Protein complexes play significant roles in cellular processes. Identifying protein complexes from protein-protein interaction (PPI) networks is an effective strategy to understand biological processes and cellular functions. A number of methods have recently been proposed to detect protein complexes. However, most of methods predict protein complexes from static PPI networks, and usually overlook the inherent dynamics and topological properties of protein complexes. In this paper, we proposed a novel method, called NABCAM (Neighbor Affinity-Based Core-Attachment Method), to identify protein complexes from dynamic PPI networks. Firstly, the centrality score of every protein is calculated. The proteins with the highest centrality scores are regarded as the seed proteins. Secondly, the seed proteins are expanded to complex cores by calculating the similarity values between the seed proteins and their neighboring proteins. Thirdly, the attachments are appended to their corresponding protein complex cores by comparing the affinity among neighbors inside the core, against that outside the core. Finally, filtering processes are carried out to obtain the final clustering result. The result in the DIP database shows that the NABCAM algorithm can predict protein complexes effectively in comparison with other state-of-the-art methods. Moreover, many protein complexes predicted by our method are biologically significant. With advances in high-throughput techniques, a lot of protein-protein interaction (PPI) data has been generated . The emeSo far, many algorithms have been proposed to predict protein complexes from PPI networks. Bader and Hogue  proposedHowever, these algorithms only focus on the static PPI networks. In fact, PPI networks in cells are dynamic; they change over environment and time . TherefoIn addition, Gavin et al.  revealedTo identify protein complexes accurately and biologically, researchers should pay attention to the structure properties of protein complexes predicted from dynamic PPI networks. In this paper, we proposed a novel algorithm, called NABCAM (Neighbor Affinity-Based Core-Attachment Method), to identify dynamic protein complexes. First, the centrality score of every protein is calculated. The proteins with the highest centrality scores are regarded as the seed proteins. Second, the seed proteins are expanded to complexes cores by calculating the similarity value between seed proteins and their neighbor proteins. Thirdly, the attachments are appended to their corresponding protein complex cores by comparing the affinity among neighbors inside the cluster against that outside the cluster. Finally, filtering processes are carried out. Therefore, we obtain the protein complexes set from dynamic PPI networks.The outline of this paper is as follows. In this section, some relative terminologies that are used in our experiments are presented. Then, we describe the NABCAM algorithm in the following subsections.The dynamic PPI networks are constructed by integrating the static PPI data and gene expression data , becausec, and the yellow protein is one of c’s candidate neighbor proteins to be merged, which is represented by v. The neighbors of v inside the core c are in the blue dotted circle, while those outside c are in the green dotted circle. For a protein v, its neighbor affinity inside core c and outside core c are defined respectively. If the NA(v) = NAI(v) − NAO(v) is more than the threshold Tn, the yellow protein will be merged into the core c as the attachment. The rest of the neighbor proteins of core c repeat such a process until no proteins are left to be merged. After the attachment formation, we can obtain the complexes.In this algorithm, we focus on the inherent organization of protein complexes. Based on the core-attachment structure, our algorithm identified protein complexes in dynamic PPI networks. On the formation process of attachment, we utilize the idea of neighbor affinity. As shown in Some analysis of protein complexes revealed the core-attachment structure of a complex . In FiguBased on core-attachment structure assumption, the formation process of predicted protein complexes sets involves five phases. The pseudo-code of the NABCAM algorithm is shown in v ϵ V, the dsc(v) is calculated by Equation (1).In the first phase a, the alv, the dense-spread centrality score [v is defined. For a protein v, its induced sub-graph is represented by vG is described as following: vV| represents the number of the proteins involved in vG and |vE| represents the number of the interactions involved in vG. The protein v is added to the seed protein set only if des(v) > Ts, where des(v) is the dense-spread centrality score and Ts is the seed threshold. A protein v is discarded if it has a des(v) value less than the threshold value Ts. This is done for all proteins in the PPI networks. The obtained seed proteins are the primary part of the complex cores.Considering the density and the size of the induced sub-graph of ty score  of protev, we compute the Pearsons correlation coefficient between seed protein v and its neighbor protein u. The PCC  is calculated by Equation (2).X = {x1, x2, ..., nx} and Y = {y1, y2, ..., ny} gives the expression values of protein X and Y for n time points, and x’ and y’ give the mean of expression values of X and Y, respectively. The Pearsons correlation coefficient (PCC) is a measure of the correlation between two proteins X and Y [u is appended to the core whose seed protein is v only if PCC  > Tp, where PCC  and Tp is the core threshold. When all of the neighbor proteins of seed proteins are traversed over, we obtain the whole complex cores.In the second phase b,c, we n X and Y . The morp of the complex core c, we compute separately its affinity among neighbors inside and outside the core c, namely the values of NAI (p) and NAO (p). NAI (p) and NAO (p) are calculated by Equations (3) and (4), respectively.v is a neighbor protein of core c, and d (u) represents the number of neighbors of protein u. NI (v) denotes neighbors of protein v inside the core c, the number of proteins in NI (v) is represented |NI (v)|. NO (v) denotes neighbors of protein v outside the core c, the number of proteins in NO (v) is represented |NO (v)|. The difference between NAI (p) and NAO (p) is denoted by NA (p). If NA (p) > Tn, the protein p is merged into the core c. When all of the neighbor proteins of complex cores are traversed over, we obtain the protein complex set.In the third phase d,e, we fIn the fourth phase, we should remove redundant protein complexes from the protein complex set. This is a significant step to purify the experimental results. For a protein complex, it may be included in other complexes. In our experiment, for the identified complexes that completely overlap with others, only one can be retained, while the others should be removed as redundant. Moreover, a predicted protein complex may only contain a protein, which also should be removed.Finally, the NABCAM algorithm is performed on dynamic PPI networks, thereby generating the predicted protein complex set as the result.Ts, the core threshold Tp and the neighbor affinity threshold Tn, used in the algorithm NABCAM, decide the seed protein’s selection, complex cores formation, and protein complexes acquirement, respectively. To find the appropriate thresholds, NABCAM is run with various values of Ts, Tp and Tn on the DIP, MIPS, and Krogan networks, respectively. In this paper, the appropriate thresholds of Ts, Tp and Tn are 0.3, 0.3 and 0.Moreover, the seed threshold S. cerevisiae from the DIP [In the present paper, the PPI data of  the DIP , MIPS [2 the DIP  and Krog the DIP  database the DIP , which cprecision, recall and f-measure [OS) [p| is the size of the identified protein complex, |g| is the size of the standard protein complex, and |p∩g| is the common protein number from the identified and gold complexes. If OS  ≥ w, we claim that p and g have been matched. In this paper, we set w to be equal to 0.2, which is consistent with previous articles [To assess the performance of methods, there are three evaluation indicators: -measure . We presure [OS)  between articles .precision denotes the proportion of the predicted protein complexes perfectly matched by the standard protein complexes in the prediction of the complex. It can be defined by the following Equation (6):P| represents the number of predicted protein complexes, and cpN indicates that the number of the predicted complexes perfectly matched by the known protein complexes. The higher precision is, the more accurate the algorithm is.The recall indicates the proportion of the known protein complexes perfectly matched by the predicted protein complexes in the standard of the protein complex. It can be defined by the following Equation (7):B| represents the number of known protein complexes, and cbN indicates the number of standard protein complexes perfectly matched by the predicted protein complexes. The higher recall is, the more accurate the algorithm is for predicting protein complexes.The precision and recall describe the effectiveness of the algorithm from different aspects. In order to consider these indicators synthetically, the f-measure is defined as the harmonic mean of precision and recall, which can access the overall performance of a method. It is defined by the following Equation (8):The precision and f-measure have a relationship of positive correlation. Similarly, recall and f-measure also have a relationship of positive correlation. From the formula of harmonic mean, we can see that p-value [N is the number of proteins in the PPI network, M is the number of proteins in a GO term, and n is the number of proteins that are annotated with the same GO term. Generally, the smaller the p-value of a protein complex, the stronger the biological significance of the complex processes will be. In this paper, a detected complex is considered to be significant if its p-value is less than 0.01.In order to further validate the biological significance of protein complexes, we need to carry out the functional enrichment analysis by using the p-value  formulatIn this section, the predicted protein complexes are compared with the standard protein complexes. In precision, recall and f-measure values of 0.6903, 0.4917 and 0.5743, respectively. It is obvious that the precision value of our method is much more excellent than other prediction methods. Compared with other methods, our algorithm’s recall value is a little lower than the recall values of MOEPGA, DPClus, COACH and CMC. However, the f-measure is higher for the NABCAM algorithm than its counterpart methods. The other methods MOEPGA, HC-PIN, MCL, DPClus, RNSC, COACH, CORE, ClusterOne, CFinder, MCODE and CMC achieved f-measure values of 0.4510, 0.3600, 0.3717, 0.4653, 0.4359, 0.5019, 0.4766, 0.3680, 0.4331, 0.3342 and 0.4100.As shown in precision, recall and f-measure in the MIPS and Krogran datasets, respectively, as shown in f-measure of 0.5382, recall of 0.5094, and precision of 0.5706 in MIPS dataset, which obviously outperforms other methods. In f-measure of 0.5575, recall of 0.4259 and precision of 0.8068 in the Krogan dataset, which obviously outperforms other methods.Moreover, we also compare our method with the following established leading protein complex prediction methods: CSO , Clusterp-value is less than 0.01. In this experiment, we use the tool GO::TermFinder [p-value of identified complexes whose size is greater than two.A complex is considered significant when its rmFinder  to calcup-value is in the range of <10−15, [10−15, 10−10), [10−10, 10−5), [10−5, 0.01), ≥0.01. p-values greater than 0.01 fall into corresponding intervals. We can see from p-value is greater than 0.01 in predicted complexes by the NABCAM algorithm is the smallest. So, most of the predicted protein complexes by the NABCAM algorithm are significant. Similarly, we can obtain results on the MIPS and Krogan datasets. The results illustrate that the NABCAM algorithm is competent at identifying significant protein complexes in PPI networks.p-value of protein complexes, cluster frequency, and the Gene Ontology term.To further reveal the biological significance of predicted complexes, five identified protein complexes with different datasets are presented in In the post-genomic era, it’s significant to understand the topological organization of PPI networks, predict protein complexes and discover the functions of proteins. For the sake of these goals, a number of prediction algorithms have been proposed. In this paper, we proposed a novel algorithm, NABCAM, for the computational prediction of protein complexes on dynamic PPI networks. In the NABCAM method, first, some proteins with high dense-spread centrality scores are regarded as seed proteins. Second, the seed proteins are expanded to complexes cores by calculating the similarity value between the seed protein and its neighbor protein. And then the attachments are appended to their corresponding protein complex cores by comparing the affinity among neighbors inside the cluster against that outside the cluster. Our method considers the dynamic properties of PPI networks and the inherent organization of complexes.precision, recall and f-measure. Experimental results show that the NABCAM algorithm has a better performance than other methods. Moreover, a number of protein complexes with strong biological significance are identified from dynamic PPI networks by our algorithm. In the future, we will attempt to apply our algorithm to other organisms.Our algorithm is evaluated and analyzed by comparing it with other state-of-the-art algorithms in terms of


