Identification of the structural domains of proteins is important for our understanding of the organizational principles and mechanisms of protein folding, and for insights into protein function and evolution. Algorithmic methods of dissecting protein of known structure into domains developed so far are based on an examination of multiple geometrical, physical and topological features. Successful as many of these approaches are, they employ a lot of heuristics, and it is not clear whether they illuminate any deep underlying principles of protein domain organization. Other well-performing domain dissection methods rely on comparative sequence analysis. These methods are applicable to sequences with known and unknown structure alike, and their success highlights a fundamental principle of protein modularity, but this does not directly improve our understanding of protein spatial structure.We present a novel graph-theoretical algorithm for the identification of domains in proteins with known three-dimensional structure. We represent the protein structure as an undirected, unweighted and unlabeled graph whose nodes correspond to the secondary structure elements and edges represent physical proximity of at least one pair of alpha carbon atoms from two elements. Domains are identified as constrained partitions of the graph, corresponding to sets of vertices obtained by the maximization of the cycle distributions found in the graph. When a partition is found, the algorithm is iteratively applied to each of the resulting subgraphs. The decision to accept or reject a tentative cut position is based on a specific classifier. The algorithm is applied iteratively to each of the resulting subgraphs and terminates automatically if partitions are no longer accepted.  The distribution of cycles is the only type of information on which the decision about protein dissection is based. Despite the barebone simplicity of the approach, our algorithm approaches the best heuristic algorithms in accuracy.Our graph-theoretical algorithm uses only topological information present in the protein structure itself to find the domains and does not rely on any geometrical or physical information about protein molecule. Perhaps unexpectedly, these drastic constraints on resources, which result in a seemingly approximate description of protein structures and leave only a handful of parameters available for analysis, do not lead to any significant deterioration of algorithm accuracy. It appears that protein structures can be rigorously treated as topological rather than geometrical objects and that the majority of information about protein domains can be inferred from the coarse-grained measure of pairwise proximity between elements of secondary structure elements. Investigation of the structural organization of proteins is important for our understanding of the mechanisms of protein folding and function, and for insights into protein evolution. Direct determination of protein structures ,2 and coSeveral attempts have been made to identify the structural domains of proteins. The most straightforward approach is based on visual inspection of a structure by a human expert. However, this approach is difficult to formalize, and therefore it is not easily applicable for analysis of large data sets. Another approach is to employ comparative sequence analysis. This method benefits from the vast collection of sequences from diverse organisms and high sensitivity of database search and protein sequence alignment. The shortcomings of this method is that, first, it relies on sequence similarity and thus is not applicable when the homologous sequences are not known; second, that the problem of defining the exact borders of sequence domains is itself difficult -11; and β-sheets intact and reclaim short loops  is high if a cut does not destroy many mixed cycles.The decision function given in definition 1 was found empirically. The logical decision function n et al. , who speα1, α2, α3} has to be optimized separately to obtain a better performance. For this reason, we introduce for each cut a decision function Dα with different parameters. This is possible because the algorithm can keep track of the number of cuts and a specific form of the decision function can be applied automatically and iteratively until the procedure ends.The second argument evaluates the breakdown of the randomized objective function. Application of our algorithm to proteins consisting of one or more domains indicates that the set of parameters for {AM and FES conceived the study, FES developed and implemented the algorithm and analyzed the data, AM and FES wrote the manuscript.


By combining crystallographic information with protein-interaction dataobtained through traditional experimental means, this paper determinesthe most appropriate method for generating protein-interaction networksthat incorporate data derived from protein complexes. We propose thata combined method should be considered; in which complexescomposed of five chains or less are decomposed using the matrixmodel, whereas the spoke model is used to derive pairwise interactionsfor those with six chains or more. The results presented here shouldimprove the accuracy and relevance of studies investigating thetopology of protein-interaction networks. Saccharomyces cerevisiae. The majority of cellularprocesses are mediated by protein-protein interactions, includingsignal transduction pathways and the regulation of geneexpression. Thus protein-interaction networks have been affordedthe most attention, in the hope that knowledge of their structureand topology will help us to understand their functions andevolutionary history.The working of living cells is underpinned by an almostoverwhelming array of molecular interactions that form a complexand multifaceted network: “the interactome.” The explosivegrowth in both the type and volume of experimental data availableto researchers interested in elucidating the properties of theinteractome has led to a wide range of studies investigating anumber of the core biological networks. Networks of generegulation , metabolRecently, there have been a number of large-scaleprotein-interaction studies. Efforts have ranged from studies thatinvestigated only a subset of the protein interactome to attemptsidentifying all protein interactions within the cell . It is cGenerating this type of network representation is relatively easyfor studies employing technologies that identify interactions in abinary fashion, such as the yeast two-hybrid system Y2H . HoweverIn practice, a model is used, in which pairwise interactions areassigned by applying either a matrix- or spoke-based modellingmethodology to each complex , 13 Fig. Recentlα atoms within the chainscome within 7.5 Å of each other.The ability of the matrix model to define the real set of interactions within these complexes was then assessed by plottingthe actual number of interactions in a complex (as a percentage ofthose defined by the matrix model) against the number of uniquechains within that complex . Anautomated protocol was then used to triage the collection until aset of complexes that fulfilled the criterion for analysisremained. That is, they were at least heterotrimeric in nature, asanalysis of the connectivity of complexes with less than threeunique chains is clearly meaningless. This resulted inapproximately 900 protein complexes that were then furtherfiltered to identify and remove redundancy. Subcomplexes werecollapsed into their parents and redundant structures wereidentified by performing an all-against-all comparison of eachprotein complex. Those complexes sharing two thirds or more oftheir chains with others in the set were then removed. The 133protein complexes that remained after this triage procedure werethen subjected to further analysis. Actual physical interactionsbetween polypeptide chains within the complexes were identified bycomputational analysis of the crystal structure, using anempirically equivalent algorithm to the full atom contact (FAC)method employed by Gong et al. , with an complex .Saccharomycescerevisiae [e ≦ 1e−10, fraction of conserved residues ≧ 35), we were able to identify, and make use of, protein complexes determined in other species that are structural homologs of those found in Saccharomyces cerevisiae. After