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R.P.St.O. was involved in every aspect of the study, from experimental design and performance to writing the manuscript. R.M. designed and executed algorithms and performed bioinformatic analysis. J.O. performed genetic experiments and growth curves. M.P. designed custom robotics and automation software. E.F. wrote software and performed database management. R.W.D. contributed intellectually throughout to experimental design and execution. C.N. helped design the experiments and write the manuscript. F.P.R. was involved in data analysis and manuscript preparation. G.G. was involved in every aspect of the study, including manuscript preparation.
Systematic genetic interaction studies have illuminated many cellular processes. Here we quantitatively examine genetic interactions among 26 Saccharomyces cerevisiae genes conferring resistance to the DNA-damaging agent methyl methanesulfonate (MMS), as determined by chemogenomic fitness profiling of pooled deletion strains. We constructed 650 double-deletion strains, corresponding to all pairings of these 26 deletions. The fitness of single- and double-deletion strains were measured in the presence and absence of MMS. Genetic interactions were defined by combining principles from both statistical and classical genetics. The resulting network predicts that the Mph1 helicase has a role in resolving homologous recombination–derived DNA intermediates that is similar to (but distinct from) that of the Sgs1 helicase. Our results emphasize the utility of small molecules and multifactorial deletion mutants in uncovering functional relationships and pathway order.
Complicating the relationship between genotype and phenotype is the fact that individual alleles sometimes combine to produce surprising phenotypes. The word ‘epistasis’ has been used in distinct ways, in both classical and statistical genetics, to describe this phenomenon1. Theoretical statistical-genetic arguments support the expectation that deleterious fitness effects of mutant alleles in independently functioning genes should combine multiplicatively; in other words, the double-mutant fitness is expected to be the product of the single-mutant fitness values2. The frequency with which this relationship occurs in nature is consequential to theories regarding evolution and the origins of sexual reproduction3, but it remains unresolved after limited study4–6. Departure from the multiplicative model suggests that the corresponding gene products have a functional relationship, the nature of which depends on the ‘direction’ of the departure. Aggravating interactions, or ‘negative epistasis’ (in which the double-mutant fitness is lower than expected; synthetic lethality, in the extreme case), often reflect activities operating in separate but compensatory pathways7. Alleviating interactions, or ‘positive epistasis’ (in which the double-mutant fitness is greater than expected), often result when gene products operate in concert or in series within the same pathway. These interactions (also called ‘diminishing- returns’ interactions2) arise, for example, when a mutation in one gene impairs the function of a whole pathway, thereby concealing the consequence of additional mutations in other members of that pathway.
Several experimental studies and their analyses in Saccharomyces cerevisiae have illustrated the value of genome-scale screens for genetic interactions8–20. Screens for synthetic sick or lethal genetic interactions have uncovered numerous functional relationships, identified compensatory protein complexes and pathways, and offered insight into the nature of genetic robustness8–17. Most large-scale genetic interaction screens, however, have been restricted to the discovery of synthetic sick or lethal interactions and have defined such interactions by departure from the expectation that double-mutant strains will have the fitness of the least fit single mutant8,10–12,14,15.
Although recent studies have expanded to include the measurement of alleviating interactions, these interactions have not been defined in a consistent way. In one case, a range of interaction types was defined by enumerating all possible ‘greater than’, ‘less than’ and ‘equal to’ relationships among single- and double-mutant invasive growth phenotypes18. In another case, epistasis was defined with the S-score13, which identifies interactions from double mutants whose growth deviates from the median growth of all evaluated double mutants involving a given gene20. A theoretical study19 defined interaction under the multiplicative neutral model2 by using predicted growth rates, but ultimately favored an alternative measure (‘scaled epsilon’). Neither of the latter two measures was evaluated experimentally.
Here we have conducted a comprehensive and quantitative analysis of genetic interactions among a target set of genes, focusing on non-essential genes that confer resistance to the DNA-damaging agent MMS. Quantitative fitness analysis identified both aggravating and alleviating interactions on the basis of deviation from a multiplicative model. Because of the quantitative nature of our assay, we could also differentiate among ‘classical genetic’ subclasses of alleviating interactions on the basis of the relative MMS sensitivity of single-and double-deletion strains. We used a systematic, objective and automated analysis of the genetic evidence to derive an interaction network that recapitulates many known features of DNA repair pathways. This interaction network also makes predictions, including a role for the Mph1 helicase in resolving DNA intermediates resulting from homologous recombination.
