First, we focus on the large set of conserved genes (that is, genes that are conserved in all fungal species analyzed), identifying sequence co-evolutionary relationships that are manifested in the absence of major gene gain and loss events. As these co-evolutionary relationships cannot be deciphered by an analysis based on phyletic patterns, and a single evolutionary rate measure is too crude for capturing them, we set out to measure the relative evolutionary rate of each gene at every branch of the evolutionary tree. The resulting new 'relative evolutionary rate pattern' (rERP) measure characterizes a gene's pattern of evolution as a vector of all its relative evolutionary rates in the different branches of a species' phylogenetic tree. A workflow describing the determination of genes' ERPs is presented in Figure 1 (for a detailed description of the workflow described in this figure and comparison to other measures of co-evolution see Materials and methods). We analyzed genes from nine fungal species, whose phylogenetic relationship (based on the 18S rDNA 26 and on the comparison of 531 informative proteins 27) is presented in Figure 2. We first created a set of orthologous genes (lacking paralogs) that are conserved in all species, resulting in a dataset of 1,372 sets of orthologs spanning a total of 12,348 genes. Each such set of orthologous genes (SOG) was then aligned, and its ancestral sequences at the internal nodes of the phylogenetic tree were inferred using maximum likelihood. The resulting sets of orthologs and ancestral sequences were then used to estimate the evolutionary rate, dN/dS 28, along each of the tree branches. To consider the selection forces acting on synonymous (S) sites we used an approach similar to that of 29 and adjusted the evolutionary rates accordingly. These adjusted evolutionary rates are denoted dN/dS', and compose an ERP vector that specifies a dN/dS' value for each branch of the evolutionary tree, for each SOG. We next carried out an analysis of the resulting ERP matrix, whose rows are the SOGs, its columns are the tree branches, and its entries denote evolutionary rate values (dN/dS').

Our first task was to characterize the global selection regimes acting upon the genes studied. We conservatively limit this investigation to the short branches of the tree (excluding branches (7,15), (15,16), (8,16), (9,16); Figures 2 and 3) to avoid potential saturation problems that may bias the ER computation (Materials and methods). Most of the genes exhibit purifying selection (dN/dS' < 0.9) in the majority of the phylogenetic branches, as one would expect 30. A much smaller group of genes under positive (dN/dS' > 1.1) and neutral (0.9 <dN/dS' < 1.1) selection are concentrated in three branches (Figure 3), with the majority located on the branch leading from internal node 12 to internal node 11, probably following the whole genome duplication event known to have occurred at this bifurcation 31. This major duplication event probably served as a driving force underlying this surge of positive selection, by relaxing the functional constraints acting on each of the gene copies 32. This branch also represents a switch from anaerobic (Saccharomyces cerevisiae, Saccharomyces bayanus and Candida glabrata) to aerobic (Aspergillus nidulans, Candida albicans, Debaryomyces hansenii, Kluyveromyces lactis, Yarrowia lipolytica) metabolism 33, which has likely required a large burst of positive evolution in many genes. Additional data file 1 includes a table that depicts the SOGs with positive evolution along this branch (using their S. cerevisiae representative), which is indeed enriched with many metabolic genes. The other two branches under positive selection are the branch between nodes 13 and 14, leading to a subgroup (D. hansenii and C. albicans) that evolved a modified version of the genetic code 34, and the branch between nodes 13 and 15 that leads to Y. lipolytica (which is a sole member in one of the three taxonomical clusters of the Saccharomycotina 35).