collapsing subcomplexes into their parents and removing any redundant structures, we wereleft with a set of thirteen structures that were suitable for usein the final part of our analysis. Crystallographic data for eachstructure and the FAC method were used to determine the “truetopology” of the interactions within a complex and the ability ofeach model to describe it was assessed by calculating a scorebased on the following functions:N is the number of unique polypeptide chains in the crystal structure. For the spoke model We then performed a direct comparison between the matrix and spokemodels by combining crystallographic data with protein complexdata obtained experimentally for the yeast revisiae , 17, 18.Analysis of protein connectivity within complexes over a range ofsizes revealed that those complexes composed of ≤ 5 uniquepolypeptide chains are generally appropriately described by thematrix model  thematrix model performed as well or better than the spoke model forcomplexes containing up to five unique chains. The supClearly, no single model (either matrix or spoke) can provide thetrue representation of the actual interactions that occur withinprotein complexes and we make no attempt here to state that thisis the case. Rather, we aim to suggest a method by whichexperimental data from studies elucidating protein complexes arebest processed so that they most accurately depict reality, priorto their incorporation into a global protein-interaction networkand its subsequent analysis using graph-theoretical methods.It has long been assumed that the matrix model provides arelatively poor description of the true interaction space for anygiven complex, and previous work by Bader et al. demonstrated that the spoke model was more accurate (in agreement with published literature) . The preCrystal structures of large complexes provide the best way ofvalidating the protein-protein interaction networks and fordeveloping appropriate models for integrating and interpretingdata from high-throughput studies that employ techniques like Y2Hand TAP-tagging. Although, in general, the solution of proteincrystal structures is becoming more automated, the structures ofprotein complexes must still be solved by careful and painstakingvalidation of the crystallized complex at each stage. Structuralgenomic initiatives will often systematically miss these complexesbecause they generally attempt only to produce, crystallize, andsolve the structures of individual proteins. In this light, thelack of overlap between structural data and network interactiondata, while striking, is not unexpected.It should be noted that our analysis methodology regards thestructural data deposited within the PQS database as beingrepresentative of the “real” biological unit (BU). In reality,the data provided by PQS is a prediction of the BU based on thecrystallographic asymmetric unit (ASU). However, as thesepredictions have been found to be accurate in approximately 75%of tested cases , it is uWhile the paucity of overlap between the structurally solvedprotein complexes and those determined experimentally precludedany type of rigorous statistical analysis, we believe, given theresult shown in


The multitude of functions performed in the cell are largely controlled by a set of carefully orchestrated protein interactions often facilitated by specific binding of conserved domains in the interacting proteins. Interacting domains commonly exhibit distinct binding specificity to short and conserved recognition peptides called binding profiles. Although many conserved domains are known in nature, only a few have well-characterized binding profiles. Here, we describe a novel predictive method known as domain–motif interactions from structural topology (D-MIST) for elucidating the binding profiles of interacting domains. A set of domains and their corresponding binding profiles were derived from extant protein structures and protein interaction data and then used to predict novel protein interactions in yeast. A number of the predicted interactions were verified experimentally, including new interactions of the mitotic exit network, RNA polymerases, nucleotide metabolism enzymes, and the chaperone complex. These results demonstrate that new protein interactions can be predicted exclusively from sequence information. Many functions performed within a living cell are mediated by specific interactions between proteins. Precise geometric and chemical matches between segments of the protein structures facilitate those interactions. Such binding surfaces are often evolutionarily conserved elements of protein structures known as conserved domains that recognize specific binding elements on the interacting proteins. Binding domains and their corresponding interacting profiles constitute basic interacting modules that are replicated in multiple protein pairs, where they mediate similar interactions. Although many conserved domains are identified, only a handful have known, well-characterized binding elements. This paper describes a computational method that aims to elucidate the binding specificity of many domains. The utility of the derived binding specificity is demonstrated by predicting new interactions between yeast proteins. The predictions are based solely on sequence information by identifying the conserved domains and their corresponding binding sequences. A number of the predicted interactions were confirmed experimentally, demonstrating the feasibility of this approach. The interaction between two proteins is a geometric and electrostatic match between two polypeptide surfaces that results in a stable set of bonds between amino acid side chains or backbone atoms. The interacting amino acids are often part of conserved sequence features such as domains or short linear motifs that constitute the interaction site between the two proteins. Despite the increased coverage and sensitivity of experimental techniques for detecting protein interactions –6 , is based on a two-step approach. First, potential domain-binding motifs are extracted from structural data. Second, these motifs are converted to sequence profiles in the form of position-specific scoring matrices (PSSMs). These PSSMs are derived using a subset of experimentally determined binary interactions that contain the domain of interest . Gibbs sThe library of 3-D structures of protein complexes contains a detailed description of the binding interfaces between interacting proteins that include atom contacts and residue side-chain interactions . Using mThe binding specificity of a domain is determined by a combination of physiochemical properties and structural constraints at the binding site that can be satisfied by multiple variations of the consensus sequence motif . The intWe collected a set of 87,894 nonredundant protein interactions from four databases containing binary protein interactions from multiple species. Interactions derived from structural studies were excluded to preclude self-identification, as well as high-throughput protein complexes identification experiments ,31 see . Gibbs sp = 1.0 × 10−13; The learned PSSMs were used to predict interactions for 703 yeast proteins with domains for which we successfully derived binding profiles. A physical interaction was predicted between proteins containing interacting domains and proteins with one or more of the interacting profiles associated with those domains C. A totaExperimental verification of a subset of the predicted interactions was performed by a one-step immunoaffinity purification of one of the two interaction partners, followed by mass spectrometric identification of associated proteins (IP-MS) as previously described . The IP-+) Adh7 and Prs5, the latter being a member of the PRS complex. This result suggests a possible direct link between NADP/NADPH balance, which is controlled by Adh7 [Among the experimentally confirmed predictions were interactions between the five components of the PRS complex, which together compose the 5-phosphoribosyl-1(a)-pyrophosphate synthetase enzyme (EC number 2.7.6.1). This complex is a key component in the production of the precursors for purine, pyrmidine, and pyridine nucleotides . An addi by Adh7 , and the by Adh7 . Another by Adh7 . We also by Adh7 . Additio by Adh7 .One might argue that the above successful predictions