A common assumption in comparative genomics is that orthologous genes share greater functional similarity than do paralogous genes (the “ortholog conjecture”). Many methods used to computationally predict protein function are based on this assumption, even though it is largely untested. Here we present the first large-scale test of the ortholog conjecture using comparative functional genomic data from human and mouse. We use the experimentally derived functions of more than 8,900 genes, as well as an independent microarray dataset, to directly assess our ability to predict function using both orthologs and paralogs. Both datasets show that paralogs are often a much better predictor of function than are orthologs, even at lower sequence identities. Among paralogs, those found within the same species are consistently more functionally similar than those found in a different species. We also find that paralogous pairs residing on the same chromosome are more functionally similar than those on different chromosomes, perhaps due to higher levels of interlocus gene conversion between these pairs. In addition to offering implications for the computational prediction of protein function, our results shed light on the relationship between sequence divergence and functional divergence. We conclude that the most important factor in the evolution of function is not amino acid sequence, but rather the cellular context in which proteins act. The use of model organisms in biological research rests upon the assumption that gene and protein functions discovered in one organism are likely to be the same or similar in another organism. Hence, the assumption that experiments in mouse will tell us about the function of genes in humans. A guiding principle in the assignment of function from one organism to another is that single-copy genes (“orthologs”) are statistically more likely to provide functional information than are multi-copy genes, whether in the same organism or different organisms. Here we have tested this idea by examining genes with known functions in human and mouse. Surprisingly, we find that multi-copy genes are equally or more likely to provide accurate functional information than are single-copy genes. Our results suggest that the organism itself plays at least as large a role in determining the function of genes as does the particular sequence of the gene alone. This insight will benefit the assignment of function to genes whose roles are not yet known by widening the pool of appropriate genes from which function can be inferred. The potential for gene duplication to generate evolutionary novelty was first noted in 1918 by Calvin Bridges cited in , and thehttp://www.ncbi.nlm.nih.gov/About/primer/phylo.html).As the first protein-sequence data became available, Zuckerkandl and Pauling hypothesis about functional similarity We refer to the hypothesis that orthologs are more likely to be functionally similar than are paralogs as the “ortholog conjecture” cf. . In factA large number of methods have been developed to identify orthologous relationships among proteins. These methods range from simple pairwise comparisons, to standard phylogenetic tree-building, to probabilistic assignment using Bayesian analyses In this paper we directly test the ortholog conjecture using comparative functional genomic data. We use experimentally derived functional assignments of more than 8,900 genes from mouse and human, as well as a microarray dataset that includes 25 tissues in both mouse and human, to directly assess our ability to predict function using orthologs and paralogs. We use this pair of species both because they are two of the best-studied and best-annotated organisms and because homologous relationships are easy to identify due to their relatively recent divergence time. Because paralogs are almost always either more- or less-related to a focal gene than an ortholog , it is meaningless to compare the predictive power of all orthologs to all paralogs; it seems obvious that closely related orthologs will be more similar in function than distantly related paralogs, and vice versa. Instead, we focus on the predictive power of both orthologs and paralogs as a function of protein sequence divergence. Our results demonstrate that paralogous genes from the same species are often a much better predictor of functional divergence than are orthologs or paralogs from different species, even at lower sequence identities.Functional similarity was calculated between all pairs of homologous proteins (i.e. those in the same gene family) in human and mouse for which there is experimentally defined function for both members of the pair. These pairs include 2,579 one-to-one orthologs between human and mouse and 21,771 paralogous comparisons of any type. The experiments used to annotate these genes come from 12,204 unique published papers whose results are collected in the Gene Ontology (GO) database; in a later section we carry out an independent analysis using microarray data to measure functional similarity. dN/dS) and functional similarity  and functional similarity is nearly the same for the different types of homologs as sequence identity approaches 50%. The curves do not provide comparable information for sequence identities below 50% because of an insufficient number of 1-to-1 orthologous pairs with very low identity.Contrary to a common assumption (the “ortholog conjecture”), the functional similarity between paralogs is significantly higher than that between orthologs for high sequence identities  was selected uniformly randomly from all proteins with at least one ortholog and at least one paralog in the family, and all its functionally annotated homologs were collected. We then asked whether at least one of the paralogs had higher sequence similarity than the ortholog, and then whether it had higher or lower functional similarity. This analysis required functionally annotated triples within gene families ; thus 1-to-many and many-to-many orthologous relationships were included in this analysis. In cases where multiple genes were co-orthologous to the target, the ortholog having the highest sequence identity with the selected target protein was used for comparison. Note that each gene family was counted only once in this analysis, preventing families with large numbers of lineage-specific duplications from biasing the results. Finally, to ensure that the choice of target protein did not unduly affect the results, we repeated the analysis 100 times, choosing a new target protein from the 1145 unique families containing experimentally annotated triples each time . The family-based analysis showed similar trends to those observed in previous sections. In the Biological Process category, if the orthologous sequence was more similar to the target protein, the ortholog had higher functional similarity to the target protein than all of its paralogs in only 33.4±0.1% of the cases (mean ± standard error). In contrast, in 82.9±0.4% of protein families in which a paralogous sequence was most similar to the target protein, it was also functionally most similar. In the Molecular Function category, the observed difference between orthologs and paralogs was similar: an ortholog had higher functional similarity to the target protein than all of its paralogs in only 49.5±0.1% of the cases. On the other hand, if the most similar sequence to a target protein was a paralog, the paralog was functionally most similar to the target protein in 71.1±0.5% of families.It is known that paralogous sequences residing on the same chromosome are more likely to undergo non-allelic gene conversion in mammals We examined two families in further detail. (1) We compared the functional similarity of orthologs and paralogs in the full set of nuclear receptors in human and mouse, a well-studied group of proteins. Out of the 48 and 49 nuclear receptors identified in human and mouse, respectively mMAP4K2), 3 human outparalogs , and 3 mouse outparalogs  . In contrast, its functional similarity with its own outparalogs was 69% on average, including 82% similarity with hMAP4K3, a within-species outparalog.(2) Another example of a violation of the ortholog conjecture is found in the mitogen-activated protein kinase kinase kinase kinase 2 (MAP4K2) family. MAP4K2 is a serine/threonine protein kinase, expressed in lymph nodes, but also in other tissues such as lung, brain, and placenta mMAP4K5) . Of thesWe analyzed multiple potential biases in the data that could impact the conclusions of this work. They included: 1) Functional annotation that is organism-specific, i.e. certain functions may be studied only in humans while others may be studied only in mice. To address this possibility we repeated our analysis using only the subset of functions studied in both human and mouse; there was no significant difference in the shape of the functional similarity curves relative to that shown in Because all of the above analyses are based on user-reported or curator-based determinations of function, they may still be affected by individual researcher biases that we cannot control for. The only way to avoid this potential problem is to obtain a measure of function that is not dependent on an individual's interpretation of experiments. Therefore, we conducted a parallel analysis of the relationship between protein similarity and functional similarity using microarray data from 25 homologous tissues in human and mouse P<0.01; Wilcoxon test) and a strong positive correlation with the sequence identity of paralogs but not orthologs. Our results were not dependent on the distance measure used to quantify functional similarity , paralogous genes from the same species (either human or mouse) are better predictors of function than are orthologs from the other species. A similar result was previously obtained among yeast, fly, and worm when comparing conserved protein-protein interactions between homologs within the same species and homologs from different species , in situ (e.g. tissue-specific expression), or in vitro but with species-specific conditions and/or interactors (e.g. yeast two-hybrid). Function is therefore assessed in the context of individual organisms, not in a common laboratory setting.In addition to a general lack of support for the ortholog conjecture, our analyses revealed several surprising patterns. One of the most surprising is the lack of any discernible relationship between protein similarity and functional similarity for orthologs, whether considering Biological Process or Molecular Function annotations . AverageThe importance of cellular and organismal context in defining protein function may go a long way toward explaining many aspects of our results, including the lack of a relationship between functional and sequence similarity for orthologs, the presence of this relationship for paralogs, and the differences between different types of paralogs . We propose that the key to understanding the rate at which protein function evolves is not how quickly the protein sequence itself evolves, but rather the rate at which its cellular context—including directly and indirectly interacting molecules—evolves. To further explain this hypothesis, note that all of the orthologous pairs studied here are the same age: that is, they all share a last common ancestor at the split between the human and mouse lineages, regardless of their level of sequence identity. Unlike orthologs, the paralogs studied here shared common ancestors at many different times in the past, with some paralogs having split only a few million years ago while others split >100 million years ago. We propose that this difference in divergence times is the key to understanding the difference in relationships between functional and sequence similarity. The orthologs all share the same age—and therefore the same average functional similarity—but the paralogous pairs are of many different ages—and therefore different functional similarities.Why should proteins of the same age share the same level of functional similarity? While there is no direct role for “time” in evolution that is not tied to mutation, we suggest that what time represents here is the evolution of the cellular context: the sum of the evolutionary changes over all of the directly and indirectly interacting molecules. If this context evolves at a steady rate , then protein function will appear to evolve at a steady rate, a rate largely disconnected from the level of an individual protein's sequence divergence. Several pieces of evidence support this conjecture. First, our results above show that even orthologous proteins that are 100% identical have different functions. Since it is obvious that the proteins themselves have not changed, the change must be due to regulation or downstream effects of these molecules. For example, Liao and Zhang in vitro environment orthologous proteins really would be more functionally similar than paralogous proteins—after all, studies of rates of protein sequence evolution suggest an increased rate of sequence change among paralogs Some researchers may be concerned that the function being measured here is not independent of the organism, and is therefore not appropriate for testing the ortholog conjecture. Of course it is possible that if measured in a common The results of our study suggest that neither sequence similarity nor identification of orthologous assignments alone can be considered an accurate predictor of protein function. We find that orthologous proteins between human and mouse share a constant level of functional similarity over a wide range of  sequence identities, while the functional similarity between paralogs is dependent on the type of paralogy, level of sequence identity, relative chromosomal location of duplicated genes, and organismal context. We