Modeling macromolecular assemblies with restraints from crosslinking mass spectrometry (XL-MS) tends to focus solely on distance violation. Recently, we identified three different modeling features inherent in crosslink data: (1) expected distance between crosslinked residues; (2) violation of the crosslinker's maximum bound; and (3) solvent accessibility of crosslinked residues. Here, we implement these features in a scoring function. cMNXL, and demonstrate that it outperforms the commonlyused crosslink distance violation. We compare the different methods of calculating the distance between crosslinked residues, which shows no significant change in performance when using Euclidean distance compared with the solvent-accessible surface distance. Finally, we create a combined score that incorporates information from 3D electron microscopy maps as well as crosslinking. This achieves, on average, better results than either information type alone and demonstrates the potential of integrative modeling with XL-MS and low-resolution cryoelectron microscopy.  •A scoring function that outperforms more commonly used crosslink scoring methods•A comparison of methods to calculate the distance between crosslinked residues•Combining low-resolution 3D-EM and crosslinking information improves scoring Bullock et al. present a scoring function for modeling protein complexes based on crosslink data (cMNXL) that outperforms other functions currently in use. They also combine this method with a 3D-EM fitting score to create a combined scoring function that outperforms each score alone. Protein complexes play a critical role in the cell, either through transient cell signaling complexes or via the specialized functions of macromolecular machines. Determining the structures of protein complexes is therefore essential for a mechanistic understanding of the cell. Unfortunately, protein complexes can be problematic to study with traditional structural techniques, such as X-ray crystallography, nuclear magnetic resonance (NMR), or cryo electron microscopy (EM), due to their size, heterogeneity, or resistance to crystallization . A recenXL-MS is a technique typically used to generate distance restraints, which can be used for protein modeling. The concept of protein crosslinking has been around a long time, although it is not until recently that its popularity has increased, due to technical advances in detector design , crossliA typical crosslinking experiment consists of first reacting the protein complex with crosslinker, which covalently binds specific amino acids  within a given distance (from 0 to 50 Å) depending on the length of the crosslinker. The crosslinked complex is then digested by proteases and the crosslinked peptides are analyzed and identified via MS . From thAnother aspect of crosslinking that is commonly overlooked is that crosslinks can only form on residues that are solvent accessible; therefore, crosslinks can act as a proxy for solvent accessibility. We previously made use of this solvent accessibility information by defining a non-accessible crosslink, i.e., a crosslink that has been experimentally observed but where one or both of the crosslinked residues are non-solvent accessible in the model. Incorporating this solvent accessibility information was shown to be very beneficial to the modeling of protein monomers .The distance between two crosslinked residues is usually calculated in one of two ways. The most common method is the Euclidean distance (ED), i.e., a direct line between the two crosslinked residues. By virtue of its simplicity, it is a very quick calculation to perform; however, as this does not take into account the fact that a crosslinker cannot travel through protein mass, it can be inaccurate. This is in contrast to the solvent-accessible surface distance (SASD), defined as the shortest path between two residues across the surface of the protein , which cPreviously, when crosslinking restraints have been used for scoring models of protein monomers and complexes the most common approach has been to use only violation of the maximum bound of the crosslinker (number of violations [NoV]). This scoring can be done either via a step function, i.e., a crosslink is either violating or not , a smootTo improve upon existing crosslink scoring regimes, here we combine the three potential types of modeling restraint encoded in crosslinking information: (1) the maximum bound of crosslinker; (2) the expected distance between crosslinked residues; and (3) the solvent accessibility information of crosslinked residues. Previously, we incorporated these three sources into the scoring function Matched and Non-accessible Crosslink (MNXL) score, and showed it to outperform the NoV method when modeling protein monomers . Here weWe updated our previous scoring function to create cMNXL. cMNXL is made up of the number of non-accessible (NoNA) feature of both intra- and inter-subunit crosslinks and the number of violations and expected SASD of inter-subunit crosslinks .ExSASD is the expected SASD between inter-subunit crosslinked residues, NoV is the number of inter-subunit crosslinks that violate the theoretical maximum bound of the crosslinker, NoNA is the number of crosslinks that are non-accessible , and the subscripts inter and intra refer to inter-subunit and intra-subunit crosslinks, respectively. During the study, the score from each of these terms was calculated separately and a systematic investigation into the different weighting was performed in order to return the best results  or a thTo statistically evaluate this scoring function, we tested cMNXL on a theoretical benchmark of 68 protein dimers, each with 100 models at a range of qualities. The models were scored using theoretical crosslinks. To replicate a more realistic scenario, we bootstrapped crosslinks at 15% recovery with a minimum of 2 inter-subunit crosslinks see .Overall, cMNXL achieves an average precision of 0.560 and average area under the curve (AUC) of 0.901 . This is1QA9 or 1FQJ, which contain 27 and 38 lysines across the complex, respectively  perform the least, with low precisions when used on their own  (The best-performing term of cMNXL is the ctively) . HoweverTo discover how cMNXL performed with experimental crosslinking data, we then tested cMNXL on a second benchmark of 9 protein complexes, each with 100 models at a range of quality, using experimental crosslinks taken from the XLinkDB2.0.cMNXL achieves a higher average precision of 0.644 and AUC of 0.908. Although overall on this small benchmark the NoV score performs similarly to cMNXL, with non-significant increase in precision and a non-significant decrease in AUC , the FPR is significantly worse . In the 3 out of 9 individual cases where NoV outperforms cMNXL, NoV has a much higher FPR .1U8F, which has 162 crosslinks (42 inter- and 120 intra-subunit) . Here, the inter-subunit crosslinks are located in three discrete regions across the protein interface, which triangulates the protein orientation and optimizes the scoring.Generally across the benchmark, the higher the number of crosslinks, the more successful the modeling, as is the case for PDB: subunit) . However1F05  is severely affected. With PDB: 1F05  there arolerated . In thisolerated , given tolerated  and S2.Next, we compared the effect on modeling performance when using either SASD or ED to calculate the distance between crosslinked residues. While SASD is theoretically more correct, using Jwalk to calculate SASD is around 5 orders of magnitude slower than ED . This can become prohibitive when dealing with large numbers of models and crosslinks.ED) to make a direct comparison between the distance types and retain the solvent accessibility information that would otherwise be lost when solely using ED. Upon use of ED, there is no significant change in precision  or AUC  (ED) and comparing with NoV does result in a significant decrease in performance, in both precision and AUC .We substituted ED for SASD in cMNXL (cMNXLctively) . LookingED . This can be attributed to two benchmark cases, PDB: 1UJZ and 2PSN, whose performances decrease more dramatically , and therefore the crosslink restraints tolerate a large range of non-native models. When the ED is used the tolerance is increased further, therefore accepting an even greater range of non-native models  from γ-TEMPy , a genetScoring the theoretical benchmark with each scoring function (F score and cMNXL) separately reveals that on average the F score performs significantly better than cMNXL at each resolution in terms of both AUC  and precision . However, the combination of F score with cMNXL significantly improves the average performance at every resolution compared with F score alone in terms of AUC  and precision  .Figure 71XD3 from the theoretical benchmark, where globular subunits are difficult to orientate accurately (fnat of 0) in the top 10, resulting in a precision of 0.40. The combination of crosslinking and 3D-EM, even when the crosslinking alone is unable to successfully model the protein complex, improves the orientation of the subunits, increasing the precision to 0.90.Crosslinks are especially useful in cases such as PDB: curately A. Here, 1F05, cMNXL alone performs badly because it has only 2 inter-subunit crosslinks (see above) . In terms of precision, the F score alone already performs excellently so there is little room for additional improvement . In bence above) B. Again,ExSASD); (2) the number of violations of the crosslinker maximum bound between two crosslinked residues (NoV); (3) the solvent accessibility of the crosslinked residues (NoNA). By making use of all three of these aspects, we were able to create a scoring function that improves upon the commonly used inter-subunit NoV or the expected distance between inter-subunit ExSASD.Our previous investigation into modeling monomeric proteins  and our We tested our score on both an experimental and a theoretical benchmark. The theoretical benchmark was scored at a 15% recovery rate in order to more accurately replicate an experimental scenario . Scanning of the recovery rates shows us, however, that at ∼50% recovery the modeling precision begins to plateau. Future technical improvements in the collection of crosslinks should therefore increase the performance of XL-MS modeling.Lysine crosslinkers are also able to crosslink serine and threonine residues, albeit at much lower frequencies . As of yNoNA contributed the most performance to the scoring function, whereas NoV and ExSASD contributed only smaller gains. Interestingly, this has not been the case with our current results on protein complexes, where out of all the scoring aspects, NoNA contributes the least (and the inter-subunit ones less than the intra-subunit), while both NoV and ExSASD deliver similar high performance.Previously we showed that non-accessible crosslinks play an important role in modeling the structure of monomeric proteins . In a beNoV and ExSASD contribute less . However, solvent accessibility can in theory guide subunit orientation once rigid bodies reach close proximity (both inter- and intra-), which may explain the small but significant increase in performance seen