The major goal of this work is to study the co-evolution of gene pairs and of cellular processes. To this end we utilized the ERP matrix to compute the rERP of each conserved SOG. The rERP is a vector containing the relative, ranked dN/dS' (rER) of each SOG in every branch of the evolutionary tree, thus comparing the evolutionary rate of each individual SOG to that of all other SOGs. The ranking procedure is employed to attenuate the effects of noisy estimations of ER values, especially in long branches of the phylogenetic tree (see Note 1 in Additional data file 2). Defining the rERP of a Gene Ontology (GO) process to be the mean rERP of all the genes it contains, we asked which GO processes have the rERP with the highest mean and the highest variance across the different branches of the evolutionary tree (Figure 4). Notably, processes related to energy production, such as the tricarboxylic acid cycle (involved in cellular respiration), and ATP synthesis-coupled proton transport (which includes genes encoding the mitochondrial ATPase) have the highest mean rERP and also exhibit the highest variance of their rERP. This reflects the primary role that energy production has played in fungal evolution, and the effects that changes from anaerobic to aerobic metabolism have had on the development of fungal species. Additional high rERP energy-related GO terms include aerobic respiration and heme biosynthesis. Interestingly, biological functions related to information flow within the cell exhibit high mean rERP values (tRNA export from nucleus, DNA recombination) or high rERP variance (transcription initiation from polymerase II promoter, RNA processing, transcription termination from RNA polymerase II promoter). The trend, however, is not identical for all processes: protein import to the nucleus, for example, has a high rERP value but very little variance. Full lists of conserved genes and GO groups sorted according to their mean rERP and rERP variance appear in Additional data file 3.

We carried out a hierarchical clustering of GO-slim functions according to their rERP values, which is depicted in Figure 5. Many GO-slim groups exhibit correlated rERP values. For example, processes related to metabolic activity (such as cellular respiration, carbohydrate metabolism, and generation of precursor metabolites and energy) exhibit high rERP values across the tree, whereas others (cell cycle and meiosis) exhibit markedly lower values. Interestingly, processes related to polarized growth and budding exhibit the lowest overall rERPs. Importantly, the figure shows that rERP values can provide additional information to that contained in the global relative evolutionary rates (that is, those measured by aggregating the whole tree). For example, the two GO-slim process groups plasma membrane and microtubule organization center (Figure 5, middle) have relatively similar (low) relative global evolutionary rates but markedly different rERPs (as they appear in the two extreme parts of the hierarchical clustering). While the standard ER measure checks if the average ER of genes is similar (that is, |ER₁ - ER₂|), rERP compares the fluctuations in the ER of genes. Thus, two SOGs may appear similar by one measure and very different when applying the other. Figure 6 shows two examples in which the two measures provide opposite results. Notably, the correlation between these two measures is significant but rather low (r = -0.055, P < 10^-16). Overall, GO groups with functionally related gene sets (that is, those that map closer on the GO ontology network) tend to have similar rERP values (the correlation between distance in the GO graph and average correlation of rERP is -0.96, P-value < 4.5 × 10^-4; see more details in Figure 7, Additional data file 4, and Materials and methods; this comparison is made using the S. cerevisiae GO ontology and mapping all the SOGs to this ontology).

Having a representative rERP vector for each SOG/process enables us to examine the correlations between them and to learn about their co-evolutionary history. A positive rERP correlation arises when two SOGs/processes exhibit a similar pattern of change in the different branches of the evolutionary tree and have evolved in a coordinated, cooperative C-type fashion. A simple example of such a co-evolution is the mitochondrial genome maintenance and mitochondrial electron transport categories. A marked negative rERP correlation denotes reciprocal, R-type co-evolution where periods of rapid evolution of one SOG/process are coupled with slow evolution in the other; this may arise when the rapid evolution of one process creates a new niche or biochemical activity that, in turn, enables, or selects for, the rapid evolution of the other process. An illustrative R-type example involves the category of methionine biosynthesis, which has a negative rERP correlation with phosphatidylcholine (PC) biosynthesis. PC is synthesized by three successive transfers of methyl groups from S-adenosyl-methionine to phosphatidyl-ethanolamine 3637. Thus, the evolution of the PC biosynthetic pathway may be conditioned on the evolution of the methionine biosynthesis pathway, and thus follow it with some time lag (Figure 8). Interestingly, genes that co-evolve in a C-type manner do provide functional backups to each other, having a statistically significant enrichment in genetic interactions (hypergeometric P-value < 0.0039), while genes co-evolving in an R-type manner do not (where the enrichment is studied using the S. cerevisiae genes in each of the pertaining SOGs). We also found that the fraction of sequence-similar SOGs is significantly larger among pairs of C-type co-evolving genes than among pairs of R-type co-evolving genes (Note 2 in Additional data file 2).