could be easily predicted from the orthology of the interacting proteins to the structural complexes used, such as the interactions between members of the PRS complex. We therefore tested several nonobvious predicted interactions that cannot be easily inferred from structural or sequence homology to other interacting pairs. The critical downstream effector of the mitotic exit network is the phosphatase Cdc14, which activates Clb degradation and Sic1 accumulation by dephosphorylation of key substrates . We confAs noted previously, we excluded additional experimental evidence, such as localization and expression data from our prediction method. Although additional experimental information and functional annotation would likely improve prediction accuracy, it may also limit predictions only to those proteins with prior experimental or functional information. In addition, the use of functional annotation such as Gene Ontology terms  in a prediction method will penalize predicted interactions between proteins with unrelated functions. Therefore, it restricts the ability to predict interactions between apparently unrelated proteins that could illuminate new cellular functions .trans-membrane and disordered domains are underrepresented due to limitations in structure determination [The D-MIST method for identifying domain-binding modules is currently limited in a number of ways. The first limitation is the availability of detailed binding information, as attained primarily through structural studies and peptide-based approaches such as phage display  and randmination ,47. Consmination . Last, mmination , the pow−6 and then converted to InterPro identifiers [The domain-binding motifs were extracted from BIND protein interaction records that were generated from 10,064 structures . Interacntifiers . Bindingj at position i in the PSSM  is computed as follows:i,jc is the observed counts of residue j at position i in the sampled proteins, jb is pseudocounts for residue j, N is the number of sequences sampled, and B is the total number of pseudocounts for all residues. By increasing the pseudocount term (jb) for specific positions in the PSSM, the sampling algorithm is biased to favour positions where the residue at position i in the sampled protein is similar to the residue at position i of the structural motif. We set the pseudocounts to equal 62% of the residue counts in the sampled proteins.A total of 87,894 nonredundant protein interactions were collected from 204 species from four database sources: BIND , DIP 5353, Mint Two proteins were predicted to interact if one protein had a domain and a second protein matched one or more of the binding profiles for that domain C. We atthttp://www.invitrogen.com). Bait complexes were immunopurified on anti-FLAG M2 antibody resin, resolved by denaturing gel electrophoresis, and visualized by colloidal Coomassie stain. Protein identification by automated liquid chromatography tandem mass spectrometry on a Finnigan LCQ DECA ion trap  mass spectrometer was as described previously [3 epitope fusions and detection with 12CA5 anti-HA or 9E10 anti-Myc monoclonal antibodies, respectively . The probability of the observed overlap between the predicted interactions and the literature curated is approximated by a Poisson distribution. A random variable Y has a Poisson distribution ifλ = Np, N is the sample size, and p is the probability of a single event; i.e., the probability of selecting a true interaction by random chance. In the current analysis, N is the number of predicted interactions , y is the number of literature-validated predictions (609), and p is the probability of predicting a correct interaction by random chance for the 703 proteins for which interactions were predicted. The value of p is approximated as the frequency of true interactions among all possible protein pairs that were considered. Since there is no known complete set of interactions for any reference organism, we cautiously assume an upper bound of 100 physiological interactions per bait protein. This number is likely an order of magnitude larger than the true value. Potential interactors for the 703 proteins containing domains with derived binding profiles were identified by scanning the entire yeast proteome  for proteins that matched the domains binding profiles. Hence, the total number of proteins pairs that were considered  is 703 × 6,000. The value of p is then P (y ≥ 609) under a Poisson distribution is 1.0 × 10−13. Similar calculation using a hypergeometric distribution (sampling without replacement) yields a p-value of 1.0 × 10−8.The predicted interactions were compared to a new set of yeast curated interactions collected from more than 50,000 abstracts and publications  (availabDataset S1http://www.cytoscape.org.A Cytoscape session file containing the complete set of predicted interactions as well as the networks in (2.0 MB ZIP)Click here for additional data file.Figure S1The predicted interactions were compared to a new and exhaustive set of curated interactions extracted from the literature that includes physical interactions from both high-throughput and directed studies as well as genetic interactions. The overlap contains 609 interactions that represent ∼3% of the predicted interactions. Proteins are coloured according to Gene Ontology biological process annotation.(519 KB PDF)Click here for additional data file.Figure S2Bait proteins were purified using FLAG antibodies, and their interacting proteins were detected by antibodies specific to C-terminal HA or Myc3 epitopes.(325 KB PDF)Click here for additional data file.Text S1http://www.people.fas.harvard.edu/~junliu/index1.html#Computational_Biology.Each domain-binding profile is specified as a list of sequence motifs. The sequence motifs are used as input to a PSSM search program . Source (2.7 MB TXT)Click here for additional data file.


One main research challenge in the post-genomic era is to understand the relationship between protein sequences and their biological functions. In recent years, several automated annotation systems have been developed for the functional assignment of uncharacterized proteins. The underlying assumption of these systems is that similar sequences imply similar biological functions. However, it has been noted that matching sequences do not always infer similar functions.In this paper, we present the correlation between protein sequences and protein functions for the yeast proteome in the context of gene ontology. A novel measure is introduced to define the overall similarity between two protein sequences. The effects of the level as well as the size of a gene ontology group on the degree of similarity were studied. The similarity distributions at different levels of gene ontology trees are presented. To evaluate the theoretical prediction power of similar sequences, we computed the posterior probability of correct predictions.The results indicate that protein pairs of similar biological functions tend to have higher sequence similarity, although the similarity distribution in each functional group is heterogeneous and varies from group to group. We conclude that sequence similarity can serve as a key measure in protein function prediction. However, the resulting annotations must be verified through other means. A method that combines a broader range of measures is more likely to provide more accurate prediction. Our study indicates that the posterior probability of a correct prediction could serve as one of the key measures. The human genome project and numerous other genome projects have produced a large and ever increasing amount of sequence data. One of the main research challenges in the post-genomic era is to understand the relationship between the nucleotide sequences of genes and the functions of the proteins they encode. Traditionally, the functional annotation of genes has been done manually by experienced individual curators with the help of advanced searching tools. However, to unlock the potential of the huge amount of genomic-wide sequence data, it is necessary to develop large-scale approaches for the functional assignment of uncharacterized proteins -10. In rThe Gene Ontology (GO) consortium provides a vocabulary to describe gene and gene product attributes in any organism . GO inclSince the establishment of