proteins in the dataset are recognized by looking at the top 8 predictions, and two third by looking at the top 17.
This is a very encouraging result with respect to the potential applicability of this in silico predictive approach to the reconstruction of PPI networks. In fact, proposing to a biologist a set of less than 20 interactions to test is very reasonable. The analysis on the average IR for the enzyme-inhibitor subset highlights that an average IR threshold ƒ10 allows the method to propose about 12 partners, a reasonable number of proteins to be selected for experimental tests. In 38 cases over 46 (Figure  6 ), the true partner is present in the retained subset showing a very high sensitivity. For the whole Mintseris benchmark, for roughly the half of the dataset (82 proteins), the true partner is retrieved with an average IR ƒ10. Notice that when considering the experimental binding site of each partner, 138 proteins over 168 display an average IR ƒ10.
Taking into account these possibilities, this set of highly potential partners becomes interesting for further studies. For instance, these interactions would deserve to be experimentally tested to see how strongly they interact, and whether they form a structurally well-defined complex. Also, for a given protein and a set of highly potential partners, one could ask whether general structural (geometrical or physico-chemical) features of the interface exist and in the positive case, classify these interfaces. These further studies could contribute to give important insights into protein partnership discrimination. For each protein P, we defined a signature representing the strength of interaction of P with all other proteins. As mentioned above, signatures found for all P's in the Mintseris dataset demonstrate the existence of strong interactions with some proteins, but also the absence of interactions with other proteins, and so on.
The spectrum of strengths of interactions suggests the notion of PPI to be revisited so to include the larger panel of potential complex formations between a protein and its potential partners. Several questions could then be asked on proteins presenting similar signatures  [44] , but they go beyond the aim of this work. We have shown that evolutionary information can also be used to restrict the conformational space of the docking exploration without an important loss in sensitivity. This result is very important in view of reducing the computational cost of highly time demanding docking calculations (all atom description and precise energy functions) and the perspective of enlarging the dataset size for future CC-D calculations. To conclude, we are the first to perform a CC-D of a pool of proteins covering a large spectrum of functions and interaction modes, performing it on unbound structures and providing energy values (even though simplified) taking into account electrostatic forces.
Our approach is the first combining evolutionary information with CC-D simulations. The evaluation of the performance of these two contributions to the problem of partner identification, suggests that there is still room for improvement in the solution. In particular, we have shown that a precise identification of protein binding sites allows for very satisfactory predictions. Data coming from the CC-D calculations and the evolutionary analysis are provided and they will help the community to evaluate further CC-D studies and methodological developments. In particular, the decoy set constitutes a unique dataset of ''negative'' partners. For them, we provide about 2000 conformations and an associated coarse-grain energy score. It might be extremely useful to suitably parametrize docking scoring functions, more refined than our coarse-grain scoring function, to discriminate partners.
The protein dataset The Docking Benchmark 2. 0  [25]  is constituted by 168 proteins belonging to 84 known complexes. We used the unbound conformations of the proteins with the exception of 12 antibodies for which the unbound structure is unavailable. For those, the bound structure is used instead. Any reference to the proteins uses either their name or the Protein Data Bank (PDB) code  [45]  of the experimental complex they belong to with the r or l extension denoting a receptor or a ligand protein respectively. For example, 1AY7_r and 1AY7_l refer to barnase (receptor) and barstar (ligand) in the barnase-barstar complex 1AY7. The coordinates for the bound and unbound structures of both receptor and ligand proteins are available in the PDB and can be found at http://zlab. bu. edu/zdock/benchmark.
For every protein pair P 1 P 2 , we calculate an energy-weighted optimal interaction index (II) defined in Eq. (1). To allow comparison among different partners we defined a normalized index NII P1,P2 by taking into account all of the four lines/columns that feature either P 1 or P 2 in the II matrix as follows: min(II where P are the 168 proteins of our dataset. NII values vary between 0 and 1. Values close to zero imply that two proteins cannot form an interface involving a significant fraction of the experimentally identified residues, or that interfaces involving these residues have poor interaction energies. Values close to one indicate predicted interfaces with good energies and composed of experimentally identified residues. For each protein P 1 , we define as predicted partner of P 1 , the protein P i that leads to NII P1,Pi ~1.
