The characterization of functional redundancy and divergence between duplicate genes is an important step in understanding the evolution of genetic systems. Large‐scale genetic network analysis in Saccharomyces cerevisiae provides a powerful perspective for addressing these questions through quantitative measurements of genetic interactions between pairs of duplicated genes, and more generally, through the study of genome‐wide genetic interaction profiles associated with duplicated genes. We show that duplicate genes exhibit fewer genetic interactions than other genes because they tend to buffer one another functionally, whereas observed interactions are non‐overlapping and reflect their divergent roles. We also show that duplicate gene pairs are highly imbalanced in their number of genetic interactions with other genes, a pattern that appears to result from asymmetric evolution, such that one duplicate evolves or degrades faster than the other and often becomes functionally or conditionally specialized. The differences in genetic interactions are predictive of differences in several other evolutionary and physiological properties of duplicate pairs.
Gene duplication and divergence serves as a primary source for new genes and new functions, and as such has broad implications on the evolutionary process. Duplicate genes within S. cerevisiae have been shown to retain a high degree of similarity with regard to many of their functional properties (Papp et al, 2004; Guan et al, 2007; Wapinski et al, 2007; Musso et al, 2008), and perturbation of duplicate genes has been shown to result in smaller fitness defects than singleton genes (Gu et al, 2003; DeLuna et al, 2008; Dean et al, 2008; Musso et al, 2008). Individual genetic interactions between pairs of genes and profiles of such interactions across the entire genome provide a new context in which to examine the properties of duplicate compensation.
In this study we use the most recent and comprehensive set of genetic interactions in yeast produced to date (Costanzo et al, 2010) to address questions of duplicate retention and redundancy. We show that the ability for duplicate genes to buffer the deletion of a partner has three main consequences. First it agrees with previous work demonstrating that a high proportion of duplicate pairs are synthetic lethal, a classic indication of the ability to buffer one another functionally (DeLuna et al, 2008; Dean et al, 2008; Musso et al, 2008). Second, it reduces the number of genetic interactions observed between duplicate genes and the rest of the genome by masking interactions relating to common function from experimental detection. Third, this buffering of common interactions serves to reduce profile similarity in spite of common function (Figure 1). The compensatory ability of functionally similar duplicates buffers genetic interactions related to their common function (reducing the number of genetic interactions overall), while allowing the measurement of interactions related to any divergent function. Thus, even functionally similar duplicates may have dissimilar genetic interaction profiles. As previously surmised (Ihmels et al, 2007), duplicate genes under selection for dosage amplification have differing profile characteristics. We show that dosage‐mediated duplicates have much higher genetic interaction profile similarity than do other duplicate pairs. Furthermore, we show in a comparison with local neighbors on a protein–protein interaction (PPI) network, that although dosage‐mediated duplicates more often have higher similarity to each other than they do to their neighbors, the reverse is true for duplicates in general. That is, slightly divergent duplicate genes more often exhibit a higher similarity with a common neighbor on the PPI network than they do with each other, and that observation is consistent with the idea that common interactions are buffered while interactions corresponding to divergent functions are observed.
We then asked whether duplicates’ genetic interactions that are not buffered appear in a symmetric or an asymmetric fashion. Previous work has established asymmetric patterns with regard to PPI degree (Wagner, 2002; He and Zhang, 2005), sequence divergence (Conant and Wagner, 2003; Zhang et al, 2003; Kellis et al, 2004; Scannell and Wolfe, 2008) and expression patterns (Gu et al, 2002b; Tirosh and Barkai, 2007). Although genetic interactions are further removed from mechanism than protein–protein interactions, for example, they do offer a more direct measurement of functional consequence and, thus, may give a better indication of the functional differences between a duplicate pair. We found that duplicates exhibit a strikingly asymmetric pattern of genetic interactions, with the ratio of interactions between sisters commonly exceeding 7:1 (Figure 4A). The observations differ significantly from random simulations in which genetic interactions were redistributed between sisters with equal probability (Figure 4A). Moreover, the directionality of this interaction asymmetry agrees with other physiological properties of duplicate pairs. For example, the sister with more genetic interactions also tends to have more protein–protein interactions and also tends to evolve at a slower rate (Figure 4B).
Genetic interaction degree and profiles can be used to understand the functional divergence of particular duplicates pairs. As a case example, we consider the whole‐genome‐duplication pair CIK1–VIK1. Each of these genes encode proteins that form distinct heterodimeric complexes with the microtubule motor protein Kar3 (Manning et al, 1999). Although each of these proteins depend on a direct physical interaction with Kar3, Cik1 has a much higher profile similarity to Kar3 than does Vik1 (r=0.5 and r=0.3, respectively). Consistent with its higher similarity, Δcik1 and Δkar3 exhibit several similar phenotypes, including abnormally short spindles, chromosome loss and delayed cell cycle progression (Page et al, 1994; Manning et al, 1999). In contrast, a Δvik1 mutant strain exhibits no overt phenotype (Manning et al, 1999).
Duplicate genes show significantly fewer interactions than singleton genes, and functionally similar duplicates can exhibit dissimilar profiles because common interactions are ‘hidden’ due to buffering.
Genetic interaction profiles provide insights into evolutionary mechanisms of duplicate retention by distinguishing duplicates under dosage selection from those retained because of some divergence in function.
The genetic interactions of duplicate genes evolve in an extremely asymmetric way and the directionality of this asymmetry correlates well with other evolutionary properties of duplicate genes.
Genetic interaction profiles can be used to elucidate the divergent function of specific duplicate pairs.