find that sequence identity thresholds as a means of function transfer are generally applicable only to within-species paralogs. Moreover, these thresholds depend on the type of paralogy and a specific duplication event, with inparalogs typically having lower thresholds for similarly accurate functional transfer than outparalogs. On the other hand, in the absence of within-species paralogs, our data indicates that orthologs and between-species outparalogs are similarly accurate in predicting protein function. In general, however, such relationships cannot be deemed ideal for function transfer of GO terms, as the average accuracy of predictions using orthologs and between-species outparalogs were consistently lower than 0.70 . Though Functional annotation of genes with unknown function is often carried out by researchers working on particular proteins. In these cases—far from being an automated process of ortholog identification and functional transfer—individual researchers may examine the function of many closely related homologs before making decisions about functional annotations, or even before designing experiments. If they are available, researchers may be using the functions of both orthologs and paralogs to guide their own functional annotations. When inparalogs are available and happen to have the highest sequence identity, these genes may actually be the ones having the largest influence on the functional annotations in common databases; such a process of individual functional inference would create a pattern much like the one we observe. While our analysis of microarray data is consistent with the high functional similarity of within-species paralogs and is free from individual researcher or curator bias, we cannot rule out the possibility that such bias exists in widely used databases. However, such biases are likely to only apply to organisms already being studied by a large community of researchers in molecular biology. Many new genomes are being sequenced solely for the evolutionary or environmental importance of a species, and are therefore unlikely to have much prior data on gene and protein function. In these cases, our results suggest that functional transfer need not be dependent on the identification of orthologous genes in a model organism.There are 31,479 proteins in the Swiss-Prot database with experimentally characterized function and 40,951 proteins in the Gene Ontology database . The functions of this relatively small group of proteins have been transferred to a much larger number of homologous proteins and propagated across biological databases, often with gross inaccuracies human and mouse: if the main purpose of biomedical research into model organisms is to understand the function of genes and proteins in humans, then we might expect these studies to be predictive of function in humans. While our results certainly show that mouse proteins are predictive of the function of human proteins . Though we cannot control for each type of error, the fact that within-species gene pairs cannot be confused with between-species gene pairs (of any kind) means that our main results are robust to the exact tree topologies. In total, our dataset consisted of 26,467 gene trees containing 22,137 human and 22,039 mouse genes  gene trees were used to identify all homologous human-human, mouse-mouse, and human-mouse gene pairs. Though there are many methods and databases available for identifying homologous relationships, they provide qualitatively similar results se genes .Biological Process and Molecular Function protein function information was retrieved from the Gene Ontology (GO) database. Only the curated GO term annotations were used in the analysis. These include all experimentally inferred annotations: inferred from direct assay (IDA), expression pattern (IEP), genetic interaction (IGI), mutant phenotype (IMP), and physical interaction (IPI) evidence codes. We also included the traceable author statement (TAS) and inferred by curator (IC) evidence codes. Since both the Biological Process and Molecular Function ontologies are represented by directed acyclic graphs (DAGs), the original functional terms were propagated towards the root of each DAG (with the root node excluded) thus producing a complete set of terms for each protein. The GO seqdblite database (release 2009-01-18) was used for term propagation. In total, 4,854 human and 4,089 mouse proteins had functional annotation in at least one GO DAG. This reduced the number of gene trees with at least two functionally annotated genes to 2,448; the total number of ortholog pairs is 2,579, inparalog pairs is 597, within-species outparalogs is 11,334, and between-species outparalogs is 9,840 .Microarray data presented in Su et al. z-score method, forcing expression values within a tissue to have a mean of 0 and a standard deviation of 1. After expression values were normalized within a tissue, they were again normalized for individual probesets across tissues, forcing expression values for a single probeset to have a mean of 0 and a standard deviation of 1 across tissues. Specifically, if we represent the expression value of a probeset i in a tissue j as ijs, we can define the tissue-normalized expression value, ijt, as:jμ and jσ are the mean and standard deviation of expression values in tissue j. The final normalized expression value for a probeset i in tissue j, ijn, is defined as:iμ and iσ are the mean and standard deviation of i·t values for gene i in all tissues. After these two steps of normalization, we averaged probesets that match to the same gene and then averaged duplicate samples for the same tissue.Expression data was normalized within each platform individually. Expression values were first normalized within each individual tissue using the In total, we were able to obtain expression data for 15,907 human genes and 15,552 mouse genes. This reduced the number of gene trees with at least two functionally annotated genes to 7,495; the total number of data pairs used for orthologs is 10,863, for inparalog pairs is 2,014, for within-species outparalogs is 10,396, and for between-species outparalogs is 9,370 .losum62 scoring matrix . We divided the number of matching residues by the length of the alignment. For the calculation of dN/dS and dS, we used the Goldman and Yang method We calculated protein sequence identity by using Needleman-Wunsch alignments of protein sequences with the BT(p) be a set of propagated GO terms for protein p and T(q) be a set of propagated GO terms for protein q. Then, the functional similarity fs between p and q was calculated as:To calculate functional similarity for the GO data, let p when protein q is used to predict p's function , and the fraction of correctly predicted functional terms in q when protein p is used to predict q's function fs≤1, with 0 corresponding to proteins with disjoint sets of functional terms and 1 corresponding to proteins with identical sets of terms. Functional similarity of 0 may occur because we removed the root node from each ontology.This formula can be interpreted as the average of the fraction of correctly predicted functional terms in corr between genes p and q (in a somewhat abused notation where p and q represent both genes and their indices in microarrays) for normalized data was calculated as:T is the index set of tissues being considered, pjn is the normalized expression for gene p in tissue j, and pµ is the mean expression level for gene p over all tissues in T.To calculate functional similarity for the microarray data, we used the Pearson correlation coefficient (the Euclidean distance provided similar results). The correlation coefficient Figure S1A) The figure shows four hypothetical genes in humans (H1–H4) and two in mouse (M1–M2). There are four types of homologs shown: 1) M1 is an ortholog of H1, H2, and H3 because their last common ancestor is a speciation event (one-to-many orthology). 2) H1 is an inparalog of H2 and H3, with respect to the human-mouse split, because their last common ancestor is a duplication event more recent than the human-mouse split. 3) M1 is a within-species outparalog of M2 because they are related by a duplication event that occurred before the human-mouse split. 4) M1 is also a between-species outparalog of H4 because they are related by a duplication event before the human-mouse split (and in different genomes). B) The figure shows two hypothetical genes in humans (H1 and H2) and two in mouse (M1 and M2). There are three types of homologs shown: 1) M1 and H1 are one-to-one orthologs, as are M2 and H2. 2) M1 is a within-species outparalog of M2 because they are related by a duplication event that occurred before the human-mouse split, as are H1 and H2. 3) M1 is a between-species outparalog of H2 because they are related by a duplication event before the human-mouse split (and in different genomes), as are H1 and M2.Different types of homology relationships among genes. (PDF)Click here for additional data file.Figure S2dN/dS calculated using the Goldman and Yang method. A) human-mouse orthologs (red) and all paralogs (blue). B) human-mouse orthologs (red), inparalogs (green), within-species (W-s) outparalogs (blue), between-species (B-s) outparalogs (purple). Counts of gene pairs in each bin are listed below each figure. Note that estimates of dS (and therefore dN/dS) are inaccurate for long divergence times due to multiple substitutions at the same site; this likely affects the values for outparalogs.The relationship between functional similarity and (PDF)Click here for additional data file.Figure S3The phylogenetic relationships between functionally annotated members of the MAP4K family, and counts of overlapping and non-overlapping GO terms for the target protein human MAP4K2 (red circles) and each of its homologs (blue circles). Tree branch lengths are not drawn to scale.(PDF)Click here for additional data file.Figure S4A) human-mouse orthologs (red) and all paralogs (blue). B) human-mouse orthologs (red), inparalogs (green), within-species (W-s) outparalogs (blue), between-species (B-s) outparalogs (purple). Counts of gene pairs in each bin are listed below each figure.The relationship between functional similarity and sequence identity using only the subset of GO terms assigned to at least one human and at least one mouse protein. (PDF)Click here for additional data file.Figure S5A) human-mouse orthologs (red) and all paralogs (blue). B) human-mouse orthologs (red), inparalogs (green), within-species (W-s) outparalogs (blue), between-species (B-s) outparalogs (purple). Counts of gene pairs in each bin are listed below each figure.The relationship between functional similarity and sequence identity using a constant GO term annotation depth for all members of the gene family. For each family, the maximum depth of annotation (measured as the distance from the root node) for each protein was calculated, and then the minimum of the individual maximum annotation depths was found. All GO terms below this minimum were removed for all proteins in the family. (PDF)Click here for additional data file.Figure S6A) human-mouse orthologs (red) and all paralogs (blue). B) human-mouse orthologs (red), inparalogs (green), within-species (W-s) outparalogs (blue), between-species (B-s) outparalogs (purple). Parts C) and D) show the same relationship using only GO term annotations derived from the same publication (based on PubMed ID) for both members of the homologous protein pair. Counts of gene pairs in each bin are listed below each figure.The relationship between functional similarity and sequence identity excluding all GO term annotations derived from the same publication (based on PubMed ID) for both members of the homologous protein pair. During annotation, the same GO term can be assigned to a protein by two or more distinct PubMed IDs. In these cases, GO term annotations were not considered to have come from the same publication if different PubMed IDs could be assigned to the annotations for each member of the pair. (PDF)Click here for additional data file.Figure S7A) human-mouse orthologs (red) and all paralogs (blue). B) human-mouse orthologs (red), inparalogs (green), within-species (W-s) outparalogs (blue), between-species (B-s) outparalogs (purple). Parts C) and D) show the same relationship using all experimental and curator inferred evidence codes, but excluding traceable author statements (TAS). Counts of gene pairs in each bin are listed below each figure.The relationship between functional similarity and sequence identity using only protein pairs annotated with GO terms assigned by the same evidence code. All experimental , curator inferred (IC), and traceable author statement (TAS) evidence codes are included. (PDF)Click here for additional data file.Figure S8dS calculated using the Goldman and Yang method for inparalogs only.The relationship between functional similarity and (PDF)Click here for additional data file.Table S1Functional similarity within the nuclear receptor family in human and mouse. Of the total number of annotated proteins with both an ortholog and a paralog, the counts show the number in each category. Paralogs with higher functional similarity are further distinguished by whether the within-species or between-species outparalog was most similar.(DOC)Click here for additional data file.Dataset S1Measures of functional similarity, sequence similarity, and homology relationships between proteins, as well as GO codes associated with each protein used in the study.(TXT)Click here for additional data file.Dataset S2Correlation in gene expression profiles between proteins, tissues used from the human and mouse array experiments, mappings of probesets to genes, as well as normalized expression values for each gene.(TXT)Click here for additional data file.