We systematically assessed genetic interactions among a target subset of genes that confer resistance to the compound MMS. These genes were selected on the basis of the results of a chemogenomic fitness screen of pooled homozygous yeast deletion strains21,22 (Fig. 1 and Supplementary Table 1 online). Deletion strains that were among the most sensitive to MMS (Fig. 1) were used to construct all possible combinations of double-deletion strains for quantitative fitness analysis (see Methods). To facilitate construction of these mutants, each gene was deleted in haploid strains of both mating types. In MATa haploids (BY4741), genes were replaced with a gene encoding the kanamycin resistance marker gene (Kanr). In the MATα haploid strain (Y5563), genes were replaced with a gene encoding the nourseothricin resistance marker gene (Natr). Y5563 contains the can1Δ::MFApr-HIS3 marker necessary for the selection of double-deletion haploid mutants14. The doubling time (D) of all single-deletion strains in rich growth medium (YPD) with and without 0.002% MMS was measured by using a highly quantitative growth assay (Methods and Fig. 2a). Deletion strains for which the doubling time of the Kanr strain was inconsistent with that of the Natr strain were either reconstructed and verified to eliminate inconsistencies or omitted from further analysis (data not shown).
The doubling times of single mutants (with and without MMS) ranged from 1.3 h to 8 h, and the average coefficient of variation (CV), calculated from not fewer than five replicates, was 5.2%. Only a modest increase in CV was observed for strains with the most severe growth defects (Supplementary Fig. 1 online). This method provided the sensitivity and precision necessary for distinguishing small differences in growth rate, which were essential for our subsequent analysis (Supplementary Fig. 1). The fitness of each deletion strain was defined by its growth rate relative to that of wild type (calculated as the doubling time of the parental wild-type strain divided by that of the mutant). The average fitness values of single-deletion strains used for further analysis are shown in Figure 2b. Notably, all 26 gene deletions resulted in reduced fitness relative to the wild-type control.
We used the 26 Kanr haploid deletion strains and 26 Natr haploid deletion strains to construct 650 double-deletion strains. Four of these strains could not be constructed because of genetic linkage between genes. Ten other strains were nonviable (synthetically lethal) and were assigned a fitness of zero. The fitness of the remaining 636 double-deletion strains was measured in YPD media both with and without MMS (see Methods). A benefit of this approach is that each gene pair is represented by two independently constructed double-deletion strains (referred to as the ‘Kanr-Natr’ and ‘Natr - Kanr’ strains). To quantify the robustness of our strain construction and fitness assay, we plotted the fitness (calculated in both the presence and the absence of MMS) of the Kanr-Natr double-deletion strains against that of the Natr-Kanr deletion strains (Fig. 2c). We obtained a highly significant correlation (R = 0.981) with a slope near to 1, consistent with the idea that strain construction contributed negligibly to fitness.
If the deleterious effects of two distinct mutations are truly independent of one another, then their fitness defects are predicted to combine multiplicatively2. In other words, if a strain deleted for gene x has a fitness Wx and a strain deleted for gene y has a fitness Wy, then the fitness of the double mutant strain Wxy is expected to be Wx × Wy. Using the double- and single-deletion fitness values calculated in Figure 2, we measured the deviation ε from this expectation (where εxy = Wxy − Wx × Wy) and found that ε values were highly correlated between reciprocal double-deletion pairs (R = 0.896; data not shown). The ε values derived from averaging the fitness of the Kanr-Natr and Natr-Kanr mutants are given in Supplementary Table 2 online and are represented as a heat map in Figure 3a.
Given that deviation from neutrality (nonzero ε) suggests a functional relationship, we assessed how well current knowledge of these genes was reflected in the ε values. We examined the distribution of ε value for gene pairs with or without a specific functional link—in other words, gene pairs that either do or do not share a specific gene ontology (GO) term23. Whereas the distribution of ε values for genes without a specific functional link is centered near zero, the ε values of the 35 functionally linked gene pairs are clearly centered away from zero and are predominantly positive (Fig. 3b).