Gene duplication is a primary mechanism for generating functional novelty, because it allows for the relaxation of selective constraints and thus provides an opportunity for functional innovation or specialization (Ohno, 1970). Genome sequencing studies in several species have revealed that a sizable fraction of many genomes are duplicated and that paralogous genes retain a relatively high degree of sequence similarity (Kellis et al, 2004; Byrne and Wolfe, 2005). In addition to the similarity of nucleotide/amino‐acid sequence, functional genomic studies have identified significant overlap between duplicate genes in terms of their physical interactions (Baudot et al, 2004; Guan et al, 2007; Musso et al, 2007; Wapinski et al, 2007), fitness effects (Gu et al, 2003), metabolic activity (Papp et al, 2004; Kuepfer et al, 2005) and gene expression patterns (Gu et al, 2002b), providing further evidence to suggest that functional similarity among duplicate gene families has been actively retained for over millions of years (Kellis et al, 2004; Kafri et al, 2006).
Genetic interaction analysis offers another means to assess functional relationships between duplicated genes. A genetic interaction refers to an unexpected phenotype not easily explained by combining the effects of the individual genetic variants (Dixon et al, 2009). This phenomenon is also generally referred to as epistasis by the statistical genetics and evolution communities and can refer to phenotypes that are either aggravated (synergistic combinations) or alleviated (antagonistic combinations) in combination with other variants. Synthetic lethality represents an extreme form of negative genetic interaction in which mutation of a single gene, although having little or no effect on the organism, results in cell death when combined with mutation of a second gene (Dobzhansky, 1946; Novick et al, 1989). Negative genetic interactions are often taken as evidence of a functional relationship and, as a result, can be used to directly assess the extent of functional redundancy between genes. Indeed, a systematic survey identified negative interactions between 35% of gene pairs arising from the whole‐genome duplication (WGD) event (Musso et al, 2008). This rate represents an approximately 20‐fold enrichment over random pairs and confirms that functional redundancy is pervasive among duplicate pairs (DeLuna et al, 2008; Dean et al, 2008; Musso et al, 2008). Despite this wealth of data, we lack models that reconcile the long‐term preservation of redundancy among duplicate genes with their patterns of functional divergence.
Synthetic genetic array (SGA) methodology enables large‐scale analysis of genetic interactions in yeast (Tong et al, 2001, 2004; Costanzo et al, 2010), which can extend our view beyond individual duplicate pair interactions to systematically examine the subsets of genetic interactions between duplicate genes and the rest of the genome. Analogous to studies based on protein–protein interactions (PPIs), the number of negative genetic interactions for a given duplicate pair and the extent to which their interactions overlap should provide insight into functional similarities and relationships between duplicate gene pairs. Furthermore, genes belonging to the same biological pathway or protein complex often share similar profiles or patterns of genetic interactions (Tong et al, 2004). As a result, genes can be assigned into specific pathways or complexes by virtue of their genetic interaction profile similarity, as measured across a large fraction of the genome (Tong et al, 2004; Costanzo et al, 2010). This approach was adopted to examine the interaction profiles for 90 duplicate genes within a functionally biased subset of gene deletion mutants queried against itself (Ihmels et al, 2007). This analysis showed that even though duplicate genes display negative genetic interactions with each other, they also appear to behave like singleton genes, in that they exhibit numerous unique genetic interactions; the authors suggest that duplicates are functionally redundant but have divergent roles because they often fail to provide a genuine backup when another gene is deleted (Ihmels et al, 2007).
In the current work, we explore evidence for duplicate gene redundancy in their genetic interaction profiles and further explain the previously observed lack of similarity among the interaction profiles of duplicate gene pairs (Ihmels et al, 2007). Specifically, we propose that the established ability for many duplicate genes to buffer one another under certain conditions should cause genetic interactions related to common functions to be hidden from our experimental method. Furthermore, as duplicates evolve away from complete redundancy, non‐overlapping genetic interactions should appear, reflecting their divergent roles. We find evidence to support these hypotheses in a genome‐wide collection of quantitative genetic interactions in Saccharomyces cerevisiae (Costanzo et al, 2010). We show that exceptions to the model provide insight into evolutionary mechanisms of duplicate gene retention by distinguishing partially redundant genes maintained because of their functional divergence (Ohno, 1970; Hughes, 1994; Force et al, 1999; Conant and Wolfe, 2008; Marques et al, 2008) from those pairs retained because increased gene dosage is beneficial to the organism (Kondrashov and Kondrashov, 2006; Conant and Wolfe, 2007; Ihmels et al, 2007). Finally, we provide evidence based on genetic interaction profiles supporting an asymmetric model of divergence, and show a connection between genetic interaction asymmetry and other physiological and phylogenetic properties.
A hypothesis about the buffering of genetic interactions after gene duplication
We hypothesize that immediately after a duplication event, duplicate genes are identical and presumably redundant, and thus, the only genetic interaction that either paralog exhibits should be with its sister gene (Figure 1A and B). Such a scenario cannot persist without selection pressure to maintain the now redundant copies (Brookfield, 1992). As the pair diverges, the selective pressures that maintained the ancestral gene will begin to act on each duplicate copy individually, creating unique genetic interactions (Figure 1C). Implicit in this hypothesis is the fact that genetic interactions are buffered and undetectable immediately after a duplication event, and then are gradually revealed in one sister duplicate or the other as the pair diverges (Figure 1C). The interactions that emerge after duplication may include the original ancestral genetic interactions that were buffered by the duplication or they may reflect a new function unique to one member of the pair, instances of sub‐ or neo‐functionalization, respectively. On the basis of this hypothesis in which common functions are buffered, genetic interactions should reveal how paralogs have diverged, but seldomly reveal their common functions. Requisite to this reduction in common interactions is the ability of a duplicate gene to partially compensate for the loss of its sister, which has been well established in previous studies (Supplementary Figure 1; Gu et al, 2003; Ihmels et al, 2007; DeLuna et al, 2008; Dean et al, 2008; Musso et al, 2008).