when incorporating non-accessible crosslinks into cMNXL. This is in contrast to modeling different conformations of protein monomers, whereby the distance between crosslinked residues is unlikely to differ dramatically between models, and backbone flexibility opens up the possibility of burying or exposing different residues. In this instance, non-accessible crosslinks markedly increase the performance while ute less .ED, where the latter's performance collapsed completely (precision of 0.06). However, in this benchmark on protein complexes, the difference in performance is much less marked. This is likely because in protein monomers, physically the crosslink must curve around the protein surface, which creates a larger discrepancy between the ED and SASD. In the case of complexes, there is a higher chance of the crosslink to be more “linear” when connecting two residues, thereby making the ED a reasonable approximation for inter-subunit crosslinker paths in protein complexes. This would be even more so when using crosslinkers shorter than BS3  or zero-length crosslinkers . These results again highlight how rigid-body modeling of protein complexes has information requirements different from those of the flexible modeling of protein monomers.In our previous study on monomers, the effect of using SASD over ED was pronounced, especially in the comparison between MNXL and NoVSASD and NoVED). This is similar to the observation made by ED to NoVSASD. This observation contrasts with what is seen in our experimental benchmark, where the performance is significantly different only in the expected distance term (ExED performing worse than ExSASD). However, as shwon, this result is due to two specific cases (PDB: 1UJZ and 2PSN) that perform badly, and is therefore not indicative of a more general trend.In our theoretical benchmark, the performance between SASD and ED only differs significantly when using the NoV term  are usedistance ).As the crosslinking experiment happens in solution at room temperature, it is possible that crosslinking datasets are capturing more than one conformation of the complex. This could be a result of the protein complex adopting multiple native conformations, but it could also be due to crosslinks capturing a partly dissociated complex. Consequently, this might lead to conflicting sets of crosslinks that correspond to (in terms of distance restraints and solvent accessibility information) two or more structural states. Modeling procedures that use crosslinking in the sampling stage are more likely to identify these events, either by specifically processing these events during sampling  or by clAdditionally, during the crosslink identification process it is likely that a small percentage of the identified crosslinks will be false positives. Experimental methods for assessing the quality of crosslinks are becoming more rigorous ; howeversimulated, which gave the F score an advantage over the crosslinking data , the results confirmed that the combination of crosslinking and 3D-EM information is complementary at all resolutions and can capture subunit orientation better than 3D-EM alone. This is most notable in certain cases such as PDB: 1XD3, where models ranked in the top 10 by the F score have completely incorrect interfaces. Even in cases where the crosslinking information is insufficient to successfully model protein complexes on its own , the combination of crosslinking with 3D-EM information still generates an improvement.Finally, we wanted to demonstrate that crosslinking and 3D-EM information at resolution range of 10–20 Å are complementary to each other in the modeling process. By combining cMNXL with the fitness score (F score) from γ-TEMPy, we created a combined score that performed better overall on the benchmark than each score alone. Even though the 3D-EM maps were in-cell crosslinking and cryo-ET should improve the structural characterization of macromolecular complexes within the native environment.Using a combination of crosslinks and 3D-EM data could be especially relevant to applications in cryo-ET where the maps resulting from subtomogram averaging are still often in the intermediate- to low-resolution range . Combinim.topf@cryst.bbk.ac.uk)Further information and requests for data should be directed to and will be fulfilled by the Lead Contact, Maya Topf (http://topf-group.ismb.lon.ac.uk/Software.html and in the TEMPy software (http://tempy.lon.ismb.ac.uk)The theory behind the cMNXL score is described in the main text. cMNXL is freely available as a python package from The weighting of each scoring aspect in the final cMNXL scoring function was reached via a systematic scan of weights for each aspect from 0 to 1 (in steps of 0.1), simultaneously. This scan was performed on the larger theoretical benchmark (see below) and the weights that gave the highest precision were chosen.et al. . The minimum criteria for selecting a set of theoretical cross-links was for it to have at least 2 inter-subunit cross-links. The choice of 15% recovery reflects the typical recovery from an XL-MS experiment . This process was repeated 1000 times and the average precision and AUC taken. The performance of cMNXL on this benchmark was also tested at 1/5/10/20/30/40/50/60/70/80/90 and 100% recovery .The experimental benchmark, taken specifically from XLinkDB2.0 based on the in-cell cross-linking datasets  and Cha, was useUsing TEMPy , for eacFor the purposes of this study, all homo-complexes in the benchmark have been treated like hetero-complexes, i.e. all identical subunits and associated cross-links were treated as unique subunits, with individual cross-links specified to each subunit . In order to determine if a homo-complex cross-link should be intra- or inter-subunit, the SASDs of all the possible combinations were calculated and the lowest SASD was chosen (if no SASD under 32 Å was present in the native the lowest SASD was still taken). All reciprocal crosslink combinations were reproduced.NoV at different maximum bounds. The precision peaks at 32 Å  which combines a mutual information (MI) score and a clash penalty score (PS):tal data . The PS tal data . The comThe weighting of cMNXL was chosen as a result of a systematic scan of weightings between 0 and 2.Models are assessed via mean Cα-RMSD (meanRMSD) calculated using an in-house script and MODELLER-v9.18 . Iteratiand an fnat score of ≥ 0.3, and FP  is defined as a model that is scored in the top 10 by the scoring function but has a meanRMSD > 4 Å or fnat ≤ 0.3. The False Positive Rate (FPR) is calculated as FP/(FP+TN) where TN (True Negative) is defined as a model that is not scored in the top 10 by the scoring function and has a meanRMSD > 4 Å or fnat ≤ 0.3. The fnat criteria matches the criteria for a medium model in CAPRI (We assessed the effectiveness of our scoring function using Precision and Area-Under-Curve (AUC) taken from the Receiver-Operating-Characteristic (ROC) curve. Precision is calculated as TP/(TP + FP), where TP (True Positive) is defined as a model that is scored in the top 10 by the scoring function and has a meanRMSD of ≤ 4 Å in CAPRI . In the and fnat ≥ 0.3. ROC systematically lowers the scoring threshold to assess whether a model is a true positive, instead of the top 10 ranked models. ROC and AUC calculations were calculated using the ROCR package in R (https://www.r-project.org/).ROC curves were calculated with a model being defined as Positive if the meanRMSD is ≤ 4 Å www.r-project.org/). For example, the precision values of each benchmark case for the NoV score were compared directly to the precision values for each benchmark case for cMNXL (i.e. each case was paired together instead of simply combining them into one distribution). The alternative hypothesis was that the mean of the precision of cMNXL was greater than the mean of the precision of the NoV score (i.e. one-sided). In all cases, a significance threshold p-value of 0.05 was used, however p-values were often much smaller. Relevant p-values have been included in the main text.The statistical significance between the precision and AUC of different scoring methods was calculated using a one-sided paired t-test, as implemented in R  can be found in the http://topf-group.ismb.lon.ac.uk.The experimental cross-links used to score the experimental benchmark can be found in the


Their connectivity network needs to be considered for the full understanding of biological phenomena, but the available information on protein–protein associations is incomplete and exhibits varying levels of annotation granularity and reliability. The STRING database aims to collect, score and integrate all publicly available sources of protein–protein interaction information, and to complement these with computational predictions. Its goal is to achieve a comprehensive and objective global network, including direct  as well as indirect  interactions. The latest version of STRING (11.0) more than doubles the number of organisms it covers, to 5090. The most important new feature is an option to upload entire, genome-wide datasets as input, allowing users to visualize subsets as interaction networks and to perform gene-set enrichment analysis on the entire input. For the enrichment analysis, STRING implements well-known classification systems such as Gene Ontology and KEGG, but also offers additional, new classification systems based on high-throughput text-mining as well as on a hierarchical clustering of the association network itself. The STRING resource is available online at  While an impressive amount of structural and functional information on individual proteins has been amassed , our knoad hoc discovery and annotation.Arguably, the common denominator of the various forms of protein–protein associations is information flow—biologically meaningful interfaces have evolved to allow the flow of information through the cell, and they are ultimately essential for implementing a functional system. Hence, it is desirable to collect and integrate all types of protein–protein interactions under one framework; this then provides support for data analysis pipelines in diverse areas, ranging from disease module identification ,8 to bioIMEx consortium , as nsortium . They prnsortium ,21. Lastnsortium , FunCoupnsortium , I2D , as well as download pages covering individual species networks and associated data. The website allows users to log on and store their searches and gene sets, and contains evidence viewers to inspect the underlying evidence of any given interaction. It also provides users with high-level information regarding their input/search data, including network enrichment statistics and functional enrichment detection, using two different conceptual frameworks for the latter (see below). Many of the features of STRING have been made available and described earlier (STRING is one of the earliest efforts  and stri earlier  and the  earlier ), small  earlier ), protei earlier ), tissue earlier ) and vir earlier ), respecTogether with other online resources , the STRING database has recently been awarded the status of a European Core Data Resource by ELIXIR, a pan-European bioinformatics initiative dedicated to sustainable bioinformatics infrastructure . As a prThe basic interaction unit in STRING is the ‘functional association’, i.e. a link between two proteins that both contribute jointly to a specific biological function . For twoAll of the association evidence in the STRING database is categorized into one of seven independent ‘channels’: three prediction channels based on genomic context information (see below), and one channel each for (i) co-expression, (ii) text-mining, (iii) biochemical/genetic data (‘experiments’) and (iv) previously curated pathway and protein-complex knowledge (‘databases’). Users can disable all channels individually or in combinations. For each channel, separate interaction scores are available as well as viewers for inspecting the underlying evidence Figure . In geneWithin each channel, the evidence is further subdivided into two sub-scores, one of which represents evidence stemming from the organism itself, and the other represents evidence transferred from other organisms. For the latter transfer, the ‘interolog’ concept is applied ,43; STRIThe individual protein associations in the various channels are derived, briefly, as follows:The three genomic context prediction channels  are the result of systematic