We previously suggested that comparing the sets of interactors for different proteins should allow detection of functional similarity independently of the sequence information 19. We therefore developed the PRODISTIN method based on the principle that the more two proteins share common interactors, the more likely they are to be functionally related. In practice, starting from a list of binary protein-protein interactions, the PRODISTIN method consists of three different and successive bioinformatic steps (Figure 1, see Materials and methods for details). First, a graph comprising all proteins connected by a specific relation is constructed and a functional distance is calculated between all possible pairs of proteins in the graph with regard to the number of interactors they share. Second, all distance values are clustered, leading to a classification tree. Third, the tree is visualized and subdivided into formal classes. We thus define a PRODISTIN class as the largest possible subtree composed of at least three proteins sharing the same functional annotation and representing at least 50% (the absolute majority) of the individual class members for which a functional annotation is available. Classes of proteins are then analyzed for their biological relevance and tested for their statistical robustness.

In the first experiment, we analyzed 2,946 yeast protein-protein interactions involving 2,139 proteins, that is, 38% of the Saccharomyces cerevisiae proteome 2021. The classification tree obtained contains 602 proteins (Figure 2).

To understand the biological foundation of PRODISTIN clustering, we examined different possibilities that could explain protein segregation in the tree. First, we tested whether sequence similarity correlates with our clustering results, given the abundance of proteins involved in related functions that exhibit similarity in their sequences. Pairwise alignments between the sequences of the 602 yeast proteins classified by PRODISTIN were computed using a global and a local alignment algorithm. Given that the obtained distances (expressed as the percentage of similarity for global and the score for local alignments, respectively) do not fit with tree distances, the tree model is not appropriate to represent these huge alignments 22. We thus directly compared the distance values obtained with PRODISTIN, the global and the local alignments (as described above), by identifying for each distance matrix the nonredundant pairs of proteins (x, y) for which y is the closest neighbour of x or vice versa.

Among the 611 closest pairs of proteins identified with PRODISTIN, the 546 obtained with the global and the 527 obtained with the local alignment, 112 are shared between both alignments (21.2%), 32 between PRODISTIN and the global alignment (5.8%) and 38 between PRODISTIN and the local alignment (7.2%). This result strongly suggests that sequence alignments do not cluster the same proteins that PRODISTIN does, leading to the conclusion that PRODISTIN clustering is only moderately dependent on sequence similarity.

As sequence similarity is not a key determinant of PRODISTIN clustering, we then investigated the capacity of PRODISTIN to cluster proteins with identical or related functions. To do so, we separately analyzed PRODISTIN classes using two types of protein functional annotations described in the Yeast Proteome Database (YPD) 23: the 'functional category' corresponding to the biochemical function(s) and the 'cellular role' describing the cellular function(s) (see 1924 for discussions about the notion of function). Both types of function are known for 420 proteins in the tree. For comparison, PRODISTIN classes were separately constructed as defined above according to either the cellular or the biochemical function of proteins, using the 420/602 proteins annotated for both types of function (Figure 2a). Among the total of 369 proteins belonging to PRODISTIN classes, 212 (57%) are clustered according to both types of function, and 157 (43%) according to only one type of function. Strikingly, 69% of the latter (108/157) are clustered according to the cellular function whereas the remaining 31% (49/157) are grouped according to the biochemical function. Therefore, the PRODISTIN method clusters proteins more efficiently by their cellular function than by their biochemical function. This result is further validated by the following observations. First, when the subcellular localization of the classified proteins is investigated, proteins belonging to the same subcellular compartment are found clustered in the tree, as would be expected from clustering based on cellular function (data not shown). Second, when the biochemical function of proteins is considered, proteins with functions such as 'protein kinase' or 'hydrolase' are found broadly scattered in the tree. Given that proteins with such biochemical functions are likely to be involved in a large number of different cellular processes, their scattering throughout the tree is to be expected from clustering on the basis of the cellular function. Third, sequence-similarity classification of proteins differs from PRODISTIN protein clustering, as described above. Consequently, from now on, we will only consider PRODISTIN classes based on the cellular function of proteins.