Large‐scale SGA data confirms an enrichment of negative genetic interactions among duplicates
To first affirm previous evidence for duplicate redundancy, we extracted genetic interactions for 576 duplicated S. cerevisae gene pairs (461 WGDs and 115 small‐scale duplicates (SSD); see Materials and methods) from our recent quantitative and genome‐scale SGA analysis (Costanzo et al, 2010). This study captures both negative interactions, those in which the double mutant was less fit than expected (synergism of mutation effects), and positive interactions, those in which the double mutant was more fit than expected (antagonism of mutation effects). Because our SGA study focused on only genetic interactions involving two genes, we restricted our analysis to two‐gene duplicate families.
A primary requisite of the duplicate buffering hypothesis is that sister duplicates should show negative genetic interactions with each other, indicating at least partial redundancy among paralogs (Figure 1C). We found a striking enrichment for negative genetic interactions between sister duplicates (67/205 pairs; 33%; Figure 2A; Supplementary Table 1), which was consistent with previous findings (35% (Musso et al, 2008); 34% (Dean et al, 2008); 55% (DeLuna et al, 2008)). This is substantially higher than the negative genetic interaction rate among randomly selected gene pairs (1.8%; Costanzo et al, 2010), as well as the corresponding rate between physically interacting pairs (7%, P<5 × 10−23; Figure 2A; see Materials and methods) or pairs sharing specific functional annotations (4%; Myers et al, 2006). Although enrichment was observed for both WGD and SSD paralogs, the genetic interaction rate was significantly higher among WGD pairs (P<5 × 10−2; Figure 2B; see Materials and methods), supporting the greater retained functional overlap observed in general among WGD paralogs (Guan et al, 2007; Hakes et al, 2007). However, when ribosomal duplicates are removed from consideration, the difference between WGD and SSD is no longer significant (See Supplementary Note 1 for more information on ribosomal duplicates).
Genetic redundancy between duplicates causes disparate interaction profiles
Our hypothesis about duplicate gene buffering suggests that duplicate genes will show fewer genetic interactions with other genes, because they functionally buffer one another (Figure 1). Indeed, we found that duplicate genes, on average, exhibit 34 interactions compared with 55 interactions observed for singletons when assayed against a set of ∼1700 functionally diverse query mutant strains (P<6 × 10−16; Figure 2C). Notably, the decrease in negative genetic interactions is more apparent on gene families consisting of more than two members. Only 5% (29/554; P<1 × 10−27; see Materials and methods) of duplicates belonging to large gene families exhibit negative genetic interactions with each other, illustrating the impact of higher‐order buffering and/or condition specificity among repeatedly duplicated genes. To control for the tendency of certain classes of genes toward duplication (Marland et al, 2004; He and Zhang, 2006), we examined the number of genetic interactions (union) across a range of double‐mutant fitness values, and confirmed that the deficit in genetic interactions is not due to a bias in duplicates toward gene pairs that are not important under the experimental conditions studied (Supplementary Figure 2).
In addition to fewer genetic interactions, our hypothesis suggests that sister duplicates should not share many interactions in common despite common function (Figure 1C). Indeed, we found that sister duplicates share an average of 1.2 negative genetic interaction partners, whereas genes encoding physically interacting proteins (a proxy for functionally related genes) share an average of 7.2 negative interactions (see Materials and methods). This trend extends beyond the counting of discrete interactions to more continuous measures of genetic interaction profile similarity. Duplicate pairs exhibit lower interaction profile similarity than functionally related gene pairs or genes encoding physically interacting proteins (P<5 × 10−6; Figure 2D; Materials and methods; Supplementary Table 2). The lack of genetic interaction profile similarity among a number of partially redundant duplicate pairs was previously observed in Ihmels et al (2007), in which the authors attribute the phenomenon to incomplete buffering, that is, divergence. Differing genetic interactions certainly convey differentiation of function; however, our updated model (Figure 1) allows us to additionally explain how profile dissimilarity can also be a consequence of retained functional overlap. Thus, genetic interaction profiles for duplicate pairs are dissimilar, both for reasons of functional redundancy and divergence.
Dosage duplicates are exceptions to the buffering model
Assuming duplicate redundancy, our hypothesis about duplicate gene buffering suggests that only genetic interactions resulting from functional divergence will be observable. However, this reasoning should not apply to an important class of duplicate genes, namely, those selected for increased protein product (Ohno, 1970; Ihmels et al, 2007). For example, Ihmels et al, noted that duplicates expressed in high abundance have retained very similar expression profiles, indicating the cell's need for both copies simultaneously. In general, if the cell benefits from higher gene dosage immediately on duplication, then the overlapping function of the duplicate copies is not truly redundant and should induce interactions in both sisters' profiles. Indeed Ihmels et al (2007), noted several examples of high‐abundance duplicates with significantly correlated genetic interaction profiles. Thus, dosage duplicates appear to behave differently in the genetic interaction network than duplicates retained because of functional divergence.