To track down the co-evolution of SOGs, we generated a co-evolution network where two SOGs (termed, for convenience, according to the S. cerevisiae genes they contain) are connected by an edge only if there is a significant (either positive or negative) Spearman rank correlation (with P < 0.05) between their rERPs. The node degrees in the co-evolution network follow a power-law distribution (Figure 9) and the network has small world properties (the average distance between two nodes is 5.03). Many biological networks (for example, see 3839) exhibit similar properties. The degree in the co-evolutionary network is significantly correlated with the degree in the S. cerevisiae protein interaction network (r = 0.0726, P = 0.0125) but is not significantly correlated with the degree in the S. cerevisiae genetic interaction network, or with the degree in its gene expression network.

A co-evolution network of cellular functional categories was built for each of the three GO ontologies (biological process, cellular component, molecular function), using two significance cutoff values (Spearman P-value < 0.01 and Spearman P-value < 0.001) to determine significant correlations between GO categories. A list of highly correlated pairs of GO terms is provided in Additional data file 5. The correlation between the distance of GO groups in the 0.001 cutoff co-evolution network (that is, their evolutionary distance) and their distance in the corresponding GO ontology network (that is, their functional distance) is highly significant: 0.38 for cellular component, 0.16 for biological process and 0.43 for molecular function (all three with P-values <10^-16; a similar trend is observed using the 0.01 cutoff network). A similarly marked correlation between evolutionary and functional relationships of GO groups is also found when considering positive and negative co-evolution networks separately (Note 3 in Additional data file 2).

Similar results were observed when we considered classification according to Enzyme Commission (EC) number 40, which is a numerical classification scheme for enzymes based on the chemical reactions they catalyze. By this classification, the code of each enzyme consists of the letters 'EC' followed by four numbers separated by periods. Those numbers represent progressively finer classifications of the enzyme. Thus, it induces a functional distance. Our analysis shows that pairs of orthologs with smaller functional distance (genes whose first two roughest classification levels are identical) exhibit higher levels of correlation between their rERP than other pairs of orthologs (mean rERP correlation of 0.31 versus 0.27, P = 1.23 × 10^-7).

We did not find a parallel significant correlation between the genomic co-localization of GO groups and their co-evolutionary score (see Materials and methods for a description of how we computed the co-localization score of pairs of GO groups). The co-evolution of genes and their chromosomal location are not correlated even when considering each chromosome separately. Thus, we conclude that cellular functionality is a more important force driving gene co-evolution than their genomic organization.

The rERP measure correlates well with other systemic qualities such as genetic and physical interactions. The average Spearman correlation between rERP levels of interacting proteins in the S. cerevisiae protein interaction network is 0.063, which is 155 times higher than the average correlation (4.05 × 10^-4) for non-interacting proteins (P < 10^-16). Proteins that are part of a complex show a correlation of 0.05 between their rERPs, 100 times higher than the average correlation for proteins that are not a part of the same complex (P < 10^-16). The Spearman correlation between rERP levels of genetically interacting proteins is 0.02, which is 32 times higher than the average correlation (6.08 × 10^-4) for non-interacting proteins (P = 2.71 × 10^-6). Protein rERPs are also correlated with the co-expression of their genes (Spearman correlation 0.063, P < 10^-16). The significant correlation between co-evolution and physical/functional interactions suggests that physical interactions between the products of conserved genes play a part in their co-evolution. Namely, to maintain the functionality of an interaction, a change in one protein is likely to facilitate the evolution of the proteins interacting with it, as has already been shown 5. Yet, as the magnitude of this correlation is rather low, it is likely that other co-evolutionary forces play a part in determining co-evolution, such as the sharing of common and varying growth environments during evolutionary history.