Using the 509 yeast proteins of the tree annotated in YPD for 'cellular role', 64 different PRODISTIN classes were constructed, containing 3 to 36 members each. They contain two-thirds (408/602) of the tree proteins and cover 29 different 'cellular roles' out of 44 possible (Figure 2b; see also Additional data file 1). Whereas some 'cellular roles' are associated with only one class in the tree (such as 'meiosis', which is class 27 (Figure 2b, see also Additional data file 1)), several classes have the same cellular role. This generally corresponds to different aspects of a given cellular process: for instance, the six classes accounting for 'vesicular transport' (Figure 2b) are specifically devoted to autophagy (class 45), structural proteins related to actin (class 55), endoplasmic reticulum to Golgi transport (classes 56, 57), endocytosis (class 58) and exocytosis (class 59), respectively (see Additional data file 1).

A detailed analysis of the PRODISTIN classes shows that several types of classes are encountered when class functional homogeneity is considered. In the simplest case, proteins are associated with the same molecular complex or involved in a particular cellular process. Nearly half of the classes fall into this category; for instance, class 23 (Figure 3a) consists solely of five members of the peroxisomal import complex 25, and class 22 'DNA synthesis' (Figure 3d; see also Additional data file 1) contains 9 out of 12 proteins involved in DNA replication (labelled with an asterisk on Figure 3d). The two other characterized proteins belonging to this class are implicated in related and/or overlapping processes such as 'cell cycle control' and 'chromatin and chromosome structure' (Cdc23 and Spt2, respectively).

The second case corresponds to classes annotated with two different cellular roles. These classes either cluster multifunctional proteins that are doubly annotated (all the peroxisomal proteins forming class 23 are involved in 'lipid fatty acid and sterol metabolism' as well as in 'protein translocation' (Table 1; see also Additional data file 1) or contain at least 50% of the proteins annotated for a cellular role, at least 50% annotated for another cellular function, and certain proteins annotated for dual functions (Table 1). For instance, three out of six proteins in class 17 'chromatin and chromosome structure/mitosis' (Figure 3b) are associated with the kinetochore (Dam1, Spc19 and Spc34, annotated 'chromatin and chromosome structure'), and five play a part in the maintenance of the spindle-pole body (Dam1, Spc19, Dad2, Dad1 and Duo1, annotated 'mitosis'), with two proteins involved in both processes (Dam1 and Spc19). Such situations illustrate cross-talk between superimposed or partially overlapping cellular processes, via the dual function of some proteins.

Finally, a third case is encountered, in which small classes are nested within larger classes (Table 1) representing another example of cross-talk between cellular processes. The example given is for class 1 'amino acid metabolism' (Figure 3c; see also Additional data file 1). The metabolism of amino acids is related to cell-cycle control (class 3, Figure 3c) through the ubiquitin-dependent proteolysis pathway mediated by the ubiquitin protein ligase complex SCF (Skp1-Cdc53-F-box protein). This complex contains two core proteins - Skp1 and Cdc53 - and a F-box motif-containing protein required for the specific targeting of certain proteins to the degradation pathway 26. Consequently, a 'cell cycle control' class containing Skp1, Cdc53 and the F-box protein Cdc4, which targets Sic1 to degradation at the G1-S transition of the cell cycle, is nested within an 'amino acid metabolism' class enclosing the F-box protein Met30, which targets the transcription activator Met4 towards degradation during methionine biosynthesis. It is interesting to note that these classes encompass the uncharacterized F-box-containing protein Flm1 which, on the basis of its position in the classification tree (Figure 3c), is a candidate to target Csm3, a protein needed for chromosome segregation at meiosis 27, towards the ubiquitin-dependent proteolysis pathway.

The detailed analysis of the classes shows that the PRODISTIN method clusters proteins belonging to the same molecular complex, pathway or cellular process, and underlines cross-talk between functions. Therefore, the method enables the extraction of complex functional information from interaction networks by considerably reducing their complexity.

Among the 602 tree proteins, 93 had no defined 'cellular role' in YPD when we retrieved annotations (see Materials and methods). As 42 of them belong to a defined PRODISTIN class, a cellular function could consequently be proposed. Our predictions (Table 2; see also Additional data file 2) were compared with predictions obtained by others using several bioinformatics methods 81828, the association of the protein to a complex of known functions 29 and recent experimental results described in the literature and reported in the Saccharomyces Genome Database (SGD) 30.