To determine whether genetic interaction profiles could generally distinguish duplicates under dosage selection, we first compiled a set of likely dosage‐related duplicates based on independent phylogenetic and genomic data (see Materials and methods). Using a combination of sequence and gene expression‐related metrics, we defined a class of 80 putative ‘dosage’ duplicate pairs (Supplementary Table 1). Importantly, this class was enriched for known dosage‐mediated paralogs (Kondrashov and Kondrashov, 2006; Conant and Wolfe, 2007; Ihmels et al, 2007). For example, 23 of the 80 pairs were ribosomal duplicates, which represents a significant enrichment (‘Translation’ GO term; P<3 × 10−5; hypergeometric cdf). Furthermore, deletion of one of the dosage paralogs resulted in a more severe fitness defect than other paralogs, suggesting that the dosage duplicates tend to lack the redundancy exhibited by other duplicates (Supplementary Figures 4, 5). The overall proportion of dosage pairs in our set is relatively low (∼14%), but this is likely a conservative estimate for duplicates in general (Supplementary Figure 3).
Indeed, we found that dosage duplicates exhibit strikingly different characteristics in the genetic interaction network. Specifically, dosage duplicates show significantly greater genetic interaction profile similarity than other duplicates (Figure 3A). In fact, dosage duplicates are statistically indistinguishable from highly correlated singleton gene pairs that encode physically interacting proteins (Figure 3A; P>0.4; Wilcoxon rank‐sum test; Materials and methods).
We speculated that the buffered interactions of non‐dosage duplicates (for example, A′‐Z and A″‐Z in Figure 1C) could be present in the genetic interaction profiles of functionally related genes that lack a duplicated partner. To identify these functionally related ‘proxy’ genes, we focused on genes encoding proteins that exhibit physical interaction with both protein products of a duplicate gene pair (Figure 3B; Materials and methods). We reasoned that these proxy proteins may have physically interacted with the ancestor of the duplicates and, thus, have a genetic interaction profile resembling that of the ancestor gene. Subsequent to duplication, either these interactions were distributed uniquely between the modern copies (sub‐functionalization) or new functions arose (neo‐functionalization) as the pair diverged. Comparing the genetic interaction profiles of the duplicate genes with their corresponding proxy, we found that the large majority of divergent duplicate gene profiles are more similar to the proxy gene profile than to their corresponding sister′s profile (Figure 3C). In contrast, dosage‐mediated duplicates more often show higher profile similarity to each other than they do to the proxy gene (Figure 3C), suggesting that these genes tend not to buffer one another. Thus, genetic interaction profile similarity appears to be an effective way to distinguish dosage duplicates from duplicates undergoing functional divergence.
Duplicates exhibit asymmetric genetic interaction patterns
On the basis of the buffering model, genetic interaction profiles should reflect the unique roles of duplicate genes undergoing functional divergence. Ohno (1970) hypothesized that once a duplicate begins to accumulate mutations, the selection pressure will focus on the duplicate retaining the ancestral function and, therefore, most of the divergent changes should be confined to one copy. Although controversial (Wagner, 2002; Lynch and Katju, 2004; Fares et al, 2006; Byrne and Wolfe, 2007), evidence supporting such asymmetric divergence has been extracted from duplicate sequence data (Conant and Wagner, 2003; Zhang et al, 2003; Kellis et al, 2004; Scannell and Wolfe, 2008), PPIs (Wagner, 2002; He and Zhang, 2005) and expression patterns (Gu et al, 2002b; Tirosh and Barkai, 2007).
The distribution of genetic interactions within each duplicate pair strongly supports a model of asymmetric evolution. We examined the ratio of unique negative genetic interactions for each pair of duplicates (max:min, see Materials and methods) and found that the ratio exceeds 4:1 for >30% of gene pairs surveyed (109/351), and more than 17% (60/351) of duplicate pairs exhibit a ratio greater than 7:1 (Figure 4A). The observed interaction ratios are significantly greater than expected under a null model of symmetric interaction (P<1 × 10−100; Wilcoxon rank‐sum test; see Materials and methods), suggesting that genetic interactions tend to appear preferentially in one member of each duplicate pair.
We suspected that the asymmetric distribution of genetic interactions could be partially explained by asymmetric rates of sequence evolution, which provide an independent measure of selection pressure. Previous work showed a correlation between protein dispensability and evolutionary rate among duplicate genes (Yang et al, 2003). A recent study of WGD pairs has also shown that both sisters undergo a period of accelerated change, but while one of them evolves much slower and is preferentially retained across different yeast species, the other evolves much faster and is preferentially lost (Byrne and Wolfe, 2007; Scannell and Wolfe, 2008). Interestingly, we found a related trend in which the rapidly evolving member had fewer genetic interactions than the more slowly evolving partner in 34/51 of previously defined asymmetric duplicate pairs (Kellis et al, 2004; P<0.02; binomial). The bias was more pronounced for pairs whose unique genetic interaction degree ratio exceeded 7:1. In this case, the rapidly evolving member was associated with a lower interaction degree for 27/38 pairs belonging to this group (Figure 4B; P<7 × 10−3). Furthermore, there was a significant correlation between the disparity in sequence evolution rates and the asymmetry of interaction degree (r=0.318, P<0.03), suggesting that the magnitude of asymmetry in genetic interaction degree was predictive of asymmetry in selection pressure acting on duplicate gene sequences. Interestingly, the set of duplicates with asymmetric evolution rates is significantly depleted for dosage‐mediated pairs (P<2 × 10−3; hypergeometric cdf; Supplementary Note 2).