Current approaches of predicting protein functions from a protein-protein interaction (PPI) dataset are based on an assumption that the available functions of the proteins (a.k.a. annotated proteins) will determine the functions of the proteins whose functions are unknown yet at the moment (a.k.a. un-annotated proteins). Therefore, the protein function prediction is a mono-directed and one-off procedure, i.e. from annotated proteins to un-annotated proteins. However, the interactions between proteins are mutual rather than static and mono-directed, although functions of some proteins are unknown for some reasons at present. That means when we use the similarity-based approach to predict functions of un-annotated proteins, the un-annotated proteins, once their functions are predicted, will affect the similarities between proteins, which in turn will affect the prediction results. In other words, the function prediction is a dynamic and mutual procedure. This dynamic feature of protein interactions, however, was not considered in the existing prediction algorithms.In this paper, we propose a new prediction approach that predicts protein functions iteratively. This iterative approach incorporates the dynamic and mutual features of PPI interactions, as well as the local and global semantic influence of protein functions, into the prediction. To guarantee predicting functions iteratively, we propose a new protein similarity from protein functions. We adapt new evaluation metrics to evaluate the prediction quality of our algorithm and other similar algorithms. Experiments on real PPI datasets were conducted to evaluate the effectiveness of the proposed approach in predicting unknown protein functions.The iterative approach is more likely to reflect the real biological nature between proteins when predicting functions. A proper definition of protein similarity from protein functions is the key to predicting functions iteratively. The evaluation results demonstrated that in most cases, the iterative approach outperformed non-iterative ones with higher prediction quality in terms of prediction precision, recall and F-value. Assigning biological functions to uncharacterized/un-annotated proteins is one of the major challenges in post-genomics due to the importance of proteins in various biological processes and the high cost of biological experiments . On the The past decade has seen a rapid development of computational methods for predicting protein functions from PPI datasets. To predict functions computationally, protein interactions in a PPI dataset are usually modelled as an undirected acyclic network. The nodes in the network represent unique proteins and the edges represent the interactions between proteins . With thThe current approaches can predict functions effectively to some extent for some but not all cases. In addition to the factors such as incompleteness and noisy data of the PPI datasets, whether a computational algorithm can more reasonably reflect the nature of protein interactions will determine the quality of prediction. In fact the existing approaches, whether they are semantic or not, are based on an assumption that the functions to be predicted for an un-annotated protein are determined by the functions of annotated proteins in the dataset. That means the prediction is mono-directed from annotated proteins to un-annotated ones, and once the functions of un-annotated proteins are predicted, the prediction is finished (i.e. a one-off procedure). This assumption, however, only reflects one aspect of protein interactions. As a matter of fact, in real biological processes, proteins have high mobility and have dynamic interplay that produces a framework which is ever-changing but overall stable . ProteinConsidering the above issues, in this paper, we propose an innovative approach to predict protein functions iteratively. The iterative prediction method simulates the dynamic process of protein interactions in terms of protein and function similarities when predicting functions. Meanwhile, in our algorithm the local and global semantic influence of the available protein functions in the dataset is also taken into account, which more reasonably counts the contribution of available functions to the prediction results. The iterative prediction starts with assigning initial predicted functions to the un-annotated protein, and then calculates the initial similarities between the un-annotated protein and its neighbour proteins. With these initial similarities, a kNN-based prediction method is applied to get the new predicted functions for the un-annotated protein. Replacing the initial/old predicted functions of the un-annotated protein, the new predicted functions are then used to recalculate the similarities between the un-annotated protein and its neighbour proteins for the next round of prediction. This prediction process is repeated until the similarities between the un-annotated protein and its neighbour proteins reach a stable state, which represents a dynamic stable status among the protein interactions in terms of similarities. To guarantee the prediction being conducted iteratively, a similarity between proteins must be properly defined. This is also one of our contributions in this paper.The paper is organized as follows. In Section "Methods", we present the iterative prediction algorithm in detail. In Section "Results", we provide the evaluation results of our algorithm and the comparison results with the methods that are similar to our method. We discuss the concerns and issues that are related to our algorithm in Section "Discussion". We finally conclude our work in Section "Conclusions" and discuss some future work about iterative approach improvement.The idea of our prediction algorithm is to iteratively count the contribution of the available functions in the neighbours of the un-annotated protein to the final determination of predicted functions. The contribution of a function to the prediction is primarily dependent on the number of neighbour proteins that have the function and the similarities between the un-annotated protein and these neighbour proteins. In our algorithm, we also consider the similarities between the functions in the neighbour, as well as the global and local influence of the functions, in the prediction. The details of this iterative prediction algorithm are presented as follows. It can be seen that the base of our algorithm is the definitions of protein similarity and protein function similarity. Therefore, we firstly define these similarities, and then give the prediction algorithm.p, we denote the neighbour proteins of p as a set N(p). The neighbour proteins of a protein p are those that have direct and/or indirect interactions with p in the PPI network. In this paper, we only select those proteins that have direct interactions with p as the neighbour proteins of p. We also denote the functions of a protein p' as a set F(p'), and the functions of all the neighbour proteins of p as another set Suppose the un-annotated protein is GO terms  to annotp and p', suppose the size of the set F(p) is m (i.e. the number of functions in F(p)), and the size of the set F(p') is n. The similarity between two proteins p and p' is defined asNow we give the definitions of protein similarity and protein function similarity. For any two proteins δf,f' is an indicator function, i.e. if f and f' are the same, its value is 1, otherwise, it is 0.where f and f', they can be represented as two vectors t, the dimension of each function vector t. Since the GO is represented as a directed acyclic graph in which a GO term may have multiple parent GO terms, we call all parent terms of a GO term the ancestors of the term. If a function is annotated by a GO term, it is also annotated by the ancestors of the GO term. Therefore, the vector element values at the index positions that correspond to these ancestors are set to 1, otherwise set to 0. For example, suppose we have five GO terms for functional annotation (just for demonstration only), the function f is annotated by the fourth term whose ancestors are the second and third terms, and another function f' is annotated by the fifth term whose ancestors are the third and fourth terms, then these two functions f and f' can be represented as two vectors For any two functions f and f' is then defined asThe similarity between two functions f sim  ≤ 1. For the above two function vectors f sim  = 2/3.where p being annotated by a function f ∈ FN(p), i.e. the contribution of function f to the final prediction results, is defined as:With the above protein and protein function similarities, the score of the un-annotated protein N is the number of all proteins in the dataset and nf' is the number of proteins in the dataset that have the function f'. It can be seen from the equation (3) that the value of f sim  refers to the local impact of available functions within the local domain N(p) on the prediction results, while the value f' is common to almost all proteins, i.e. almost all proteins in the dataset have the function f', then the importance as well as influence of f' decreases, otherwise it will increase.where f ∈ FN(p), its contribution to the final prediction results is calculated by the score defined in (3). Therefore, all the functions in FN(p) can be ordered by their scores from the highest to the lowest, and then the first k functions with the k highest scores are selected as the predicted functions of the un-annotated protein p. The value of k is determined empirically or by the prediction requirements. In this paper, we select k as the average number of functions each protein has in the dataset. With the predicted functions of the un-annotated protein p, the similarities between the un-annotated protein p and its neighbour proteins, i.e. sim  in (3), as well as the function scores are recalculated. With the recalculated scores, all the available functions in FN(p) are re-ordered and a new prediction is made. This procedure is repeated until the similarities between the un-annotated protein p and its neighbour proteins achieve a stable state.The iterative function prediction is conducted based on the equation (3). In fact, for each available function p, so that the similarities between the un-annotated protein p and its neighbour proteins in (3) can be calculated. The selection of initial functions for the un-annotated protein p is determined by the initial function scores calculated by the equation (3) but with the similarity sim  = 1 for any p' ∈ N(p), i.e. for each function f ∈ FN(p), its initial score isTo start the above iterative prediction procedure, we need to assign initial functions to the un-annotated protein We set the threshold for initial function selection as follows:size (FN (p)) is the number of functions in the set FN(p). The functions whose scores calculated by (4) are over the threshold (5) are selected as the initial predicted functions of the un-annotated protein p.where sim  is the key to conducting the function prediction iteratively. If the protein similarity is defined in other ways rather than from protein functions, the prediction algorithm based on (3) is just a normal weighted kNN algorithm and the prediction cannot be conducted iteratively. So the prediction does not reflect the dynamic features of protein interactions, and it is just a one-off process. What makes our algorithm different from existing algorithms is that our protein similarity sim  of two proteins p,p' is defined from their functions. With this similarity definition, the prediction algorithm based on (3) can go through an iterative process to predict functions until the similarities achieve a stable state. In other words, the prediction algorithm with our protein similarity definition reflects the dynamic features of protein interactions.It is observed from the above iterative prediction algorithm that the similarity definition of two proteins S. Cerevisiae protein-protein interaction (PPI) dataset derived from the BioGrid site (http://thebiogrid.org/) to build a protein interaction network for computational experiments. This dataset contained 232,239 interactions. To reduce the influence of noise data, we removed from the dataset the duplicated interactions, self interactions and all proteins that do not have GO annotation information. The filtered dataset for the experiments then contained 4,905 proteins, 3,260 GO terms and 155,662 interactions. The GO terms [http://www.geneontology.org/. We only used the biological process ontology and the GO annotations of S. Cerevisiae in our experiments.To