For each protein P, 10 runs of JET were launched and we defined a score JET P (i) for each surface residue i to be the number of occurrences of the residue in extended patches divided by 10. This score reveals the likelihood of the residue to belong to the interface. Predictions by combining docking and evolutionary information. For each residue i in protein P, we define a score JETzNIP(i)~aNIP P (i)zbJET P (i), where JET(i), NIP(i),a,b range between 0 and 1. Different combinations of a,b have been tested and our final results are obtained with a~0:4,b~0:6. Since Antibody-Antigens evolve more rapidly than other interface surfaces, the conservation signal is less sharp and predictions are intrinsically difficult. For this, we lowered the weight of JET contribution by fixing a~0:6,b~0:4. Evaluation of the performance of the score ''JET½0:6zNIP½0:4'' for partner prediction compared to the performance of NIP alone or JET alone on the Mintseris dataset and its subsets is illustrated in Figure  S77  and Table  S10  in Text S1.
HEX docking CC-D of the Mintseris' Enzyme-Inhibitors dataset was performed with HEX v6. 3 using the shape complementarity basedonly score  [42]. Docked conformations were clustered using a 3 A cutoff and the best-scored conformations of the 500 first clusters were retained for the analysis. A protocol similar to that described for MAXDo was applied to evaluate partner prediction based on HEX results, (i) by assuming knowledge of the experimental interfaces and (ii) by crossing docking scores with evolutionary information. All 500 conformations were considered for residue scoring based on docking and for protein interaction index calculation. Parameter values are reported in Table  S7  in Text S1.
Analysis of the origins for the proteins in the Mintseris dataset Given a protein P 1 , we searched in the Mintseris dataset for those proteins P 2 that have a homolog coming from the same species as P 1. Namely, for each P 2 , we searched with Blast (Evalue threshold at 10e {4 , alignment coverage 70%) for the set of sequences that are at least 100%, or 80% or 60% identical to the P 2 original sequence. This provides a set of species that we say to be representing P 2. We then checked that the species of P 1 is included in the set of the species representing P 2. Notice that the protocol does not necessarily provide the same answer when it is applied to the protein pairs P 1 ,P 2 or P 2 ,P 1 due to the nonsymmetrical Blast result.
Data release We release the first large decoy database comprising not only structures of true complexes but also structures of non-functional complexes potentially forming in the cell. For the 28224 possible protein pairs (involving the 168 proteins) of the Mintseris Benchmark 2. 0, we considered about 2000 best ligand orientations (represented on w and h angles as described above) for each receptor. We provide the associated decoys together with the corresponding energy values. A program to reconstruct the PDB structure of the conformation given w and h angles is also provided. For each protein in the Mintseris dataset, we also furnish the evolutionary analysis for the detection of the binding sites. The download site is http://www. lgm. upmc. fr/CCDMintseris/.
Figure3. The protocol. The protocol is based on docking calculations and JET predictions and produces an interaction matrix for the proteins in a database. Here, two protein structures, the receptor 1AY7 and the ligand 2MTA, are analyzed. The first step consists in cross-docking 1AY7 and 2MTA respectively, against all structures in the database (see cyan box for 1AY7 and blue box for 2MTA). A structure will be crossed dock against another in several conformations (from 100000 up to 450000, depending on the size of the proteins). In the schema, 1AY7 and 2MTA are also docked one against the other (see intersection between blue and cyan boxes). As a result of the cross-docking, a NIP score is associated to each protein leading to the prediction of an interaction site (color range from light blue to dark blue, corresponding to weak and strong signals respectively).