For two proteins (5%), no cellular function has ever been proposed by any other method. For 27 proteins (64%), our prediction is in accordance with or related to previously proposed ones, or the experimental results. For 13 proteins (30%), our predictions disagree (Table 2; see also Additional data file 2). When only the 19 experimentally determined functions are considered, PRODISTIN predictions are in accordance with 11/19 (58%) of them. Noticeably, when the functional predictions obtained by the global optimization method (GOM 18) for the same proteins are considered, only 4/13 (31%) predictions are in accordance with the experimentally determined functions. Taken together, these observations strengthen the relevance of the PRODISTIN predictions for the uncharacterized proteins.

Interestingly enough, the PRODISTIN method also reveals the existence of clusters containing only proteins of unknown function. In one case, a cellular function can now be proposed for the entire cluster: as class 62 (annotated 'unknown') is nested into class 56 (annotated 'vesicular transport'), all its members can therefore be associated with 'vesicular transport' and a posteriori recent experimental results strengthen our predictions (Table 2) 3132.

Finally, the putative involvement of proteins of already known function in new cellular processes is also encountered. Class 52 (Figure 3e) contains proteins involved in RNA processing, including the members of the two LSM complexes which play a part in mRNA decapping (Lsm1-7) and pre-mRNA splicing (Lsm2-8) 33. Given that two small subunit ribosomal proteins Rps28A and B have been found to interact with Lsm2, Lsm4, and Lsm8 in the two-hybrid screen from Uetz et al. 15, these authors suggested either a possible involvement of Lsm proteins in translation/ribosomal biogenesis or an unforeseen role of the ribosomal proteins in RNA splicing. As both proteins share all their interactors with Dcp1 (mRNA-decapping enzyme), PRODISTIN rather suggests a novel implication of Rps28A and B in mRNA decay.

Altogether, these results lend further support to the ability of the PRODISTIN method to directly derive a cellular function for proteins from the information contained within the interaction network, without using any additional sequence or structure information.

To evaluate the quality of PRODISTIN classifications and predictions on a more statistical basis, four different types of control experiments have been performed in order to assess the influence of various parameters.

First, given that annotations taken from databases may contain inconsistencies, our classification for the yeast proteome (originally established with YPD annotations) was further tested using the Gene Ontology (GO) annotations 34. We used the GO Term Finder tool from the SGD database to search for significant shared GO terms (or their parents) used to describe the genes of interest and to calculate a p value for the occurrence of common terms (for details see Help in 35). Lists of genes constituting all PRODISTIN classes were successively processed with the GO term finder for the 'biological process' ontology. On average, for 87.3% of the PRODISTIN classes, the best hit, that is, the common GO term with the lowest p value, is in accordance with the class annotation proposed using YPD annotations. These terms are highly statistically significant as a p value < 1e^-6 is encountered for 83.63% of the classes. Moreover, these terms applied to 77% of the class members on average. As GO terms represent an independent source of functional annotation from YPD, these congruent results confirm that PRODISTIN efficiently clusters proteins having common or related cellular functions.

In a second control experiment, the overall accuracy of our functional predictions was estimated on the basis of the ability of PRODISTIN to predict correctly the function of already known proteins. For this, we first supposed that members of a given PRODISTIN class all perform the function attributed to the class (independently of their actual function) and then compared these predictions to the known functions. We defined the prediction success rate as the ratio between the number of correctly predicted functions and the total number of predictions. In this test, PRODISTIN performances were compared with those of a 'majority rule' algorithm (MRA 28), which assigns to a given protein the function most frequently found among its neighbors in the original protein-protein network. As shown in Table 3, the highest success rate for function predictions is attained with PRODISTIN. In fact, 67% of the predictions made with PRODISTIN are correct against only 43% of the ones proposed by the MRA.