evaluate the effectiveness of our iterative prediction algorithm, as well as to compare our method with other related methods, we used a real GO terms  used in precision, recall and F-value, which are defined as follows:Usually, the quality of a prediction algorithm is evaluated by its NP is the number of correctly predicted functions for a given protein p, NA is the number of all predicted functions for protein p, NR is the number of real functions of protein p. For these evaluation metrics, NP is usually the number of predicted functions that exactly match the real functions. However, the function annotations of proteins have their specific features in the context of an annotation scheme such as the GO. It is known that the GO terms are organized in a hierarchical structure with the nodes representing the GO terms and the edges representing ancestor-child relationships. If a protein p is annotated by a node, it is also annotated by all ancestor nodes of that node. The ancestors of a node mean the more general function categories in biology. In other words, if two functions share some ancestors in the GO structure, even if they are not exactly the same, they are still similar to some extent at higher levels of functional categories. Therefore in our evaluations, in addition to evaluating how many functions we can predict that exactly match the real functions, we also evaluated to which extent the predicted functions are similar to the real functions over the function ancestor terms in GO. For this purpose, we adapted the evaluation method in [fo1, fo2, fo3,..., fon}, and the predicted functional annotations are {fp1, fp2, fp3, ..., fpm}. The success of the prediction for a real function foi  is defined as:where ethod in  with ourfpj  is defined as:and the success of a predicted function recall and precision are defined as follows:The measures of new F-value is defined as before but with the above new recall and precision definitions. These new recall and precision measures do make sense in biology because although two proteins interact with each other, they do not necessarily have the exact same functions, but they might be in more general function categories (i.e. the ancestors in GO). Therefore, the above new measures of recall and precision are more reasonable when assessing prediction quality in real biological applications.The new Since our iterative algorithm is based on the cosine similarity between two function vectors, we named our algorithm the Cosine Iterative Algorithm (CIA). Due to the lack of existing similar iterative prediction algorithms, in our evaluation, we compared our CIA with two algorithms that were also based on the kNN method. One is Neighbour Counting (NC)  which prf ∈ FN(p) being assigned to the un-annotated protein p is calculated as follows:With the INC algorithm, the score of a function If,p' is defined as followwhere the function The initial score is calculated as follows:The initial function selection for kicking off the iterative function prediction, as well as the iterative prediction procedure, is similar to our algorithm described above.If,p' in the above INC algorithm was replaced by the Lin's similarities between functions. Our previous evaluation results showed that the INC algorithm outperformed the Lin's similarity-based iteration algorithm in terms of precision, recall and F-value when predicting protein functions from different protein interaction datasets. Therefore in this paper, we focused on the comparison of CIA algorithm with the INC algorithm with respect to the iterative prediction quality.In our previous work , we haveFigures To further evaluate the effectiveness of our algorithm, we conducted ten-fold cross-validation experiments. The original protein dataset was randomly divided into ten parts in the experiments. For each round of validation, one part was treated as a testing dataset and the remaining nine parts were treated as training datasets. The evaluation results for the three algorithms in terms of precision-recall are shown in Figures We also conducted cross-validation experiments on the protein interaction networks inferred by Affinity-MS and Two-Hybrid assays in the original BIOGRID database. The evaluation results for the three algorithms in terms of precision-recall are shown in Figures To demonstrate the effectiveness of our iterative approach, in Table f is determined by two factors, one is the influence of the function f, i.e. p and its neighbour proteins, i.e. sim . For a given function f ∈ FN(p), its influence is fixed and will not be changed with the iterations. Therefore, the convergence of the algorithm depends on whether the similarities sim , where p' ∈ N(p), will be stable after finite iterations. In fact, according to equation (1), the similarity between two proteins depends on the functions they possess. Once their functions, especially the functions of the un-annotated protein p, are fixed, their similarity is fixed or stable. From the iterative algorithm, it can be seen that the final predicted functions should be those that have the highest influence and are highly similar to the functions of those proteins that are highly similar to the un-annotated protein p. However, those functions with an average influence but are highly similar to the functions of those proteins that are highly similar to the un-annotated protein p, or those functions with a higher influence but are on average similar to the functions of those proteins that are highly similar to the un-annotated protein p, are also the candidates of predicted functions. The initial function selection of the iteration algorithm only selects the most frequent functions that have the higher influence, without considering the impact of the protein similarity on the prediction results. After the first round of iteration, those functions are selected that have the highest influence and are highly similar to the functions of those proteins that are highly similar to the un-annotated protein p. As indicated above, since the neighbour of the protein p and the influence of the selected functions are fixed, the functions with the highest scores after the first round of iteration will still keep the highest scores in other iterations once they are assigned to the protein p, because the highest scored functions and protein similarities endorse each other in the iterations. Therefore, the second round of iteration is to select those candidate functions that have the second highest scores, and so on. That means the highest scores from the previous iteration will not be changed in the next iteration. Since the number of predicted functions is finite, after finite iterations  the similarities between the un-annotated protein p and its neighbour proteins will not be changed any more, i.e. be stable. Therefore, the iterative algorithm is convergent. Our experiments also demonstrated that usually after two or three iterations, the predicted functions are stable.In this section, we discuss the concerns and issues related to our algorithm. The first concern is about the convergence of our iterative prediction algorithm. As stated in the section "Methods", the iterative prediction is based on iteratively updating the function scores calculated by equation (3). It can be seen from equation (3) that the score of a function k which determines the number of predicted functions. As analyzed above, the algorithm predicts functions by iteratively adjusting the similarities between the un-annotated protein and its neighbour proteins, and calculating the function scores. This iterative process has no specific constraints on the selection of initial functions, provided the candidate functions for iterations are selected as many as possible. Theoretically, we can select all available functions within the neighbour of the un-annotated protein as the initial functions for iterations. In our algorithm, we select initial functions according to their influence. This selection method is based on our prediction algorithm and an assumption that functions with higher influence are more likely to be the candidates of predicted functions. Therefore, this initial function selection method concentrates on those most likely candidate functions and reduces the computational cost. Our observation from the experiments demonstrated the effectiveness and efficiency of this initial function selection method, as we did not see significant differences between the prediction results produced from the method that selects all available functions in the neighbour as the initial functions and the prediction results produced from our initial function selection method. We believe that other existing prediction algorithms can also be used to select initial functions for our algorithm. Regarding the value of parameter k in the prediction, it is obvious that its value has impact on the prediction precision and recall, as well as the F-value. Ideally, this parameter value should be determined objectively. We tried to determine this value to be the number of functions whose scores were above the average score, or by ranking the function scores first and then determining the value of k to be the number of functions whose scores did not decrease sharply (e.g. less than 50%) between two adjacent functions in the ranking list. Our experiments showed that the current method of determining the value of k, i.e. the value of k is the average number of functions each protein has in the neighbour, achieved the best prediction results compared with other methods we tried. Whether there are better methods for determining the value of k is an issue we will address in the future research.Another concern about the iterative algorithm is whether the prediction results are sensitive to the initial function selection and the value of parameter This paper proposed a novel iterative approach trying to incorporate dynamic features of protein interactions into the protein function prediction. The iterative prediction algorithm also takes into account the local and global semantic influence of available functions within the protein interaction dataset on the prediction results. Therefore our approach is more likely to reflect the real biological nature between proteins when predicting functions. We adapted new evaluation metrics accordingly to evaluate the prediction quality of our algorithm and other similar algorithms. The evaluation results demonstrated that in most cases, the iterative approach outperformed non-iterative ones with higher prediction precisions and recalls. The prediction results also showed the feasibility and effectiveness of the proposed iterative approach. Since the iterations of the prediction algorithm occur within the neighbour of the un-annotated protein only, our iterative prediction algorithm can be scaled to other larger protein databases. It is concluded that the functions of an un-annotated proteins are mainly determined by the functions within the local domain (e.g. the neighbour) of the un-annotated protein, and those functions that are highly similar to all functions in the local domain and rare within the whole dataset are more likely to be the predicted functions of the un-annotated protein.As we noticed, in our algorithm the prediction is based on the neighbour proteins of the un-annotated protein and their available information. In this paper, we only select those proteins that directly interact with the un-annotated protein as the neighbours. This neighbour selection method might lead to the genuine functions of the un-annotated protein being excluded from the final predicted functions. Further research is needed to select neighbours more reasonably to improve the prediction quality while reducing the impact of noise data. Another issue that comes to our notice is that in our algorithm we use a simple method to calculate the similarity of two proteins from their functions. Although this similarity calculation method significantly reduces the computational cost, it might not be able to precisely reflect the real similarity between proteins. Certain aggregation methods that make use of different data sources could be used to derive a more precise and reasonable protein similarity, and in turn, improve the prediction quality.XC participated in the study of prediction algorithms, carried out experiments and result analyses, and drafted the manuscript. JH conceived of and coordinated the study, carried out the study of prediction algorithms, participated in experimental result analyses, revised and finalized the manuscript. All authors read and approved the final manuscript.