In searching for physiological evidence to corroborate the marked asymmetry in interaction degree, we examined PPIs involving gene pairs with the most extreme ratio of genetic interactions (7:1). Of these, 35 pairs exhibit at least one PPI for each member, and for 25/35 (71%) of these pairs, the partner with more genetic interactions also tended to have retained or gained more physical interactions (P<9 × 10−3; binomial; Figure 4B). Genetic interaction degree asymmetry as a measure of selection pressure is also predictive of measurements of single‐mutant fitness, wherein we observed that the partner with more genetic interactions has a larger impact on fitness when deleted (P<2 × 10−8; binomial; Figure 4B). We observed a similar trend with the number of chemical environments in which each duplicate sister displays a phenotype (Hillenmeyer et al, 2008), wherein the duplicate sister with the higher genetic interaction degree generally had a higher chemical‐genetic degree (P<3 × 10−5; binomial; Figure 4B; see Materials and methods). Interestingly, these trends between duplicate sisters mirror similar trends related to genetic interaction degree across the whole genome (Costanzo et al, 2010; Lehner, 2010).
We also found that WGD sisters with more genetic interactions tend to have higher sequence similarity to the remaining member of the pair in other WGD species (S. castellii, P<2 × 10−3; Candida glabrata, P<1 × 10−2; binomial; Figure 4B; see Materials and methods). Specifically, in 11 of 13 instances in S. castellii and in 12 of 16 such cases in C. glabrata, the higher degree sister showed higher sequence identity to the single remaining WGD sister. Additionally, the duplicate sister with more genetic interactions tended to have a greater mRNA expression level (Holstege, 1998) for 32 out of the 51 pairs (63%; P<0.046; binomial), although this difference was not significant in an independent expression level study (Nagalakshmi et al, 2008). Interestingly, we found that the rate of negative interactions between sisters in the asymmetric set was 46%, which is no less than the background rate for duplicates (Supplementary Figure 6), indicating retained functional overlap for even these highly skewed pairs.
The asymmetric distribution of genetic interactions among duplicate pairs motivated us to question whether the overall deficit of genetic interactions among duplicate genes is a result of buffered interactions distributed in both duplicate copies evenly or rather in only one paralog. Strikingly, we found that, on average, one of the two duplicates had a comparable or larger number of interactions than singletons while the sister has significantly fewer interactions (Figure 4C). The slightly higher number of interactions for the high‐degree duplicate gene appears to be a result of an important bias among the ancestors of the duplicates, as they became statistically indistinguishable from singleton genes after controlling for gene importance (Supplementary Figure 7). Thus, the overall deficiency of duplicate genes for genetic interactions (Figure 2C) as well as the asymmetric distribution of modern interactions (Figure 4A) suggests that the majority of the interactions of the common ancestor are associated with a single member of the pair.
Dissecting the divergent functions of duplicates through genetic interaction profiles
Genes belonging to the same biological pathway or protein complex tend to share similar patterns of genetic interactions, and similarity between genetic interaction profiles has proven effective for predicting gene function and defining pathway and complex membership (Costanzo et al, 2010). In this study, we exploited genome‐wide genetic interaction profiles along with specific interactions to identify the functional differences that distinguish divergent gene pairs. For example, SSO1 and SSO2 encode SNARE proteins, core components critical for the specificity of membrane fusion and intracellular transport in eukaryotic cells (Jahn and Scheller, 2006; Yang et al, 2008). Although vesicle fusion with the plasma membrane is dependent on either SSO1 or SSO2 gene function, previous studies have shown an SSO1‐specific requirement for prospore membrane formation during sporulation (Jantti et al, 2002; Yang et al, 2008). We noticed that genes involved in chitin biosynthesis (CHS3, CHS5 and SKT5) and polarized cell growth (BUD6, BEM3 and AXL2) shared genetic interactions in common with SSO1 (r>0.14; Supplementary Table 4; see Materials and methods) but not with SSO2 (r<0.04), suggesting a specific role for SSO1 in these processes during vegetative growth. These genetic interaction profile similarities support previous observations from high‐content screening experiments, indicating that SSO1 is important for normal actin localization, and deletion of SSO1 results in more severe actin mis‐localization (21%) compared with a sso2Δ mutant strain (Ohya et al, 2005; 4%; Supplementary Figure 8).
We found that SSO1 and SSO2 also varied extensively in terms of their interaction degree. In fact, the ratio of SSO1:SSO2 interactions was among the most asymmetric, with 149 negative interactions for SSO2 compared with only 15 negative interactions involving SSO1 (Supplementary Table 3). Consistent with evolution of a condition‐specialized function, previous studies suggest that functional divergence has led to a more prominent sporulation‐specific function for SSO1 (Jantti et al, 2002; Yang et al, 2008). The reduced number of interactions observed for SSO1 may reflect its specialized function, in part, because genetic interactions were mapped under vegetative conditions when sporulation is not required. In a similar example, highly asymmetric genetic interaction degree may reflect sporulation or meiosis‐specialized function for cell wall assembly duplicates GAS1 and GAS2, suggesting that this may be a common basis for imbalances in genetic interaction degree (Supplementary Note 3).
Genetic interaction profile examination yielded another interesting example in duplicate pair CIK1/VIK1. Comparison of profile similarity and interaction degree of CIK1 and VIK1 demonstrates the ability of genetic interaction analysis to distinguish subtle functional differences between paralogous genes. CIK1 and VIK1, which arose from the WGD event, encode kinesin‐associated proteins that form separate heterodimeric complexes with Kar3, a minus‐end‐directed microtubule motor protein, to mediate a diverse set of microtubule‐dependent processes (Manning et al, 1999). Despite strong sequence and structural similarities, CIK1 and VIK1 exhibit different genetic interaction profiles, suggesting that these proteins have specialized functional roles. Although both proteins depend on physical interaction with Kar3 for proper function, CIK1 has more genetic interactions in common and is more closely correlated to the KAR3 interaction profile (CIK1–KAR3; r=0.5; see Materials and methods) compared with its duplicate VIK1 (VIK1–KAR3; r=0.3). Consistent with closely related interaction profiles (Figure 5A), kar3Δ and cik1Δ deletion mutants share several phenotypes including abnormally short spindles, chromosome loss and delayed cell cycle progression (Page et al, 1994; Manning et al, 1999). In contrast, a vik1Δ mutant strain does not exhibit any overt phenotype (Manning et al, 1999).
