From an evolutionary perspective, functional overlaps of gene duplicates may serve to increase the evolvability of organisms (5) but are also expected to be unstable (6, 7). Specifically, if a gene's function can be compensated for by a redundant duplicate, mutations in that gene would have no effect on the phenotype. As a result, such mutations could not be selected against, and redundancy would be gradually lost (8).

Because of the inherently unstable nature of functional overlaps, it is thought that they are rapidly eliminated on evolutionary time scales (8–10). In line with this assumption, recent estimates suggest that the proportion of duplicate pairs that can effectively compensate for each other's loss is low [10% (3, 11)], compared with the majority of duplicates with little or no compensation (or “backup”) capacity. These considerations have recently sparked controversy as to whether functionally overlapping duplicates play any significant biological role, other than accelerating evolutionary rates (8, 11, 12).

Notably, although evidence suggests that a rapid loss of functional overlap indeed describes the fate of most duplicated genes, this hypothesis is also violated by numerous well documented examples (13, 14). In one such case, recent knockdown experiments in Caenorhabditis elegans have revealed duplicate genes that have been conserved in a functionally redundant state for >80 million years of evolution (15). Furthermore, it was demonstrated in both S. cerevisiae and in C. elegans that duplicate genes evolve more slowly than singletons, despite an initial increased evolutionary rate (16, 17), indicating that some essential functions are more likely endowed with redundancies. More recently, a combined proteomic and phenotypic analysis in yeast suggested that a preponderance of redundancy could also exist between alternative pathways (18). Taken together, these pieces of evidence suggest that, in particular types of systems, genetic redundancy may play an as-yet-unidentified role that could provide a basis for its extended conservation. Although it is unlikely that functional overlaps have been conserved solely for the sake of buffering the mutations (8, 19, 20), the possibility that they could be advantageously used for a range of different functionalities is intriguing (4, 6). If such functionalities do exist, they pose two evolutionary questions. One is how these functional overlaps have initially been fixated in the population after the duplication event. The second is how the system has evolved to use these functional overlaps. Models have been proposed that may explain the first stage, namely fixation of the duplicated state (6, 7). These models are based on differential properties of the redundant duplicates with respect to their functional efficiency and/or mutation rates.

To quantify this statement, we estimated the proportion of redundant duplicates, f_rd(k), for any given degree of connectivity, k, through where N_k^Obs is the number of observed essential duplicates at degree k, and N_k^Exp is the number of duplicates with degree k that would have been expected to be essential if there were no redundancy among duplicates. We then calculated N_k^Exp by N_k^Exp = N_k^totalf_s(k), where f_s(k) is the fraction of singletons at degree k that are essential for viability, and N_k^total is the total number of duplicate genes with degree k. The estimated proportion of redundant duplicate pairs as a function of the duplicates' connectivity is plotted in Fig. 1B. These results demonstrate that highly connected proteins are more likely than lowly connected proteins to have retained a potentially compensating duplicate.

We next turned to examine how another feature of duplicates—the extent of their coregulation interacts with their degree of connectivity in affecting essentiality. It was suggested that gene duplicates that are consistently coexpressed are unlikely to have redundant functions (4, 22). The rationale is that systematically coregulated duplicate genes may be simultaneously required for a given functionality and therefore cannot substitute for each other's absence. Fig. 2 shows the proportion of nonessential duplicates as a function of both the expression similarity of the duplicate pairs and their connectivity within the protein network. Duplicates that physically interact with only a few partners (Fig. 2A; connectivity values <3) appear to be nonessential, almost regardless of their expression similarity. The dispensability of these genes may attest to the dispensability of their biochemical functions.

Intriguingly, however, as we examine gene duplicates with higher connectivity values (Fig. 2A), the question of whether they are essential or dispensable becomes highly dependent on whether or not the duplicate copies are coexpressed (Fig. 2). Specifically, if a protein has many interaction partners and its expression is tightly coregulated with that of its duplicate copy, it will, in most cases, appear to be essential in knockout experiments. In contrast, proteins that have equally high interaction partners but whose expression is not coregulated with that of their duplicate copies are typically dispensable, implying functional redundancy (Fig. 2A). Thus, by analyzing the dependency between essentiality, expression similarity, and connectivity [see also supporting information (SI) Appendix 1], we demonstrate here that dispensability of gene duplicates is strongly associated with how these duplicates are regulated and the number of different binding partners with which they interact. Specifically, we found that, especially among the noncoregulated duplicates, backup capacity is distributed nonrandomly, demonstrating preferential tendency to concentrate in the network's hubs (see SI Appendix 2).