Third, we tested the robustness of PRODISTIN towards the presence of both spurious and missing interactions in the dataset because, despite the fact that it was carefully assembled (see Materials and methods), the actual accuracy of our dataset is difficult to estimate. This prompted us to test PRODISTIN's reliability when the topology of the network is disturbed by false or missing edges. For this, we rewired the network by randomly removing edges and putting them back in between pairs of proteins not already connected. PRODISTIN and the MRA were applied to these rewired networks and the pattern of change of the prediction rate was monitored when the percentage of modified edges gradually increases from 0 to 50%. Interestingly, the rate of correct predictions stays remarkably even (between 64 to 67%) (Figure 4). The number of proteins for which a prediction is possible (because they belong to a PRODISTIN class of known function) also remains quite stable (from 389 for the initial network to 471 on average for 50% rewired networks), although the actual number of proteins in the tree increases from 601 to 1,493 on average for 50% rewired networks. Comparison with the MRA clearly shows that, although this algorithm is able to offer a prediction for a larger number of proteins in the network, its success rate is always two to three times lower than that of PRODISTIN. In addition, it is also very sensitive to the introduction of false interactions, as its success rate drops dramatically from 43% for the initial network to 20% on average with 50% rewired networks. In summary, it is possible to conclude that clustering proteins within classes according to their cellular functions has a positive buffering effect on the prediction rate and that PRODISTIN is thus very robust against the presence of false interactions in the dataset.

We then tested PRODISTIN's performance on random networks of identical topologies in order to assess whether PRODISTIN clustering would have occurred by chance. For this, all protein names were reshuffled and randomly assigned to nodes in the network. The PRODISTIN analysis of such networks only allows the construction of a tiny number of classes (15 on average, instead of 63), consequently leading to a very low number of proteins for which a prediction is possible (51 on average instead of 389 in the current study). Finally, the prediction rate drops to 60%. This clearly indicates that random interaction networks never lead to both a high number of PRODISTIN classes and a correct prediction rate, as true networks do.

A final statistical assessment of PRODISTIN has been performed by measuring the robustness of the protein clusters with another criterion based on tree topology (see Materials and methods for details). For this, we applied PRODISTIN to the protein-protein interaction network of the bacterium Helicobacter pylori 14, for which information on putative true/false positives is available. Using the PBS^® algorithm, these interactions had been ranked in five experimental categories of decreasing biological confidence (from A to E) 14. A recent assessment has further confirmed the existence of a positive correlation between this reliability score and the true-positive rate 36. Classification trees built with five datasets corresponding to the interactions of categories A, A+B, A+B+C, A+B+C+D, and A+B+C+D+E were computed and tested for the robustness of their subtrees and the average robustness value was calculated for each tree (see Materials and methods for details). As expected, this value decreases as more interactions of lower biological significance occur in the dataset (Figure 5). This correlation between PBS categories and the average statistical robustness of the trees represents a fourth and independent support for the reliability of the PRODISTIN approach. In addition, the fact that the average robustness value of the yeast tree is almost equivalent to that of the H. pylori A tree reinforces the conclusion that the Saccharomyces tree is biologically meaningful.

We present here a new bioinformatics method that is able to compute a functional clustering of proteins on the basis of protein-protein interaction data. When applied to the yeast interactome, our method classified 602 proteins, representing a significant part of the proteome (11%), into 64 classes of functionally related proteins.

Our method was based on the assumption that a distance formula (the Czekanovski-Dice distance) that uses information on shared interactors could potentially mirror a functional distance between proteins. The demonstration that the classification and the protein clustering resulting from PRODISTIN are essentially driven by the cellular function of proteins gives strong support to our initial assumption. This also may be explained by the fact that the chosen distance formula makes it possible to take into account not only the functional information carried by the nearest neighbors in the protein-protein network, but also by proteins two edges away. Therefore, the obtained distance values, once clustered, are able to highlight subgraphs in the network, such as those formed by proteins involved in the same pathway(s) or cellular process(es).

As we also showed that the PRODISTIN functional distance clusters proteins independently of their sequence similarities and their actual biochemical function, we now have the opportunity to quantify functional relationships between proteins in the same way that sequence alignments make it possible to quantify protein-sequence similarity. PRODISTIN thus represents a useful complement to sequence-comparison methods, which rather point towards proteins that have the same molecular function. It is interesting to note that the majority of proteins with the same biochemical function are not clustered in the tree despite their sequence similarity. This moderate dependence of cellular function on sequence similarities clearly means that many functional similarities are at present missed by sequence-based methods, emphasizing the importance of using other types of data than sequence and structure as a basis for function assessment.

