Sulfolobus acidocaldarius, bind DNA preventing its denaturation. Thanks to their stability and small size (60–66 residues in length) they have been considered as ideal candidates for engineering and have been used for more than 10 years now, for different applications. The individuation of a mutant able to recognize a specific target does not imply the knowledge of the binding geometry between the two proteins. However, its identification is of undoubted importance but not always experimentally accessible. For this reason, computational approaches such as protein-protein docking can be helpful for an initial structural characterization of the complex. This method, which produces tens of putative binding geometries ordered according to a binding score, needs to be followed by a further reranking procedure for finding the most plausible one. In the present paper, we use the server ClusPro for generating docking models of affitins with different protein partners whose experimental structures are available in the Protein Data Bank. Then, we apply two protocols for reranking the docking models. The first one investigates their stability by means of Molecular Dynamics simulations; the second one, instead, compares the docking models with the interacting residues predicted by the Matrix of Local Coupling Energies method. Results show that the more efficient way to deal with the reranking problem is to consider the information given by the two protocols together, i.e. employing a consensus approach.Affitins constitute a class of small proteins belonging to Sul7d family, which, in microorganisms such as  Sulfolobus acidocaldarius and Sulfolobus solfataricus, and act to prevent DNA denaturation thanks to their stability in a broad range of temperature (up to 100°C) and pH (from 0 up to 12). The general topology of Sac7d is that of the OB-fold family. Its tertiary structure consists of a five-stranded incomplete ß-barrel , capped at the opening by a three-turn C-terminal α-helix (residues 53–63). The triple-stranded ß-sheet (β3-β4-β5) has been identified as the DNA binding surface . This probe is constituted of an affitin (Nanofitin B10) which has been engineered in such a way to recognize the pharmacological target epidermal growth-factor receptor (EGFR) and to exhibit a unique cysteine moiety at its C-terminus. The latter is used for a fast and site-specific radiolabeling procedure necessary for the Positron Emission Tomography (PET) .Affitins engineering is usually accomplished by generating large libraries of mutants, which are subsequently screened for their affinity for the selected protein target. However, once the desired mutant is obtained, no structural information about the affitin-protein complex is readily available. In such a contest, as far as computational approaches are concerned, molecular docking can be considered for an initial structural characterization.To date, no docking program can always identify a correct solution, especially in the context of the protein-protein interactions; instead, docking results consist of a ranking of the best putative binding poses, according to the docking-score function. These require a post-docking processing, in the attempt of identifying the correct binding geometry through the analysis, scoring and, if need be, reranking of the docking models. The post-docking step can be based on energy-, knowledge-, consensus-, and evolution-based algorithms and includes, for example, the contact analysis, the prediction of the interface, the flexible refinement of the model and the energy minimization of the latter .In the perspective of using affitins as targeting scaffolds, our work focuses on the validation of the docking poses obtained for different affitin-partner complexes available in the Protein Data Bank (PDB) through two procedures described hereafter. The aim is to develop a robust protocol for the initial prediction of the most probable binding geometry between a specific target and a new engineered affitin.Two post-docking strategies are considered in the present paper: the first one involves the investigation of the stability of docked complexes through Molecular Dynamics (MD) simulations and evaluation of CAPRI, DockQ, and other structural and energetic parameters ; the secThis paper is organized as follows. The first part presents the results of docking between seven affitins with as many protein partners whose binding experimental structures are available in the PDB. The reliability of the ranking of the docking poses is then checked by means of MD simulations and MLCE approach. Finally, we show how the coupled use of such two methods can improve the identification of the correct docking models.Protein structures were selected by doing a sequence similarity (threshold 60%) search in PDB, starting from the sequence of the wild-type affitin (PDB code: 1AZQ), which resulted in 55 entries. For our study, we selected the seven complexes made up by engineered affitins and protein partners. When available, structures of the proteins partners in the complexes were superimposed to the respective unbound forms, to check whether a significant change in their fold occurred upon binding. As this is not the case, we hold that bound structures of these proteins can be used for rigid docking calculations. All protein structures retrieved from the PDB were prepared using the tool Protein Preparation Wizard included in the Schrödinger package . The proProtein-protein docking calculations have been carried out using the web server ClusPro . The strα atoms of the “receptor” (the bigger protein) of the docking models on the same atoms of the crystallographic structure; 2) calculating the RMSD of the Cα atoms of the “ligand”  of the docking models with respect to the crystallographic structure. We considered as “Native” docking poses having crystal_RMSD ≤0.5 nm, while docking poses with crystal_RMSD >0.5 nm were considered as “Non-Native”.We evaluated the performance of the four available scoring schemes  using as a measure of the capability of identifying the experimental assembly a parameter  describing the distance of the docking model from the crystallographic structure. crystal_RMSD was calculated by: 1) fitting the CThe reranking of the first ten docking poses based on the crystal_RMSD parameter highlights that, for these complexes, the “balanced” scoring scheme performs better than the others , therefoAmong the methods available for the reranking of docking binding poses, the protocol proposed by Jandova et al. was applied. Briefly, it consists in performing MD simulations of the docking poses and monitoring parameters that describe their stability along the simulation time, thus allowing to discriminate among stable poses, i.e. probably Native, and not stable ones, probably Non-Native.A, and the one with the second lowest value as B. C and D are the labels for the poses having the second highest and the first highest crystal_RMSD values, respectively.For each complex listed in −1 nm−1 was reached. Atoms motion equations have been integrated with leap-frog algorithm every 2 fs. A 1.4 nm cut-off was applied to van der Waals and electrostatics interactions, beyond whom the latter have been treated with PME (−1 nm−2). Production runs have been performed in NPT ensemble at 1 bar and 300 K. Proteins and solvent have been coupled to two velocity-rescaling thermostats  of the ligand  is calculated during the MD simulation after the superimposition of the same atoms of the receptor (the larger protein) on the reference structure; 3) Fnat. Pairs of residues on different sides of the interface were considered to be in contact if any of their atoms were within 5 Å. Fnat is calculated as the number of native (correct) residue–residue contacts during the MD simulation divided by the number of contacts in the reference structure. DockQ parameter  was performed on the correlation matrix of Spearman coefficients of average values of the CAPRI parameters and of relative standard deviations (rSD) of BSA, HB and EPP. The analysis was conducted on the whole trajectories (production run).MLCE method was used for identifying areas on the partners of the affitins prone to an interaction . This approach combines the analysis of a given protein’s energetic properties with that of its structural determinants, to identify protein areas that are prone to interact with potential partners.via a MM/GBSA calculation. The resulting symmetric MLCE is based on the hypothesis that some residues stabilize the protein folding, while others establish interactions with partners. The analysis of the interaction energy that each residue establishes with all other residues of the protein accounts for these different roles: residues which strongly interact with the rest of the protein are related to the stabilization of the folding core, while the recognition sites may have weaker pair interactions, as in this way they can easily undergo conformational changes which can make the protein able to recognize and bind a partner. More specifically, the analysis of the interaction energies of all the amino acids in a protein consists in calculating for each residue the non-bonded part of the potential energy  https://github.com/colombolab/MLCE), was used in cluster mode. Calculations were performed on centrotypes of clusters which cover at least 90% of the conformation variability sampled during three independent MD simulations (100 ns each). Patches were predicted on the centrotype of the most populated cluster considering the top 15% or top 10% of spatially contiguous residue pairs with the lowest-energy interactions. Then, they were compared with residues interacting with the affitins in the crystallographic structures and in the docking poses.For the calculations, REBELOT program, version 1.3.2 . Superimposition of the crystallographic structures and the docking poses are shown in MD simulations of complexes 4CJ0, 4CJ1, 4CJ2, 5ZAU, 6QBA, 5UFE and 5UFQ were carried out for the crystal structures and for the four docking poses A , B , C and D (the latter two Non-Native).The average values of three parameters i-RMSD, L-RMSD and Fnat were calculated from MD trajectories every 500 ps and