GO, many ontology-based sequence annotation approaches have been developed -23, inclIn this study, we investigate the mathematical underpinnings of the automated sequence annotation approaches that are based on sequence similarity and gene ontology. We explore the structures of the three ontology categories and re-evaluate the assumption that similar sequences give rise to similar biological functions. We introduce a novel measure of overall similarity between two protein sequences based on a set of local BLAST alignments. Using the complete proteome from the model organism yeast, we study the degree of overall similarity of yeast protein sequences in each functional group defined by GO terms. We examine the effects of the level of GO terms and the size of GO groups on the degree of similarity. We present the sequence similarity distributions at different levels of GO DAGs and the distributions of siblings of GO groups. To evaluate the theoretical prediction power of similar sequences, we compute the posterior probability of the hypothesis that protein A possesses the same biological function as protein B, given B's biological function is known and A and B are similar.p-values were calculated based on a novel measure (Equation (2) in Methods section) of overall similarity of two protein sequences. The distributions of the p-values are shown in Table p-value distribution of protein sequence pairs from the complete yeast proteome. This distribution serves as a control for the distribution of the whole population. The second, third and fourth columns show the distributions for sequences annotated for biological processes, molecular functions and cellular components, respectively. As we can see, the four distributions are quite similar, indicating that the annotated proteins in each of the three gene ontology categories provide a representative sample set of sequences from the complete yeast proteome. On the other hand, we clearly see that the majority of sequence pairs are not similar. Only about 4% of the sequence pairs have p-values less than 0.01.All-to-all pair-wise protein sequence local alignments were performed using the alignment tool for blasting two sequences (I) which was retrieved from the NCBI ftp site . The p-vThe distributions of the number of GO groups at different levels of the gene ontologies are shown in Figure p-value distributions of protein sequence pairs annotated for molecular function, biological process and cellular component GO terms at different levels of GO categories. Each curve in the figures represents the percentages of sequence pairs of less than or equal to a certain p-value across different levels of GO categories. Some curves do not include the percentages for all levels because no sequence pair on those levels has a p-value less than or equal to certain thresholds. For the sequences annotated for molecular function and cellular component GO terms, we see clearly that the majority of the sequence pairs are considered non-similar throughout the levels. Over 59% of sequence pairs at all levels have p-values greater than 0.01. However, the number of similar sequence pairs does increase steadily with their GO levels. In particular, the percentage of pairs with high similarity scores (p ≤ 10-10) has a steep increase from the root level to level 5. Level 9 has the highest percentage of similar pairs for molecular function ontology. At this level over 35% of the sequence pairs have similarity p-values less or equal to 10-3 while for levels 5 through 8, over 13% of the sequence pairs have p-values less or equal to 10-3. These percentages are significantly higher than the 1.8% extracted from the p-value distribution of the entire population of sequence pairs annotated for molecular functions  at levels 5 or above than those at levels below 5. For the biological process ontology, the increase of the number of similar pairs starts to level off around level 7, apparently much higher than for molecular function and cellular component ontologies. About 6.2% of pairs at levels 7 through 11 have the similarity p-values less than and equal to 10-3, compared to an average of 1.74% at levels below 7. Similar to the two other ontologies, there are significantly more pairs annotated for biology process GO terms having high similarity scores (p ≥ 10-10) at levels 7 and above than at levels below 7.Figures p-value distributions of sequence pairs for each GO group of the three ontologies are shown in the supplement tables I, II, III . This result indicates the strong correlation between sequence similarity and function similarity/specificity.The complete p-values less than or equal to 10-5 for molecular function ontology is about -0.124. The coefficients for biological process and cellular component are -0.137 and -0.136, respectively. As an example, the protein kinase activity group has 94 annotated sequences. About 70% of the 4371 sequence pairs have p-values less than or equal to 10-5. On the other hand, the nucleobase, nucleoside, nucleotide kinase activity group has only 10 annotated sequences. Only 10 out of the 45 pairs have p-values less than or equal to 10-5, although both groups are at the same level (level 5) of the molecular function ontology tree. The fact that most child groups have higher similarity scores than their parents might be the main factor contributing to the weak negative correlation between sizes and similarity scores.The dependence of sequence similarity on group size was also examined. No strong correlation was found although there is a vague trend of increasing degree of sequence similarity as the group gets smaller. The Pearson correlation coefficient of group size versus percentage of sequence pairs with p-value distributions of sequence pairs for the branch are shown in Table p-value less than or equal to 10-100, one can almost be certain that the protein with that query sequence belongs to the nucleotide kinase activity group. On the other hand a hit to the protein kinase activity group with the same p-value would carry only 13% of the confidence that the protein belongs to the group. We believe that the high degree of variation observed in the posterior probabilities indicate that the posterior probability could serve as a key measure in protein function predictions.The above results indicate that proteins of similar biological functions tend to have higher sequence similarity. The level of GO groups on a gene ontology tree depicts to a certain degree the functional similarity of the groups, although it's far from being able to accurately characterize the relationship between protein sequence similarity and biological function similarity. To evaluate how much protein sequence similarity can contribute to biological function prediction, we computed the posterior probabilities of correct predictions using equation 4). The results for the protein kinase activity branch of the molecular function ontology tree are presented in Table . The resp-value distributions of sequence pairs in GO groups are heterogeneous and vary from group to group. We conclude that sequence similarity can serve as one of the key measures in protein function prediction. However, the results do not directly translate into a high confidence of the function prediction provided by automated protein annotation systems that are solely based on sequence similarity and GO definitions. These methods can serve as a preliminary tool for functional predictions. The resulting annotations have to be verified through other means. A method that combines a broader range of measures, including sequence similarity, GO definitions, gene expression patterns, as well as available knowledge of the organism under study, is more likely to provide more accurate function prediction. Our study indicates that the posterior probability of a correct prediction could serve as one of those key measures.In this paper, we studied the correlation between protein sequence similarity and function similarity for the yeast proteome in the context of the three gene ontologies. The results indicate that protein pairs in a GO group tend to have higher sequence similarity than a randomly drawn sequence pair, although the Sacchyromyces cerevisiae) proteome was obtained from Swiss-Prot [st of 2005, there are 19094 GO terms including 9856 biological process