Prediction of specific functional linkage on the basis of the ε value alone achieved a sensitivity of 80% at a false-positive rate of 20% (Fig. 3c), as assessed by cross-validation. Hierarchical clustering of genes by genetic congruence (that is, correlation of ε profiles15,24; see Methods) showed that the similarity between the spectrum of genetic interactions of two genes was also a robust predictor of functional links (Fig. 3c). This is consistent with the observation that genetic congruence can predict shared function15,24. We found that a combination of ε, genetic congruence, and a measure of the difference between the MMS sensitivity of the double mutant and each single mutant (described in more detail below) was the most robust predictor of specific functional links. Using the combined predictor, we achieve a sensitivity of 84% at a false-positive rate of 20%. Moreover, at a lower false-positive rate of 2%, the combined predictor achieves 54% sensitivity, as compared with 20% achieved with ε alone (Fig. 3c). We also note that ‘scaled epsilon’, a previously proposed measure of genetic interaction19, was not as effective at predicting functional links (Supplementary Fig. 2 online).
Because two gene pairs with the same ε value may have different susceptibilities to measurement error, we used a Z-test based on estimated errors in fitness measurements of single- and double-deletion strains to detect significant departure (P < 0.01) of each gene pair from the multiplicative model (see Methods). We applied this method to fitness measurements obtained both with and without MMS, and found that the addition of MMS increased the number of both aggravating and alleviating interactions (Fig. 4). In the presence of MMS, 113 out of 323 pairs were found to deviate significantly from the multiplicative model. Of these, 45 were classified as alleviating interactions (significantly positive ε) and 68 were classified as aggravating interactions (significantly negative ε). Classification results for all 323 gene pairs are given in Supplementary Table 2.
Of the 45 gene pairs with significantly positive ε (see below), 24 had a functional link. Of the 21 alleviating interactions that did not have a functional link, many have well-documented interactions including MUS81-MMS4 (ref. 25), SGS1-SHU1, SGS1-SHU2 and SGS1-PSY3 (ref. 26); HPR5-RAD18 and HPR5-RAD5 (ref. 27); RAD5-RAD18 (ref. 28); and SHU1-SHU2 (ref. 29). Most gene pairs in our data set were classified as neutral, even when cells were grown in the presence of MMS. The limited connectivity of alleviating interactions was marked given that the genes studied were already enriched for a common function (conferring resistance to MMS). This observation suggests that the functional information provided by alleviating interactions is specific rather than general.
We focused further on the 45 gene pairs classified as alleviating in MMS, dividing them into five distinct categories based on the relative MMS sensitivity (S; see Methods) of single- and double-deletion strains (Fig. 5a). Restricting these analyses to MMS-induced growth defects enabled us to focus on pathways responding specifically to MMS-induced lesions, which was important because approximately half of the deletion strains studied showed fitness defects even in the absence of MMS (data not shown). Fourteen pairs showed ‘masking epistasis’ (Sxy = Sx > Sy), whereas four showed partial masking epistasis (Sxy > Sx > Sy). This scenario may be intuitively viewed as the deletion in gene x ‘masking’ the effects of the deletion in gene y. In addition, 2 gene pairs showed complete suppression (Sxy = Sy < Sx) and 15 showed partial suppression (Sy < Sxy < Sx). In this scenario the deletion in gene y improves the phenotype associated with the gene x deletion. Lastly, we observed ten gene pairs for which the MMS sensitivity of the single- and double-deletion strains was statistically indistinguishable (Sxy = Sx = Sy). These interactions, which we call ‘coequal’, are related to ‘complementary gene action’, ‘complementary epistasis’ or ‘asynthetic’ relationship types that have been previously described18,30,31.
Coequal relationships suggest that the genes function as cohesive units. For example, if two genes encode distinct subunits of a given protein complex, then we would expect these genes to show a coequal relationship (if neither gene has an additional function and if the protein complex requires both subunits for its function). Nine of the ten coequal interactions that we detected (all but PSY3-HPR5) encode, or are predicted to encode, physically interacting proteins25,26,28,32,33 (Fig. 5b). This suggests that disruption of each gene alone is sufficient to disrupt the function of the protein complex to which it contributes, and that neither gene has a separate function under the conditions examined. Apart from the PSY3-HPR5 pair, the coequal interacting pairs tended to have the highest congruence scores (Fig. 3a).