the DockQ values have been evaluated (see Methods section). As described in the Methods section, the quality of a model is defined as high/medium/acceptable/incorrect if the DockQ value is ≥0.80/≥ 0.49/≥ 0.23/< 0.23 . It has A, three out of seven  are classified as medium quality ones. All of them are very close to the crystallographic structure of the complex  DockQ values of the poses A fall in the acceptable quality range, with 4CJ1 being close to be classified as an incorrect model despite its optimal superimposition with the crystallographic structure . On the other hand, many DockQ values falling in the acceptable range were found for the poses C and D, even though they are Non-Native poses. The lowest DockQ values were obtained for Non-Native poses (C or D) only for three out of four complexes . As for the other complexes, low DockQ values correspond to poses B, with some of them being good models , the number of hydrogen bonds (HB) and the protein-protein interaction energy (EPP). Our focus was addressed to their relative Standard Deviations (rSD), rather than on average values, as the former directly reflects the docking pose changes during the MD simulations.To get more insights on the capability of these parameters (or a linear combination of these parameters) in determining the quality of the models, Principal Component Analysis (PCA) was performed on the correlation matrix of Spearman coefficients of CAPRI parameters  and of BSA, HB and EPP (rSD). The analysis was conducted on the parameters extracted from the whole trajectory (production run) and led to first two principal components (PCs) describing almost the 85% of the whole data set variability. The overlay of loadings and scores plots (biplot) obtained from the PCA is shown in This analysis shows that i-RMSD, L-RMSD and Fnat are highly correlated, with Fnat pointing in the opposite direction: as expected, a high value of the latter is related to low values of i-RMSD and L-RMSD . Only for complexes 4CJ0 and 4CJ2, affitins of pose A have the highest number of interacting residues with a patch. In other words, two (plus two doubtful cases) poses A can be identified based on MLCE analysis. These results indicates that a decision on the quality of a docking model cannot be based on this parameter only but, at the same time, it can be useful if coupled to another one, as shown in the following.As shown in In the present work, we used two different approaches to identify the correct binding mode of two interacting proteins, among the ones predicted through docking calculations. The first one is related to parameters that account for the stability of the binding pose, while the other is based on the prediction of the possible interacting residues of one of the two partners, through the analysis of the energetic and structural-dynamical properties of this protein.A were identified as the best ones; in addition, for 6QBA, model A could not be distinguished from D. Considering instead MLCE results, only two poses A were identified, plus two doubtful cases in which poses A could not be distinguished from B or C.In the sections above we showed that these methods, if applied individually, can lead to some misleading results, as they are not always able to identify the native binding mode among the predicted docking poses. Concerning DockQ, four poses However, since both methods show general good capabilities in discriminating the quality of the docking poses, and they rely on totally different assumptions, we apply a consensus approach which combine these two procedures into a single, more powerful method to identify the native conformation of complexes predicted through docking calculations.In A and 4CJ2-A); 2) if the previous point does not apply, exclude the poses characterized by one best- and one worst-scoring parameter at the same time ; 3) select the pose presenting the highest values of both parameters, i.e. repeat the first step ; 4) if the previous point does not apply, select the poses presenting the highest value of each parameter, respectively . Following this procedure, we identified unique poses in five cases: only for 4CJ1 and 5UFQ identification was not possible. This protocol is also described in a flowchart  select the pose presenting the highest values of both parameters , significantly improving the prediction obtained applying the two approaches individually.Considering that 4CJ1-In the present paper, we focused on the reliability of docking and post-docking procedures in predicting the binding geometries between affitins and several protein partners, by testing them on PDB-available complexes.A  led to medium-quality (≥0.49) DockQ values. The remaining ones are acceptable, with two of them (4CJ1 and 5ZAU) characterized by values close to the incorrect range. Moreover, for some of the complexes , the obtained DockQ values for Native poses were sometimes too similar or even lower than the ones obtained for Non-Native poses. Summing up, DockQ was able to identify four out of seven poses A. Thus, we decided to look for other parameters, descriptive of the protein-protein interface, able to correctly rerank the poses. Among them, our attention was addressed to the number of hydrogen bonds between the two partners (HB), the buried surface area (BSA) and the protein-protein interaction energy (EPP). Principal component analysis (PCA) was performed on the correlation matrix of the Spearman coefficients of CAPRI parameters  and of BSA, HB and EPP (rSD). The analysis was conducted on the whole trajectory (production run) and allowed us to observe that the first principal component is able to discriminate around 70% of Native and Non-Native poses. Concerning MLCE, the method showed to be an adequate tool for the prediction of the interacting residues in most cases. Thus, it was used for the reranking of docking poses, considering the number of residues of the affitins interacting with the patches identified on their partners. However, only two poses A, plus two doubtful cases, were identified. We thus decided to evaluate the quality of the docked poses by combining the results obtained through DockQ and MLCE methods, i.e. to employ a consensus approach. In this way, five out of seven correct models were detected.ClusPro proved to be a suitable docking approach for identifying putative binding geometries of complexes containing affitins. In fact, for all the seven complexes considered , at least one docking pose among the first ten well overlapping to the crystallographic structure was obtained, with crystal_RMSD values ranging from 0.13 to 0.28 nm. However, as it is known, the predicted binding modes obtained by the docking algorithm and the ranking, could be far from reality. Hence, we applied a method based on the monitoring, during MD simulations, of CAPRI parameters and the global parameter DockQ, in order to identify discriminants among Native and Non-Native poses. The idea at the basis of such an approach is that Native poses should be more stable during the MD simulations, i.e. the mutual arrangement of the two proteins should not change significantly. On the contrary, Non-Native models should undergo larger conformational changes, driving the two proteins away from the initial spatial arrangement. The results obtained showed that only three of the simulations performed on poses Affitins are small and highly stable proteins, features that make them easily engineerable. This results in them being ideal candidates for the development of molecular probes, entities that, through the specific recognition of a biomarker, are nowadays largely employed for the diagnosis of serious diseases such as tumor pathologies. Thanks to their structural stability, affitins-partners interactions can be studied by means of a simple protocol, as it is the one described in this paper. The protocol consists in the employment of ClusPro, a freely available server for protein-protein docking, which, treating the partners as rigid bodies, supplies the potential binding modes of the selected affitins and their partners.The evaluation of the quality of the docking models is then addressed with two totally distinct approaches. The modeling of the full structural flexibility of the complex is introduced with MD simulations, in order to evaluate, at high atomic resolution, the structural details of the interface regions. Several parameters, including the CAPRI ones and the DockQ, are monitored and overall analyzed with PCA for quantifying the stability of docking models.A totally different approach, the MLCE, is used in parallel to identify putative binding patches on the surfaces of the proteins. Docking models are reranked on the basis of the match with MLCE results.DockQ and MLCE, if considered alone, are not fully able to discriminate among the docking poses. However, applying a consensus approach involving both the methods significantly improves the capability of identifying the correct binding mode among the predicted docking models.Our work thus demonstrates that the combination of the MLCE method, which is completely unbiased, as it is based on the protein’s energetic properties and differs from the algorithm used by ClusPro to determine the potential binding surfaces, together with the dynamic evaluation of the stability of the predicted binding poses obtained with a rigid docking approach, is a fast and effective method to quickly discriminate correct from incorrect predictions generated by initial-stage docking and leads to better quality outcomes.The overall approach we present here may represent an effective tool for evaluating a large number of affitins, and for selecting and designing new ones that are specific and selective for a target of interest.We finally highlight that the presented protocol does not aim to be suitable for all protein-protein complexes. However, while applied to the case of affitins and known protein partners, no information about the characteristics of these specific complexes has been used to define it. In principle, the protocol can be transferable to other systems with similar characteristics, specifically, to those ones where no significant conformational rearrangement upon binding occurs.