terms, 7559 molecular function terms, and 1679 cellular component terms. Among the 6467 protein sequences, 4175 are annotated with 1084 biological process terms, 3317 are annotated with 1060 molecular function terms, and 4735 are annotated with 354 cellular component terms.The complete yeast  in the list to measure the overall similarity of the two protein sequences, we use the following score S to measure the overall similarity of two sequences:Sequence similarities can be measured through pair-wise global alignments or local alignments. Homologous protein sequences are usually similar over active domains and thus share common folds and functions. Therefore, local alignment is a more appropriate method for comparing protein sequences for their functional similarity. There are several local alignment schemes for comparing protein sequences, including BLAST that can be used together with different scoring systems such as BLOSUM62 and BLOSUM80. The program returns a list of local alignments of certain statistical significance. However, how to measure the overall similarity of two protein sequences is not obvious. For example, proteins with two similar domains with certain similarity scores could be considered to be much more similar than proteins with only one domain with a higher similarity score. In this study, we introduce a novel measure of overall similarity of two protein sequences. We utilize the alignment tool for blasting two sequences to obtain the list of optimal local alignments. Let {S stands for the probability of finding a high-scoring segment pair (HSP) with a local alignment score of at least Si, and Ei is the expected number of HSPs of score at least Si and can be obtained directly from the alignment tool. Assuming the HSPs are independent of each other, the p-value:where S1, ..., Sn}. The corresponding E-value for the overall similarity  therefore can be written as:measures the probability of finding a pair of protein sequences with a list of scores at least {E = -ln(1 - eS-).     (3)p-values and the E-values to measure the overall similarity of a pair of protein sequences. Since when |x| < 1, -ln(1 - x) = x + x2/2 + O(x3), the E- and p-values are essentially the same when they are small. For example, when p = 10-5, |p - E| is of order 10-10. For convenience, we use p-values to present our results in this paper. The alignment tool used for blasting two sequences (b12seq) was retrieved from the NCBI ftp site [We use the ftp site . We usedGO terms in each of the three ontology categories were parsed and stored in a tree structure similar to the one used in AmiGO  to form To evaluate how much protein sequence similarity can contribute to biological function prediction, the posterior probabilities of correct predictions can be computed using Bayes' theorem :ε represents the p-value threshold for a sequence pair s1 and s2, while the p-value p is calculated based on equation (2).where G represents a GO group, ZHD proposed the research idea, designed and implemented the research approaches, and drafted the manuscript. BH participated in the implementation of the research approaches and the result analysis. LR contributed to the idea of introducing a novel measure for the overall similarity of two protein sequences and participated in the result discussion and the manuscript writing. DMP and TS participated in developing the research idea, provided the explanation of the biological meaning of the results, and contributed to the manuscript writing. All authors read and approved the final manuscript.The p-value distribution of sequence pairs in GO groups of molecular function ontology. The p-value distribution of sequence pairs in GO groups of molecular function ontology. This file contains the p-value distribution of sequence pairs in all GO groups of molecular function ontologyClick here for fileThe p-value distribution of sequence pairs in GO groups of biological process ontology. The p-value distribution of sequence pairs in GO groups of biological process ontology. This file contains the p-value distribution of sequence pairs in all GO groups of biological process ontologyClick here for fileThe p-value distribution of sequence pairs in GO groups of cellular component ontology. The p-value distribution of sequence pairs in GO groups of cellular component ontology. This file contains the p-value distribution of sequence pairs in all GO groups of cellular component ontologyClick here for file


Elucidating biological networks between proteins appears nowadays as one of the most important challenges in systems biology. Computational approaches to this problem are important to complement high-throughput technologies and to help biologists in designing new experiments. In this work, we focus on the completion of a biological network from various sources of experimental data.S. cerevisiae: a protein-protein interaction network and an enzyme network. In both cases, we obtained results competitive with existing approaches. We also show that our method provides relevant insights on input data regarding their potential relationship with the existence of interactions. Furthermore, we confirm the biological validity of our predictions in the context of an analysis of gene expression data.We propose a new machine learning approach for the supervised inference of biological networks, which is based on a kernelization of the output space of regression trees. It inherits several features of tree-based algorithms such as interpretability, robustness to irrelevant variables, and input scalability. We applied this method to the inference of two kinds of networks in the yeast Output kernel tree based methods provide an efficient tool for the inference of biological networks from experimental data. Their simplicity and interpretability should make them of great value for biologists. In this domain, the main challenge is to infer the structure of the networks from all available data for a given organism. Both supervised and unsupervised methods have been proposed to address this problem. Unsupervised methods derive some interaction score for each protein pair on the basis of single or multiple sources of data . The gra  be an undirected graph with vertices V and edges E ⊂ V × V·|V| = m is the number of nodes in the graph. We suppose that each vertex vi , i = 1...m, can be described by some features in some input space x(vi) = xi ∈ Gn =  of G is available during the training phase: without loosing generality, we enumerate the nodes belonging to Vn as v1,....,vn where n is the number of nodes in the subgraph denoted by Gn =  with Vn ⊂ V and En = { ∈ E|v, v' ∈ Vn}. The goal of supervised graph inference is then to determine from the knowledge of Gn a function e(x(v), x(v')): V × V → {0,1}, ideally such that e(x(v), x(v')) = 1 ⇔  ∈ E.Let k: V × V → k = ⟨ φ(v), φ((v')⟩. To solve the problem of graph inference, we first define a kernel k such that adjacent vertices lead to high values of k and non-adjacent ones lead to smaller ones. The mapping of this kernel is thus such that φ(v) is close to φ(v') in v and v' are connected. Then, the problem of graph inference may be solved as follows: from the n × n Gram matrix K with Ki, j = k and the input feature vectors xi, find an approximation of the kernel values between pairs of new vertices described by their input values. A graph on unseen vertices is then obtained from the learnt kernel by connecting those vertices that correspond to a kernel prediction above some threshold.Following  and 5],,5], our k between nodes vi and vj as the -element of the matrix K = exp(-βL), where L = D - A is the Laplacian matrix of the graph, with D the diagonal matrix of node connectivities and A the adjacency matrix, and β > 0 is a user-defined parameter that controls the degree of diffusion. With respect to the adjacency matrix, the diffusion kernel defines a more global and smoother similarity measure between two nodes that takes into account all paths in the graph (even non direct) between these two nodes. When β increases, the kernel diffuses more deeply into the graph, making distant vertices in the graph closer in A natural kernel between nodes of a graph is the diffusion kernel proposed in . It defiOutput Kernel Trees  are a kv1,...,vn} described by their input vectors xi = x(vi), i = 1,...,n and a Gram matrix K with Ki,j = k, the idea of our method is to recursively split the training set with binary tests based on the input features. A test T is a boolean function of the input feature vector that usually involves only one feature at the same time: for a numerical variable, it compares its value to a threshold and for a categorical variable, it checks whether its value belongs to a subset of all possible values of the variable. Each split of a tree node aims at reducing as much as possible the variance of the output feature vector ϕ(v) in the left and right subsets of graph vertices corresponding to the two issues of the test.  