Two major advantages result from the fact that PRODISTIN computes all interactions constitutive to an interaction network at once. First, it produces a large functional tree, allowing direct comparison in terms of cellular function for any pair or group of proteins. Second, it makes it possible to visualize a large number of cellular processes and their main actors in a single integrated view, thus offering the possibility of examining the links between cellular functions, and more broadly, the organization of cellular functions within the interaction network. In doing so, PRODISTIN functional trees can capture the essential part of the functional information buried in complex interaction networks, something which is at present impossible to deduce from the intricate graphical representations. Consequently, PRODISTIN can be considered to be one of the first cellular bioinformatics tools available that allows not only comparison of the function of individual proteins but also the ability to study cell function more globally. For instance, the dissection of given cellular functions into sub-functions visible at network level or the study of the functional relationships between known cellular functions can be investigated. As discussed in Results, PRODISTIN has shown that the 'vesicular transport' general function can be separated into distinct subfunctions. An analytic approach of this kind could be systematically undertaken for all known yeast cellular functions, as they are statistically represented in the tree, and later on for those of other organisms. As far as the second question of the relationships between functions is concerned, PRODISTIN could represent a valuable functional data-mining tool. It is, for instance, interesting to note that, although there exist 44 different YPD 'cellular roles' to describe the complete yeast proteome, of which 42 are represented by more than one protein in the tree, our PRODISTIN classes at present cover only 29 of them. Despite the existence of biases in the interaction dataset generally, due to a deeper investigation of certain proteins and to methodological flaws, this observation could suggest a predominant role for these 29 cellular functions in the organization of the network.

Comparison of the results of PRODISTIN with those of other computational methods for assessing and comparing protein functions is not straightforward. Because of the lack of common interaction sets, functional annotations, common evaluation tools and sometimes insufficient description of the algorithms used, no simple benchmarking comparative analyses are yet possible. However, in an attempt to evaluate the relative advantages and disadvantages of the different methods, we compared their results when available. For this purpose, we evaluated PRODISTIN against the MRA 28 and two networks-based methods, the GOM 18 and the Rives and Galitski method (RGM 17). We measured their relative behavior in terms of success rate in the prediction of the function of already known proteins (PRODISTIN vs MRA vs GOM), functional assignment of unclassified proteins (PRODISTIN vs GOM), and ability to cope with false-positive and false-negative interactions in the dataset (PRODISTIN vs GOM vs MRA).

Our results (see Table 3) and those of the GOM (Table 1 in 18) both agree that the MRA has a lower success rate than PRODISTIN or GOM in predicting the function of known proteins. When the ability of GOM and PRODISTIN to predict a function for 42 otherwise uncharacterized proteins is compared to recently published experimental results as a reference, the latter performs better (Table 2). We found that 58% of PRODISTIN predictions are in accordance with the literature, whereas only 31% of the predictions made by the GOM are.

Finally, when robustness towards the presence of false-positive and false negative interactions is assayed by changing the topology of the network, the MRA again performs less efficiently than PRODISTIN (Figure 4). In addition, on random networks of identical topology, both PRODISTIN and the RGM (Table 1 in 17) show that clustering of proteins in true networks is always higher than clustering observed in random networks.

Unlike GOM, PRODISTIN and RGM produce functional trees as an output. But PRODISTIN goes one step further, by finding functional classes on the tree according to two parameters (the minimal number of annotated proteins for the same function in the class and their minimal representation in the class - 3 and 50%, respectively, in this study). This considerably facilitates the process of function assessment, as it minimizes the ambiguity inherent in tree representation. This class construction also has a positive buffering effect that limits the influence of false interactions on the classification and makes it possible to maintain high prediction rates, as already discussed. One may argue that constructing classes limits the number of proteins for which a prediction is possible. It is then important to note that PRODISTIN settings may be changed easily at different levels. Depending on the goal of the user (favoring class coverage of the tree, for instance), the number of proteins per class can be increased by juggling with the two parameters defining the PRODISTIN classes, but at the unavoidable price of a slight decrease in the overall accuracy of the predictions. Switching from the YPD annotation system to the GO system using GO slim categories also increases the number of classified proteins in the tree and consequently, of possible predictions (D.M., B.J. and C.B., unpublished data).