RNA-protein interactions (RPIs) play important roles in a wide variety of cellular processes, ranging from transcriptional and post-transcriptional regulation of gene expression to host defense against pathogens. High throughput experiments to identify RNA-protein interactions are beginning to provide valuable information about the complexity of RNA-protein interaction networks, but are expensive and time consuming. Hence, there is a need for reliable computational methods for predicting RNA-protein interactions.RPISeq, a family of classifiers for predicting RNA-protein interactions using only sequence information. Given the sequences of an RNA and a protein as input, RPIseq predicts whether or not the RNA-protein pair interact. The RNA sequence is encoded as a normalized vector of its ribonucleotide 4-mer composition, and the protein sequence is encoded as a normalized vector of its 3-mer composition, based on a 7-letter reduced alphabet representation. Two variants of RPISeq are presented: RPISeq-SVM, which uses a Support Vector Machine (SVM) classifier and RPISeq-RF, which uses a Random Forest classifier. On two non-redundant benchmark datasets extracted from the Protein-RNA Interface Database (PRIDB), RPISeq achieved an AUC (Area Under the Receiver Operating Characteristic (ROC) curve) of 0.96 and 0.92. On a third dataset containing only mRNA-protein interactions, the performance of RPISeq was competitive with that of a published method that requires information regarding many different features  of the putative RNA and protein partners. In addition, RPISeq classifiers trained using the PRIDB data correctly predicted the majority (57-99%) of non-coding RNA-protein interactions in NPInter-derived networks from E. coli, S. cerevisiae, D. melanogaster, M. musculus, and H. sapiens.We propose RPISeq demonstrate that RNA-protein interactions can be reliably predicted using only sequence-derived information. RPISeq offers an inexpensive method for computational construction of RNA-protein interaction networks, and should provide useful insights into the function of non-coding RNAs. RPISeq is freely available as a web-based server at http://pridb.gdcb.iastate.edu/RPISeq/.Our experiments with  Most of the essential molecular functions of cells are governed by interactions of proteins with other proteins, nucleic acids and small ligands. Computational studies of protein interaction data have helped identify protein-protein interaction PPI networks in various organisms ,2. SimilComputational studies of RNA-protein interactions have largely focused on the "interface prediction problem", i.e., the problem of identifying the amino acid residues in a protein that are likely to bind to an RNA -22. OnlyMachine learning offers one of the most cost-effective approaches to constructing predictive models in settings where experimentally validated training data are available. At present, however, it is unclear whether the available experimental data regarding RNA-protein interactions are sufficient for successfully training classifiers using machine learning algorithms. Against this background, this study explores machine learning approaches to train sequence-based classifiers for predicting RPIs.et al.  does not directly report predictions as to whether or not a specific RNA-protein pair is expected to interact (the "partner prediction problem"), we were not able to directly compare our results with their method [Bellucci et al.  used a vr method .et al. [et al. [RPISeq-RF, which uses only sequence information. Our RF classifier achieved an accuracy of 68%, based on 500 trees, results comparable to the 70% reported for the RF classifier of Pancaldi and Bähler [Pancaldi and Bähler et al.  also emp [et al. , and 5,1 [et al. . They ald Bähler . Our SVMd Bähler .In the Pancaldi and Bähler study, only 5,166 out of a total of 13,243 positive mRNA-protein pairs were actually used for prediction, because some of the features required by the classifiers were not available for the remaining 8,000 pairs . When weRPISeq is computational construction of RNA-protein interaction networks. Recently, Nacher and Araki [RPISeq could be useful for constructing networks of ncRNA-protein interactions, we evaluated our method in predicting RPIs in networks derived from NPInter. Because the NPInter RPI pairs do not include any pairs derived from ribosomes, in this experiment, we also compared the performance of models trained on the RPI369  versus RPI2241, to evaluate the potential effect of strong ribosomal sequence bias on performance.An important potential application of nd Araki  used RPInd Araki , a databRPISeq are estimates of interaction propensities for a specific RNA-protein pair. In Tables Tables In contrast, when trained on the RPI369 dataset, the SVM classifiers out-performed the RF classifiers  versus an RF classifier trained on the RPI369 dataset (46.9%). In contrast, for predicting human and mouse RNA-protein interactions, SVM classifiers trained on the RPI369 dataset  provide the best prediction performance. For yeast RPIs, both the RF and SVM classifiers trained on RPI2241 generated excellent predictions, 98.0% and 99.2%, respectively, whereas classifiers trained on RPI369 made more errors, with correct predictions for 66.1% (RF) and 89.0% (SVM) of the cases.With regard to the effects of ribosomal sequence bias, these results are somewhat difficult to interpret. The best "overall" prediction performance was obtained using the SVM classifier trained on the RPI369 dataset , with 83.4% interactions correctly predicted; the RF classifier trained on the RPI2241 dataset  correctly predicted 80.2% of the total interactions. Differences in performance of classifiers trained on the two different datasets are significant when predictions for each model organism are considered individually. For example, for S. cerevisiae, based on the data in NPInter. In Figure PISeq predictions obtained using classifiers trained on the RPI2241 dataset are mapped onto the network. As described above, the SVM classifier (right) makes more correct predictions (green edges) and fewer incorrect predictions, i.e., false negatives, (red edges) than the RF classifier (left). In Figure Seq predictions made using classifiers trained on the RPI369 dataset, which results in more errors, are shown.Figure One protein hub (highlighted in yellow), which appears as a green square node with connections to several RNA nodes (pink circles), is apparent in these views of the network. It corresponds to the yeast SEN-1 helicase, which is known to interact with several snoRNAs . SeveralFigure RPISeq, for predicting RNA-protein interaction partners, using only sequence information, with up to 90% average accuracy. We also demonstrate, that RPISeq can effectively predict RNA-protein interaction networks, based on evaluation using available data from five model organisms.Regulation of gene expression at the post-transcriptional level is often mediated by interactions between RNA binding proteins and mRNAs or ncRNAs ,11,40. Iin vivo or in vitro cross-linking studies focused on individual proteins . rRNA-ribosomal protein pairs constitute ~ 40% of the total, reflecting the predominance of ribosomal structures in the current version of the PDB. To investigate the impact of this bias on machine learning methods for predicting RPIs, we also generated a smaller dataset of 369 RNA-protein partners (RPI369), from which all rRNA-containing complexes had been removed (see Methods for details).We used RPI2241 and RPI369 as non-redundant benchmark datasets for developing and rigorously evaluating the performance of various machine learning classifiers. In cross-validation experiments, classifiers trained and tested on the larger dataset had superior prediction performance, indicating that the greater number and diversity of complexes in RPI2241, relative to RPI369, has a stronger positive effect on classification accuracy than the potentially negative effect of sequence bias in RPI2241. When we evaluated classifiers using independent datasets of RPIs from NPInter, however, classifiers trained on RPI369, in some cases, had better prediction performance. The basis for this observation is currently under investigation.Methods for details).To identify sequence features of the proteins and RNA important in determining their specific interactions, we analyzed the features most frequently used by the Random Forest classifier to predict interacting partners . The complete list of important RNA and protein features is provided as Supplemental data S1  in combination with appropriate machine learning methods, provide an effective approach to construct RPI predictors. Because the data used in this study represent only a small fraction of cellular RNA-protein complexes and interactions, we anticipate that more accurate predictions will be possible when larger and more diverse datasets of experimentally validated RPIs become available.In this study, RPISeq methods do not suffer from this limitation because they require only sequence-derived features to make reliable predictions. In fact, the performance of RPISeq improved substantially (by 8% in accuracy) when evaluated on the entire dataset of Pancaldi and Bähler. Thus, for predicting mRNA-protein interactions, the sequence-based approach implemented in RPISeq provides performance comparable to that of classifiers that require a more extensive set of features, including those that cannot be extracted from RNA and protein sequences alone.The method of Pancaldi and Bähler , which wRPISeq in predicting specific RPIs, we examined its effectiveness in constructing RNA-protein interaction networks in several model organisms, using only information derived from RNA and protein sequences. The networks were extracted from the "ncRNA binds protein" category of NPInter [RPISeq was able to successfully predict the interactions of a single protein with multiple RNAs (protein hubs), as well as interactions of a single RNA with multiple proteins (RNA hubs).Encouraged by the success of  NPInter , currentS. cerevisiae, RPISeq provided excellent predictions of RPIs: both the RF and SVM classifiers trained on the RPI2241 dataset correctly predicted > 98% of interactions in the NPInter database [RPISeq-RF classifier trained on the RPI2241 dataset also correctly identified a large majority of interactions in the D. melanogaster (99%) and E. coli (92%) networks. For human and mouse networks, however, classifiers trained on the RPI369 dataset gave better performance, with the RPISeq-SVM classifier correctly identifying 83% of the interactions in human and 93% in the mouse. It is important to note that these evaluations are based on predicting only known "positive" interactions currently available in NPInter ["negative" data regarding non-interacting protein-RNA-protein pairs are not included in NPInter. Because the experimental data in NPInter are incomplete, it is problematic to assume that RNA-protein pairs not included in NPInter do not, in fact, interact. Also, some experimentally-determined RPIs included in NPInter could correspond to false positives.In the case of the yeast, database . The RPI NPInter ; "negatiRPISeq should be valuable for constructing and analyzing regulatory RNA-protein interaction networks.Given the relatively small sizes of the RNA-protein networks analyzed in this study, differences in the results obtained using different classifiers to predict RPIs in different species must be interpreted with caution. It will be important to evaluate these methods on