Given the definition of the output kernel, this amounts at dividing the set of vertices corresponding to that node into two subsets in which vertices are as much as possible connected between each other in the training graph.Our algorithm follows the main steps of the CART algorithm . StartinT given the local learning sample S at the current node is defined as follows:More precisely, the score used to evaluate and select a test N is the size of S, Sl and Sr are its left and right successors of size Nl and Nr respectively  and var{ϕ(v)|S} is the empirical variance of the output feature vector in the subset S, computed using the kernel trick by:where S (ie. variance (2) is null) or some stopping criterion is met .Like in the standard CART algorithm, an exhaustive search is carried out at each tree node to find the test that maximizes this score. The splitting of a node is stopped when the output feature vector is constant in x(v)) of the output feature vector ϕ(v) corresponding to a vertex v from its input vector x(v). The loss function that it minimizes (in average) over the learning sample is the square distance in x(v)) - φ(v)||2.By analogy with regression trees, this algorithm actually tries to find implicitly an approximation L of the tree is labeled with a prediction L in Again, by analogy with regression trees, each leaf NL is the number of learning cases that reach this leaf. Our final goal however is to make predictions about the kernel value between two vertices v and v' described by their input vectors x(v) and x(v'). Let us suppose that x(v) (resp. x(v')) reaches leaf L1 (resp. L2) that contains vertices v and v' is approximated by:where v and v'.which makes use of kernel values only. Then, this kernel can be thresholded to make a prediction about the existence of an edge between By construction, our method, called Output Kernel Trees (OK3), shares several features of standard tree-based methods. The most attractive ones being the interpretability of the model and the ability of the method to rank the features (see below).While useful for interpretability reasons, single trees are usually not competitive with other methods in terms of accuracy, essentially because of their high variance. Thus, in the context of classification and regression problems, ensemble methods have been proposed to reduce variance and improve accuracy. In general, these methods grow an ensemble of diverse trees instead of a single one and then combine in some fashion the predictions of these trees to yield a final prediction. Among these methods, those which only rely on score computations to grow the ensemble of trees and which combine predictions by simply averaging them, can be directly extended to OK3. As a matter of fact, the prediction of an ensemble of trees in posed in . In thisposed in  for the N × Score (see Eqn. 1), and by summing these reductions. Thus, attributes that do not appear in a tree have an importance of zero, and those that are selected close to the root nodes of the trees typically receive high scores.An important feature of tree-based methods is that they can be exploited to rank attributes according to their importance for predicting the output value. The computation of this ranking is especially interesting with ensemble methods which are not interpretable by themselves. In the context of OK3, we propose to compute the importance of an attribute by computing for each split  where the attribute is used the total reduction of variance brought by the split, which is actually S. cerevisiae. The first one is a network of physical protein-protein interactions borrowed from [We carry out experiments on two kinds of protein networks in the yeast wed from  that conwed from . It is cwed from  by 4] a aS. cerewed from  and subswed from .) 184 prβ of the diffusion kernel was fixed to 3.0 for the protein-protein interaction network and to 1.0 for the metabolic network. We have nevertheless tried different values of β ∈  but did not notice any important change in accuracy.As described in the Methods section, both networks were smoothed by a diffusion kernel. For comparison purpose with  and 4],,4], the Different sources of data could be used for the inference of these biological networks. Experimental data obtained from various large scale methods are natural candidates but other kinds of data such as GO or KEGG annotations have also been used for this task . In thisWe considered two sets of gene expression data. The first dataset comes from the study in  and the The existence of orthologs of a given gene in a set of species is potentially an important source of information for the prediction of biological networks. In our experiments, we use the phylogenetic profiles gathered by . They weThe localization of a protein in the cell is also potentially influencing its interactions with other proteins. The vector of features in this case consists of 23 binary values coding for the presence/absence of the protein in a given intracellular location. This data was obtained from the experiment in .Such data is considered as a very noisy version of the true protein-protein interaction network and has been shown to contain many false positives. In our experiments, we use the networks obtained from the assays in  and 17]17].β = 1.0. This kernel is then transformed into a input feature vector for each protein by computing the first 50 directions with kernel PCA.Because of its pairwise nature, this kind of data can not be directly handled by tree-based methods that require that all proteins are described by an input feature vector. To still accommodate with it, we use the following procedure: following , we consFor both networks, we use an ensemble of 100 output kernel trees grown with the extra-trees method with default parameters. To match the protocols used in  and 5],,5], we eWe analyze ROC curves obtained by varying the threshold, the true positive rate being the proportion of existing edges correctly predicted and the false positive rate the proportion of non existing edges erroneously predicted. We  average the ROC curves obtained on the different folds and we also compute (average) areas under the ROC curves .We distinguish two types of edges for the computation of ROC curves: edges connecting an unseen protein  to a seen protein  and edges connecting an unseen protein to another unseen protein (TF vs TF). We expect that the latter will be more difficult to predict than the former. Hence, we compute in each experiment three ROC curves and AUC values: the ROC curve computed on TF vs TF edges, on TF vs LF edges, and on both kinds of edges simultaneously. The TF vs. LF and TF vs. TF ROC curves with different sets of variable are given in Figure Overall, the results are quite good. They are better for the protein-protein interaction network than for the metabolic network. The way the method exploits each data source is very different in both networks. For the protein-protein interaction network, the most important source of information is the expression data followed by the y2h network, localization data, and phylogenetic profiles. For the prediction of the metabolic network, the most important source of information is the phylogenetic profiles followed by the expression data. Localization and y2h data are on the other hand not very useful on this latter database. On both networks, combining all data sources allows to improve the AUC values with respect to the use of each data source separately. As expected, TF vs. LF edges are easier to predict than TF vs. TF edges. The difference between the two kinds of edges is however less important on the protein-protein network than on the metabolic network.This