all-against-all genome comparisons, aiming to assess the consequences of past genome rearrangements, gene gains and losses, as well as gene fusion events. These evolutionary events are known to be retained non-randomly with respect to the functional roles of genes, and thus allow the inference of functional associations between genes even for otherwise rarely studied organisms .The co-expression channel is based on gene-by-gene correlation tests across a large number of gene expression datasets (using both transcriptome measurements as well as proteome measurements). In the case of transcript data, STRING re-processes and maps the large number of experiments stored in the NCBI Gene Expression Omnibus , followeas is: namely the ProteomeHD dataset of the Juri Rappsilber lab , covering 294 biological conditions measured using SILAC in human cells. ProteomeHD is not based on Pearson correlation, but instead uses the treeClust algorithm , are re-mapped and re-processed: first, duplicate records and datasets are removed, and then entire groups of records are benchmarked against KEGG and scored accordingly.The database channel is based on manually curated interaction records assembled by expert curators, at KEGG , Reactomhttps://arxiv.org/abs/1804.05957) (last updated on 17 April 2018). Full-text articles that were not classified as English-language articles were removed (using fastText and a pretrained language identification model for 176 languages (https://arxiv.org/abs/1607.01759)), as were those that could not be mapped to PubMed. We also removed highly unspecific articles that mention more than 200 relevant biomedical entities such as proteins, chemicals, diseases or tissues. The final corpus consists of 28 579 637 scientific publications, of which 2 106 542 are available as full-text articles and the remainder as abstracts. While the text-mining pipeline itself has remained unchanged , its diFor users that query the STRING database with a set of proteins (as opposed to a single query protein only), the website computes a functional enrichment analysis in the background; this can then be inspected and browsed by the user, and includes interactive projections of the results onto the user's protein network. This functionality has been available since version 9.1, and is based on straightforward over-representation analysis using hypergeometric tests.However, this analysis uses only a small part of the information that the user might have about his or her protein list. First, the original list of proteins might have been much longer, and the user would have had to truncate it . Second, the list might have had a biologically meaningful ranking, which would have been lost during submission to STRING. Third, each protein might have been associated with some numerical information from the underlying experiment or study . For this type of genome-wide measurements, simple overlap-based over-representation analysis is not the best choice .Thus, beginning with version 11.0, STRING offers such users a second option for conducting enrichment analysis. It specifically asks for genome-scale input, with each protein or gene having an associated numerical value . Of the available methods for searching functional enrichments in such a set, we chose a permutation-based, non-parametric test that performs well in a number of settings, termed ‘Aggregate Fold Change’ . BrieflyFollowing the computation of the entire new enrichment option, users are presented with a three-panel view of the results Figure . There, Over the coming years, the STRING team aims to continue tracking all available protein association evidence types and prediction algorithms. One particular focus will be to expand the protein-based co-expression channel, where advances in proteomics throughput and scope lead us to expect growing data support for association searches. With regard to the STRING website, we expect to provide tighter integration of functional enrichment and network search results, and are exploring options to provide more context on the various networks . We will also strive to provide better interoperability options and increase our list of partnered, crosslinked resources as well as applicable direct data import options to facilitate our regular data updates.


Translational and post-translational control mechanisms in the cell result in widely observable differences between measured gene transcription and protein abundances. Herein, protein complexes are among the most tightly controlled entities by selective degradation of their individual proteins. They furthermore act as control hubs that regulate highly important processes in the cell and exhibit a high functional diversity due to their ability to change their composition and their structure. Better understanding and prediction of these functional states demands methods for the characterization of complex composition, behavior, and abundance across multiple cell states. Mass spectrometry provides an unbiased approach to directly determine protein abundances across different cell populations and thus to profile a comprehensive abundance map of proteins.http://computproteomics.bmb.sdu.dk/Apps/CoExpresso.We provide a tool to investigate the behavior of protein subunits in known complexes by comparing their abundance profiles across up to 140 cell types available in ProteomicsDB. Thorough assessment of different randomization methods and statistical scoring algorithms allows determining the significance of concurrent profiles within a complex, therefore providing insights into the conservation of their composition across human cell types as well as the identification of intrinsic structures in complex behavior to determine which proteins orchestrate complex function. This analysis can be extended to investigate common profiles within arbitrary protein groups. CoExpresso can be accessed through With the CoExpresso web service, we offer a potent scoring scheme to assess proteins for their co-regulation and thereby offer insight into their potential for forming functional groups like protein complexes.The online version of this article (10.1186/s12859-018-2573-8) contains supplementary material, which is available to authorized users. Biological systems are governed by a multitude of entangled interactions between biomolecules with an immense number of physical and chemical properties. Protein complexes are large biomolecules with a wide range of tasks in the cell and consist of multiple subunits linked by non-covalent interactions. These interactions can lead to a variety of stable or transient states where the complexes display different compositions of their subunits or different structures that are often fine-tuned by post-translational modifications. An example of functional diversity are ribosomes that are known to contribute differentially to translation of distinct subpopulations of mRNAs . There iVarious experimental methods exist to identify protein complexes and to determine and quantify which protein subunits they are composed of. Determination of protein interaction partners within a complex provides valuable knowledge about complex and protein function and thus their potential behavior . Most prThere is an increasing amount of evidence supporting the hypothesis that the majority of protein complexes are tightly controlled in the cell. Post-transcriptional regulation occurs predominantly for protein complex members, leading to strong co-regulation of complex subunits. This could be shown by systematic investigation of protein and gene expression levels in human cancer , 7, in aIn contrast to most proteomics data repositories where only raw data and identification results are available, ProteomicsDB , 12 is aHere, we apply three scoring models on the ProteomicsDB data to assess the significance of subunit co-regulation in protein complexes. We compare and benchmark different randomization and scoring approaches on known complexes and reveal particular substructures of complex behavior for a few selected use cases. The scoring and extensive visualization is implemented in the web service CoExpresso that allows investigating co-regulatory patterns in any group of human proteins.Quantifications of proteins and IDs of known complexes were downloaded from ProteomicsDB , 12 and Quantitative abundance profiles of SwissProt proteins were extracted from ProteomicsDB hosting mass spectrometry based protein abundances for distinct human cell types including cell tissues, cell lines and fluids. In ProteomicsDB, proteins and samples are annotated according to UniProtKB and Brenda Tissue Ontology , respectFrom the downloaded profiles (summer 2016), we retained only cell types with more than 1000 proteins and which were tagged by Brenda ontology terms. Proteins not available in at least 2 cell types were removed. This reduced the data to comprise 15,409 proteins and 140 tissues. Uniprot accession numbers for annotated human complexes were downloaded from CORUM and filtered for duplicates, leading to a total of 2175 reported complex compositions.C, only the nt cell types with full coverage, t= [ 1..nt], i.e. having quantitative values for all proteins p= [ 1..np], were considered, resulting in a nt by np matrix EC.For each protein group C. The often relatively low coverage of proteins over multiple cell types required creating randomized sets for each combination of number of cell types and number of proteins.We applied 3 different forms of randomization to obtain random protein groups being quantified in the same number of cell types as the proteins of protein group nt by np randomized values were obtained by sampling, independently at random, ntnp values from all quantitative values of all proteins in all tissues. 10,000 random groups were created for each combination of nt and np.Randomization of quantitative values of all proteins in all tissues comprised sets with the same dimensions as the to be tested protein group. That is, the np and number of cell types nt: nt cell typesTake all proteins being each quantified in at least np proteins IDs and count full cell type coverage of the protein groupRepeat the following 5000 times: sample Keep unique protein combinations with coverage over at least five cell typesRandomization of proteins and categorization into cell type coverage. This randomization type turned out to be more complex and a sufficient large coverage of random groups was achieved by the following procedure. For each combination of number of proteins With this procedure, we obtained 1000–20,000 unique and random protein groups for each relevant combination giving a total of more than 20,000,000 randomized groups. Obtaining random protein groups with low coverage was computationally most demanding. Our method is scalable with respect to data coverage and will also perform within a similar time frame when increasing the number of considered cell types.np proteins are sampled independently at random from all proteins that appear in the same cell types as the tested protein group, and their observed values in those cell types are considered.All proteins simultaneously found in the same cell types as the tested protein group were randomized to create 10,000 samples. That is, Mean correlation model (MCOM): Protein abundances were averaged for each cell type, restricting to cell types covered by the entire protein group, M(t)=<EC>p. For each protein p, Pearson’s correlation to the means M(t) provides a measure of how much the protein follows the common profile of the protein group, SMCOM(p)=cor(M(t),EC), where cor(x(t),y(t)) denotes Pearson’s correlation between samples x and y.Pairwise correlation model (PCOM): Pearson’s correlation was calculated between all proteins pairs using the abundances in the cell types covered by all proteins. The score is then given by the sum, Factor analysis model (FAMS): The model is based on factor analysis developed for microarray analysis  counting the number of all valid cases within the brackets.For each model, randomization method, and a given combination of p-values from multiple protein groups, correction for multiple testing was carried out via the Benjamini-Hochberg procedure.For Tight regulation of protein complexes by translational and post-translational control mechanisms may result in the degradation of more abundant proteins that do not form the complex. Then the proteins of known complexes, such as the ones