In addition, VIK1 and CIK1 differ in their gene expression and protein localization (Manning et al, 1999). Interestingly, we found that CIK1 and KAR3 interaction profiles more closely resemble the profiles of genes involved in chromosome cohesion and segregation (GO:0000070; P<8 × 10−8; hypergeometric cdf; Figure 5A), whereas VIK1 was more correlated to genes involved in microtubule assembly and stabilization (GO:0007017; P<2 × 10−8; Figure 5A). Our findings support a previous hypothesis (Manning et al, 1999) and suggest that the Cik1–Kar3 and Vik1–Kar3 heterodimers serve distinct, yet related, roles during cell division. In addition to profile similarity, examination of individual genetic interactions also highlight potential functional differences between these microtubule motor‐associated proteins. We noticed strong asymmetry in the ratio of CIK1:VIK1 interaction degree and, consistent with a more severe deletion phenotype, we found that CIK1 has 4.5‐fold more negative genetic interactions than VIK1 (Supplementary Table 3). Interestingly, several genetic interactions connecting VIK1 and CIK1 to common partners differ in their type. In particular, the plus‐end microtubule motor‐encoding gene, CIN8, shares a modest positive genetic interaction with VIK1, whereas a cik1Δ‐cin8Δ double mutant displayed a synthetic sick/lethal phenotype (Figure 5B). Findings derived from our large‐scale survey of genetic interactions support previous observations that disruption of VIK1, but not CIK1, partially suppresses the temperature‐sensitive growth defect of a cin8‐3 kip1Δ double mutant (Manning et al, 1999). One role for the Kar3 microtubule motor during vegetative growth is thought to involve opposing the action of the Cin8 and Kip1 motor proteins. The VIK1‐specific positive genetic interactions reported here and elsewhere (Manning et al, 1999) suggest that a CIN8 and KIP1 antagonistic function may be unique to the Vik1–Kar3 heterodimer, thus distinguishing between Vik1–Kar3‐ and Cik1–Kar3‐related functions. In another example, we found that BIM1 shared a positive interaction with CIK1 (bim1Δ suppressed the cik1Δ growth defect) and a negative interaction with VIK1 (Figure 5B). Bim1 is a microtubule‐binding protein that localizes to the plus end of the microtubules where it is required for proper positioning of the nucleus during nuclear migration (Tirnauer et al, 1999; Lee et al, 2000). Recent studies have shown that Bim1 also localizes to the spindle midzone to stabilize microtubules during anaphase (Gardner et al, 2008). Interestingly, Kar3 also exhibits different sub‐cellular localization patterns that are dependent on physical interaction with Vik1 or Cik1. During vegetative growth, Kar3 associates with the spindle midzone in a Cik1‐dependent manner (Sproul et al, 2005), whereas the Kar3–Vik1 heterodimer localizes to the spindle poles (Manning et al, 1999; Allingham et al, 2007). Although the nature of the genetic interactions is unclear, the negative interaction between BIM1 and VIK1 might reflect the failure in nuclear positioning due to unstable microtubules while positive interaction observed between BIM1–CIK1 might reflect opposing functions involved in stabilizing and destabilizing the microtubules (Sproul et al, 2005; Gardner et al, 2008).
In both pairs of duplicates we investigated in detail (SSO1–SSO2 and CIK1–VIK1), the duplicate genes exhibited a strong negative interaction between sisters. This suggests that despite evidence for functional specialization and dramatic asymmetry in their overall interaction degree, sister duplicates retain the ability to partially compensate for the loss of one another, and this trend appears to be relatively common across duplicates in yeast (Supplementary Figure 6). We also noted that, although genetic interactions can resolve functional differences between sisters, in these cases, the differences appear to be relatively subtle: context or conditional specialization in the case of SSO1–SSO2 and localization specialization in the case of CIK1–VIK1.
We examined how partial redundancy and the functional divergence of duplicate gene pairs relates to their genetic interaction profiles. We found evidence for the hypothesis that immediately after duplication, duplicated gene pairs will mask each other's interactions with other genes, and that as the pair evolves apart, interactions reappear, highlighting functional differences between them. We have also shown that genome‐wide genetic interaction profiles provide insight into the mechanisms of duplicate gene evolution by distinguishing duplicate pairs maintained for gene dosage effects from those retained because of functional divergence. These findings clarify previous observations about the surprising prevalence of genetic interactions for apparently redundant duplicate genes (Ihmels et al, 2007), and provide evidence that they do indeed reflect functional redundancy as well as functional divergence. Finally, we also showed that a disproportionate distribution of genetic interactions among gene pairs supports the asymmetric evolution of duplicate genes whereby one member of a duplicate pair is under stronger selective pressure. The skewed distribution is correlated with differences in rates of sequence evolution, PPI degree, single‐mutant fitness defects and sensitivity to a variety of chemical environments, suggesting that one member of the gene pair assumes a predominant role under standard vegetative growth conditions.