difference in AUC between the two networks probably reflects the biological significance of the input data. Actually, localization and y2h data directly reflect protein-protein interactions. In contrast, though interacting proteins belong per se to a same metabolic pathway, the inverse is not true. Indeed, non interacting proteins can participate to distant steps of a same pathway. In that case the localization and y2h network data would poorly contribute to prediction. Phylogenetic profiles are related to protein-protein interactions as well as pathway distribution since one expects all enzymes of the same pathway to be conserved or lost during evolution. The order of the different data set contributions to prediction nicely reflects all these biological constraints. Interestingly, expression data appear to be a good predictor for protein-protein interactions. This result could reflect the requirement that different partners of a protein complex should be co-expressed.For comparison, the last column of Table Looking at the AUC obtained when integrating all data sources (except y2h for the metabolic network that was not used in ), we getKernel-based methods are usually not as efficient as tree-based ensemble methods to detect irrelevant inputs . This may explain why they are not as good as our tree-based ensemble method on the expression data, which potentially contain irrelevant and noisy information. On the other hand, tests on phylogenetic variables in our trees are based on the presence or the absence of an ortholog protein in only one organism at a time. For the prediction of protein-protein interactions, the whole profile should be considered and hence these very local tests are somewhat inappropriate. For the prediction of the metabolic network, however, it is known that different organisms have developed different pathways.Hence, the presence of an ortholog of the protein in a given organism is potentially informative. This may explain why our trees make a better use of phylogenetic profiles for the metabolic network than for the protein-protein network, while the opposite is true for kernel-based methods.One of the main advantages of our tree-based approach is that it provides interpretable results. We illustrate this feature in this section., where N is the number of proteins in its cluster and p is the percentage of protein pairs that interact in the cluster. For comparison, the percentage of interactions in the whole learning sample is 0.5%. Of course, since the problem is quite difficult and noisy, several leaves do not correspond to significantly connected proteins. We projected the more significant leaves (arbitrarily defined as those that contain more than 5 proteins and 5% of connections) on the protein-protein interaction network . However, their positions in the inferred network suggest that they participate in ribosome biogenesis. For some of them, it is indeed possible to find some clues that they are related to this process. For example, YNL175C shares some sequence similarity with YOL041C, which is itself involved in ribosome biogenesis. As a strong evidence in favor of our prediction, we note that a recent computational analysis  based onWe proposed a new method for the supervised inference of biological networks. This method is based on a kernelization of the output space of tree-based methods. It yields competitive results with respect to full kernel-based methods on a protein-protein interaction network and on an enzyme network. In addition, it provides interpretable results in the form of a rule based clustering of the network and a ranking of the variables according to their importance at predicting new edges. The ability to discover new information about unannotated proteins was further illustrated on a small-scale study. These results suggest that our tool could be helpful to point out proteins that are worth further experimental investigations.PG developed the algorithm, carried out the experiments, and drafted the manuscript. FAB coordinated the collaboration, participated in the design of the algorithm, and helped in writing the manuscript. NT and MD helped in collecting and interpreting the data and did the biological validation of the results. All authors read and approved the final manuscript.


Identification of protein interaction networks has received considerable attention in the post-genomic era. The currently available biochemical approaches used to detect protein-protein interactions are all time and labour intensive. Consequently there is a growing need for the development of computational tools that are capable of effectively identifying such interactions.Here we explain the development and implementation of a novel Protein-Protein Interaction Prediction Engine termed PIPE. This tool is capable of predicting protein-protein interactions for any target pair of the yeast Saccharomyces cerevisiae proteins from their primary structure and without the need for any additional information or predictions about the proteins. PIPE showed a sensitivity of 61% for detecting any yeast protein interaction with 89% specificity and an overall accuracy of 75%. This rate of success is comparable to those associated with the most commonly used biochemical techniques. Using PIPE, we identified a novel interaction between YGL227W (vid30) and YMR135C (gid8) yeast proteins. This lead us to the identification of a novel yeast complex that here we term vid30 complex (vid30c). The observed interaction was confirmed by tandem affinity purification (TAP tag), verifying the ability of PIPE to predict novel protein-protein interactions. We then used PIPE analysis to investigate the internal architecture of vid30c. It appeared from PIPE analysis that vid30c may consist of a core and a secondary component. Generation of yeast gene deletion strains combined with TAP tagging analysis indicated that the deletion of a member of the core component interfered with the formation of vid30c, however, deletion of a member of the secondary component had little effect (if any) on the formation of vid30c. Also, PIPE can be used to analyse yeast proteins for which TAP tagging fails, thereby allowing us to predict protein interactions that are not included in genome-wide yeast TAP tagging projects.PIPE analysis can predict yeast protein-protein interactions. Also, PIPE analysis can be used to study the internal architecture of yeast protein complexes. The data also suggests that a finite set of short polypeptide signals seem to be responsible for the majority of the yeast protein-protein interactions. Proteins carry out the majority of the biological processes in cells. Most often, proteins accomplish this task in association with protein partners, forming stable or transient protein complexes. It is therefore generally accepted that protein-protein interactions are responsible for the cell's behaviour and its responses to various stimuli -3. FurthSaccharomyces cerevisiae has emerged as the model organism for studying functional proteomics. Very recently, we used protein interaction analysis to assign putative functions to different yeast proteins , its specificity as (TN/(TN+FP)) [%], and its accuracy as ((TP+TN)/(TP+FN+FP+TN)) [%] where TP is the number of true positive, FN the number of false negatives, TN the number of true negatives, and FP the number of false positives. We note that a major source of false positives reported by PIPE is motifs with frequent occurrence in the database. Pairs of such motifs can have a high co-occurrence simply because they are very frequent.The following yeast strains were used in this study: OshB6 MATa ura3-1 leu2-3,112 his3-11,15 trp1 ade2-1 YGL227W-TAP::TRP1 and OshB7 MATa ura3-1 leu2-3,112 his3-11,15 trp1 ade2-1 YMR135C -TAP:TRP1. TAP-tagged YGL227W and YMR135C proteins were purified as in ,10. In bPIPE program was written in C++ with Linux as the operating system. The source code is subjected to the terms established by GNU and is available free of charge from the authors on request or can be downloaded from . We haveAG, SP, FD, AC, JC contributed to the conceptual development of PIPE. SP and XL contributed to the implementation of PIPE. AD, AE, MG, JG, MJ, NK, AG contributed towards the TAP tagging experiments and data collection. All authors read and approved the final manuscript.