collected in the CORUM database, will show similar abundance protein profiles when compared across different cell types. Given that proteins often have multiple functions, a protein complex might present itself in different compositions or the complex does not change in abundance, we did not assume all complexes to show highly similar abundance profiles of their proteins but merely investigated how much co-regulation can be observed.p-values from comparison of the score of a protein to the scores obtained from appropriately randomized data. Therefore, we investigated different ways of randomizing the ProteomicsDB data to identify the best performing combination of scoring scheme and randomization procedure.We applied different scoring systems to evaluate whether proteins in human complexes exhibit similar regulatory behavior when compared over multiple cell types. Despite of having a large set of available protein abundances, coverage of the proteins over the 140 cell types was often sparse  by scores obtained from randomizations. By comparing the scores of the different models to scores from randomly sampled data, we obtained probabilities to discard the observed abundance profiles as result of randomly chosen proteins. Thus the false discovery rates (FDRs), represented by p-values calculated for each model and randomization. More “realistic” randomization (IS <PCS<PTCS) resulted in lower number of complexes with significant abundance profiles. MCOM and PCOM, both models being based on Pearson’s correlation, produced nearly the same results on complex level  for all three scoring models.Use case A: Condensin I . MRPS12 and MRPS12 are known to be altered in many and different cancer types [We looked into more examples of subgroups with highly co-regulated abundances. Higher coverage over cell types for these subgroups allows gathering further insight into their co-regulation. MRPS17, MRPS36 and MRPS12 show very low correlation  with high correlations . AvailaOur comparison showed that appropriate randomizations are crucial to achieve results with simultaneously high recall and considerable robustness to noise. The results speak against complete randomization of all values, where global differences amongst cell types and proteins are neglected. We found that protein identities (PCS method) needed to be maintained to reach robust results. On the other hand, maintaining the identity of the tissues (PCTS method) in the investigated protein group did not lead to lower robustness. We therefore conclude that testing properties of protein profiles in general should be compared to a randomized set where protein identity is kept. In data with many missing values, this randomization requires categorizing the random protein groups into their tissue coverage which can be computationally expensive. We therefore provide a web service that stores the randomizations and where arbitrary protein groups can be tested for their significance. By testing annotated complexes from the CORUM database for the significance of their concurrent protein abundance profiles, we could confirm almost 50% (500–600 depending on scoring model) of the protein groups being co-regulated with an FDR below 0.1. This confirms the tight regulation of complex proteins previously reported and extends this observation to be valid generally in human cells. Given the lack of coverage over sufficient cell types in many cases, resulting in rather low statistical power, we predict that most protein complexes will be found to be translationally and post-translationally regulated. While most insight into dysregulation of complex subunits comes from gene expression data, our tool allows extending the analysis by determination and comparison of complex behavior on protein level. Instead of analyzing and comparing protein behavior alone, our user-friendly tool characterizes protein changes with respect to the complex or a in general to a protein group. Thus we provide direct insight into the functional behavior of a protein group.Our analysis additionally confirmed and extended details about protein complex substructure that indicates regulatory features that orchestrate complex function by changes in complex composition or by here not investigated post-translational modifications.We furthermore tested whether the large database of randomized protein groups could be used to identify novel protein assemblies that represent highly interacting functional modules such as complexes. We did not find enrichment for known protein-protein interactions in the most significant protein groups. This means that investigating protein co-regulation by random sampling alone is not a good source to search for novel complexes but remains highly valuable to test for complex behavior and confirm their composition across cell types. Given the combinatorial explosion when considering the number of possible protein groupings, the random sampling strategy used here considers only a small fraction of all protein groups that contain highly co-regulated proteins. Novel protein assemblies could still be found by selective and iterative algorithms that determine protein groups with highest co-regulation within all possible combinations.The here presented study provides deep insight into protein complex behavior in human cells. The data for all 1414 investigated protein groups can be accessed via the CoExpresso web service. Arbitrary protein groups can be tested for their significance with respect to their co-regulation in human cell, such as investigating prior hypotheses about protein groups with common strongly co-regulated functional behavior. With more data on hand, we expect to improve statistical power and accuracy by including more data sets and by characterizing the role of quantified post-translational modifications.Project name: CoExpressoProject home page:http://computproteomics.bmb.sdu.dk/Apps/CoExpresso and https://bitbucket.org/veitveit/coexpressofor source code and R scripts.Operating system(s): Platform independent (web service)Programming language: R and javascriptOther requirements: We recommend a modern web browser (e.g. Firefox or Chrome)License: Apache 2.0Additional file 1Supplementary Figures to CoExpresso: Assess the quantitative behavior of protein complexes in human cells. (PDF 5647 kb)


Protein interactions involving intrinsically disordered proteins (IDPs) greatly extend the range of binding mechanisms available to proteins. In interactions employing coupled folding and binding, IDPs undergo disorder-to-order transitions to form a complex with a well-defined structure. In many other cases, IDPs retain structural plasticity in the final complexes, which have been defined as the fuzzy complexes. While a large number of fuzzy complexes have been characterized with variety of fuzzy patterns, many of the interactions are between an IDP and a structured protein. Thus, whether two IDPs can interact directly to form a fuzzy complex without disorder-to-order transition remains an open question. Recently, two studies of interactions between IDPs (4.1G-CTD/NuMA and H1/ProTα) have found a definite answer to this question. Detailed characterizations combined with nuclear magnetic resonance (NMR), single-molecule Förster resonance energy transfer (smFRET) and molecular dynamics (MD) simulation demonstrate that direct interactions between these two pairs of IDPs do form fuzzy complexes while retaining the conformational dynamics of the isolated proteins, which we name as the extremely fuzzy complexes. Extreme fuzziness completes the full spectrum of protein-protein interaction modes, suggesting that a more generalized model beyond existing binding mechanisms is required. Previous models of protein interaction could be applicable to some aspects of the extremely fuzzy interactions, but in more general sense, the distinction between native and nonnative contacts, which was used to understand protein folding and binding, becomes obscure. Exploring the phenomenon of extreme fuzziness may shed new light on molecular recognition and drug design. A stable three-dimensional structure of a protein is the key to understanding protein function in the conventional structure-function paradigm . On the Intrinsically disordered proteins do not have a unique stable structure, or a unique folding funnel on the free energy landscape . IntrinsUnderstanding protein-protein interaction involving IDPs is a central theme for experimental and theoretical studies of IDPs . Our knoThe first clearly characterized extremely fuzzy complex is 4.1G-CTD/NuMA . Proteinele) and the electrostatic contribution to the solvation free energy (ΔGpolar) are both large in magnitude. On the other hand, the magnitudes of van der Waals interaction (ΔEvdW) and nonelectrostatic contributions to solvation free energy (ΔGnonpolar) are relatively moderate. The summation of ΔEele and ΔGpolar is positive, i.e., unfavorable for binding, while the nonelectrostatic contributions are all negative. This rough estimation suggests that the binding of 4.1G-CTD to NuMA is not mainly driven by electrostatic interactions and nonpolar interactions have important contribute. This is consistent with the mutagenesis experiments in [Another clearly characterized extremely fuzzy complex is H1 chaperone/prothymosin-α (H1/ProTα) . Human lments in , where mSo far, 4.1G-CTD/NuMA and H1/ProTα are the only two clearly characterized extremely fuzzy complexes at high resolution, i.e., residue specific and/or atomic level information have been obtained. However, new evidence of extremely fuzzy complexes between two or more IDPs is emerging. For example, evidence for formation of extremely fuzzy complex between human α, β and γ synuclein have been recently reported ,47.kon of H1/Pro-Tα interaction is at the diffusion limit (3.1 ± 0.1 × 109 M−1 s−1), suggesting that the binding process is basically barrierless. It is anticipated that for extremely fuzzy complexes similar to H1/Pro-Tα, i.e., with extended conformations and very broad binding interface, the association is basically diffusion limited.The thermodynamics and kinetics of protein-protein association are far more complicated than those of small molecules ,50,51. TAlthough the binding mechanism of extremely fuzzy complex lacks a simple picture, some established explanations for other types of IDP-mediated interactions with different degrees of fuzziness could be applicable in certain aspect. In coupled folding and binding model, it has been proposed that structure element similar to those in complex are preformed in unbound IDPs  and the http://frustratometer.qb.fcen.uba.ar/) [From the perspective of energy landscape , the binuba.ar/)  As shownAs mentioned above, it is difficult to define native and nonnative contacts in the binding of two IDPs. This situation is especially obvious in the case of H1/Pro-Tα. As for the 4.1G-CTD/NuMA complex, it might be possible to identify these two contact types since specific binding sites have been found. Thus, even for the two complexes representing the extremely fuzzy interactions, the detailed binding mechanisms could be different. In general, the task of achieving a holistic understanding of the mechanism for IDP-mediated interactions with various degrees of fuzziness will require the identification and evaluation of relative contributions of native and nonnative contacts, which is beyond conventional conformational selection and induced-fit models ,58,59. TThe studies of fuzzy complexes in the past two decades have provided hints on our understanding of the extreme fuzziness. The fuzzy complexes database (FuzDB) has collected dozens of fuzzy complexes characterized in detail . The assThe two extremely fuzzy complexes reported recently have given a definite answer to the question of whether fuzzy complexes can be formed by two IDPs while retaining structural dynamics. This type of fuzziness represents the dynamic extreme in the spectrum of IDP interactions, suggesting that a more general model beyond all previously proposed mechanisms is required to understand protein interactions. In the perspective of energy landscape, the whole pathway of specific protein binding may occur without marked reduction of frustration, and therefore the reconsideration of ‘native’ and ‘nonnative’ contact is necessary. Both mechanistic understanding and functional importance of the extremely fuzzy interactions are exciting aspects in IDP studies.