larger, more complete datasets of experimentally validated RNA-protein interactions as they become available. On the whole, our results suggest that RPISeq, a family of purely sequence-based classifiers, can be used to predict whether a specific RNA-protein pair is likely to interact. Our results demonstrate that the corresponding RNA and protein sequences alone contain sufficient information to allow reliable prediction of RPIs. Such predictions can be used to: (i) identify putative RNA partners of a target protein, or protein partners of a target RNA; and (ii) computationally construct RNA-protein interaction networks. The datasets used in this study are relatively small compared with the large number of RNA-protein complexes and diverse interactions that occur in cells. The increasing availability of transcriptome-wide experimental data should lead to improvements in computational methods for predicting RNA-protein interactions and for modelling regulatory networks of RNA-protein interactions. RPISeq is freely available as a web-based server at http://pridb.gdcb.iastate.edu/RPISeq/.In this work, we tested whether For training and testing classifiers, two benchmark non-redundant datasets of RNA-protein interacting pairs were extracted from 943 protein-RNA complexes in PRIDB using an 8 Å distance cut-off . PRIDB iTo generate a balanced dataset of "non-interacting RNA-protein pairs" (negative examples), we randomly paired the RNAs and proteins from the 943 protein-RNA complexes and removed similar interacting RNA-protein pairs . Because ~40% of RNA-protein complexes in the PDB correspond to ribosomal structures, the RPI2241 dataset is also strongly biased towards ribosomal RPIs. Thus, we constructed a second dataset, RPI369, which is a subset of RPI2241 generated by removing all RPIs that contain ribosomal proteins or ribosomal RNAs and is provided as Supplemental data S3  dimensional vector, where each element of the vector corresponds to the normalized frequency of the corresponding 3-mer in the sequence Each RNA-protein pair is represented as a 599-feature vector, in which 343 features are used to encode the protein sequence and 256 features are used to encode the RNA sequence. Proteins are encoded using the conjoint triad feature (CTF) representation previously used by Shen et al . In thisnce  dimensional kernel-induced feature space in which the patterns become separable or nearly separable. Given a training set consisting labeled examples of the form  where Xi is an n-dimensional input vector and yi = 0/1 is its label , the SVM learning algorithm effectively selects the hyperplane that maximizes the margin of separation between the training samples of the two classes from among all separating hyperplanes. If the examples are not perfectly separable in the kernel-induced feature space, a user-chosen parameter C is used to trade off training error (the number of misclassified training examples) against margin for the correctly classified training examples.The SVM classifier  classifiε = 1.0E-12. We set C = 1.0 and tolerance parameter T = 0.0010. We then used the option to fit a logistic model to the output of the resulting SVM classifier to obtain the posterior probability of class from the SVM output for any given input.In our study, the input to the SVM classifier is a 599-dimensional vector that encodes features of a given pair of RNA and protein sequences as described above. The output of the SVM is a binary label indicating whether the given RNA-protein pair interact or not. We used the Sequential Minimal Optimization SMO implementation in Weka 3.7  to trainm variables selected at random from the set of input features. Given a query instance, the majority vote of all the classifiers is returned as the RF prediction. We used the Random Forest implementation in Weka 3.7. By default, Weka builds a RF classifier as an ensemble of 10 trees and sets the value of m = log_2 (number of features) + 1. For most of our experiments, we set the number of trees to 20 and 10 features were evaluated at each node. For comparison with the method of Pancaldi and Bähler [RandomForest (RF)  is an end Bähler , we set AttributeSelection class in Weka toolkit. We used wrapper subset evaluator in combination with Random Forest classifier and best first search method.For performing feature selection, we used Standard 10-fold cross-validation procedures were used to evaluate and compare classifier performance on the benchmark datasets. For the RF classifier, we also performed leave-one-out cross-validation; results were not significantly different from those obtained using 10-fold cross-validation (data not shown).et al. [We computed the following statistics, as described in Baldi et al. , to measwhere TP is the number of true positives, FP is the number of false positives, TN is the number of true negatives, and FN is the number of false negatives.The F-Measure is a composite indicator of performance that attempts to "balance" precision and recall. F-Measure values range from 0 to 1, with values close to 1 indicating better performance. The area under the curve (AUC) of the receiver operating characteristic curve (ROC) was also computed. AUC values also range from 0 to 1: the AUC = 1 for a perfect classifier and for a random classifier = 0.5.RPISeq webserver and prepared the initial draft of the manuscript. DD and VGH contributed to the experimental design, supervised the work, and edited the manuscript. All authors read and approved the final manuscript.UKM conceived the study (with DD and VGH), carried out the experiments, implemented the List of RNA and protein features important for distinguishing interacting and non-interacting RNA-protein pairs (S1).Click here for filePositive RPIs in the RPI2241 dataset. This is a tab-delimited file with two columns. The first column is a list of proteins and the second column is a list of corresponding RNAs (S2).Click here for filePositive RPIs in RPI369 dataset. This is a tab-delimited file with two columns. The first column is a list of proteins and the second column is a list of corresponding RNAs (S3).Click here for file


The iRefIndex consolidates protein interaction data from ten databases in a rigorous manner using sequence-based hash keys. Working with consolidated interaction data comes with distinct challenges: data are redundant, overlapping, highly interconnected and may be collected and represented using different curation practices. These phenomena were quantified in our previous studies.The iRefScape plug-in for the Cytoscape graphical viewer addresses these challenges. We show how these factors impact on data-mining tasks and how our solutions resolve them in a simple and efficient manner. A uniform accession space is used to limit redundancy and support search expansion and searching on multiple accession types. Multiple node and edge features support data filtering and mining. Node colours and features supply information about search result provenance. Overlapping evidence is presented using a multi-graph and a bi-partite representation is used to distinguish binary and n-ary source data. Searching for interactions between sets of proteins is supported and specifically includes searches on disease-related genes found in OMIM. Finally, a synchronized adjacency-matrix view facilitates visualization of relationships between sets of user defined groups.The iRefScape plug-in will be of interest to advanced users of interaction data. The plug-in provides access to a consolidated data set in a uniform accession space while remaining faithful to the underlying source data. Tools are provided to facilitate a range of tasks from a simple search to knowledge discovery. The plug-in uses a number of strategies that will be of interest to other plug-in developers. Each protein interactor is assigned a "Redundant Object Group Identifier" or ROGID using its primary amino acid sequence, NCBI taxonomy identifier and the SHA-1 digest algorithm ,15. ROGIUsing interaction data can be difficult due to a number of challenges that are distinct to this data type: multiple accession systems for protein data, high redundancy between interaction databases, multiple methods for complex representation, the scale-free nature of interaction networks and the resulting impact on visualization. Some of these issues have been discussed at length in our previous papers ,16,17. Hhttp://irefindex.uio.no. Corrections made to source data were essential for legacy databases  that are no longer updated.Version 8.0 of the iRefIndex accompanies the release of iRefScape (1.16) described in this paper (see Methods). The final data set is based on 1,057,642 source interaction records but is only composed of 480,368 distinct interactions (RIGID's) involving 86,757 distinct protein interactors (ROGIDs). Version 8 includes 2,580 updates for protein database accessions, 4,748 corrections to malformed accessions, 19,278 corrections to taxonomy identifiers and more than 8,084 resolutions of ambiguous identifiers. Terms describing interaction type, interaction detection method and interactor detection method were normalized to PSI-MI ontology terms. Full statistics for each release are provided at The highly redundant nature of protein interaction data from multiple sources has been described previously . CentralInstallation of the iRefScape plug-in is a two step process. First, the plug-in itself is installed using the Cytoscape "plug-in manager". Second, the plug-in queries the user for a permissible location to store data and then retrieves the entire iRefIndex dataset via File Transfer Protocol (FTP). An "Installation and index handler" module executes these functions with a minimum of user intervention.All iRefScape operations are performed on this local dataset. We chose this local approach (as opposed to web-services) for a number of reasons. Data retrieval is independent of connectivity over a network and it is not subject to communication overhead or server outages; therefore, it is fast and reliable. Local search is also private; a concern among commercial users. A local dataset, being static, ensures that results can be reliably reproduced and compared over the course of a study where multiple search strategies may be examined. Finally, a local dataset also affords the possibility for the plug-in's functions to operate over an entire interactome and a large set of attributes: something that would be impractical if the data were not already available locally. In addition, the user can include and search on a private set of attributes for any node or edge in the iRefIndex data set.We found that this approach was a feasible option for data delivery in terms of both required disk space and search times. Download and indexing of the 362 MB package for release 8.0 of iRefIndex required less than 10 minutes using a remote, 10 Mbps internet connection. The data package is compressed on arrival and is dynamically uncompressed as required by user searches (see Data access optimizations in Methods). Thus, a search will take less time to return results after it has been performed once. For example, it takes 9 seconds to retrieve interactions involving UniProt:Q39009 and UniProt:Q9ZNV8 for the first time while the same operation subsequently takes only 2 seconds.originalReference search type.An identifier for a protein (or a list of identifiers for multiple proteins) may be entered via a query box or from a file. Multiple accession-types are supported including those from RefSeq and UniProt. Entrez Gene IDs and official gene