It is known from previous work that gene duplication accompanied by conservation of interactions is common in PINs for both homomers and interactions between non-homologous proteins 919. We have calculated the frequency of interactions between paralogues in four independent datasets of protein interaction networks studied here (Table 1). We used structural assignments to detect homology, thus considering even very distant evolutionary relationships, as described in Materials and methods. We found that interactions between paralogues are significantly more frequent than expected by chance (Figure 2). In order to investigate the evolutionary origins of interactions between paralogues, we determined the conditional probabilities for a protein that forms a paralogous dimer to also be a homodimer. The observation that interactions in homodimers and paralogous dimers are not independent (Table 2) supports an evolutionary link between these two types of dimers, such that paralogous dimers evolved by duplication of homodimers. These observations support the corollary that duplication of homomers is frequently accompanied by conservation of interactions.

We next investigated whether the duplication of homodimers is associated with protein complexes in PINs. We consider the average clustering coefficient (C) of a network as a descriptor of the extent of modularity of that network. Clusters frequently correspond to known protein complexes, as shown by 41213 and by us (Supplementary material S1 in Additional data file 1; illustrated in Figure 3a). This parameter captures the frequency of densely connected subgraphs in the network 14, and allows us to measure modularity in a PIN without specific knowledge of the identity of the protein complexes. We show here that PINs are more clustered than randomized networks with exactly the same broad degree distributions as the real yeast PIN (Figure 3b), extending previous analysis where it was shown that protein interaction networks were more clustered than random Erdõs-Rényi networks and random power-law networks 24. This provides strong support for the biological significance of clusters in networks.

We investigated whether duplication plays a role in determining the clustering levels of the network. The duplication and conservation scenarios in Figure 3c suggest that only duplication of proteins that form homodimers, and not other proteins, will lead to an increase in the clustering coefficient of the network. To investigate this, we implemented a theoretical model of network growth by duplication-divergence 112526 and asked whether inclusion of self-interactions in the model increases the global clustering coefficient.

As shown in Figure 3d, the presence of self-interacting proteins increases the clustering of the network in this model. In particular, the higher the initial proportion of self-interactors, the higher the clustering of the resulting networks (see Materials and methods and Supplementary material S2 in Additional data file 1 for details of the modeling procedure). This is consistent with the result obtained in a previous theoretical study of network evolution by duplication-divergence 10. The increases in clustering levels in this simplified model are modest, suggesting that additional mechanisms must operate in the evolution of real networks, and that only a subset of protein complexes are derived by the mechanism proposed here.

Conversely, when we consider the four real PINs (Table 1) and ask the opposite question, whether selective removal of interactions between paralogous proteins reduces the global clustering of the network, we find that this is the case. Clustering levels are reduced by between 7% and 15% (Supplementary material S3 in Additional data file 1). This is significantly more than obtained by removal of other interactions, which has negligible effects on the global clustering of the network. These small but significant reductions are consistent with the modeling results, further supporting that this mechanism operates in the evolution of a subset of protein complexes.

This result is subject to the following caveats. First, in some cases the formation of a cluster is not due to a single multi-protein complex, but many alternative ones, which may not co-exist in time and in space. This has been described in transcription factor families 2728, and is illustrated in Figure 3a. Secondly, the graph representation we use for PINs is, in itself, limited; for example, it ignores the stoichiometry of the different subunits within protein complexes. For example, a protein complex composed of six identical subunits forming a ring would be depicted as a single self-interacting node, and not captured as a cluster in the PIN. Thus, although considering PINs gives us a network perspective on protein complexes and also large numbers of interactions and increased statistical power, we need to consider alternative definitions of protein complexes to substantiate the above result. So, we next investigated experimentally derived protein complexes.

We tested the corollary that there is an over-representation of interactions between paralogous proteins within protein complexes. We considered two distinct types of protein complex data. The first is composed of three independent data sets of protein complexes in S. cerevisiae (Table 1) and is discussed in this section; the second is composed of protein complexes of known three-dimensional structure, and will be considered in the next section.

First, we found that in all three S. cerevisiae datasets, about one-third of the protein complexes contain duplicated proteins, which is more than expected by chance (Figure 4a). We then wanted to check whether the duplicates physically contact each other within these complexes. However, the three S. cerevisiae protein complex datasets lack information on the physical interactions, or interfaces, formed between the constituent proteins of a complex, as well as the stoichiometry of the complexes, that is, how many copies of each protein are present. Therefore, we computationally overlaid all the protein interactions (Yeast and Yeast-large) onto the protein complexes and asked whether the paralogous subunits of complexes physically interact. Of the complexes for which protein interactions can be superimposed, 27% to 30% have interacting homologous proteins (Table 1). The TAP and HMS-PCI datasets are the result of large-scale experiments, and some redundancy may exist, deriving from multiple baits picking up the same complex. For the TAP dataset, the authors provide a smaller set of predicted complexes based on bioinformatics methods. We repeated the calculation on this set of predicted TAP complexes and found that the frequencies at which the complexes contain homodimers (F(HD)) or dimers of paralogous proteins (F(PD)) are 43% and 34%, respectively. In all cases we found that this enrichment is highly significant at p < 10^-4.