AFP) require the availability of both positive examples  and negative examples (corresponding to proteins not associated with that function). Unfortunately, publicly available proteome and genome data sources such as the Gene Ontology rarely store the functions not possessed by a protein. Thus the negative selection, consisting in identifying informative negative examples, is currently a central and challenging problem in AFP. Several heuristics have been proposed through the years to solve this problem; nevertheless, despite their effectiveness, to the best of our knowledge no previous existing work studied which protein features are more relevant to this task, that is, which protein features help more in discriminating reliable and unreliable negatives.Supervised machine learning methods when applied to the problem of automated protein-function prediction  and term-unaware . We validated the informativeness of each feature utilizing a temporal holdout in three different experiments on yeast, mouse and human proteomes: (i) feature selection to detect which protein features are more helpful for the negative selection; (ii) protein function prediction to verify whether the features considered are also useful to predict GO terms; (iii) negative selection by applying two different negative selection algorithms on proteins represented through the proposed features.The present work analyses the impact of several features on the selection of negative proteins for the Gene Ontology (GO) terms. The analysis is network-based: it exploits the fact that proteins can be naturally structured in a network, considering the pairwise relationships coming from several sources of data, such as protein-protein and genetic interactions. Overall, the proposed protein features, including local and global graph centrality measures and protein multifunctionality, can be betweenness, which is the most relevant among term-unaware features. The node positive neighborhood instead is the most predictive feature for the AFP problem, while experiment (iii) showed that the proposed features allow negative selection algorithms to select effectively negative instances in the temporal holdout setting, with better results when nonlinear combinations of features are also exploited.Term-aware features (with some exceptions) resulted more informative for problem (i), together with node The online version of this article (10.1186/s12859-018-2385-x) contains supplementary material, which is available to authorized users. Thus, if a protein is not associated with a function, this could be simply due to a lack of information. Indeed, in such cases it is not possible to exclude that future studies could in principle associate that protein with that function.The publicly available databases devoted to record protein functions  are often (positively) annotated solely to a small number of proteins. Therefore, remaining proteins either do not possess the function, or correspond to not yet discovered positive annotations.Among the available protein function taxonomies, this work considers the Gene Ontology (GO), a hierarchy composed of three branches, biological process (BP), molecular function (MF), and cellular component (CC), each structured as a direct acyclic graph . The funAFP), consisting in discovering novel associations of proteins with biological functions through computational methodologies. Indeed, the automated prediction process is typically based on supervised/semi-supervised machine learning techniques, requiring both positive and negative associations of proteins with functions  in order to infer accurate predictors. In this context, selecting the negative examples is a central issue for AFP  encode some notion of intra-protein functional similarity (with Wij=0 when the corresponding nodes are not connected). The matrix W is obtained from the STRING connections D is a diagonal matrix with non-null elements m GO terms {1,…m}: each matrix refers to a different temporal release of the ontology (assuming Y as the older one). If we denote the r-th column and the i-th row of a matrix X by Xr. and Xi. respectively, then Yk. and k to the proteins in V at the beginning and at the end of the houldout period. Moreover, Ni:={j∈V|Wij≠0} denotes the neighborhood of node i∈V, and for a given GO term k, k .Protein networks are represented as an undirected graph k, Cnp⊆V is the set of proteins that received a new annotation in the holdout period, that is, We recall that fixed a term G which effectively discriminate proteins belonging to Cnp from proteins negatively annotated in both releases, as shown in the next section.As mentioned in the previous section, the main aim of this paper is extracting features from nodes in The protein features studied in this work are selected in order to consider on the one hand information about the network topology, including both local and global ‘standard’ node centrality measures, on the other hand information about protein annotations. The resulting set of protein features is shown in Table G: some of them are purely local, in the sense that they exploit a limited local neighborhood around the protein of interest (f1– f4); other features are more global in nature (f6– f9), and correspond broadly to some of the most common parameter-free centrality measures in network analysis. A second group of features, besides using the network structure, takes also into consideration the annotations (f5) or refers to the term-aware variant of some of the features of the first two groups (f10– f14). The considered features are summarized in Table f1Neighborhood mean: mean of connection weights in the protein neighborhood. f2Neighborhood variance: variance of connection weights in the protein neighborhood. f3Weighted degree: sum of connection weights in the protein neighborhood. f4Weighted clustering coefficient: weighted proportion of triplets centered in the protein of interest that turn out to be closed (i.e. triangles). f5Number of annotations: number of GO terms for which the protein is annotated in the older release. f6Closeness centrality: reciprocal of the sum of shortest-path distances from the protein to all the other proteins in the same connected component. f7Lin’s index: an adjusted version of closeness, obtained multiplying it by the square of the size of the component. f8Harmonic centrality: sum of the reciprocal of all the shortest-path distances from the protein to all the other reachable proteins. f9Betweenness: sum of the fractions of shortest paths that pass through the given protein. f10Positive neighborhood: sum of connection weights in the protein positive neighborhood. f11Mean of positive neighborhood: mean of connection weights in the protein positive neighborhood. f12Positive closeness centrality: reciprocal of the sum of shortest-path distances from the protein to all the positive proteins in the same connected component. f13Positive Lin’s index: an adjusted version of positive closeness, obtained multiplying it by the square of the number of positive proteins in the same connected component. f14Positive harmonic centrality: sum of the reciprocal of all the shortest-path distances from the protein to all the positive reachable proteins.A first group of features depends only on the structure of the network est f1– f; other fThe first two features refer to the first moments of the distribution of connection weights in the neighborhood of a node. The third feature provides information about the node connectivity, and moreover has been suggested in the literature as a proxy for gene multifunctionality , 27. Joif4 is the weighted-aware version of the local clustering coefficient [Measure fficient  of the nfficient  that takf5 is related to the ability of a protein to play different roles: in its computation, the current GO term has been excluded in order to not introduce bias.Feature f6– f8 are among the most classical geometric centrality measures. As many authors observe [f6 [f7 [f8 [f8, originally defined by Anthonisse for edges [Features  observe , 32, cloerve [f6  . A special case is represented by the feature f5, which uses an information not directly related to the annotations for the current GO term, but encompassing GO terms; hence, we did not include it in the group of term-aware features. Conversely, features f10 and f11 are the term-aware versions of f1 and f3, respectively, and similarly f12– f14 are the term-aware equivalent of f6– f8.Feature on score . Togethek∈{1,2,…14}.In order to have comparable ranges, features have been normalized so as to sum up to one across proteins, that is It is worth pointing out that the centrality measures considered here do not cover all the indices examined in the literature , and in 3Prop features have also been considered: originally proposed to extract features from biological networks, this algorithm describes a protein i∈V with three features j=1,2,3, each representing the probability that a random walk  which starts from a positive (annotated) node ends in i [k, recalling the previously introduced diagonal matrix D, and setting To further enrich our analysis, the state-of-the-art nds in i . Namely,with components j∈{1,2,3} . Features f15– f17 in Table it holds that f1– f17 described in Table Cnp for GO terms in Table CART algorithm [Sequential floating forward Search (SFFS) method [CART, which in addition is able to exploit feature interactions. To prevent selection bias and overfitting, data were partitioned into three non-overlapping subsets  method  to deterposed in ). On eacF1 measure was selected as performance criterion to be maximized both in the inner and the outer CV loops. Finally, we ranked features through the proportion of times they have been selected in all the experiments over the three data subsets.In order to deal with the scarcity of positive instances, the f1– f14, f15– f17, and f1– f17. In order not to have any bias toward a specific classifier, two state-of-the-art methods were used to solve the binary classification problems where instances were represented through feature vectors: linear support vector machines (SVM) with class weights [Random Forests (RF) [C and mtry, respectively for SVM and RF models. To counterbalance the large presence of negative examples and to avoid learning trivial models, the class weights of the SVM for term k have been set to 1 and F1 measure has been adopted both to select the model and to measure the classification performance (averaged across folds), since this measure is more informative when positive instances are rare. Furthermore, results are also reported in terms of Precision (proportion of annotated proteins among those classified as positive) and Recall (proportion of annotated proteins that were positively classified).The proposed features have also been tested in classifying node/proteins to the Gene Ontology terms, to assess their capability in capturing network structures useful for the automated protein-function prediction. For each term previously described and summarized in Table  weights  and Randsts (RF) . The perested in . The F1 f15– f17,f1– f14 - top q,f1– f14 - mean,f1– f14,f1– f17 - top q,f1– f17 - mean,f1– f17,In order to study further the subsets of features that help detecting reliable negatives, the features described in Table q’ denotes the selection of the top q=5 features in the corresponding ranking in Fig. q=5 derives from the observation of