We employed the PRISM algorithm 41 to partition each of the three GO co-evolution networks (biological process, cellular component, molecular function) into clusters of nodes, such that nodes from one cluster have similar sign connections (denoting positive or negative rERP correlations) with nodes from other clusters. We focus here on biological processes at a significance cutoff value of P < 0.01 (Figure 10). PRISM clusters the process terms into coherent groups in a statistically significant manner (P < 0.001; see Materials and methods), where most of the groups are enriched for particular types of processes: Cluster A7 contains many processes related to DNA metabolism, chromatin formation and RNA processing. This cluster shows strong negative correlations with clusters A6 (amino acid biosynthesis, tricarboxylic acid cycle, glucose oxidization and energy production) and cluster A8 (protein processing and modification). It has also strong positive correlations with cluster A4 (nuclear traffic and DNA repair) and with cluster A5. We note that among the RNA-related processes in cluster A7, some (such as mRNA export from nucleus and poly-A dependent mRNA degradation) show R-type correlations with functions such as protein degradation via the multivesicular pathway. This relationship points to a mode of evolution in which the two catabolic processes (protein and RNA) require coordination, so that changes in one are dependent on preceding changes in the other. Similarly, cluster A6 shows strong coordinated co-evolution with cluster A3 (amino acid and purine biosynthesis, glucose oxidization, energy production and ribosome biology). Both clusters include GO functions related to the production of energy and, thus, coordinated evolution is expected. An overview of the results shows that genes that affect regulatory or information-related processes (DNA metabolism, chromatin formation and RNA processing (cluster A7)) are 'master players'. These master genes/processes exert reciprocal selection forces on many other metabolic process (clusters A8, A3 and A6) and participate in the co-evolution of other processes such as nuclear traffic (cluster A4).

The results presented above were focused on the analysis of a conserved set of genes whose orthologs appear in all nine fungal species studied, comprising 1,372 SOGs and spanning a total of 12,348 genes. The fungal dataset additionally includes 2,168 orthologous sets spanning more than 74,851 genes that exhibit at least one change in their copy number along the phylogenetic tree (and hence have undergone gene loss and/or gene duplication events). The 'propensity for gene loss' (PGL) 17 was shown to correlate with gene essentiality, the number of protein-protein interactions and the expression levels of genes. PGL has been used in methods for predicting functional gene linkage 4243, extending upon previous methods that used the occurrence pattern of a gene in different organisms for the same aim 121314. Recently, a probabilistic approach related to the PGL was developed 42. A related measure, which is also based on a gene's phyletic pattern (the occurrence pattern of a gene in different current organisms), is phylogenetic profiling (PP) 151643. This measure has been employed in previous small scale studies to identify sets of genes with a shared evolutionary history 1213141543. We describe a new measure of co-evolution that is a generalization/unification of both PGL and PP, termed the copy number pattern (CNP). Like PP, it characterizes each gene by examining its phyletic pattern (but additionally takes into account the number of paralogous copies of each gene in the genome). Like PGL, it exploits the information embedded in a species' phylogenetic tree to more accurately characterize the evolutionary history of each gene (in comparison, PP carries out a similar computation based on just the phyletic pattern). We used the new CNP measure to analyze orthologous sets that exhibit at least one change in copy number along the analyzed phylogentic tree. This set of genes is, by definition, not completely conserved, and complements the conserved set of genes analyzed by the rERP measure.

Figure 11 provides a stepwise overview of CNP computation. Steps A to F are essentially similar to those used to generate the rERP (see Materials and methods): we first generate a set of 2,168 orthologous sets that exhibit at least one change in copy number along the analyzed phylogentic tree. We then translate the resulting set of orthologs to copy numbers in each organism (the number of paralogs in an organism), and reconstruct the ancestral gene copy number using CAFE' 44 (step F in Figure 11). Finally, using the copy number in each internal node, we compute the change (the difference) in copy number for orthologous sets along each edge (step G in Figure 11). The orthologous sets used for the rERP analysis and the orthologous sets used for the CNP analysis include two different, exclusive groups of conserved versus less-conserved genes, respectively. Analysis of these sets reveals that the first group is enriched with metabolic processes while the second is enriched with functional processes such as reproduction and cell differentiation (Additional data file 6).