Thus, analysis of the three sets of S. cerevisiae protein complex datasets supports the corollary that interacting paralogues are over-represented amongst protein complexes.

Next we concentrated on the set of protein complexes with known three- dimensional structure (Table 1) to further test the corollary that there is an over-representation of interfaces between paralogues within each protein complex. This dataset, obtained from the PQS database, is an automatically generated subset of the PDB containing solely oligomers 29. In PQS, the proportion of complexes with paralogues is comparable to the S. cerevisiae complex datasets, at 30% (Figure 4b). The advantage of studying this dataset is that it can provide stoichiometry and interaction maps for complexes, that is, we can test directly whether paralogues interact.

Consistent with our hypothesis, we found that the frequency of interactions between paralogues within a protein complex is higher than would be expected by chance, while that of homomeric interactions is lower (Figure 5a; see Materials and methods for an explanation on how the expected values are calculated). One example is the mitochondrial F1/Fo ATP synthase complex (Figure 5b), which contains interacting paralogous subunits 30. While it could potentially establish homomeric contacts, no such contacts exist in the complex, illustrating how homomeric interactions can be under-represented compared to the random scenario. Thus, we have shown that paralogues not only frequently interact within protein complexes, but also appear to interact preferentially compared to homomeric interactions and interactions between evolutionarily unrelated proteins.

To further investigate this, we repeated the experiment shown in Figure 5a, but considering only subunits that can establish homo-interactions as well as interactions between paralogues. This is equivalent to determining what choice is made in a situation such as that represented in Figure 5b. We found that given a choice, in almost all cases a preference for interactions between paralogues will be made, as shown in Figure 5c. The reason for this is likely to be that this type of geometrical arrangement of proteins within complexes requires the smallest number of different interfaces to be formed, and so is the most parsimonious evolutionary scenario. In the F1 sub-complex, the three α and three β subunits alternate within the hexameric ring 30, so that only two different interfaces are formed (α:β and β:α; Figure 5b, left).

Our hypothesis is that many protein complexes start with homomeric interactions that duplicate and diversify, and serve as a seed for the coalescence of further subunits. The photosystem I shown in Figure 1 illustrates this concept. In Heliobacteria, the complex contains a homodimer at its core (PshA₂), whereas the eukaryotic complex contains a dimer of paralogues (PsaA:PsaB). These two paralogous polypeptide chains are each decorated by different peripheral subunits, suggesting that in this class of photosystem (Type-I RC), the core was established prior to the accretion of further subunits 2122. Another example is RNA polymerase II, which contains at its core a large dimer of homologous subunits, and is believed to have evolved from an ancestral generic nucleic acid binding homodimer 3132.

To investigate whether this is a frequent mechanism of evolution of complexes, we tested the fifth corollary and asked whether homomeric interactions and interactions between homologous proteins precede interactions between unrelated proteins in evolution. Then we tested whether paralogues within complexes of known three-dimensional structure have asymmetric interactions.

To answer the first question, we compared PINs in different organisms and asked whether homomeric interactions and interactions between paralogues in one organism are likely to be conserved in the PINs in other organisms, that is, whether the protein(s) have orthologues that interact. Such pairs of interactions have been termed interologs in 33. In Table 3 we show that self-interactions and dimers of paralogues are three to seven times more likely to be conserved from yeast to fly and worm than interactions between unrelated proteins. However, due to the small number of conserved interactions, these results are not definitive. To gain a larger coverage of the yeast proteins, we tested whether proteins that establish interactions with identical and/or with homologous proteins are older than other proteins. We estimated the likely time of origin of each gene in S. cerevisiae by phylogenetic profiling and analyzed both the Yeast and Yeast-large PINs as described in Materials and methods. Homomeric proteins and those that interact with paralogues are significantly older than other proteins, tending to be present in all Eukaryotes and either in Bacteria or Archaea (Yeast) or all Eukaryota (Yeast-large). Other proteins tend to be present only in Fungi and Metazoa, but not in other Eukaryota. The difference in evolutionary conservation is statistically significant in both data sets (p = 0.003 for yeast and p < 0.001 for Yeast-large, Wilcoxon-Mann-Whitney test). These two results support the corollary that the establishment of homomeric interactions and the duplication to dimers of paralogous chains are early events in the emergence of a protein complex.