Previous studies suggest that the asymmetric accumulation of loss‐of‐function mutations in many duplicate pairs is established quickly based on sequence evidence from the WGD event that indicates that the identity of the quickly evolving sister is consistent across several yeast species (Fares et al, 2006; Byrne and Wolfe, 2007; Scannell and Wolfe, 2008). On the basis of these observations combined with results from this study, we propose a refined model of duplicate evolution (Figure 6). Following a duplication event that does not provide a dosage‐dependent fitness advantage, we argue that one member of a duplicate pair should accumulate loss‐of‐function mutations more quickly due to relaxed purifying selection alone (Supplementary Note 4; Supplementary Figures 9–11). In essence, a degenerate paralog is more accommodating of mutations and stands a higher chance of sustaining a mutation affecting any remaining redundant functions (Supplementary Note 4). In many cases, the fast evolving duplicate meets the common fate of non‐functionality and eventual gene loss. If early function loss is complementary, the pair is put on a path toward functional partition. Gene properties that are necessary for multiple functions may be preserved in both copies if previous mutations caused these functions to fall to different sisters. Such an arrangement would render a complete functional divergence impossible. We note that this natural progression of asymmetry should occur for any duplication event, either whole‐genome or small‐scale, although the means of preservation of a duplicate pair might be distinct depending on the context. Presumably, in some cases, sister duplicates simply maintain complementary but essential roles despite their asymmetry, whereas in other cases, the asymmetric configuration provides some fitness advantage that ultimately enables a selective sweep.
We cannot rule out the possibility that neo‐functionalization may have a role in the preservation of some duplicate pairs and their subsequent asymmetric evolution, but if that is the case, the quickly evolving duplicate appears to take on a more inconspicuous functional role in most pairs. Our data argues against dramatic neo‐functionalization and instead suggests that the rapidly evolving duplicate retains a subset of the ancestral function for which it has become optimized (Figure 6). Importantly, despite specialization, the high rate of negative genetic interactions observed between asymmetric duplicate pairs (Supplementary Figure 6) indicates that the lower degree sister often retains some ability to compensate for the loss of the more constrained sister. We do not interpret this as evidence for selection on their redundancy, rather that the function or context for which the quickly evolving duplicate has been specialized allows or requires it to at least partially maintain the ancestral role (Supplementary Figure 9).
Our observations are consistent with previously proposed models of sub‐functionalization, including the Duplication–Degeneration–Complementation and Escape from Adaptive Conflict models (Hughes, 1994; Des Marais and Rausher, 2008; Innan and Kondrashov, 2010). Both these schemes describe ancestral functions being split between duplicates, the latter allowing for optimizations previously constrained by other functions. Indeed, we identified several gene pairs in the yeast genetic interaction network that support specialization driven by adaptation to different environmental or developmental conditions, leading us to speculate that a special case of the Escape from Adaptive Conflict or Duplication–Degeneration–Complementation models may apply to a large fraction of duplicates in S. cerevisiae, in which this specialization is driven by adaptation to different environmental or developmental conditions. For example, several of the most asymmetric pairs involve a gene specialized for sporulation or meiosis. Sporulation requires formation of a membrane structure known as the prospore membrane, which is dependent on the Sso1–Spo20 t‐SNARE complex. Although in vitro experiments indicate that both Sso1 and Sso2 can bind to Spo20 to form a functional t‐SNARE, the Sso2–Spo20 complex exhibits much weaker membrane‐fusion capacity and, thus, may explain why only Sso1 is able to support sporulation (Liu et al, 2007). Furthermore, studies have shown that Sso1 can interact with phosphatidic acid, which is necessary for Spo20 localization and function (Liu et al, 2007). Although the exact cause of functional divergence remains unclear, it is possible that the SSO1 gene product acquired a specialized role after duplication, which is important for modulating SPO21 function in non‐dividing cells. This example supports our model illustrating that changes in protein function are often relatively subtle, and condition or developmental specialization may instead be the driving force behind duplicate gene retention.
Although genome sequences provide a wealth of information about gene ancestry, they fail to address the functional efficacy of genes on which selection ultimately acts. Network analysis of PPIs (Presser et al, 2008) provide a complementary view, but common physical interactions shared by a duplicate pair still do not reveal whether interaction with a specific member of a duplicate pair has a functional consequence to the cell under a given experimental condition. Genetic interactions address both of these shortcomings by revealing exactly which relationships have an impact on fitness, and which do not, and thus provide a powerful perspective for understanding duplicate gene evolution.
Materials and methods
Definition of duplicates and singletons
The full list of duplicate pairs consists of those identified as the result of the WGD event, as reconciled from several sources (Byrne and Wolfe, 2005). Additionally, any pair of genes fulfilling established similarity requirements (Gu et al, 2002a) was reasoned to be a duplicate pair resulting from a SSD event. Specifically, the gene pair must have a sufficient sequence similarity score (FASTA Blast, E=10) and sufficient protein alignment length(>80% of the longer protein). The pair must also have an amino‐acid level identity of at least 30% for proteins with aligned regions longer than 150 amino acid, and for shorter proteins, the identity must exceed 0.01n+4.8 L(−0.32(1+exp(−L/1000))), where L is the aligned length and n=6 (Rost, 1999; Gu et al, 2002a).
After combining pairs from the WGD event, with pairs determined through sequence alone (SSD), families with more than two members as a result of multiple pairings were completely removed from analysis to control for potential buffering from a third member affecting the interactions of the first two, and any gene not involved in any pairings was deemed an unambiguous singleton.
Functionally related pairs
As a proxy for non‐duplicated yet functionally related gene pairs, we have used pairs that exhibited a PPI in at least one of two high‐throughput TAP‐MS studies (Gavin et al, 2006; Krogan et al, 2006). To increase the number of duplicate pairs considered in the analysis relating sister–sister profile similarity to sister–proxy similarity, we did not limit PPI interactions to TAP‐MS (see next section). Interactions for this analysis were included from BioGrid if they fell into one of the following categories: affinity capture‐RNA, affinity capture‐Western, two‐hybrid, PCA, affinity capture‐MS, co‐fractionation, biochemical activity, co‐crystal structure, co‐purification, far western, FRET, protein–peptide, protein–RNA or reconstituted complex.