frequency distributions: in some cases just three features are above the mean, while in other ones the distribution has a lower variance with seven features overcoming the mean frequency value. The value of q has been tuned as a compromise between these two different conditions.where ‘top x% of the total number of proteins, with x∈{1,5,10,15,20,25,30}.The selection of reliable negatives was performed through protein ranking, both exploiting the decision function values for SVMs and leveraging the probability to belong to a given class in RFs. The negative proteins selected as reliable are those bottom-ranked by the models. Following the temporal holdout setting, the models were trained on the older annotation release, by fixing a budget of negatives to be selected, subsequently computing the number of false negatives averaged across terms ; this outcome is in line with the general observation that betweenness is scarcely correlated with most of the remaining centrality indices, and it may be associated to the fact that the considered networks have a relatively small diameter.Number of annotations seems to carry a significant signal on mouse, mainly for CC and BP branches , and for Neighborhood mean (yeast – MF).f1– f14 and f1– f17 provide to some extent analogous results, with some differences that however seem not to be related to an underlying physical topology: for instance, Neighborhood mean has a significantly higher frequency when discarding 3Prop features on yeast CC data . Such results are confirmed also in terms of Recall. On mouse and human data, f1– f14 representation is still more informative than f1– f17 when employing RFs, performing similarly to 3Prop representation. Conversely, SVMs achieve the best results when using all features, and this is likely due to the ability of RFs in capturing the combined effect of features, thus making some of them redundant; on the other hand, SVMs need a more complex protein representation to achieve nearly the same results. SVMs also tend to have a higher Recall, while RFs are more precise. This is probably due to the adoption of cost-sensitive SVM learning, which, by attributing a larger misclassification weight to positive instances, tends to increase both the number of true and false positives.The classification performances in terms of F1 are summarized in Fig. 3Prop features have been excluded from this experiment because their effectiveness in predicting GO functions has already been assessed in [In addition, to give an insight about the impact of each feature on the automated protein-function prediction, each classification experiment was repeated removing in turn one feature and using all the remaining features to represent proteins. The results in terms of essed in . Due to Positive neighborhood (f10), whose removal causes the largest decrease in F1 values. The removal of Number of annotations (f5) leads to a significant decay for both classifiers, whereas when singularly eliminating the other features just negligible differences can be observed. These results clearly show that some features are redundant for this task, and the application of feature selection methodologies may lead to better results than those depicted in Fig. Clearly, the most informative measure is f1– f17 mean is slightly the most informative, whereas f15– f17 (3Prop) achieve the (largely) worst performance. On BP terms most feature sets perform similarly, whereas on MF data the f1– f14 set has the top performance. On human data, again f1– f14 and f1– f14mean achieve the top performance, with close results, while on mouse data the combination including all features (f1– f17) is the top performing one.Figure f1– f14 and f1– f17 feature sets are the top performing ones, likely due to the fact that eliminating even the features with low absolute frequencies wastes some useful combined effects that the RF model, for its nonlinear nature, is able to exploit. Indeed, the top 5 and mean feature sets have been selected on the basis of the absolute individual frequencies reported in Fig. 3Prop features: along with the above mentioned set of features, it represents the top performing set, as opposed to SVM results. Thus these three features, appropriately combined, may also provide information similar to that encoded in the features f1– f17. On the other side, this requires more complex selection algorithms, thus features f1– f14 are preferable when, for complexity reasons, simpler models must be adopted.Different behaviors are observed when RF model is adopted as negative selection procedure: in all the experiments, f1– f14 seem to be more informative for selection algorithms not able to capture nonlinear combined effects among feature subsets, whereas they perform similarly to the 3Prop feature set when selection methods with higher classification capabilities are adopted. Nevertheless, by excluding features f12– f14, since they are rarely selected by the feature selection algorithm, the computation of the remaining features can nicely scale when input size increases, since features f1– f9 can be computed offline, being not term-specific, and features f10 and f11 can be computed efficiently. Conversely, the 3Prop features need to simulate 6 random walks on the whole network, which also should be row-normalized, affecting thereby scalability.In summary, features AFP context. State-of-the-art graph centrality measures, GO term-aware measures, and protein multifunctionality have been considered. Term-aware features resulted more informative for selecting reliable negative proteins through a state-of-the-art feature selection method in a temporal holdout setting, where the validation is carried out on the proteins that received novel annotations in the temporal holdout period. Among the remaining features, the node (protein) betweenness showed an interesting pattern, in particular on mouse data, where it is close to being the most relevant feature. The protein positive neighborhood instead is the most predictive feature for the AFP problem . Finally, by supplying the proposed features as input to linear and nonlinear negative selection algorithms, we discovered that there is little or no redundancy among the features when their linear combination is adopted, whereas their nonlinear interaction also provides novel discriminative abilities to negative selection algorithms.Seventeen protein features in biological networks have been studied in this work to assess their ‘usefulness’ for selecting relevant negatives in the Overall, apart for those mentioned above, a clear and regular trend did not arise, thus suggesting further analyses under different settings and/or adding (discarding) some features as future investigations.Additional file 1Figure S1. Proportion of times each feature is selected by the SFFS algorithm on mouse data and CC (a-d), MF (b-e) and BP (c-f) terms. Same notations as in Fig. Additional file 2Figure S2. Performance in terms on Precision (a-b) and Recall (c-d) measures averaged across GO branch terms when proteins are represented through f1– f14, 3Prop (f15– f17), and f1– f17 features. Left and right columns correspond to SVM and RF results, respectively. (PNG 130 kb)Additional file 3Figure S3. Evaluation of the impact of features f1– f14 on the classification performance. Bars correspond to the Precision results averaged cross GO branch terms on yeast data when removing the related feature. (PNG 47 kb)Additional file 4Figure S4. Evaluation of the impact of features f1– f14 on the classification performance. Bars correspond to the Recall results averaged cross GO branch terms on yeast data when removing the related feature. (PNG 54 kb)Additional file 5Figure S5. Number of false negative averaged across GO terms on the mouse data. First (resp. second) row shows the results of the SVM (resp. RF) selection algorithm. (PNG 203 kb)


Recent reports concerning interactions between proteins and different types of polyelectrolytes, that is, linear polyelectrolytes and polyelectrolyte modified nanoparticles, are summarized with their binding differences systematically discussed and compared based on the two major titration techniques. We believe this short review could provide valuable insight in the understanding of the structure–property relationship and the design of applied biomedical PE-based systems with optimal performance.This review discussed the mechanisms including theories and binding stages concerning the protein–polyelectrolyte (PE) interaction, as well as the applications for both complexation and coacervation states of protein–PE pairs. In particular, this review focused on the applications of titration techniques, that is, turbidimetric titration and isothermal titration calorimetry (ITC), in understanding the protein–PE binding process. To be specific, by providing thermodynamic information such as pH The investigation of the interaction between polyelectrolyte (PE) and proteins remains one of the most important research fields in biotechnology. It is well-established that proteins and PEs could form complexes and coacervates/precipitates at certain conditions, driven by non-specific and non-covalent interactions, primarily electrostatic interactions ,2,3. ComTo understand the protein–PE interaction, different analysis methods, such as dynamic light scattering (DLS) , small-aOn the basis of the thermodynamic studies on the interaction between proteins and PE for both linear and colloidal, we discussed the mechanisms explored by thermodynamic analysis and possible applications of protein–PE interactions in this short review. In particular, we briefly reviewed two theories significantly promoted by Paul Dubin, that is, charge regulation and charge anisotropy theory, and three binding stages in protein–PE binding, and explored the application of titration techniques, that is, turbidimetric titration and ITC, in understanding the protein–PE binding process. We hope this review can promote the understanding of the protein–PE complexation process and provide guidance for developing applied biomedical PE-based materials with optimal performance. In this section, we discussed the microscopic process behind the protein–PE complexation, as well as analytical methods to characterize these processes. In particular, the application of titration techniques, for example, turbidimetric titration and ITC, in understanding the protein–PE interaction process has been extensively reviewed.pI”. According to charge regulation theory in pH > pI. Bonsson et al. utilized this theory to analyze different protein–PE binding and proved its effectiveness by Monte-Carlo simulations, especially at lower ionic strength . Th. Th34]. pI” between protein and SPB could be clearly observed and could be attributed to the entropy-driven process because of counter ion release [Among various PE-modified nanoparticles, spherical polyelectrolyte brushes have been widely used in proteins because of their high loading capacity, stable micro-environment, and tunable performance. Ballauff et al. firstly used SPB as nanocarriers for proteins and studied their interaction via DLS, small angle X-ray scattering (SAXS), and ITC supplemented by model simulation ,28,67. B release . However release . Interes release ,69. With release . It is n release ,72,73, sH/T△S) obtained by ITC exhibited a linear relationship, revealing the resemblance between nanoparticle–protein and protein–protein