The effects of amino acid insertions and deletions (InDels) remain a rather under-explored area of structural biology. These variations oftentimes are the cause of numerous disease phenotypes. In spite of this, research to study InDels and their structural significance remains limited, primarily due to a lack of experimental information and computational methods. In this work, we fill this gap by modeling InDels computationally; we investigate the rigidity differences between the wildtype and a mutant variant with one or more InDels. Further, we compare how structural effects due to InDels differ from the effects of amino acid substitutions, which are another type of amino acid mutation. We finish by performing a correlation analysis between our rigidity-based metrics and wet lab data for their ability to infer the effects of InDels on protein fitness. A common type of mutation in protein structures are amino acid insertions and deletions, or InDels. InDels are caused by non-frameshifting insertion or deletion variants in the genome ,2. WhileThe location of an InDel can be anywhere in the sequence of a protein but frequently they occur in the loop regions . AvailabResearch indicates that many disease phenotypes are caused by InDels. An example is the widely studied cystic fibrosis, where several mutants are known . The F50The size of an InDel is found to correlate positively with the impact and extent of the changes to the structure of a protein. Predominantly, InDels that involve two or more more amino acids are found to have a greater impact on a protein’s structure whereas a single InDel tends to have a less pronounced effect . Since tInDels should also be examined relative to other mutations. InDels are thought to have a greater impact on the structure of a protein, but substitutions are the most common type of mutation, for which abundant experimental data is available. A comparison of what happens when a residue is inserted or deleted at a location versus when a residue is substituted for another, could offer valuable insights to the effects of InDels, as it is a near-direct comparison with a far more studied type of mutation.Currently there are no well-established tools to model structural or functional changes in proteins caused by InDel mutations. Nor are there are any tools that systematically catalog mutants of a protein structure with InDels or substitutions. A previous effort, InDelPDB , used prIn this work, we employ inverse kinematics, ab initio energy minimization and rigidity analysis, to extend our previous work to model and analyze InDels in protein structures . The metOur methodology consists of identifying wildtype-mutant pairs for InDels from the PDB  followedinsertion, deletion, and mutation, in the primary publications for protein structures, and we relied on UniProt [Because there are no widely accepted methods to identify mutant structures in the PDB, this was our first task. We performed an expanded search on the PDB, looking for certain keywords, including  UniProt  to identThe PDB files containing InDels were further investigated in order to identify the location and the size of the mutation, where size refers to the count of amino acids that are inserted or deleted. This yielded a total of 35 mutants with InDels of size 1–6 in loop regions or in secondary structures. This was followed by using UniProtKB  to identComputational mutants were generated from the wildtype protein PDB files using Rosetta . It is aStructural bioinformatics researchers have been utilizing robotics-based geometric algorithms for modeling and elucidating various properties of proteins. In proteomics, these algorithms are used to model protein structures and their dynamics .For motiOne of the uses of IK in protein structure prediction is for modeling of loops by manipulating the rotational DoF of the loop region in order to find likely loop conformations that attach to the rest of the protein structure. An idea branched from IK is kinematic closure (KIC) . KIC is The kinematic closure  process Close the loop using geometric modeling without applying a refinement step;Employ kinematic closure to refine the loop region.For a kinematic articulated chain with a gap, that represents deletion of an amino acid or a position where one or more amino acids are inserted, we need to solve the problem in a systematic manner. The solution entails finding a balance between global adjustments of the torsion angles as well as the modification of angles and regions next to the residues that were inserted or deleted. Our approach to resolve this problem is as follows:remodel protocol [loop protocol [The specific protocols used to achieve the above are Rosetta’s protocol , used toprotocol ,35.remodel protocol’s quick and dirty variant closes the gap but the resulting structures have steric clashes. To resolve the structure, the loop protocol uses KIC to refine the region of closure in order to find a low energy conformation. This approach yields structures with good energy scores. In some cases the resulting structures were further enhanced by using all-atom refinement using Rosetta’s relax [The explanation for this particular combination is that structures that are generated by simply closing the gap do not have good energy scores. The is due to the reason that the ’s relax  protocolIn order to validate our ability to generate mutants computationally, we compared the structures of the PDB mutants with their respective in silico counterparts. We performed the evaluation based on the RMSD of the loop region or the secondary structure where the InDel existed and computed all-atom RMSD before performing rigidity analysis of the mutant structures.In Previous research shows that InDels are more tolerated in the loop region of a protein . HoweverClose the gap without refinement of resulting structure using geometric modeling.Perform all-atom refinement on the resulting structure for the purpose of energy minimization.The methodology to perform insertions and deletions in secondary structures differs from loop regions as follows:Escherichia coli thioredoxin (PDB: 1txx) where an arrow is pointing towards the region where insertion is performed. The right panel shows the computationally generated mutant superimposed on the experimentally available structure (PDB:1tho). The global all atom RMSD is 0.685 Å, and the local RMSD score is 0.221 Å. Again Rosetta’s remodel protocol was used to close the gap and then Rosetta’s relax protocol was used in the second step to resolve the structures for achieving better energy scores. The rationale for this particular combination is that using KIC on the secondary structure did not yield structures similar to the PDB mutants. However, all-atom refinement results in structures that are more similar to their PDB counterparts.In G for 2700 single and multiple point mutations, using a combination of the rigidity analysis metrics (RDSMs) and structural features that include solvent accessible surface area (SASA), temperature, pH, secondary structure element, and the type of mutated amino acid. We used these as features for Support Vector Regression (SVR), Random Forest (RF), and Deep Neural Network (DNN) methods. Our results showed high correlation (0.81) between rigidity and ΔΔG. Finding and correlating ΔΔG information with rigidity for InDels is more challenging, due to the dearth of experimental data. However, there exists some information about specific families, for example luciferase [G information exists, we used other fitness measures for baseline validation of our results. The rigidity and flexibility of protein domains provide insights into a protein’s structural stability . A compuciferase , TEM-1 βactamase  among otWe measured the differences between the in silico generated InDel mutants and their wild types, and between the PDB InDel mutants and the wildtype, using RMSD measurements, and via a visual inspection via PyMol. The similarities and differences in these scores give us insights into the ability of our method to accurately generate in silico InDels.i is the rigid cluster size, and LRC = Largest Rigid Cluster in the wild type. i in the wildtype and mutant, respectively. This provides a measure of the accumulated differences between the sizes of each protein’s rigid clusters. If the wildtype of a protein does not have a rigid cluster of size i, but the mutant does, then that particular term in the summation is negative. Conversely, if the wildtype but not the mutant, has a rigid cluster of size i, then that term in the summation is positive. The term For a quantitative analysis of the structural differences between our wildtype and InDel mutants, we used our previously developed Rigidity Distance Similarity Metric (RDSM). It tells us information about the sizes and amounts of identified rigid clusters in the wildtype when compared to the generated mutant . For RDSThe RDSM measurement was developed in order to quantify differences in rigidity properties between two proteins. It accounts for the difference in the size and numbers of rigid clusters, while weighing the difference between the largest clusters in the mutant and wild type more heavily than the differences among the smallest clusters. This is because differences among the largest rigid clusters are usually considered to have a bigger effect on protein rigidity than small clusters, which have a more localized effect.We calculated the RDSM scores for each of the wildtype–experimental mutant, wildtype–computational mutant, and experimental mutant–computational mutant pairs. This allows us to evaluate the quality of our computational approach for creating these InDels. Lower RDSM scores mean the rigid clusters of a given wildtype and mutant are more structurally similar to one another. Due to variations in protein size, the RDSM scores were normalized by the number of atoms in that protein. This lets us better assess the differences as relative and not absolute.In addition to the RDSM metric, we computed the Two Largest Cluster Comparison Score (TLCCS)  between Its particular use is in providing a quantitative score of how much structural change is caused by the mutation, because modeling more impactful mutations is of greater priority than modeling mutations that had little effect. The closer the TLCCS value is to 1, the less effect the mutation has on the protein’s rigid clusters. InDels that result in a TLCCS of near 0.5 and below will be treated as a having a significant impact in the protein’s rigidity.Lastly, we performed visual analysis via a custom Python program, focusing on the rigid clusters at the InDel site. This elucidates important information about the effect on the protein’s rigid clusters in the proximity of the InDel site(s), providing new information that global analysis does not offer.In order to further validate our rigidity analysis metrics in capturing the structural properties of proteins, we tested how small changes to a protein structure affect its rigidity properties. To do this, we subjected six protein structures from our data set to a small number of minimization steps using NAMD . We creaBorreliella burgdorferi. In all, the table represents 25 examples of deletions and 11 insertions. The maximum number of inserted residues is three. We were able to insert up to four residues in the loop region of the human lysozyme, but we were unable to find any preexisting InDel mutants in the PDB that contained more than three amino acid insertions. Three of the deletions are of length 6. The letters “l”, “s”, or “h” in the table represent whether the InDel exists in the loop region, beta sheet, or alpha helix of protein, respectively.Some of the entries refer to varying-length InDels from the same protein. For instance, 6AIS and 6ICS represent deletions of two and four amino acids, respectively, from the loop region of outer surface protein A of Both the global and local RMSD values, in angstroms, are all less than 1.0 Å, with several as low as 0.13 Å. Therefore our in silico approach for creating InDel protein mutants using the robotics-inspired inverse kinematics approach and ab initio energy minimization yields structures that are similar to InDel mutants whose structures are resolved experimentally.Using our RDSM scores, we determine the similarity between the effects of our computational InDel versus the experimental one. Previous research  found thunctions , produceThese scores, RDSM2 and RDSM3, for the wildtype, PDB, and in silico generated mutants, are shown in One initial shortcoming of our RDSM approach, is that it fails to show the magnitude of the structural change of the InDel in the real world. This information is important, because computationally modeling InDels that have little to no effect on a protein’s structure would not be as useful as modeling an InDel that fundamentally changes it. Consequently, we calculated the TLCCS between each wildtype and PDB mutant, with the results in X indicate the RDSM score between wildtype and PDB mutant and let the RDSM score between the wildtype and computational mutant be represented by Y. This is indicated by orange and blue bars in the graphs, respectively. We used Spearman correlation test [We carried out a statistical analysis of the results in order to evaluate the choice of RDSM metric as an equitable approach to gauge the impact of an InDel. We describe the problem as follows: Let ion test  in orderThe evaluation was conducted for five RDSM values. These values varied in their weight X and Y with the RDSM score between the PDB mutant and the computationally derived mutant. The problem is now comprised of performing comparison of W with X and Y. Which means that we could not simply use 2-sample t- or z-test. Thus, we used the subsequent approach to resolve this.The other part of the analysis comprised of finding the relationship between X and Y versus W. Once the difference, denoted by variable D, is computed, the probability of it being less than zero was computed—i.e., The first step was to compute the probability of the third variable being smaller than the minimum of other, i.e., ndicator  that theTo further investigate the effects of InDel mutations, they should be compared with existing mutations. In To assess the predictive power of our rigidity-based approach to infer the effects of InDels on protein structure, we applied our method on TEM-1 sistance . We geneAs can be seen, the Pearson Correlation Coefficient R values for RDSM1, RDSM2, RDSM3, and RDSM5 of −0.423, −0.191, −0.153, and −0.2547 reveal a negative weak correlation between these rigidity-based metrics and the experimentally derived fitness values for the 10 InDels. Although the correlations for the rigidity-based metrics are not strong, they nonetheless reveal that there is a relationship between the experimental fitness values and rigidity metrics for these 10 mutants.G [G against the rigidity-based prediction of the effect of the mutation. Thus, when combining rigidity metrics with other features of the InDel mutants, we can expect similar or better performance, which we leave for future work.In our previous study involving single- and multiple-substitution only mutations, RDSM1, RDMS2, RDSM3, and RDSM5 metrics had much weaker negative correlation values of −0.053, −0.059, −0.063, and −0.022 against ΔΔG . For thaFully elucidating the effects of substitutions versus InDels is out of the scope of this project, but we provide a case study nonetheless. The Cypovirus Polyhedra protein has multiple crystal structures: PDB 5YR9 has a substitution at position 190, 5GQI has one deletion near that position, 5GQJ has two deletions, and 5GQN has three deletions. When compared to substitutions, InDels are responsible for more structural and functional changes in proteins. In spite of that, they are not as well studied. One of the main reasons is the lack of experimental and computational data. In this study, we attempted to develop a better understanding of InDels as well as their structural implications.In this work, we computationally generated short InDels, and also assessed their effects on a protein’s rigidity. For this study, we identified 36 InDels of lengths 1–6 amino acids, that were in the loop regions and secondary structures of protein. Those InDels were computationally generated, and then rigidity analysis was performed on the resulting structures. We demonstrated that the methods generate InDel mutants that are structurally similar to PDB InDel mutants.The rigidity analysis of the computationally generated InDels proved that we are capable of producing InDels computationally with similar rigidity properties to the InDel mutant structures in the PDB, with respect to the size and location of rigid clusters and flexible regions.Further, our statistical analysis revealed that computational and experimental PDB mutants both are significantly different from the wildtype while their rigidity properties are similar to one another.This preliminary study highlights our ability to create computational InDel mutants, thus attempting to bridge the gap that exists due to lack of experimental and computational InDel data.Furthermore, there is currently no widely known resource for identifying mutant proteins (InDels or substitutions) which mines the PDB for mutants of a desired protein. In our future work we plan to create a web-based tool that will directly mine the PDB for InDel and substitution mutant structures given a wildtype. Eventually we plan to incorporate a substitution mutant generator into a compute pipeline, which will permit us to create and analyze different types of protein mutants. Another future direction is to incorporate larger InDels and model them, possibly with the help of AlphaFold or other new modeling techniques.