Yeast protein-protein interactions were extracted from the MIPS database 37. Only direct binary interactions were selected, based on the method used for their identification (two-hybrid, excluding high-throughput experiments, in vitro binding, far western, gel retardation and biochemical experiments). For high-throughput two-hybrid experiments, 948 interactions were taken from Uetz et al. 15 and 839 from Ito's core data 12. This yielded a total of 2,946 interactions involving 2,139 proteins (average connectivity 2.6 interactions per protein). The 1,517 protein-protein interactions involving 730 proteins from Helicobacter pylori and their corresponding PBS categories were taken from Rain et al. 14.

Only proteins involved in at least three binary interactions were selected for further classification. Taking into account that the existence of false-positive and false-negative interactions weights more for poorly connected proteins, and that the estimated number of interactions per protein is close to five 3839, we chose to rule out proteins for which the contribution of such false interactions may blur the analysis. Proteins in our dataset have 2.6 interactors on average. We thus chose to set the connectivity threshold to be classified to 3, which means that proteins implicated in one or two interactions were not classified but taken into account for the computation. First, it is stated that a relation between two proteins to be classified exists if either they interact with each other and/or they share at least one common interactor. Subsequently, a graph in which vertices are proteins and edges correspond to this relation, was computed. The connected components are computed and the main one containing almost all of the proteins was selected. Second, the Czekanovski-Dice distance between all pairs of proteins of this class was then calculated. This classical distance on graphs corresponds to the formula

D(i,j) = #(Int(i) Δ Int(j))/ [#(Int(i) ∪ Int(j)) + #(Int(i) ∩ Int(j))]

in which i and j denote two proteins, Int(i) and Int(j) are the lists of their interactors plus themselves (to decrease the distance between proteins interacting with each other) and Δ is the symmetrical difference between the two sets. This distance was chosen because it increases the weight of the shared interactors by giving more weight to the similarities than to the differences; it is very close to an ultrametric distance because the vast majority of distance values between protein pairs is at a maximum (for two proteins that do not share any interactor, the distance value is 1, the highest value, whereas for two proteins interacting with each other and sharing exactly the same interactors, the distance value is 0, the lowest value). Consequently, the advantage of choosing this distance is that it authorizes the use of tree representation. With such distance values, only one tree structure fits the initial distance values, independently of the chosen clustering algorithm. We have used the BioNJ algorithm 40 to build a tree from our distance matrices. This is an improvement of the neighbor-joining algorithm 41, which takes into account the variance of the distance between proteins to evaluate the length of the branches in the tree. A circular classification tree was then drawn using the TreeDyn package 42.

Pairwise sequence alignments have been performed on the set of 602 protein sequences classified with the PRODISTIN method. Both Needleman-Wunsch (global alignment) and Smith-Waterman (local alignment) algorithms have been applied. The programs used for the two algorithms are available at 43 and 44, respectively. The chosen alignment matrix was BLOSUM50, and the gap-opening and gap-extension penalties were set to 12 and 2, respectively. The resulting 363,004 alignments have been processed to calculate the distance corresponding to the percentage of similarity for each protein pair in the global alignment and for the score in the local alignment.

The robustness of each subtree was computed by measuring its homogeneity using a criterion based on topology. Considering triples made of two elements within a given subtree and one outside the subtree (possibly restricted to the sibling subtree), we evaluated the percentage of these triples for which the two elements belonging to the same subtree are separated by the smallest distance value. This allowed us to calculate a class robustness index (CRI) for each inner branch, which was computed by the Qualitree program 22 as a measurement of robustness/quality of the downward class. CRI may be considered as functionally equivalent to the bootstrap index usually used to assess the quality of phylogenetic subtrees. CRI values for PRODISTIN classes are available in Additional data file 1. The average CRI per tree corresponds to the sum of all triples for which the two elements belonging to the same subtree are separated by the smallest distance value divided by the sum of possible triples.

We downloaded the 'cellular role', 'functional categories' and 'sub-cellular localization' annotation files for yeast proteins from YPD 23 on 28 May 2002. The category labels were then loaded into Treedyn 42 for a direct class visualization on the trees as displayed in Figure 2b.