Asymmetric alleviating interactions (where Sx ≠ Sy) can be used to infer the order of biochemical events in a pathway34. For example, the phenotype of an xΔyΔ mutant resembling that of xΔ, but not yΔ, could be explained by protein X operating upstream of protein Y in a pathway (under the positive regulatory model of Avery and Wasserman34). We found that the genetic interactions among five genes central to homologous recombination (RAD51, RAD52, RAD54, RAD55 and RAD57; hereafter termed ‘homologous recombination genes’) can recapitulate the current model for the biochemical steps carried out by their encoded proteins (Fig. 5c). The first step of this process involves recruitment of the Rad51 protein to single-stranded DNA by Rad52. Extension of the resulting Rad51-nucleoprotein filament is then mediated by the Rad55-Rad57 heterodimer. Subsequent strand displacement at a region of homology is mediated by interactions with Rad54 (reviewed in ref. 35). This order is also consistent with the genetic dependencies for relocalization of these proteins to sites of DNA damage36.
The most highly connected module of alleviating interactions involved four genes (SHU1, SHU2, CSM2 and PSY3) that encode members of a protein complex collectively referred to hereafter as the ‘Shu complex’. Notably, we found coequal interactions between all pairs of Shu complex genes. Consistent with a previous report, deletions in each of these four genes partially suppressed the MMS sensitivity of the sgs1Δ strain26.We found that these four deletions also partially suppressed the rad54Δ deletion phenotype (Fig. 5d) and rescued the synthetic lethality between rad54Δ and hpr5Δ (Supplementary Fig. 3 online). These results extend previous findings supporting the idea that the Shu complex has a role in homologous recombination26 and place it upstream of Rad54.
SGS1 encodes a highly conserved member of the bacterial RecQ helicase family and shares homology with human BLM, which has mutations associated with Bloom’s syndrome37. Sgs1 has been proposed to function closely with the homologous recombination machinery. The synthetic lethality of sgs1Δmus81Δ and sgs1Δmms4Δ double-deletion strains can be rescued by eliminating early steps in homologous recombination (for example, the triple mutant sgs1Δmms4Δrad51Δ is viable38). This observation has led to the hypothesis that the helicase activity of Sgs1 and the endo-nuclease activity of the Mus81-Mms4 complex25 are each important for resolving a common cytotoxic homologous recombination-generated DNA intermediate38. Consistent with this hypothesis, recombination-dependent cruciform structures have been found to accumulate in sgs1Δ cells and to be actively resolved when SGS1 is overexpressed39.
Hierarchical clustering of ε values showed that the sgs1Δ strain and the mph1Δ strain share a similar pattern of ε values (Fig. 3a). This similarity, which includes aggravating interactions with both mus81Δ and mms4Δ, is emphasized in Figure 6a. Mph1, similar to Sgs1, possesses 3′ to 5′ helicase activity40, shows alleviating interactions with components of homologous recombination41, and has a human ortholog implicated in a disorder associated with genomic instability42. We therefore tested whether the aggravating phenotype of mph1Δ mus81Δ and mph1Δmms4Δ double-deletion strains could be suppressed by mutations in homologous recombination–associated or other genes in our data set. Triple-deletion strains were created by crossing both the ‘Kanr-Natr’ and ‘Natr -Kanr’ variants of mph1Δ mus81Δ and mph1Δmms4Δ double-deletion strains to each of the remaining 24 MATα haploids in which genes were replaced with a hygBr selectable marker (see Methods). The fitness of each triple-deletion strain was then measured in the presence of MMS.
The expected fitness deviated from expectation for several triple-deletion strains, and the sign of the observed deviation tended to be same in the mph1Δ mms4Δ and mph1Δmus81Δ backgrounds (Fig. 6b). Of the 24 gene deletions, 10 were found to show alleviating interactions on both backgrounds. These ten genes are the core factors in homologous recombination (RAD51, RAD52, RAD54, RAD55 and RAD57), members of the Shu complex (SHU1, SHU2, CSM2 and PSY3) and RAD59, a homolog of RAD52 that functions in a Rad51-independent homologous recombination pathway43. In addition, all ten deletions (apart from rad52Δ) improved the fitness of both of the mph1Δmus81Δ and the mph1Δmms4Δ double-deletion strains in the presence of MMS (data not shown and Supplementary Fig. 4 online). Consistent with previous reports, each of these deletions (with the notable exception of rad59Δ) rescued the synthetic lethality of both sgs1Δmus81Δ and sgs1Δmms4Δ (ref. 38 and Supplementary Fig. 5 online). Collectively, these results suggest that Mph1 has a role in resolving homologous recombination–dependent and Shu complex–dependent toxic DNA intermediates (Fig. 6c).