Protein-protein interactions often involve a complex system of intermolecular interactions between residues and atoms at the binding site. A comprehensive exploration of these interactions can help reveal key residues involved in protein-protein recognition that are not obvious using other protein analysis techniques. This paper presents and extends DiffBond, a novel method for identifying and classifying intermolecular bonds while applying standard definitions of bonds in chemical literature to explain protein interactions. DiffBond predicted intermolecular bonds from four protein complexes: Barnase-Barstar, Rap1a-raf, SMAD2-SMAD4, and a subset of complexes formed from three-finger toxins and nAChRs. Based on validation through manual literature search and through comparison of two protein complexes from the SKEMPI dataset, DiffBond was able to identify intermolecular ionic bonds and hydrogen bonds with high precision and recall, and identify salt bridges with high precision. DiffBond predictions on bond existence were also strongly correlated with observations of Gibbs free energy change and electrostatic complementarity in mutational experiments. DiffBond can be a powerful tool for predicting and characterizing influential residues in protein-protein interactions, and its predictions can support research in mutational experiments and drug design. Chemical bonds play a crucial role in the interaction of proteins. Understanding intermolecular bonds in particular is an important part of discovering how protein-protein complexes achieve selective binding. In structural biology, the process of deducing the role of chemical bonds requires a multi-step geometric and chemical analysis. First, bonds are identified from the structure of a protein-protein complex by applying appropriate geometric and chemical constraints. Next, hypotheses are developed about the role that bonds play in the protein complex—whether the bond stabilizes the complex, assists in the binding process, or plays a different role. Finally, these hypotheses are tested in a range of experiments, such as by mutation, which alter the specific residues involved in the bond and result in changes in binding affinity. Computational methods can support the first two parts of this process, with a focus on limiting the number of necessary experiments.This paper aims to assess the predictability of intermolecular bonds while applying standard definitions of bonds in chemical literature to explain protein interactions. Our approach is to apply the textbook chemical measurements and constraints of ionic interactions, hydrogen bonds, and salt bridges at biological pH as a predictor for the presence of intermolecular bonds, and verify these predictors against experimental findings established from literature. Measurements of hydrogen bonds are extremely well defined , but staA broad range of techniques have been developed for identifying different characteristics of protein complexes that influence protein-protein interactions. Some methods analyze mutation stability from heuristic energy changes , rigiditDiffBond is the first to classify intermolecular bond interactions across the binding interface between protein-protein interactions into salt bridge, ionic bond, or hydrogen bond categories. For hydrogen bonds, DiffBond uses HBPlus for hydrogen bond identification . For salDiffBond contributes to a larger Analytic Ensemble strategy. An Analytic Ensemble strategy, mentioned first in , aims toDiffBond predicts hydrogen bonds, ionic bonds, and salt bridges using separate methods. In this section, we describe how each bond is identified from these coordinates, beginning with the atomic coordinates of a protein structure. Following that, we explain experimental methods used to verify these techniques.Hydrogen bonds are found using HBPlus , which mIntermolecular ionic bonds are found through a search algorithm for residues within a distance and electrostatic criteria. A distance less than 5 Å between two amino acid centroids is used as a standard measurement for possible interactions. A cutoff distance of 5 Å is strict enough to yield most biochemically relevant residues. Ionic bonds, rarely, can form over longer distances between 5–10 Å , and so Intermolecular salt bridges are identified using a similar procedure to that of ionic bonds. Salt bridge distance and electrostatic measurements are measured between oppositely charged residues whose side chain charged atoms, N and O, are interacting within a distance of 4 Å . Ref. 1 also estThis procedure of searching for residue pairs bound by the respective constraints of each type of intermolecular bond, allows us to identify relevant bond predictions. The implementation of DiffBond does not require dimeric protein complexes; higher order oligomers consisting of many subunits or protein-protein interactions involving multiple proteins can be assessed in a similar way as dimers without losing interface information or violating assumptions.p called an electrostatic isopotential. The electrostatic isopotential is a subset of the potential field where the potential equals p at all points on the isopotential surface. By definition, this isopotential creates a threshold k (kT/e), where one side of the threshold has potential less than k and the other side has potential greater than k. Geometrically, an isopotential guarantees a geometric solid with measurable volume, which is the metric we use for evaluating influential amino acids.An alternate method from bond prediction for finding influential amino acids is by interpreting protein electrostatic fields using VASP-E . An elecThis implementation for calculating volumetric objects representing electrostatic fields has a unique utility of enabling volumetric comparisons. VASP-E manipulates isopotential surfaces with constructive solid geometry (CSG) techniques. CSG can calculate the union, intersection, and difference of volumetric objects . SpecifiVASP-E is able to detect small-scale changes in electrostatic isopotential volume; exploiting this feature, we intentionally remove the charge contribution from single amino acids in a process called nullification . NullifiWe compare the intersection of interface fields for individual amino acids in the protein complex to their nullified variant, mirroring lab experiments that compare wild type proteins to mutant proteins with a single point mutation. Data Set B is a summary of mutations that have been performed on Barnase-Barstar, Rap1a-raf and SMAD2-SMAD4, paired with the change in binding affinity due to mutation.To demonstrate that DiffBond is able to identify and classify significant intermolecular ionic bonds, hydrogen bonds, and salt bridges, we validated DiffBond predictions against two datasets relating to two extensively studied protein complexes: Barnase-Barstar, Rap1a-raf, SMAD2-SMAD4, and complexes involving the three-finger toxin family. Data Set A contains extensively studied amino acid pairs that form intermolecular bonds for all four protein complexes. The structures in Data Set A consist of the Barnase-Barstar complex (pdb: 1brs), the Rap1A-raf complex (pdb: 1c1y), and the SMAD2-SMAD4 trimer (pdb: 1u7v). It also complexes between members of the three-finger toxin family with neuronal nicotinic acetylcholine receptors (nAChRs) . Each of these complexes have been extensively studied for specific electrostatically influential amino acids and intermolecular bond formations that affect their binding affinity.Data Set B uses some of the structures in A , but complements this structural data with 113 mutations of the proteins in these complexes (1brs(94), 1c1y(17)). These mutations, derived from the Structural database of Kinetics and Energetics of Mutant Protein Interactions (SKEMPI), are paired with experimentally measured changes in binding affinity that are caused by the mutation. Since no information on three-finger toxin proteins exists in SKEMPI and only two mutations were reported for SMAD2-SMAD4 complex, these complexes were omitted from Data Set B.Barnase is an extracellular ribonuclease of Bacillus amyloliquefaciens often co-expressed with its intracellular inhibitor barstar. Barnase can be lethal to the cell by itself, but is countered by forming a complex with barstar . BarnaseRas is a family of GTPase involved in transmitting signals to regular biological systems like cell cycle progression, cell division, apoptosis, lipid metabolism, DNA synthesis, and cytoskeletal organization . AlthougSMADs is a family of proteins that act as main signal transducers for TGF-B receptors, a super family of proteins that help regulate cell development and growth ,29. SpecThe three-finger toxins are a superfamily consisting of toxin proteins from elapid snake venom and similar structures ,32. Membarotoxin ,34,35 anbratoxin  interactbratoxin .On Dataset A, we validated DiffBond by comparing bond predictions to known protein-protein interactions published in experimental findings. Intermolecular bond formations were gathered from published journal papers where each bond was verified manually. We required two specific criteria to be met for confirming intermolecular bonds. First, the bond must verifiably exist between a pair of residues, and explicitly state the residue from each side of the interface. For salt bridges specifically, we considered existence of both a hydrogen bond and an ionic bond to imply existence of a salt bridge even if a salt bridge is not explicitly stated. Second, the