To test whether paralogous proteins break the symmetry of a complex and allow accretion of different types of subunits, we considered the protein complexes of known three-dimensional structure again. We compared the set of complexes that contain paralogues to the complexes that contain homomeric interactions and no paralogues. As shown in Figure 5d, we found that 32% of paralogues have asymmetrical interactions, while only 4% of the homomers do, a significant difference (p < 0.001). Thus, the hypothesis that duplication of homomers results in new asymmetrical complexes is supported by the data. This may represent part of the selective advantage for conservation of such duplications.

Binary physical protein-protein interactions for S. cerevisiae 3637, Drosophila melanogaster (high confidence interactions) 38 and Caenorhabditis elegans. 39, as well as protein complex datasets for S. cerevisiae 364041 and complexes of known three-dimensional structure used in this study 29 are summarized in Table 1.

A non-redundant set of protein complexes of known structure, based on the PQS database as of June 2005, was prepared by considering complexes as graphs where nodes are the protein subunits (labeled by the domain architecture and chain identity) and edges are a contact between these subunits: two complexes were considered identical when they had the same subunits (same domain architectures, that is, identical or homolgous chains) and the same contact topology between subunits. Details of this procedure can be found in 42.

We used domain architecture as defined in the Superfamily database 4344 to identify paralogous proteins in PINs, that is, those proteins resulting from duplication of the corresponding genes. The SUPERFAMILY database provides protein domain assignments, at the SCOP 'superfamily' level 45, for the predicted protein sequences in completed genomes. Domain assignments were generated using a curated set of profile hidden Markov models. In this work, two proteins are considered paralogous if they display the same amino- to carboxy-terminal domain architecture, ignoring gaps and tandem domain repetitions as described in 9. Domain assignments were based on Superfamily release 1.63 44.

In the analysis of protein complexes from PQS we considered two chains to be identical when strict sequence identity was found, and accepted gaps at the amino and carboxyl termini of the sequences. Two chains were considered homologous when they displayed the same amino- to carboxy-terminal SCOP superfamily domain architecture, and to be different when they did not satisfy any of the above criteria. We used a cut-off of five amino acids with atoms within their van der Waal's radii plus 0.5 Å for two chains to be considered in contact. The expected frequency for a given chain to form a homo- or a paralogous contact (P_h and P_p, respectively) within a complex was calculated by counting the number of times the given chain made one or more homo- or paralogous contacts (N_h and N_p, respectively) in a set resulting from 500 randomizations of that protein complex. Randomizations consisted of considering the topology of each complex fixed, and shuffling the position of each chain within the complex. The expected frequencies were estimated by P_h = N_h/500 and P_p = N_p/500.

To investigate the effect of correlations in the network in terms of evolutionary relationships or topological organization, the following randomization schemes were applied.

We implemented a theoretical model of network evolution based on the concepts proposed in 112526. In this model we started with x = 340 proteins, representing the total number of 241 protein families and 29% of unassigned proteins in the Yeast dataset. We randomly introduced an interaction between any pair of proteins with a probability 0.0059 = 2/339, leading to a classic random graph with a Poissonian degree distribution and an average degree of two. The network is then allowed to grow until it reaches the same size as the Yeast network (neglecting isolated nodes generated during the simulation). The parameter δ for the probability to delete a link under duplication and α for random re-linking of a new node to older nodes in the network was chosen with the aim of obtaining realistic network features (that is, degree distribution) in the final network, that is δ = 0.9 and α = 0 or α = 0.1. For more details, see Supplementary information S2 in Additional data file 1.

We used Smith-Waterman alignments to identify orthologs of yeast genes in the genomes of 40 organisms, representing the three branches of the tree of life, and the major taxonomical groups within each of the branches. We used the Smith-Waterman implementation of the TimeLogic's DeCypher^® accelerated hardware. The significance of each hit is based on a PSCORE statistic where the p value is a real number between 0 and 1 describing the probability of a hit being random. The significance is based on the histogram fitting method and we used a cutoff of p < 0.01. A complete list of the organisms studied is shown in Additional data file 1 (Supplementary material S5). We considered two proteins to be orthologous if they were bidirectional best hits. The 'age' groups we can define based on available genomes are, starting from the most recent, 'S. cerevisiae specific'; 'Saccharomyceta'; 'Fungi'; 'Fungi/Metazoa'; 'Fungi/Metazoa/Amoebozoa'; 'Eukaryota'; 'Eukaryota+Archaea' or 'Eukaryota+Bacteria'; 'universal'. The eukaryotic tree used as reference is that in 47.