Our analysis of double mutants did not identify previously reported interactions between MPH1 and homologous recombination genes41, between MPH1 and Shu complex genes21, or between homologous recombination genes and Shu complex genes26. Even though the ε values for these pairs were consistently positive (Fig. 6a and Supplementary Table 2), significant deviation from the multiplicative model was rarely observed. When we aggregated the ε scores for the four Shu complex genes, we detected significant positive deviation from expectation between this complex and both MPH1 and the homologous recombination genes; however, these deviations were significantly weaker than those measured for pairs of Shu complex genes (Supplementary Fig. 6 online). These differences in ε magnitude cannot be explained by variations in single-deletion fitness defects. Thus, although our results are consistent with the idea that Mph1, homologous recombination proteins and the Shu complex operate in a common pathway, they suggest that Mph1, homologous recombination proteins and the Shu complex also have cellular roles that are independent of one another. Capturing such partially overlapping relationships in future systematic studies of alleviating interactions will prove challenging.
We have described a comprehensive and quantitative analysis of genetic interactions among 26 non-essential genes involved in resistance to MMS-induced DNA damage. A conceptually simple multiplicative model was used to define genetic interactions between these genes. The validity of this model is supported here by the fact that the fitness defects of gene pairs without functional links usually combine multiplicatively, and that deviation from this model is predictive of shared function. This model has not been applied in previous large-scale genetic interaction studies8,10–12,14,15,18. As a result, some gene pairs might have been previously misinterpreted as being in common or compensatory pathways if the multiplicative neutral model adopted here is correct.
In the absence of MMS, our methods classified 12% of gene pairs as aggravating interactions and 6% as alleviating interactions (Fig. 4). Genome-wide screens have estimated the frequency of aggravating genetic interactions (synthetic lethality and synthetic sickness) to be ~0.5% among non-essential genes15. The ~24-fold enrichment in aggravating interaction frequency that we observed in the absence of MMS illustrates the utility of chemogenomic fitness screens in identifying functionally related subsets of genes and in quantitatively measuring their genetic interactions. Notably, we further enriched the number of alleviating and aggravating interactions to 21% and 14%, respectively, by growing deletion strains in the presence of MMS. The enrichment of functional links among alleviating gene pairs further underscores the value of systematic screens that can capture such interactions13,18.
The adaptive value of the sexual mode of reproduction has been much debated. The deterministic theory argues that, if aggravating epistasis is prevalent, then sexual reproduction is selective because it enables deleterious mutations to be purged from genomes3. Previous studies aimed at measuring the relative frequencies of alleviating and aggravating interactions have yielded conflicting results4–6. Here, all single-gene deletions produced a quantifiable phenotype relative to wild type (Fig. 1b); thus, every gene pair in our data set was interrogated for both alleviating and aggravating interactions. The observation that aggravating interactions occurred more frequently than alleviating interactions (Fig. 4; both with and without MMS) is consistent with the deterministic theory. An important caveat, however, is that the genes that we studied were not chosen randomly.
The relative MMS sensitivities of single and double mutants were used to distinguish distinct subtypes of alleviating genetic interactions. We found that coequal interactions (where Sxy = Sx = Sy) occur between gene pairs that typically have the highest genetic congruence scores (Fig. 3a and Fig 5b) and coequality is generally indicative of protein complexes that function as cohesive units25,26,28,32,33. Systematically discovered alleviating interactions (where Sx ≠ Sy) accurately predicted the order of previously characterized biochemical processes. In addition, we found that shu1Δ, shu2Δ, psy3Δ and csm2Δ could partially suppress the MMS sensitivity of rad54 (Fig. 5b) and, similar to deletions in homologous recombination genes44, rescue the synthetic lethality of an hpr5Δrad54Δ double-deletion mutant (Supplementary Fig. 3). These data extend previous findings linking the Shu complex to homologous recombination26 and place this complex upstream of Rad54 in homologous recombination–mediated repair of both MMS-induced and spontaneous DNA damage.