paper must explicitly classify the bond as either an ionic bond, hydrogen bond, or salt bridge, or provide biochemical information that establishes one of the three bonds. Through this verification process, we can compile intermolecular bond information for protein complexes and compare this data to DiffBond prediction.In our evaluation of DiffBond, we counted true positives (TPs), false positives (FPs), true negatives (TNs), and false negatives (FNs). A bond prediction is defined as a TP if DiffBond predicted the formation of a bond type between two specific amino acids, and experimental findings confirmed the same amino acid pair and bond type. A prediction is considered a FP if DiffBond predicted the formation of a bond, but experimental findings did not agree or did not mention the specific bond. TNs are bond predictions that were predicted to not occur by DiffBond and from experimental findings. FNs are evaluated as intermolecular bonds that DiffBond failed to predict when experimental findings confirmed the existence of the bond. From these measurements, we compute the precision and recall of DiffBond. Precision is the fraction of correctly predicted bonds among all bonds verified in experimental findings, and recall (sensitivity) is the fraction of correctly predicted bonds among all true interactions.There are two practical issues when evaluating prediction performance using the above measurements. First, we cannot fully count TNs by nature of experiments in this field; no studies to our knowledge have exhaustively analyzed the electrostatic influence of every amino acid in a protein complex. Second, FPs as we measure them include bond predictions that may not have been experimentally tested before. As a result, FP matches may include intermolecular bonds that are yet to be found in future experiments. This conservative criteria for FP matches also implies that the reported precision of DiffBond is a lower limit of the true precision.A second way to validate the authenticity of intermolecular bonds predicted by DiffBond is to evaluate how their removal corresponds to binding. If the predicted bonds actually exist and play some role in protein-protein recognition, then we expect that, on balance, removing them through mutation should reduce affinity, and that affinity is maintained in mutants that do not remove the bonds. Thus, we used data corresponding to 113 mutants of the Barnase-Barstar and Rap1a-raf.SKEMPI provides DiffBond attempts to assess electrostatic complementarity through hypothetical changes in intermolecular bond formation due to mutations. An cartoon of the region that DiffBond analyzes is shown in Volumetric comparison of interface fields and nullification has been shown to effectively predict binding affinity changes in mutational experiments ,38. ConsThe precision and recall of DiffBond predictions, on Barnase-Barstar, Rap1a-raf, SMAD2-SMAD4, and three-finger toxin-nAChR, are reported in It is important to note that amino acids in some bonds have alternate bonding partners, so the removal of one partner by mutation may result in bond formation with a third party. Although both ionic bonds and salt bridges are theoretically capable of forming in this way, Dataset B contained no mutations where this occurred. We found that normalized average DiffBond predictions on hydrogen bond breaking, staying intact, or forming are much less correlated to normalized average  bridges c. First,k = +1/−1 and k = +5/−5 for the wildtype complex and mutant complex. This results in four intersection volumes of the interface: +1/−1 for wildtype and mutant, and +5/−5 for wildtype and mutant. Each intersection volume indicates the amount of electrostatic complementarity between the two proteins in the protein complex. As a result, a large value means greater complementarity and vice versa. By computing the difference in volumes, k = +1 and −1 at the interface and normalize by group to summarize total complementarity change for positive and negative charge. By interpreting volume changes as changes in electrostatic field at the protein-protein interface, the resulting sum of interface intersection illustrates changes in electrostatic complementarity due to mutation.In addition to measuring normalized average k = +5/−5 of “Bond Broken” and “Bond Intact” for both ionic bonds and salt bridges. However, for predicting volume difference of ionic bond for the same Rap1a-raf groups there is a significant difference, contrasting with We compared electrostatic intersection volume differences computed by VASP-E for the two groups, “Bond Broken” and “Bond Intact”, to assess DiffBond predictions . We founWe present DiffBond, a novel method for identifying and classifying intermolecular bonds in protein-protein interactions. DiffBond was designed to gather structural and electrostatic information about bond formation in a biological environment through exhaustive computational analysis of a protein complex to predict influential amino acids for binding. The prediction of influential amino acids towards guiding mutational experiments is relevant in fields like protein engineering and drug design. By identifying key residues for binding, we can form hypotheses about the mechanism by which proteins interact, whether through key electrostatic bonds like ionic bonds, salt bridges, and hydrogen bonds or through other processes involving steric hindrance, electrostatic fields, hydrophobic interactions. This knowledge is key to deciding mutations that modify protein binding specificity towards a desired effect, whether towards increasing the medicinal effects or reducing harmful effects of target proteins.Identification and classification of salt bridges, ionic bonds, and hydrogen bonds using DiffBond is a novel approach that demonstrated promising capabilities through validation on a small curated data set. DiffBond predicted ionic bond and hydrogen bond formation with 87.5% precision for both ionic bond and hydrogen bond predictions and 82.4% and 74.5% recall for ionic bond and hydrogen bond predictions respectively. Similarly, salt bridge prediction maintained 85.7% precision, and a lower recall than ionic and hydrogen bonds at 50%. Although 50% recall of intermolecular salt bridges indicates that half of the verified salt bridges in literature were not predicted by DiffBond, precision for all three bonds, which was a conservative estimate of true precision, shows that DiffBond rarely predicts a bond to exist when it does not. Overall, DiffBond was effective in correctly predicting the presence of 55 bonds and only incorrectly predicting 8. As a bond prediction tool that can be incorporated into an Analytic Ensemble, strong performance in precision is preferable over performance in recall, so that incorrect predictions infrequently waste analytical effort. Incorporation of DiffBond into an Analytic Ensemble will allow other related methods to add interaction information towards improving recall.On validation with experimentally determined binding affinities from SKEMPI, DiffBond predicted whether a bond breaks or stays intact due to mutation. We found that this prediction was significantly associated with changes in binding affinity using ∆∆G  and with∆∆G  at the iDiffBond, as a bond prediction method, is most applicable as a preliminary search for significant residues in a protein structural model or as part of an Analytic Ensemble approach. Mutational experiments rely on precise algorithms for identifying significant residues to guide mutation testing; experiments are often limited in number of mutations that can be tested and so precise prediction methods can help reduce unproductive testing. In addition, structural biologists can benefit greatly from transparent implementation and explainable results. DiffBond was implemented based on the chemical definition of bonds formed between the 20 canonical amino acids at biological pH, and predictions are defined simply as whether the software identified intermolecular bonds in the crystal structure based on the bond definition. As a result, DiffBond produces explainable results which allow us to make specific inferences about the biochemical mechanism for protein binding and specificity. This design also synergizes with other approaches to analyzing protein binding. DiffBond used in conjunction with other methods in an Analytic Ensemble that identify influential electrostatic interactions may provide a more comprehensive summary of the common electrostatic interactions across the binding interface in protein-protein interactions. Further extension of DiffBond in the direction of Analytic Ensemble work and generalizability to molecules other than proteins at biological pH is a topic of interest.The capability to computationally generate biochemical explanations for the role that a specific mechanism plays in binding is novel to the analytic ensemble strategy. In contrast to the analytic ensemble approach, conventional methods like molecular docking predict structure of proteins and complexes, but do not make inferences on mechanisms involved in binding. In such cases, inferences about influential mechanisms require human experts to interpret results. These capabilities point to new applications in the analysis of protein structure and in interpreting the biochemical mechanisms in predicted structures, thereby enhancing the design of mutational experiments aimed to elucidate protein structure and the comprehensibility of computational software outputs.