symbols are converted to accessions for their corresponding protein products. This functionality is driven by lookup tables where the user's query retrieves a pre-computed redundant object group identifier (ROGID) . Since aThe canonicalization process groups together multiple proteins that are all products of the same or related genes and then chooses one of these proteins to be the canonical representative for the whole group (see Methods). Figure A query for a protein will return its nearest neighbours. However, interactions between these first order neighbours will not be returned by default unless the user opts to complete the neighbourhood once the first order neighbours have been returned. Figure A common difficulty working with graphical data is distinguishing between nodes matching search parameters from their interactors. We have addressed this issue using a number of visual cues and node/edge features.Nodes that match search parameters are coloured blue while direct interactors are green Figure . ColoursThe "Grid" layout was selected as the default arrangement for all new search results. This algorithm was the fastest amongst those investigated for reasonably sized networks . Users are likely to alter the layout while viewing search results so these alterations are preserved as subsequent search results are drawn; only newly introduced nodes are arranged in a distinctive grid layout making them easier to locate in a graphical view.interaction. However, the experimental type and interaction type for each edge in this group may be different. Each edge is listed in the edge attribute browser along with source database and supporting publication details allowing easy linking to the original data. The edge attribute browser may also be used to sort and select (or remove) edges with specific attributes. For example, the only source of predicted interaction data in iRefScape is OPHID - these edges may be located and high-lighted using the edge attribute for source database (i.src_intxn_db). As a special precaution, OPHID edges are drawn using dashed lines so they are visually distinguishable from other data. All other data in iRefScape is based on experimental observation. Again, edge attributes corresponding to experimental method (i.method_name and i.method_cv) may be used to sort, select and high-light specific edges.Search results are presented as a multi-graph . Each node represents a distinct protein sequence from some organism (ROGID). Each edge joining the same two nodes will have the same RIGID (Redundant Interaction Group Identifier) because each represents an experimental observation supporting the same This multi-graph representation can become visually cluttered. We therefore included the ability to collapse multiple edges, leaving only a single (randomly selected) edge in the view panel (see iRefScape menu/View Tools/Toggle selected multi-edges). The edge-toggle operates using the edge attribute "i.flag" so the user can manually alter the edges that are retained in the toggled view. Collapsed edges can be re-expanded by selecting the same edge-toggle function again.Multiple edges between nodes represent a mixture of records that are either duplications within or between databases or that are multiple evidences for relations between the same two proteins. These two cases are easily distinguished in iRefScape by examination of edge attributes . The observed two-fold redundancy in interaction data underscores the need for visual tools that allow the user to visually manage related data.pseudonodes. Protein nodes  adjacent to this node represent members of the record  is used to refer to interaction records that contain more than two protein participants. This term distinguishes such records from binary interaction records where only two interactors are listed. Multi-protein interaction records are used by some databases to capture the results of certain types of experiments where a physical association is detected between a number of proteins but where the presence or absence of a direct physical interaction between any given pair of proteins in the set cannot be determined . As such, n-ary data is fundamentally different from binary data and we have preserved this difference in iRefScape. N-ary records are represented by hexagonal Of the 433,617 distinct interactions (RIGID's) in iRefIndex, only 15,056 (3%) have greater than two participants. However, these records involve 20,228 distinct proteins (ROGIDs) or 24% of the dataset. The bi-partite representation described here clearly distinguishes involvement of these proteins in "n-ary" interactions from involvement in binary interactions that include evidence for direct physical interactions.Users should be cautious in reading meaning into the labels "binary" and "n-ary" data. N-ary data does not necessarily constitute evidence for a biological complex: only that a group of proteins were observed together in some experimental result. Likewise, binary data does not necessarily constitute evidence for a direct physical interaction and in some rare cases may even be a spoke representation of a complex (see section 4.1). In all cases, it is important to examine the experimental type and/or the original publication before drawing such conclusions. Links to abstracts are provided in the interface as an edge attribute (i.PMID).i.overall_degree and i.alive_degree respectively). Edge attributes include interaction type, interaction detection method, publication identifier, source interaction database and accession, and directionality (for bait-prey systems). Controlled-vocabulary terms and identifiers are provided where possible and many of the attributes allow linking out to external databases. Bibliometric scores (i.score_np and i.score_lpr) help the user to identify edges supported by multiple citations and distinguish edges supported only by high-throughput studies respectively.A large number of node and edge attributes are included with search results to facilitate further filtering and visualization of data. A complete list of these features can be found on the iRefScape wiki site . Node atUsers can create filters for search results using Cytoscape's in-built edge and attribute filters. In addition, a complementary, advanced filter utility is included that allows the user to build up and visualize more complicated queries (see Advanced Features/Filter). Instructions are provided in the plug-in.Nodes matching filter criteria reset an attribute called i.alive to TRUE. Another node attribute  is updated to reflect the degree of a node with respect to neighbours with i.alive set to TRUE. This feature is useful for identifying nodes in the view that are highly connected to a user-defined set of nodes. As a short-cut, the user may simply select a set of nodes and then select "iRefScape menu/View Tools/Select between nodes" to do the same thing. Nodes that are highly connected to the original selection can be selected and sorted on the i.alive_degree node feature.N-ary data is sometimes represented using a spoke model where a series of binary interactions between one member chosen to represent the hub and each of the other members are created . This isiRefIndex 8.0 contains more than 77,048 distinct binary interactions (RIGID's) that may belong to spoke-represented complexes: these are sets of two or more binary interactions originating from the same database that all share the same publication reference, the same experimental method (known to produce n-ary data) and a common interactor (hub node). These binary interactions can be used to identify 21,251 cases in version 8.0 of iRefIndex where a source database may be using a spoke representation of a complex. The "Show spoke-represented complexes" tool draws a grey hexagon with dashed lines to each member of the potential complex. The user must still review the source publication to confirm that they contain evidence for a protein complex .Genes that are associated with phenotypically related diseases are quite often associated in an interaction network . We haveiRefScape supports searching for OMIM identifiers corresponding to gene-disease associations. Our disease group identifiers may also be searched in order to retrieve all proteins related to the same disease group as some OMIM identifier. Partial match searching of OMIM titles is also supported. Figure Approximately 400 disease groups were constructed that contain two or more related human genes. These groups cover just fewer than 2000 genes, the majority of which have relevant interaction data in iRefIndex. A systematic survey of all statistically significant overlaps between disease groups and interaction data is being preparedDue to the complexity of the protein interactome, it is difficult for the user to arrive at inferences by visual inspection of a graphical representation alone. We have implemented an adjacency matrix view to provide a very simple overview of the connectivity between two, user-selected groups of nodes. This adjacency matrix view is synchronized with Cytoscape's graphical view allowing users to move back and forth between the two representation types. In this view, members of group A and B appear as column and row headings respectively. If a node was found in both groups it will appear as a column and row heading. A cell at the intersection of a particular column and row contains information about the relationship between the two proteins appearing in the column and row headers. There are various possibilities:A) When only direct interactions between a row protein and a column protein exist, a "¤" symbol appears in the intersection cell and the cell will be coloured red.B) When only indirect interactions or co-complexes involving the row protein and column protein exist, the cell will be coloured blue. These are interactions involving an intermediate protein or both proteins found together in an n-ary record. The intermediate protein or the complex-node will be listed in the intersection cell.C) When there are both direct and indirect interactions, the intersection cell will be coloured green. A "¤" symbol and all intermediate proteins or complex nodes will be listed in the intersecting cell.D) When there are no direct or indirect interactions involving the row and column proteins, the cell colour is black. Entire columns or rows with only black cells will be hidden by default.E) As a special case, when the row and column protein are the same (the protein is found in both groups), proteins directly interacting with this protein will be listed in the intersecting cell.Clicking on column/row headings or intersection cells will select and highlight nodes and/or relevant edges in the graphical view. Figure iRefScape uses an internal integer identifier (iROGID) as the main node identifier (see the node feature ID in the Cytoscape interface). Other plug-ins may require that a specific identifier type (Entrez Gene ID or UniProt/KB accession) is used as the primary node identifier (e.g. BinGO requires Gene Ids ). As a sHelp buttons (?) are distributed throughout the plug-in interface to provide context-relevant help. These buttons open the iRefScape info window. Help pages include macros ("Show me an example") that perform pre-recorded operations to help step users through the interface. Likewise, a "Wizard" button can be used to walk first-time users through simple searches. The iRefScape wiki provides additional details .The Cytoscape Plug-in Manager (Plug-ins/Manage Plug-ins menu) can be used to install and update the plug-in. Installation