Genetic congruence between MPH1 and SGS1 led to the hypothesis and observation that the fitness of mph1Δmus81Δ and mph1Δmms4Δ double-deletion strains in MMS can be improved by deleting genes important for homologous recombination and is consistent with the idea that the Mph1 helicase is involved in resolving homologous recombination-dependent toxic DNA intermediates (Fig. 6). Even though the Mph1 protein shows similar substrate specificity to Sgs1 in vitro40, whether it has the same substrate specificity as Sgs1 in vivo remains to be determined. Two of our results argue against this possibility: first, we did not observe any interaction between these two genes, as might be expected if they resolve the same intermediate; and second, although the rad59Δ deletion suppressed the sensitivity of mph1Δmus81Δ and mph1Δmms4Δ, it did not rescue the synthetic lethality of sgs1Δmus81Δ or sgs1Δmms4Δ. This observation suggests that Mph1 may distinguish itself from Sgs1 by acting on substrates generated by a RAD59-dependent mechanism45.
Of the roughly 6,000 genes in the yeast genome, fewer than 1,200 are essential for viability under optimal growth conditions (rich medium at 30 °C)22,46. Consistent with studies involving random mutations4,5 and computational studies of yeast metabolism19, most of our gene pairs followed a multiplicative relationship (Fig. 4). This level of robustness will undoubtedly hinder efforts to understand the functional organization of the cell on a systems level. Our results emphasize the utility of systematic and quantitative double-deletion studies, but they also show that additional perturbations, either genetic or chemical, will be necessary to reveal the full architecture of cellular pathways.
All strains were maintained on YPD media47,48. Antibiotic-resistant strains were selected with 200 µg/ml of genetecin (Agri-Bio), 100 µg/ml of nourseothricin (Werner Bioagents) and/or 300 µg/ml of hygromycin B (Agri-Bio). Single-deletion strains were obtained from the yeast deletion collection or were constructed de novo by PCR-based gene replacement49. Double-deletion strains were constructed by the synthetic genetic array (SGA) protocol14 with minor modifications. Cells were transferred manually with a 96-head pin tool and subjected to three rounds of selection before being pinned onto YPD/agar plates, grown for 2 d, and stored at 4 °C. Triple-deletion strains were constructed essentially as above, by crossing single-deletion HygBr MATα haploids to double-deletion Kanr-Natr MATa haploids and by selecting sporulated diploids on double-deletion selection media supplemented with hygromycin B.
Double- and triple-deletion strains were reconstructed by sporulating diploid heterozygotes and dissecting tetrads, or by selecting random spores if they met one of the following three criteria: (i) a viable colony was not obtained, (ii) the strain fitness was found to be higher than that of both starting strains (Wxy − max(Wx, Wy) > 0.05), or (iii) the fitness of Kanr-Natr double-deletion strains differed from that of the Natr-Kanr deletion strains . rad57Δrad61Δ and rad55Δshu2Δ double-deletion strains were not constructed because of genetic linkage between their respective gene pairs. Ten double-deletion mutants involving five confirmed synthetic lethal pairs (sgs1Δmus81Δ, sgs1Δmms4Δ, sgs1Δslx4Δ, rad54Δhpr5Δ and sgs1Δhpr5Δ) were assigned a fitness of zero.
Individual deletion strains arrayed on YPD/agar were inoculated into 80 µl of YPD using a 96-head pin tool. Cultures were grown to saturation for 20 h at 30 °C and then stored at 4 °C for 4–48 h. The cells were then resuspended by shaking for 15 min, and the optical density at 600 nm (OD600) of cultures was determined using a Tecan GENios microplate reader (Tecan). Cell concentrations were normalized by diluting each culture to a final OD600 of 0.02 with YPD using a Biomek FX Laboratory Automation Workstation (Beckman Coulter). Normalized cultures were grown in 100-µl volumes in 96-well plates in Tecan GENios microplate readers for 24 h. The growth rate of each culture was monitored by measuring the OD600 every 15 min.