Development of new methods for analysis of protein–protein interactions (PPIs) at molecular and nanometer scales gives insights into intracellular signaling pathways and will improve understanding of protein functions, as well as other nanoscale structures of biological and abiological origins. Recent advances in computational tools, particularly the ones involving modern deep learning algorithms, have been shown to complement experimental approaches for describing and rationalizing PPIs. However, most of the existing works on PPI predictions use protein-sequence information, and thus have difficulties in accounting for the three-dimensional organization of the protein chains.Struct2Graph, for identifying PPIs directly from the structural data of folded protein globules. Our method is capable of predicting the PPI with an accuracy of 98.89% on the balanced set consisting of an equal number of positive and negative pairs. On the unbalanced set with the ratio of 1:10 between positive and negative pairs, Struct2Graph achieves a fivefold cross validation average accuracy of 99.42%. Moreover, Struct2Graph can potentially identify residues that likely contribute to the formation of the protein–protein complex. The identification of important residues is tested for two different interaction types: (a) Proteins with multiple ligands competing for the same binding area, (b) Dynamic protein–protein adhesion interaction. Struct2Graph identifies interacting residues with 30% sensitivity, 89% specificity, and 87% accuracy.In this study, we address this problem and describe a PPI analysis based on a graph attention network, named https://github.com/baranwa2/Struct2Graph). Furthermore, the novel mutual attention mechanism provides insights into likely interaction sites through its unsupervised knowledge selection process. This study demonstrates that a relatively low-dimensional feature embedding learned from graph structures of individual proteins outperforms other modern machine learning classifiers based on global protein features. In addition, through the analysis of single amino acid variations, the attention mechanism shows preference for disease-causing residue variations over benign polymorphisms, demonstrating that it is not limited to interface residues.In this manuscript, we address the problem of prediction of PPIs using a first of its kind, 3D-structure-based graph attention network (code available at The online version contains supplementary material available at 10.1186/s12859-022-04910-9. Protein–protein interactions (PPIs) are fundamental to many biological processes. Analysis of the human proteome suggests that the majority of proteins function not alone but rather as part of multi-unit complexes . Indeed,A number of strategies have been employed to decode PPIs aiming primarily at molecular scale data and amino acid sequences . TraditiS. cerevisiae and human datasets, respectively. In fact, most deep learning based methods have been shown to achieve high PPI prediction accuracy [Typical computational techniques for PPI analysis use the amino acid sequences of the two proteins to determine whether interactions occur , 25. A naccuracy , 32 owinaccuracy , 33–37.Despite their success, the above sequence based approaches do not generalize to broader classes of chemical compounds of similar scale as proteins that are equally capable of forming complexes with proteins that are not based on amino acids, and thus lack of an equivalent sequence-based representation. While the interaction of proteins with DNA can be accurately predicted , the metStruct2Graph, to predict PPIs solely from 3D structural information. Instead of using several protein specific features, such as, hydrophobicity, solvent accessible surface area (SASA), charge, frequency of ngrams, etc., Struct2Graph uses a graph based representation of a protein globule obtained using only the 3D positions of atoms. This graph based interpretation allows for neural message passing [In this work, we make the first step toward a generalized method to assess supramolecular interactions of proteins with other nanostructures. The proposed method determines the probability of formation of protein–protein complexes on a nanoscale representation of proteins from crystallographic data, as contrasted to amino-acid amino sequence information. We develop a mutual graph attention network and a corresponding computational tool,  passing  for effi passing , where i passing .Beyond the high accuracy of its PPI predictions, Struct2Graph offers a number of advantages. Similarly to the ML algorithms exploiting the idea of geometrical biomimetics, Struct2Graph only requires the 3D structure of individual proteins. Furthermore, while in this paper we focus on protein interactions, by using only the positions of atoms in our analysis, this framework can be generalized to other molecular structures where 3D information is available. Moreover, Struct2Graph is also able to provide insight into the nature of the protein interactions. Through its attention mechanism, the model can potentially identify residues that likely contribute to the formation of the protein–protein complex. Unlike other models, Struct2Graph is able to produce this data in an unsupervised manner and thus does not require protein complex information which are often unavailable .Graph convolutional network for PPI prediction: Struct2Graph uses a multi-layer graph convolutional network (GCN) for PPI prediction from the structural data of folded protein globules. The proposed approach is general and can be applied to other nanoscale structures where 3D information is available.Curation of PPI database: A large PPI database comprising of only direct/physical interaction of non-homologous protein pairsState-of-the-art prediction performance: Our method is capable of correctly predicting the PPIs with an accuracy of 98.89% on the balanced set consisting of an equal number of positive and negative pairs. On the unbalanced set with the ratio of 1:10 between positive and negative pairs, Struct2Graph achieves a fivefold cross validation average accuracy of 99.42%. Struct2Graph outperforms not only the classical feature-based machine learning approaches, but also other modern deep-learning approaches, such as Deep-PPI and DeepFE-PPI that use sequence information and feature selection for PPI prediction.Unsupervised prediction of important residues: The novel mutual attention mechanism can potentially identify important residues for the formation of the protein–protein complex. This importance can stem from either direct participation in the interaction process  or indirectly through contribution to appropriate protein folding that allows formation of the correct binding site geometry. The identification of important residues is tested for two different interaction types (neither part of the training set): (a) Proteins with multiple ligands competing for the same binding area, (b) Dynamic protein–protein adhesion interaction. Struct2Graph identifies interacting residues with 30% sensitivity, 89% specificity, and 87% accuracy.Analysis of single amino acid variation (SAV) dataset: Disease-causing mutations are known to be preferentially located within the interface core, as opposed to the rim. Of the known 2724 disease-causing SAVs and 1364 polymorphisms, our attention mechanism identifies 33.55% of all disease-causing SAVs as important (attention weights within top-20%), while 85.30% of all polymorphisms are identified as unimportant by the proposed attention mechanism, indicating significant overlap between the previously established SAV study and the important residues identified by the proposed attention mechanism.The key contributions of the proposed work can be summarized as:heterologous pairs, we searched all possible databases available . Not all PPI databases use the same publications and same ontologies to report the interactions. Consequently, it is not surprising that each database reports PPI differently. Therefore, only up to a 75% concordance between all PPI databases is achieved [Saccharomyces cerevisiae, Homo sapiens, Escherichia coli, Caenorhabditis elegans and Staphylococcus aureus) PPIs. For these organisms, IntAct provides 427,503 PPIs, and STRING provides 852,327 PPIs.Struct2Graph focuses on structure-based predictions and interaction sites of the protein pairs. Our PPI database is therefore produced based on only direct/physical interactions of proteins excluding therefore weakly interacting and loosely associated nanoscale biomolecules. To build a large physical interaction database, comprising of only achieved . For Strachieved  and STRIachieved  are chosSTRING distinguishes the type of interactions as “activation”, “binding”, “catalysis”, “expression”, “inhibition” and “reaction”. IntAct, on the other hand, describe the type of interactions as “association”, “physical association”, “direct association/interaction”, and “colocalization”. Only “direct association/interactions” from IntAct and “binding” from STRING were considered as physical interactions. We only choose concordant pairs of physical interactions from both databases. Therefore, extracting only physical interaction data from the rest of the interactions reduces the actual number of PPIs to 12,676 pairs for IntAct and 446,548 pairs for STRING. Negative PPI is extracted from the work that derives negative interaction from large-scale two-hybrid experiments . The negStruct2Graph, since the inputs to the proposed GAT are coarse grained structural descriptors of a query protein–protein pair. Struct2Graph outputs the probability of interaction between the query proteins. Struct2Graph uses two graph convolutional networks (GCNs) with weight sharing, and a mutual attention network to extract relevant geometric features related to query protein pairs. These extracted features are then concatenated and fed to a feedforward neural network (FNN) coupled with a SoftMax function, which finally outputs a probability of the two classes—‘0’ (negative pairs) and ‘1’ (positive pairs). This section first describes the preprocessing and fingerprinting procedure specifying how spatial information on protein pairs are converted into corresponding protein graphs, and then elaborates on different components of the Struct2Graph deep learning architecture.We present a novel multi-layer mutual graph attention network (GAT) based architecture for PPI prediction task, summarized in Fig. The purpose of the graph construction step is to capture the salient geometry of the proteins in a way that is amenable to further dimensionality reduction by the neural network. There are many possible ways of constructing a graph from spatial coordinates of individual atoms, and each captures a different level of detail about the geometry of the protein . For insThe graph construction approach converts spatial information associated with a protein into an equivalent protein graph object entclass1pt{minimaubgraphs  induced embedding vectors in such a way that the geometry