bindings.In addition to selective binding and loading of proteins, the studies of nanoparticle–protein binding is of vital importance to their biomedical applications, because nanoparticles would preferably interact with plasma proteins such as serum albumin, and the corona around nanoparticles would ultimately affect its biological fate during circulation . Gold naOn the basis of different binding states discriminated by titration, the protein–PE interaction could be applied for different purposes. In general, the formation of a soluble protein–PE complex could endow the system with the capability to immobilize proteins for various purposes, while the coacervate or precipitate state could be utilized for protein purification by selective phase separation. To develop novel PE-based advanced materials, thermodynamic studies could provide guidance for optimizing performance for their application.As mentioned above, turbidimetric titration could help identify three different stages for protein–PE bindings, and the intermediate complexation state could be harvested to immobilize and stabilize proteins because it could prevent protein from further aggregation via electrostatic repulsion. For example, Wang et al. observed a large range of plateau during turbidimetric titration between SPB and BLG, which could be attributed to the repulsion between complexes with the same charge . Both syAs the PEs could provide proteins with a stable micro-environment and help preserve their normal functions in the second binding stages, enzymes have great potential to be incorporated into PE-based systems for various catalytic situations. At the same time, ITC can be applied to evaluate the loading capability by measuring binding constant and stoichiometry. For example, Xu et al. loaded amyloglucosidase into the brush layers of magnetic spherical polyeletrolyte brushes. According to ITC results, strong binding between enzymes and SPB could be clearly observed even on the “wrong side” of binding. In this way, enhanced enzymatic activity and magnetic recyclability could be achieved simultaneously .Moreover, PEs and charged nanoparticles could interact differentially with different proteins during complexation stages and this difference in binding affinity, as revealed by ITC, could be utilized to generate fluorescent , colorimc and ΔpHφ, could be modulated by changing ionic strength. By choosing the appropriate condition with the largest ΔpHφ and forming phase separation between PDADMAC and mixed proteins , the supernatant and coacervates feature totally different composition with relative purity increased to 90%. Moreover, the variants of BLG, BLG-A, and BLG-B could be separately condensed at the coacervate and supernatant phase after phase separation between native BLG and PDADMAC (shown in PEs could be utilized to obtain target proteins from their mixtures by forming coacervates selectively under certain conditions. According to charge anisotropy theory, proteins feature a heterogeneous surface dotted with different charge patches and hydrophobic domains. Therefore, non-specific interactions, including electrostatic and hydrophobic interactions of Pes, have the potential to achieve selective binding and phase separation with proteins. In fact, a certain degree of selectivity toward proteins has been achieved by both linear PE chains  and PE-mshown in . The purIn this review, we have described recent developments on the understanding of protein–PE interactions using titration methods, which provide guidance for various application purposes with an in-depth understanding of the interactions. The applications of titration techniques of turbidimetric titration and ITC in protein–PE binding studies have been systematically reviewed. On the basis of thermodynamic studies on the binding between proteins and PE, both linear chains and nanoparticles, the protein–PE interaction could be utilized for various biomedical applications such as protein immobilization and protein purification. As structural uncertainties and heterogeneities still prevail in complicated PE systems, as well as in proteins, a thorough understanding of the structure–property relationship still remains a challenge. In addition, although various types of PEs and proteins have been studied thermodynamically, the experimental conditions, such as stoichiometry, pH, and ionic strength, varied greatly, leading to fragmented ideas and great difficulties in establishing general rules and theories. To address these problems, binding interfaces with well-defined and controllable structures are required and a relatively uniform standard for protein–PE binding characterizations should be established so that different studies could be compared and combined. Moreover, the current titration techniques still suffer from some drawbacks, such as dependence on model selection and accurate mole concentration calculation. Therefore, they need to be cross-validated by other complementary characterizations and computational simulations. Currently, most of the studied protein–PE complexation and coacervation are electrostatically driven and the effecte of other non-specific interactions, such as hydrophobic interaction and hydrogen bonds, are still unclear. Therefore, further studies in this area could focus on the verification of the relative contributions of separation interactions, which are still rather challenging at the moment. The traditional protein–PE models could be also expanded to more complicated systems such as drugs, enzymes, and antibodies for proteins. In addition, more research attention should be paid to PE-modified nanoparticles, because the nanoparticle–protein interaction studies nowadays mainly focus on monolayer protected nanoparticles and spherical polyelectrolyte brushes. The accumulation of PE chains on nanoparticles has great potential to enlarge the discrimination in binding with proteins, endowing the system with an improved application prospect. In a word, despite the current drawbacks and limits, with deepening understanding of the structure–property relationship, protein–PE interaction could be applied to further develop biomedical PE-based materials with smart and optimal performance.


Interactions between drugs and proteins occupy a central position during the process of drug discovery and development. Numerous methods have recently been developed for identifying drug–target interactions, but few have been devoted to finding interactions between post-translationally modified proteins and drugs. We presented a machine learning-based method for identifying associations between small molecules and binding-associated S-nitrosylated (SNO-) proteins. Namely, small molecules were encoded by molecular fingerprint, SNO-proteins were encoded by the information entropy-based method, and the random forest was used to train a classifier. Ten-fold and leave-one-out cross validations achieved, respectively, 0.7235 and 0.7490 of the area under a receiver operating characteristic curve. Computational analysis of similarity suggested that SNO-proteins associated with the same drug shared statistically significant similarity, and vice versa. This method and finding are useful to identify drug–SNO associations and further facilitate the discovery and development of SNO-associated drugs. Disease is one of the most serious threats to the safety of lives. In 2006 alone, for example, 1,685,210 new cancer cases and 595,690 cancer deaths took place in the United States, and cancer was rising to become the second-leading cause of death . For anoAlthough a large number of computational methods have been proposed to predict drug–target interactions in the past decades ,17,18,19S-nitrosylation (SNO) is a type of post-translational modification where a nitric oxide is covalently attached to a cysteine residue in proteins. In addition to regulation of protein structure and functions , SNO plahttp://dbPTM.mbc.nctu.edu.tw/), an experimentally validated post-translational modification (PTM) database carbonyl]-phenylalaninyl-amino]-5-phenyl-pentane-1-sulfonic acid benzyloxy-amide (DB04427) and the tyrosine-protein phosphatase nonreceptor type 1 (P18031) protein was predicted. The small molecule DB04427 was similar to these small molecules: DB06887, DB07719, DB08003, DB08549, DB08591, DB08593, and DB02827, which all targeted the SNO-protein P18031. Thus, it seemed a rational to identify the association of DB04427 with P18031. The protein aldose reductase (P15121) catalyzes the NADPH-dependent reduction of a wide variety of carbonyl-containing compounds to their corresponding alcohols with a broad range of catalytic efficiencies [N-methyl-8-hydroguanosine-5′-diphosphate (DB01960) belongs to a type of organic compounds known as purine ribonucleoside diphosphates. The fact that the small molecule DB01960 was similar to the molecules DB02338 and DB03461, which target the SNO-protein P15121, supported predicted DB01960–P15121 associations to a certain extent. The SNO-protein cathepsin K (P43235) was closely involved in osteoclastic bone resorption and may participate partially in the disorder of bone remodeling. The small molecule l-citrulline (DB00155) was predicted to bind the SNO-protein cathepsin K. l-citrulline shares structural similarity with the small molecules DB04276, DB04523, and DB07592, which were associated with P43235. Thus, it seemed a natural inference to predict the DB00155–P43235 association. We indirectly explained the rationality of the above predicted SNO–drug associations in terms of molecular similarity. Due to limitations of conditions, we did not conduct wet experiments to validate these associations, which will be left for experimental biologists to validate in the coming future.In total, 147 of the randomly yielded negative samples in the section “Experimental data” served as negative training samples, and the remaining 331 were used as the testing samples see . Of the ciencies ,33. The For drug discovery and development, it is one of most important things to find protein targets of drugs. Although a large number of approaches have been proposed to detect new targets of drugs in the past decades ,76,77,78N-methyl-8-hydroguanosine-5′-diphosphate (DB01960) have a similarity value of 0.8358, but they were associated with different SNO-proteins. Namely, DB01960 is associated with the proteins eukaryotic translation initiation factor 4E type 3 (Q9DBB5), and DB02082 with Ras-related C3 botulinum toxin substrate 1 (P63000). The binding of the drug to the target might be subject to key substructures. Although highly similar, the small molecules DB01960 and DB02082 might lack common key substructures to bind proteins.In the areas of bioinformatics, there is a common hypothesis called the GBA principle . The comSNO-proteins are involved in the pathological processes of some diseases. There is no doubt that the identification of drug–SNO associations is helpful to discover and develop new drugs to treat SNO-mediated disease. We, for the first time, present a machine learning-based computational method to predict associations between drugs and SNO-proteins. The method is simple to implement but quite efficient. We statistically showed that SNO-proteins associated with the same drug would share high similarity, and vice versa. The finding would be useful in detecting drug-associated SNO-proteins and SNO-protein-associated drugs by the similarity search.