Since changes in the copy number of genes are infrequent events, the Spearman correlations between pairs of CNP vectors are usually very high (the average Spearman correlation is 0.63). To overcome this, we generated CNP vectors of GO processes (according to the biological processes ontology) where the CNP of a GO category is the mean CNP of all the genes it contains. These GO process vectors exhibit a wider range of CNP values. Next, we constructed a GO process co-evolution network. In this network two biological processes are connected by an edge only if they manifest an extreme co-evolution pattern - that is, if they have a Spearman rank correlation that is higher (green colored edges, denoting coordinated relationships) or lower (red, denoting reciprocal relationships) than the correlation values of X% of the total GO pairs. We examined the networks formed under two edge-selection regimes, a more stringent one where X% = 99.9% and a less stringent one where X% = 98%. The correlation between the distance of GO groups in the network with X% = 99.9% and the distance of GO groups in the different GO ontology networks is highly significant (r = 0.4209, P < 10^-16) for green, cooperative edges, and negatively correlated (r = -0.12, P < 0.04) for red, reciprocal edges. This suggests that the two types of edges are informative: the green edges represent functional relationships while the red ones represent pairs of GOs with distant functions.

To learn more about the structure of the CNP co-evolution network, we used the PRISM algorithm 41 (as in the case of the rERP analysis) to partition each of the GO terms in the less stringent network (X% = 98%; thus obtaining a larger amount of edges and a more robust clustering) into clusters of nodes, such that nodes from one cluster have similar color edge connections with nodes from other clusters. PRISM is able to separate the process terms into coherent groups according to their mutual correlations, in a statistically significant manner (P < 0.001; see Materials and methods). Figure 12 displays the results of the PRISM analysis, clustering of the GO biological processes into seven large groups. The seven interconnected groups are enriched with specific processes, and present clear interactions of the red and green edges. As clearly seen in Figure 12, some clusters show mainly reciprocal co-evolution with most of the others (for example, clusters B1 (fatty acid metabolism) and B6 (sugar metabolism). In contrast, clusters B2, B3 and B7 (nuclear traffic, transcription and DNA metabolism) show coordinated (C-type) co-evolution. Cluster B4 (protein modification, chromatin silencing) shows C-type co-evolution with transcription (cluster B3) and nuclear import (cluster B2) as well as DNA metabolism (cluster B7) but R-type relations with cluster B1, which includes fatty acid metabolism and protein glycosylation.

A comparison between the results obtained by the rERP and CNP methodologies at a global level should be done with some caution, for three main reasons. First, these two measures are applicable for the analysis of completely disjoint, complementary sets of orthologs. Second, the two methodologies measure different types of co-evolution. The rERP measures evolution via amino acid substitutions while the CNP measures co-evolution via changes in gene copy number, which are mainly driven by gene gain and loss events. Thus, third, these co-evolutionary relationships are possibly the result of the action of different evolutionary forces. However, it may be noted that some biological processes present the same type of evolutionary relationship with both methods. For example, DNA metabolism is always positively correlated with nuclear traffic, transcription and vacuolar biology (ER-Golgi traffic). Yet, some of the clusters exhibit different relationships when analyzed by the two measures. For example, a cluster containing mainly genes labeled ribosome biology and vacuolar biology exhibits reciprocal evolution with DNA metabolism by rERP (clusters A3 to A7) but coordinated evolution by CNP (clusters B5 to B7). Thus, within a certain biological process, the evolutionary pressures exerted on highly conserved genes may differ from those that apply to less conserved ones, and may thus provide different opportunities for co-evolution.