Although the prediction of protein-protein interactions has been extensively investigated for yeast, few such datasets exist for the far larger proteome in human. Furthermore, it has recently been estimated that the overall average false positive rate of available computational and high-throughput experimental interaction datasets is as high as 90%.The prediction of human protein-protein interactions was investigated by combining orthogonal protein features within a probabilistic framework. The features include co-expression, orthology to known interacting proteins and the full-Bayesian combination of subcellular localization, co-occurrence of domains and post-translational modifications. A novel scoring function for local network topology was also investigated. This topology feature greatly enhanced the predictions and together with the full-Bayes combined features, made the largest contribution to the predictions. Using a conservative threshold, our most accurate predictor identifies 37606 human interactions, 32892 (80%) of which are not present in other publicly available large human interaction datasets, thus substantially increasing the coverage of the human interaction map. A subset of the 32892 novel predicted interactions have been independently validated. Comparison of the prediction dataset to other available human interaction datasets estimates the false positive rate of the new method to be below 80% which is competitive with other methods. Since the new method scores and ranks all human protein pairs, smaller subsets of higher quality can be generated thus leading to even lower false positive prediction rates.The set of interactions predicted in this work increases the coverage of the human interaction map and will help determine the highest confidence human interactions. Protein-protein interactions perform and regulate fundamental cellular processes. The comprehensive study of such interactions on a genome-wide scale will lead to a clearer understanding of diverse cellular processes and of the molecular mechanisms of disease. Although the determination of interactions by small-scale laboratory techniques is impractical for a complete proteome on the grounds of cost and time, several experimental techniques now exist to determine protein-protein interactions in a high-throughput manner . High-thThe low coverage and variable quality of the experimental interaction datasets have prompted many groups to investigate computational methods to predict interactions or to determine the most likely interactions seen in the high-throughput datasets. The different approaches to predict interactions can be grouped into five main categories:1) Predictors based on sequence and structure exploit the observation that some pairs of sequence motifs, domains and structural families tend to interact preferentially. Some methods predict interaction from sequence-motifs found to be over-represented in interacting protein pairs , or by c2) Predictors based on comparative genomics have been exploited primarily in prokaryotes. They consider the physical location of genes, as well as their pattern of occurrence and evolutionary rate, to predict interactions or functional relationships between protein pairs. Some predictors make use of the observation that neighboring genes whose relative location is conserved across several prokaryotic organisms are likely to interact . Other p-10, it has been shown that 16–30% of yeast interactions can be transferred to the worm  and PTM[j] are distinct PTMs and I is the set of all interacting proteins that were used to train the predictor. The annotations of PTMs in human proteins were downloaded from UniProt  and HPRDcombined module.The localization, co-occurrence of domains, and PTMs were considered simultaneously to measure their predictive power in assessing the likelihood of protein interaction. To do this, all possible combinations of the 4 localization bins, 5 chi-square domain-co-occurrence bins and 4 PTM_score bins were investigated and are referred to as the It has been suggested that unstructured regions of proteins are often involved in binding interactions, particularly in the case of transient interactions . ProteinGroup A modules. Likelihood ratios for each of the Group A modules are illustrated in Figure The Expression, Orthology, Combined and Disorder modules are referred collectively as the The transitive module works on the premise that a pair of proteins is more likely to interact if it shares interacting partners. It does this by considering the local topology of the network predicted by the integration of the Group A modules as depicted in Figure c is the set of edges that connect proteins i and j to their common interactors, Ei is the set of edges that involve protein i, se is the score (likelihood ratio) of edge e and Ei\Ec refers to the set difference of Ei and Ec. For a given set of neighbors, T increases as the interactions with these neighbors become more likely (as the sum of se increases). Additionally, the topology score T of a pair of proteins increases as the proportion of likely interactors that these two proteins share increases. The topology scores were grouped into 5 bins of increasing value. It should be noted that the neighborhood topology score calculated for a given protein pair does not consider the preliminary score assigned to that protein pair. It only considers the preliminary scores of its neighbors and so is truly based on the local network topology around that protein pair. Accordingly, the likelihood ratio the transitive module outputs for a given protein pair is independent of the likelihood ratio calculated by the Group A modules for this same protein pair.where EThe Pearson correlation between pairs of modules was estimated by taking 150 samples of 10000 protein pairs each and calculating the Pearson correlation of the likelihood ratios for the two modules considered, for each sample. The reported correlation values are the average of the 150 experiments. Samples of the protein pair space were taken instead of considering the whole space as this was more computationally tractable.The accuracy of the predictors was measured by performing five-fold cross validation experiments in which the datasets were randomly divided into five non-overlapping sets, four of which were used to train the predictor while the fifth was used to test the prediction accuracy. The accuracy reported is the average measured for all combinations of training and testing sets using these five sets. Testing was done by predicting the total likelihood scores for all protein pairs in the test set using the models computed in the training phase and then counting the number of pairs that were well predicted. We used the area under partial ROC curves as a measure of accuracy. Receiver operator characteristic (ROC) curves plot the true positive rate versus the false positive rate over their full range of possible values. In some circumstances, it is more informative to use partial ROC curves (ROCn curves) which illustrate the number of true positives identified by the predictor that score higher than the n highest scoring negatives, plotted for all values from 0 to n. There are many more negatives than positives in our datasets and this is also thought to be true for the full protein interaction networks we are modeling. Since the aim is to identify the largest number of true interacting pairs while leaving out as many non-interacting pairs as possible, it is most informative to measure the performance of the predictor under conditions of very low false-positive rates. Accordingly, ROC50 and ROC100 curves were analyzed because given the size of the datasets, these curves consider all the protein pairs predicted to have a posterior odds ratio above 1.0, for all the predictors investigated. The area under ROC curves is often used as a summary measure of accuracy. For ROCn curves, it can be calculated asi is the number of positives that score higher than the ith highest scoring negative.where i takes on values from 1 to n, T is the total number of positives in the test set and TMSS conceived and designed the study, created and implemented the predictor, analyzed the predictions and drafted the manuscript. GJB participated in the design of the study, the analysis of the predictions and the writing of the manuscript. Both authors read and approved the final manuscript.High scoring InterPro domain pairs. List of InterPro domain pairs that achieve highest chi-square score of co-occurrence in our set of positive interactors.Click here for fileHigh scoring post-translational modification pairs. List of high-scoring post-translational modification pairs.Click here for fileAll LR400 predicted interactions ranked. All human protein pairs predicted to have a likelihood ratio of interaction greater than 400 and thus a posterior odds ratio of interaction greater than 1.Click here for fileAdditional methods. In depth description of the calculation of likelihood ratios for the modules.Click here for file