of the embedding vectors reflects similarities between the graphs. The embedding portion of the GCN works as follows. To each vertex d-dimensional feature vector, which encodes the 1-neighborhood subgraph induced by the neighboring vertices and edges at 1-hop distance from a vertex. This is in contrast to explicit inclusion of amino acid specific features, such as, hydrophobicity, solvent accessible surface area (SASA), charge, etc. In our encoding, similar to other studies [A graph convolutional network (GCN) maps graphs to real-valued  studies , 68, eacEach layer of the GCN updates all vertex features by first replacing each vertex feature by a normalized average over vertex features of all 1-hop neighboring vertices. This is followed by an affine transformation given by the trained weight matrices and bias parameters. In order to impart expressivity to the GCN architecture, each coordinate of the resulting affine transformed embedding vector is passed through a nonlinear activation function, such as, rectified linear unit (ReLU) or sigmoid activations. This process is repeated for all the subsequent layers, and the output of the final layer is the newly transformed embedding (feature) vector that is propagated further to the mutual attention network. Here, the number of layers is a hyperparameter, while the weight matrices are learned from the training data in order to optimize performance of the entire system on the interaction prediction task.d-dimensional embedding of the vertex subgraphs of the query protein–protein pair, respectively, an l-layer GCN updates vertex embeddings using the following update rule:More concisely, given input protein graphs mutually contribute towards prediction of physical interaction of proteins, (b) combine embedding matrices of dissimilar dimensions d). Attention mechanisms were originally introduced for interpreting sequence-to-sequence translation models by allowing the models to attend differently to different parts of the encoded inputs. Since then, it has been adapted in other fields of deep learning, such as, computer vision [The purpose of the proposed mutual attention network is two fold: (a) extract relevant features for the query protein–protein pair that r vision .i in the first protein, the GCN-embedding is denoted by d-dimensional. Similarly, the embedding of the U and V of sizes U, V and w are trained in an end-to-end fashion along with the weights of the GCN. These attention weights are then translated to context vectors d-dimensional embedding, d-dimensional embedding. Thus, while the final embedding that forms the input to the feed-forward network (FFN) is a concatenation of the context vectors The mutual attention mechanism proposed in this work computes attention weights mentclass2pt{minimmentclass2pt{minimd, which is used as input to a single-layer, fully connected feedforward neural network (FNN) represented by The context vectors n in Eq. . This ouk-nearest neighbor (k-NN) classifier, (f) Decision tree (DT) classifier, (g) Random forest (RF) classifier, (h) Adaboost classifier, and (i) Support vector classifier (SVC) [k-NN and Adaboost, we use the readily available implementation in the scikit-learn [As part of our assessment, we compare the performance of Struct2Graph for PPI predictions against a number of recent machine learning models. These methods include: (a) DeepFE model , where wer (SVC) . All modit-learn  module. it-learn  and Deepit-learn  are implit-learn , while Sit-learn .For Struct2Graph, the hyperparameters of the models are tuned in order to achieve the reported accuracies. The tuning is obtained by performing grid search over the set of possible hyperparameter settings. The hyperparameters of our Struct2Graph implementation are as follows: optimizer: Adam optimizer  with leaTable The performance is reported for various measures, such as, accuracy, precision, recall, specificity or the true negative rate, Matthews correlation coefficient (MCC), Fmentclass2pt{minimmentclass2pt{minimNote from Table k-fold cross validation study is to measure the generalization capabilities of a model. Bootstrap resampling, on the other hand, is primarily used to establish empirical distribution functions for a widespread range of statistics. It works by performing sampling with replacement from the original dataset, and at the same time assuming that the data points that have not been chosen, are the test dataset. We repeat this procedure several times and compute the average score as estimation of the performances of various classifiers. Table The primary purpose of In most practical scenarios, the number of negative pairs is expected to be larger than positive pairs, since only a small fraction of protein pairs interact within all possible pairs. We thus evaluate the performance of the deep learning models, Deep-PPI and DeepFE-PPI against the proposed Struct2Graph model on various unbalanced training sets, where the number of negative pairs outnumber the positive pairs. These results are summarized in Tables Bootstrap resampling yields a very similar conclusion, where the Struct2Graph is again shown to outperform its deep-learning counterparts, as well as the Random Forest classifier, consistently for several unbalanced cases  with such huge class imbalance, prevalence-corrected Precision-Recall Curves (PRCs) have been adopted  that rednt}r=100  for an et-test to elucidate statistically significant evidence in favor of the Struct2Graph classifier. In particular, we compare the means of the proposed Struct2Graph model with the DeepPPI and the DeepFE-PPI models, respectively, across all folds of the cross-validation set for each metric using the one-sided Welch’s t-test. Figure p-value statistical significance for rejecting the null hypothesis that means are equal. Here, the rows represent several performance measures, while the columns depict scenarios in which the model was trained beginning from the balanced (1:1), to unbalanced  datasets. Recall that a p-value less than 0.05 is typically considered to be statistically significant. It can be seen that there is statistically significant evidence in favor of superior performance of the Struct2Graph classifier.Tables The success of any machine learning algorithm is based on the quality of training data it is presented with. Of the 4698 positive and 5036 negative examples spanned across 3677 unique proteins, we first want to make sure that the learning algorithms are not biased towards memorizing the training data , since sSimilarly, of the 3677 unique proteins, 104 unique proteins are involved in negative only interactions (do not form complexes). Figure We further validate this by building a random forest classifier that is supplied with an input vector of length 3677. The specific choice of length of the input vector is directly related to the number of unique proteins in the database. We first create a dictionary of all the unique proteins and note down the order in which these unique proteins appear in the dictionary. Then, each unique protein is represented by a 3677-long unit vector with all but one coordinate being zero. The coordinate corresponding to the order of the protein in the dictionary is marked as 1. For predicting the interaction of two proteins, say proteins A and B, the unit vectors are summed and supplied to the random forest classifier as an input. Recall that the sum operation is permutation invariant, and thus interaction prediction for the pair  is identical to that for the pair . Table The success of Struct2Graph is attributed to the thorough analysis of structural 3D information embedded in the form of a graph, which predicts interactions better than sequence-based approaches . In addiindirectly important for predicting binding, but not captured by traditional analysis that focuses only on the specific interacting residues identified in the literature. Detailed results for each example are described:HMGB1 and PSMcompete for binding TLR4: Phenol soluble modulins (PSMs), short, amphipathic, helical peptides [Staphylococcus aureus virulence, one of the most common causes of human bacterial infections worldwide [S. aureus has seven PSMs . In addition, among the top 20% predicted residues of HMGB1 were the specific interacting residues TyrSdrG-Fibrinogen Adhesion: Microbial attachment to host tissues is a crucial step in most bacterial infections. Gram-positive pathogens such as Staphylococci, Streptococci, and Enterococci contain multiple cell wall-anchored proteins that act as an adhesin to mediate bacterial attachment to host tissues. These adhesin mediating interactions have been termed MSCRAMMs  [Staphylococcus epidermidis that binds to the lecules) . SdrG isechanism .A demonstration of the potential of Struct2Graph to identify specific interaction sites was performed on two example cases (neither part of the training set) with well-described interacting residues from protein pairs in the literature. Specifically, we studied two different interaction types: (1) A protein with multiple ligands competing for the same binding area ; and (2)337, Ser338, Leu340, Phe344, Gln425, Ser437, Tyr577, Asp578, and Asn579. Figure Struct2Graph was used to evaluate the interaction between SdrG (PDB:r19A) and a synthetic peptide with homologous sequence to its binding site in Fg (PDB:r17C). Interacting residues between SdrG and the synthetic Fg peptide homolog were predicted with 75% accuracy. Among the high probability residues identified in SdrG were 9 exact matches to those in the literature . This inThese results show that Struct2Graph provides insight into key residues involved in the protein–protein interaction without any training data on the specific nature of these interactions. A complete summary of the residues identified by Struct2Graph for the preceding examples is included in the supplementary material  Protein with multiple ligands competing for the same binding area, (b) Dynamic protein–protein adhesion interaction. Struct2Graph identifies interacting residues with 30% sensitivity, 89% specificity, and 87% accuracy. Finally, through the analysis of single amino acid variations, the attention mechanism shows preference for disease-causing residue variations over benign ones, demonstrating that it is not limited to interface residues. This connection between the unsupervised discovery of interaction sites and graph representation of proteins is possible thanks to the somewhat limited type of atoms and bond patterns that commonly occur in such molecules, which makes it possible to characterize properties on local atomistic arrangements. Overall, the proposed framework is general and, while subject to availability of corresponding training data, can be made to predict other kinds of complex sets of collective supramolecular interactions between proteins and nanoscale species of different chemical composition.Additional file 1: List of important residues as predicted by Struct2Graph.Additional file 2: List of missense variants annotated in UniProtKB/Swiss-Prot human entries.