instructions  are available from the iRefScape wiki . Users cWe have presented an interface that facilitates visualization, navigation and data mining on a consolidated protein interaction data set. Working with consolidated interaction data comes with distinct challenges that were identified in earlier studies. The features incorporated in the plug-in address many of these issues.The iRefScape plug-in operates on a locally downloaded dataset organized around a uniform naming space for interactions and interactors. This approach handles redundancy in the underlying data set and supports searching on multiple accession types. Searches can be expanded to retrieve data relevant to all splice isoforms of a queried protein. Visual representation of the graph distinguishes between n-ary and binary interactions. A tool is provided to help identify spoke-represented complexes. Multiple sources of evidence for a protein-protein relationship can be individually visualized, examined and filtered on. Advanced filters are provided to identify nodes that are highly connected to a user-defined set of nodes. An adjacency-matrix viewer helps users pick out and explore links between two groups of user-defined nodes. Coupled together with direct-support for disease group searching, we imagine that these functions will be useful for exploring relationships within and between complex diseases.We have quantified different aspects of the data as justification for the features included in the plug-in and as a guide to expectations for the user as well as other developers of plug-in software. We hope this effort will benefit users not only as a search interface for consolidated interaction data but also as a tool for knowledge discovery.The iRefScape plug-in was developed using guidance provided by the Cytoscape plug-in development tutorial. The development was carried out using the Java Development Kit 1.6 and NetBeans as an integrated development environment. Apache Commons was used for file download management.Version 8.0 of the iRefIndex dataset was constructed as described in . Data isEach protein interactor is assigned a canonical identifier (cROGID). This allows related proteins (say from the same or related genes) to be identified and possibly grouped together by the end user.Entrez Gene records are associated with a list of zero or more distinct protein products (as indicated by the ROGIDs for these proteins). Entrez Gene identifiers were grouped together into related gene groups (RGGs) if they shared at least one identical protein product. Therefore each RGG has an initial list of distinct protein products encoded by at least one of its member genes and represented by a set of RefSeq protein records. This initial list was expanded to include (1) distinct proteins from UniProt proteins that were isoforms related to one of the proteins already existing in this list and/or (2) UniProt proteins that cross-referenced one of the Entrez Gene identifiers in the RGG. From this expanded list of proteins, one distinct protein was chosen to represent the canonical isoform for the entire list. If one of the proteins was a canonical sequence (as defined by UniProt ) then thWe investigated three methods for data access including web-services and finally settled on a locally installed dataset for reasons given in the Results section . The indThe first step of any protein identifier search is to find the corresponding ROGID for the protein using a pre-calculated identifier-to-ROGID index. ROGIDs are used to retrieve relevant interactions (RIGIDs). Finally, attributes for each node and edge are loaded into Cytoscape's attribute browser. Attribute data is stored locally at installation time in separate jar (Java archive) files for each node and edge. These files are named after the corresponding ROGID or RIGID (in its filename-safe version ). At seaAfter evaluating 15 open-source layouts distributed with Cytoscape, we selected the "Grid" layout for initial presentation of search results as it was the fastest to draw , 2 s (force-directed), 5 s (attributes-layout) and 351 s (jgraph-gem). We defined our own visual properties for nodes and edges using the Cytoscape VizMapper (iRef style). In some cases, this style refers to node and edge attributes imported at installation time; for instance, to help distinguish between protein nodes and pseudonodes representing n-ary data. Users can change this style in Cytoscape's VizMapper tab.The adjacency table view was constructed using a Java JTable . Nodes aThe query entered into the search box for Figure COMPARE{P08254,P08588,P16671,P17302,P18825,P78504,Q14524, Q9UGJ0,Q9Y4J8|O00253,O75056,P01189,P07550,P13945,P25874,P29120,P32245,P37231,P41159,P41968,P48357,P52895,P55851,P55916,P81133,Q15466,Q16620,Q86YN6,Q9UBU3}.Iteration was set to 1, search type "UniProt_AC" and taxid = 9606(Human). During the loading process empty rows and columns were removed to make observation easier (selected by default). After the results were loaded the results were converted from ROGID to UniProt/KB to make the comparison with the original paper .Testing of the iRefScape plug-in installation and operation was carried out using version 2.8.1 of Cytoscape running on several operating systems including Mac OS X, Windows Vista, Windows 7, and Red Hat Enterprise Linux. In addition to the test procedures carried out during the iRefIndex data release process, we have also carried out spot checks on iRefScape search results to ensure that they matched data from the primary source databases. The test cases and intended results were tabulated on the iRefScape wiki site .SR was responsible for all code development. AM developed functionality to find spoke-represented complexes. KM developed disease groups. PB and SR assembled iRefIndex data. IMD supervised the project. SR and IMD wrote the manuscript. All authors participated in testing and final preparation of the manuscript.


A hub protein is one that interacts with many functional partners. The annotation of hub proteins, or more generally the protein-protein interaction “degree” of each gene, requires quality genome-wide data. Data obtained using yeast two-hybrid methods contain many false positive interactions between proteins that rarely encounter each other in living cells, and such data have fallen out of favor.Saccharomyces cerevisiae, a protein’s high stickiness, but not its high number of functional interactions, predicts low stochastic noise in gene expression, low plasticity of gene expression across different environments, and high probability of forming a homo-oligomer. Our results are robust to a multiple regression analysis correcting for other known predictors including protein abundance, presence of a TATA box and whether a gene is essential. Once the higher stickiness of homo-oligomers is controlled for, we find that homo-oligomers have noisier and more plastic gene expression than other proteins, consistent with a role for homo-oligomerization in mediating robustness.We find that protein “stickiness”, measured as network degree in ostensibly low quality yeast two-hybrid data, is a more predictive genomic metric than the number of functional protein-protein interactions, as assessed by supposedly higher quality high throughput affinity capture mass spectrometry data. In the yeast Our work validates use of the number of yeast two-hybrid interactions as a metric for protein stickiness. Sticky proteins exhibit low stochastic noise in gene expression, and low plasticity in expression across different environments. A protein that functionally interacts with many other proteins may be more sensitive to noise in gene expression. In agre2 = 0.008, p = 2e-05). Y2H and ACMS data clearly measure different things.Y2H data may indicate the non-specific “stickiness” of a protein towards a random polypeptide better than it indicates the number of functional protein-protein interactions that the protein is involved in,10. The Here we find that Y2H degree/stickiness predicts gene noise better than ACMS/“real PPI” degree does. It has previously been argued that a protein that functionally interacts with many other proteins will be more sensitive to noise. HoweverHere we also introduce a new metric of plasticity, i.e. the variation in gene expression across different experiments. Again, we find that Y2H degree/stickiness predicts plasticity better than higher quality ACMS data on the number of functional PPIs. For both noise and plasticity, our results are robust to a multiple regression analysis that controls for protein abundance and that controls noise for plasticity and vice versa. Other significant predictors include the presence of a TATA box, whether a protein forms a homo-oligomer, and gene essentiality.2 = 0.1083) included Y2H, but not ACMS, as a predictor of noise. The second numeric column shows the R2 when a single predictor is considered in isolation. These values are given as a contrast to our primary results in the first numeric column, which show the extent to which the coefficient of determination is reduced if a predictor is removed from the best model. For the purposes of more graphical illustration, FigureTableThe strongest predictor for noise is the presence of a TATA box, consistent with earlier findings: TATA boxes are associated with higher noise-13. GeneGenes that interact with themselves (form homo-oligomers) have higher noise than genes that do not self-associate. Explanations for this novel finding are explored further at the end of the Results section and in the Discussion.Genes with high noise in a single environment tend also to have high variation across different environmental conditions (plasticity), due at least in part to mechanistic coupling at the promoter level,11,15-182 rises to 0.1609), although many of the R2 values attributable to specific predictors are modestly reduced. Correlations between noise and plasticity are known to be stronger in genes containing a TATA boxn) where θ is the proportion of active protein and n is the Hill coefficient, which is related to, but often lower than, the number of subunits in the active complex  on this number, followed by a loess regression against protein abundance Figure. SubsequThe Y2H data were isolated from downloads of the BioGRID Interaction Database, Database for Interacting Proteins (DIP), IntAct database, and Molecular INTeraction Database (MINT)-59, yielSelf interaction status was assessed using Y2H data. Y2H data frequently contain false positive PPIs between proteins that would never be expressed in the same place and time. This drawback is clearly not a problem for the assessment of self-interactions, and Y2H rather than ACMS data were used to minimize false negatives.Multiple regression models were calculated using a linear regression function (lm) in the R statistical computing environment. Continuous variables  were transformed, as described above, to make the data normal or nearly so and, in the case of noise and plasticity, to control for the confounding factor of protein abundance. Note, however, that both of the log-transformed PPI variables have truncated normal distributions, due to a floor at zero. The coefficients of determination of nested models were compared using an ANOVA. See FigureThe authors declare that they have no competing interests.JM conceived the study. LB and JM contributed to the design of the study, to the analysis and interpretation of the results, and to writing the manuscript. LB carried out the study. All authors read and approved the final manuscript.