The doubling time (D) was calculated from the difference between the time tf at an arbitrary maximum OD600 (ODm) and the time ti at a point three generations earlier, divided by the number of generations: D = (tf − ti)/3). The ODm is usually in the exponential growth regime and is approximately the OD600 after five doublings from the beginning of the run. ODm is divided iteratively by 2 to calculate the ODm−3 point at three generations earlier. For growth curves that do not reach saturation or ODm during the growth run, ODm is reassigned to the maximum OD600 of the curve. The fitness (W) of a strain deleted for a given gene x was defined as the ratio of the doubling time (D) of the wild-type strain to the deletion strain (W = Dwt/Dx).
Genetic interaction between a pair of genes (x,y) was defined if the fitness phenotype of the double mutant (Wxy) deviated significantly from that predicted for non-interacting gene pairs (Wx × Wy) under the multiplicative model. For each gene pair, the test used estimates of the mean and s.d. of Wxy derived by treating Kanr-Natr and Natr-Kanr strains as replicates. In addition, the delta method was used to compute the mean and s.d. of the product Wx × Wy on the basis of the means and s.d. of Wx and Wy obtained with the replicates in the single-deletion growth analysis. Gene pairs for which the multiplicative model hypothesis could be rejected (Z-test, α = 0.01) were categorized as genetic interactions. Interacting pairs were further classified as aggravating or alleviating depending on whether the double-deletion fitness phenotype was lesser or greater, respectively, than the product of the single-deletion fitness measurements.
Alleviating interactions were subdivided into five unique categories depending on their MMS sensitivity S, where S = D+MMS/D−MMS. Z-scores were used to measure the proximity of the MMS sensitivity of a double mutant to the sensitivities of the corresponding single mutants, x and y, with the respective formulae:
where µ and σ represent, respectively, the mean and estimated error of replicate measures of the variable indicated in the subscript. Z-scores under 0.75 were judged to be roughly equal for the purposes of subclassifying alleviating interactions. Directionality was assigned to asymmetric alleviating interactions (where Sx > Sy) as follows: for masking interactions (both partial and complete), network arrows originate from the masking locus (x); for suppressing interactions (both partial and complete), network arrows originate from the suppressing locus (y).
Gene ontology (GO) links (‘specific functional links’) were assigned to each gene pair with a specific biological process GO term in common. A GO term was considered to be specific if it is associated with fewer than 30 genes. To assess the value of quantitative genetic interactions in predicting functional links, we used several predictors: ε, genetic congruence (Pearson correlation between ε profiles, calculation for genes x and y excluding εxy, and undefined εxx and εyy values), and Z-scores measuring proximity of the double-deletion MMS sensitivity to the nearest single-deletion MMS sensitivity. The final model combined all of these predictors through a single logistic regression scheme. Regression equations were calculated by using the glmfit and glmval functions in MATLAB (MathWorks). Each model was assessed for its ability to predict functional links by using sixfold cross-validation. The prediction sensitivity or true-positive rate (defined here as the fraction of functionally linked gene pairs correctly predicted to have functional links) and false-positive rate (defined here as the fraction of non-functionally linked gene pairs incorrectly predicted to have functional links) are measured at a series of score thresholds (Fig. 3c).
We thank M. Evangelista and S. Pierce for critically reading the manuscript; and B. Andrews, C. Boone, J. Greenblatt, N. Krogan and J. Weissman for discussions. R.P.S. was supported by a postdoctoral fellowship from the Canadian Institutes of Health Research. F.P.R. was supported by grant R01 HG003224 from the National Institutes of Health National Human Genome Research Institute (NIH/NHGRI). This work was supported by a grant from the NHGRI awarded to R.W.D. and G.G.
The Swiss-Prot accession numbers for the single-deletion strains are as follows: CLA4 (P48562), CSM2 (P40465), CSM3 (Q04659), HPR5 (P12954), MAG1 (P22134), MMS1 (Q06211), MMS4 (P38257), MPH1 (P40562), MUS81 (Q04149), PSY3 (Q12318), RAD5 (P32849), RAD18 (P10862), RAD51 (P25454), RAD52 (P06778), RAD54 (P32863), RAD55 (P38953), RAD57 (P25301), RAD59 (Q12223), RAD61 (Q99359), RTT101 (P47050), RTT107 (P38850), SGS1 (P35187), SHU1 (P38751), SHU2 (P38957), SLX4 (Q12098) and SWC5 (P38326).
URLs. Swiss-Prot: http://www.ebi.ac.uk/swissprot
Note: Supplementary information is available on the Nature Genetics website.
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The authors declare that they have no competing financial interests.
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