Significance of binomial proportions (synthetic sick/lethal or dosage membership)
Synthetic sick/lethal proportion rates were tested under using the following normally distributed random variable:
where P1 and P2 are the binomial proportions in the respective classes and is the binomial proportion of the combined set.
Genetic interaction data and profile similarity calculations
Genetic interaction data were taken from a recent global genetic interaction study (Costanzo et al, 2010). For the presence or absence of individual interactions, such as calculating the proportion of synthetic lethal duplicates, or counting interaction degree for a given gene magnitude, P‐value thresholds were used (e>0.08 and P<0.05). When counting discrete interactions, column degree was used. Thus, only genes in the deletion array (3885 genes) have valid degrees. This dimension was chosen to maximize the number of covered genes, as fewer genes (1712) have been screened as queries. For assessing profile similarity, we first normalized the (unthresholded) data along both rows and columns and then used inner product between any pair of array genes as their profile similarity (Rost, 1999; Gu et al, 2002a).
Definition of dosage class
A duplicate pair was labeled as a ‘dosage’ pair if it met two of the following three conditions: (1) The pair′s representative ortho‐group had a volatility score(Wapinski et al, 2007) in the top quartile. (2) The pair had a scaled difference in transcript quantity in the bottom quartile. Absolute expression data is taken from Holstege (1998) and scaled expression difference is defined as in Ihmels et al (2007):
(3) The pair had a scaled difference in expression stability in the bottom quartile, wherein stability for each gene is defined as the number of data sets (out of a possible 127 from Hibbs et al, 2007) in which the expression of the given gene is in the bottom 2% for variance.
Ancestral proxies on the PPI network
To find suitable proxy genes for a given duplicate pair, we isolated the common interaction partners on the expanded physical PPI network for each pair with the assumption that interactions common to both paralogs are not likely to have evolved independently, and are therefore tied to one or more of the pair's ancestral functions. We then measured genetic interaction profile similarity between each paralog and the neighbor for comparison with profile similarity between the duplicates themselves. Results were averaged across all common partners for a given duplicate pair.
Genetic interaction degree asymmetry
To compare genetic interaction degree and rates of evolution, we used the original rates provided in the supplement to Kellis et al, 2004. This ratio was defined as the rate of the quickly evolving or ‘derived function’ member divided by that of the slowly evolving or ‘ancestral function’ member. To test for bias in which member of the pair had more interactions, we assumed a null model in which either gene was equally probable to have the most interactions. We obtained a P‐value for this hypothesis using MATLAB's binomial cumulative distribution function binocdf(). The proposed ancestral gene generally has a higher degree; hence, the genetic interaction ratio for the pair was calculated with the ‘ancestral function’ member's property in the numerator.
To ascertain the number of chemical environments under which a gene displayed a significant phenotype, we used the original data from Hillenmeyer et al (2008). We counted the number of conditions in which the homozygous deletion displayed a significant P‐value (P<0.05) out of a possible 1144. As above, we then used a binomial cumulative distribution to test whether the correspondence between the two data sets (the number of times the gene with more genetic interactions also had more chemical interactions) could be attributed to chance.
Phylogenetic comparison for asymmetric pairs
We compared the sequence similarity of the WGD pairs in S. cerevisiae with orthologs in other post‐WGD species (S. castellii, C. glabrata and S. bayanus) in which one WGD copy had been lost as annotated in the Yeast Genome Order Browser (Byrne and Wolfe, 2005). For each such case, we produced an amino‐acid sequence alignment between each S. cerevisiae gene and the out‐group ortholog using the BLAST algorithm (Johnson et al, 2008). We then compared the percent identity score for each duplicate with the out‐group ortholog. For every pair identified as asymmetric, we used a binomial test to ascertain whether the gene with more interactions was more similar to the orthologous gene, the null hypothesis being that the lower degree and higher degree genes have equal chance of a higher percent identity score with the orthologous gene. In S. bayanus, we found only three single orthologs to asymmetric WGD pairs in S. cerevisiae, and as such that data is not included.
Biological example profile similarity
Profile correlations for specific biological examples (SSO1, SSO2; GAS1, GAS2; CIK1, VIK1) were taken from the supplement to Costanzo et al (2010). It represents a composite score using information from both array and query profiles in an attempt to give a uniform similarity score across all pairs of genes. Figure 5A shows edges from this composite network involving CIK1, VIK1 and KAR3 using a correlation threshold of 0.2.
We would like to thank Dr Tamar Lahav and Dr Judith Berman for their valuable insights and helpful comments regarding this work and also Dr Nathan Springer for his helpful comments on the manuscript. BV, JB and CLM are partially supported by funding from the University of Minnesota Biomedical Informatics and Computational Biology program, and a seed grant from the Minnesota Supercomputing Institute. CLM and JB are supported by the National Institutes of Health (1R01HG005084‐01A1) and CLM and BV are supported by the National Science Foundation (DBI 0953881). BP is supported by The International Human Frontier Science Program Organization, by the Hungarian Scientific Research Fund (OTKA) and by the ‘Lendület Program’ of the Hungarian Academy of Sciences. CB and BA are supported by Genome Canada through the Ontario Genomics Institute (2004‐OGI‐3‐01), the Canadian Institutes of Health Research (GSP‐41567) and the Canadian Institute for Advanced Research.
Conflict of Interest
The authors declare that they have no conflict of interest.
Supplementary Table S1
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