To experimentally validate our predictions, we performed double-knockout experiments involving dozens of duplicate gene pairs. We deleted protein network hubs and, as a control, sparsely connected proteins, each with their respective paralogs. In the case of protein hubs, we excluded from our analysis all hubs that are tightly coexpressed with their duplicate copies, because these are unlikely to be redundant (Fig. 2; also refs. 4 and 22). For sparsely connected proteins, we considered dispensable genes with a single duplicate copy (see Materials and Methods).

To generate the double-deletion strains, we crossed haploid cells deleted for a gene of interest with another haploids deleted for the corresponding duplicate. This procedure resulted in a collection of diploids that were heterozygous for both mutations. We then sporulated these diploids, obtaining haploid spores with varying combinations of the two mutations, and then assessed the fitness of the double-knockout strains. As shown in Fig. 3 and SI Appendix 3, in 8 of the 12 tested protein hubs, we found a significant reduction in fitness when genes were codeleted with their duplicate copies. These effects ranged from complete loss of viability (synthetic lethality; 41.6% of these 12 cases) to slow growth (synthetic sick; 8.3% of these 12 cases) or lethality under certain growth conditions (16.6% of these 12 cases). These results strongly contrast with those we obtained among the sparsely connected proteins (nonhubs), where only 11% (2/18) showed any impact on phenotype when codeleted with their duplicates. Reassuringly, for 11 of the 14 hubs in our dataset, there have been previous indications in the literature suggesting some type of compensation (see SI Table 1 and SI Appendix 3). This is in contrast to our control set of sparsely connected duplicates, in which such evidence was reported for only 2 of 18 duplicate pairs.

Because several of the hubs in the set we examined contained more than one duplicate gene copy, we investigated whether all given duplicates are equally likely to compensate for the loss originating from the deletion. Accordingly, we selected all hubs in our collection that had three or fewer duplicate copies (constituting a total of four or fewer genes). We then separately codeleted these hubs with each of their different duplicates, generating alternative double-knockouts. The results from this experiment (see SI Appendix 3) suggested that, for any given hub, there is only one gene partner whose absence generates synthetic interaction with the deletion of the hub. That said, we cannot exclude the possibility that functional redundancy exists, even in the gene pairs that did not yield a synthetic interaction; but this redundancy was not revealed by the double-knockout, e.g., due to a third redundant partner (23).

In addition, we asked whether paralogs of hubs that are compensated for by their duplicates are also highly connected. Indeed, we found that they have a significantly higher number of protein partners compared with the average gene in the genome [P value for difference in connectivity = 2.6 × 10⁻⁴ (t test)]. Furthermore, we found that in seven of the eight cases of synthetic sick or lethal phenotypes, the hub and its paralog share a significant portion of their protein interaction partners (P < 0.01 for each of the seven pairs, using a hypergeometric test).

To firmly associate these synthetic interactions with compensations, an alternative interpretation of these experimental results must have been examined. Specifically, it could be argued that the deletion of the discussed hubs could destabilize the cellular network to such an extent that many random additional deletions, on the background of the hub's deletion will also produce lethality. To rule out this possibility, we performed another set of negative control double-knockout experiments, in which we paired the hubs previously analyzed, with duplicates of other randomly selected hubs. Strikingly, none of the 12 double knockouts we performed showed any effect on cell viability (see Fig. 3 and SI Appendix 3). These results suggest that there is genuine information in the identity of the codeleted gene and that only the true paralogs may generate genetic interactions, arguably because of functional compensation to the hubs.

One possible interpretation of our results is that functional overlaps of gene duplicates have been evolutionarily conserved more frequently, among protein network hubs. To examine the evolutionary processes responsible for the association between redundancy and connectivity, we tested how the approximated age of duplication affects the correlation between the proportion of dispensable duplicates to both (i) the connectivity of duplicates in the protein network and (ii) the expression similarity of the duplicate copies (Fig. 4). [Age of duplication was roughly estimated by the extent of synonymous substitutions (Ks) (8)]. We roughly discern three separate evolutionary regimes. In the first phase, immediately after the duplication event (0 < Ks < 0.1), duplicate pairs are both tightly coexpressed and highly dispensable. This result may reflect either compensation due to the functional similarity of duplicated genes before divergence or a dispensability of the biochemical function of the duplicated gene (24). In the second phase (0.1 < Ks < 1), we observe, in line with studies reported in refs. 9, 10, 25, and 26, a decline in the expression similarity of the duplicates, concomitant with a gradual loss of their dispensability. Notably, during these first two evolutionary stages, the dependency of knockout phenotypes on both protein connectivity and expression similarity of duplicate genes is very weak. In fact, such dependency only becomes significant during what we consider to be the third evolutionary phase, corresponding to highly ancient duplication events with divergence levels of Ks > 1. Remarkably, it thus becomes evident that the correlation shown in Fig. 2 primarily reflects an association between redundancy and connectivity in ancient, rather than in recent, duplicates. This is further substantiated by a 3-way ANOVA test (P = 0.009), demonstrating the interaction between Ks and degree in affecting duplicate dispensability (Table 6 in SI Appendix 1). This finding may suggest that compensations of protein network hubs by their duplicates is not a simple epiphenomenon of gene duplication but rather represent a functionality that has evolved through purifying selection. We have further examined the proportion of remote paralogs (Ks > 1) among pairs with increasing degree connectivity (Fig. 4B). Interestingly, the proportion of remote (presumably more ancient) pairs increases with degree connectivity, consistent, although not exclusively, with a prolonged retention of duplications in involving highly connected proteins.

In an attempt to at least partially understand the additional value gained from such redundancies, we manually searched the literature for all references of duplicate gene pairs in yeast that were experimentally demonstrated to be redundant (see Materials and Methods for a description of the literature search). Specifically, we labeled genes “redundant” if literature indicates that they meet two criteria: first, clear findings in non high-throughput studies documenting their functional overlap; and second, experimental validation of compensatory interactions between the pair members. To limit the size of the dataset to one that is reasonable for a manual search of the National Center for Biotechnology Information PubMed database, we defined a sequence similarity threshold (see Materials and Methods) and only examined duplicate pairs meeting this criterion. The resulting analysis yielded 112 carefully validated redundant paralogous pairs (for a full list, see SI Table 1). Plotting the frequency of redundant genes within the total curated set as a function of their degree of connectivity, we again observed that the proportion of redundancies significantly increased, with increasing connectivity (Fig. 5) (P = 1.7 × 10⁻⁶; logistic regression).

Previously, a classification was suggested, distinguishing between hubs whose partners are coexpressed (party hubs) and hubs whose partners are differentially expressed (date hubs) (27). By examining duplicate dispensability according to these criteria, we found no significant difference in the representation of these two gene types in the data (data not shown).

It was convincingly shown that hubs are more likely than lowly connected genes to be essential (21). Not only do our results not contradict these early findings, they are in good agreement with them, because we show too increased proportion in essential functionalities among the highly connected proteins. Essentiality of the functions carried out by the hubs either manifest themselves by increased rate of essential genes among the singletons or enhanced rate of compensations by redundancies among the duplicates. Thus, we hypothesize that without redundancy, the fraction of hubs with lethal single-gene knockout phenotypes would have been even higher than is actually the case. In line with this possibility, examples of essential functions performed by pairs of redundant, and consequently dispensable, gene duplicates have been reported (4, 14, 28).

Several points of caution regarding our assumption that hubs represent proteins with essential function should be taken. These include the possibility that some essential genes have more annotated interaction partners simply because they were studied more extensively and the valid possibility that essentiality of hubs may owe itself to the high probability that at least one of their many interactions will be essential (29). Another point of caution relates to the observation that variations on experimental and modeling methodology may affect the interpreted network topology (30). Indeed, any interpretation of our results is subject to the possibility that the protein interaction data used in this study represents only a fraction of the total underlying interaction network and that some of the annotated interactions represent false positives. Together with that, because the experimental methods used for collecting the protein–protein interactions were mostly high-throughput (affinity tag, yeast two-hybrid, etc.), they are likely not biased against detecting protein associations among particular gene sets, e.g., essential genes.

Our findings raise an intriguing question: Are redundant duplicates associated with biological roles that differ from the roles played by the majority of duplicate pairs that do not functionally overlap? In principle, high connectivity in protein networks is suggestive of one of two possibilities: (i) involvement in protein complexes [party hubs (27)] or (ii) labile interactions [date hubs (27)] typically played by posttranscriptional regulators. From examination of our curated list, it is clearly apparent that most compensated hubs fall into the second category with functions varying from posttranscriptional regulators, signaling scaffolds, or isozymes. This is also consistent with the dissimilarity in the expression of redundant duplicates (see Fig. 2 and ref. 22). It is, thus, tempting to suggest that redundant duplicates tend to be associated with regulatory functionalities, such as posttranscriptional or metabolic regulation.