Validation of Phenotypic Capacitors

We validated our identification of capacitors by repeating the phenotyping of 50 C1 strains and 50 control strains in our lab. Haploid mutants in the YKO library used for the original phenotyping were passaged for an unknown number of generations. Because some knockouts might increase mutation rates and thereby cause phenotypic variability that is not associated with loss of environmental buffering, we used instead a haploid-convertible heterozygous diploid YKO library [19] and kept the number of generations between sporulation and fixation to a maximum of ∼50. C1 strains exhibited more phenotypic variability than control strains (Figures 2 and S8). Phenotypes also appeared to be highly heterogeneous among C1 strains, suggesting that knockouts are not all disrupting a small number of high-level processes that result in a limited set of phenotypes. With the phenotype means and standard deviations from only the 100 haploid-converted strains, we repeated the calculation of phenotypic potential as described above, using the 70 already identified phenotypic medoids (Figure 2, lower right). Our expectation was that this repeated analysis would have reduced power because the proportionally large number of C1 strains that exhibit high variance would bias the lowess regression to decrease the magnitude of residuals. Even with this limitation, we found the phenotypic potential scores to be clearly higher in the C1 strains (p < 9.8 × 10⁻¹⁰, Wilcoxon-Mann-Whitney test). For a less conservative measure of phenotypic potential, we sampled data from capacitor and control strains in rough proportion to their numbers in the original analysis (five to 42), calculated scores on 1,000 repeated samplings, and averaged across all the 1,000 samples to calculate final phenotypic potentials (Figure S9). While this analysis still results in a conservative bias because of a reduction of residuals at the edges of the lowess regression due to fewer data points, capacitors exhibit ∼2-fold higher phenotypic potentials than controls (p < 2.7 × 10⁻¹⁰, Wilcoxon-Mann-Whitney test). A notable exception is RAD27, which has a lower phenotypic potential than all but three of the control strains in the more conservative first analysis and all but nine in the less conservative sampling analysis. RAD27 deletion causes a strong spontaneous mutator phenotype [20], which suggests that the high phenotypic variability observed in the original YKO might have been due to mutation accumulation. We also sampled ten capacitors in the C2 or C3 classes and these too exhibited significantly higher phenotypic potential scores than control strains (p < 0.002, Wilcoxon-Mann-Whitney test).

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Figure 2. Phenotypic Capacitor YKOs Have Highly Variable and Distinct Phenotypes

Representative micrographs from examples of putative phenotypic capacitor (HPR1, KEM1, SWI6, BEM2, CLA4, DIA2, RAD52) and control (YDR279W and YCR100C) strains are shown. Cells are stained with FITC-concanavalin A (green), rhodamine phalloidin (red), and DAPI (blue). Lower right: Histograms of the phenotypic potentials of control (black) and phenotypic capacitor (red) YKOs of haploid-converted heterozygous diploid strains.

https://doi.org/10.1371/journal.pbio.0060264.g002

As additional validation, we looked for evidence in the literature of capacitors causing increased cell-to-cell variability. Indeed, knockouts of the capacitors CCR4, CLN3, and SWI6 have each been shown to result in increased variability in diploid cell size in liquid media [21]. Knockout of CCR4 also causes irregular colony morphology on solid medium, a finding consistent with increased cell-to-cell variation [22]. Two other members of the CCR4-NOT core complex, NOT5 and POP2, are identified as capacitors in our screen suggesting that disruption of this transcriptional regulatory complex is likely to result in cellular heterogeneity. Additionally, two of three knockouts that increase intrinsic expression noise of the PHO5 promoter are the capacitors ARP8 and SNF6 [23]. Lastly, knockout of the capacitor FUS3 has been shown to increase cell-to-cell variation in response to a pheromone signal [24].

Phenotypic Capacitors Are Enriched in Several Gene Ontology Categories

We next investigated the entire set of 502 capacitors for enrichment in Gene Ontology (GO; http://www.geneontology.org/) process terms (Table S2). Phenotypic capacitors are highly enriched in numerous processes, most of which can be broadly categorized into DNA maintenance and organization, cell cycle and cell organization, response to stimuli such as stress, RNA elongation, or protein modification. This diverse set of enriched terms is likely to represent processes that can result in broad cellular changes when disrupted.

Specifically, capacitors contain 123 of 565 ORFs annotated with “chromosome organization and biogenesis” and 80 of 275 ORFs annotated with its daughter term, “telomere organization and biogenesis” (p < 2.9 × 10⁻²⁷ and p < 2.1 × 10⁻²⁵, respectively, hypergeometric distribution with Bonferroni correction). These include all genes annotated with recombinase activity, the entire telomerase holoenzyme complex, the entire RecQ helicase-Topo III complex, all but one gene from the homologous recombination module, all genes involved in postreplication repair, the entire CTF18m complex involved in sister chromatid cohesion and DNA-replication check-point signaling, the entire MMS22m module thought to be involved in double strand break repair, and both genes of the HEX3m module [25]. Notably, however, other modules that are likely to cause DNA instability are absent, including the nucleotide excision repair module, the DNA damage checkpoint module RAD9m, the MUS81m module involved in cleaving branched DNA, and the TOF1m module involved in promoting sister chromatid cohesion to repair DNA damage [25].

Capacitors also include 28 transcriptional regulators; numerous gene products involved in global mRNA production, including all members of the carboxy-terminal domain protein kinase complex; most members of the THO complex, which is thought to couple transcriptional elongation with mRNA metabolism and export; numerous nuclear pore-associated proteins, including both members of the mRNA export SAC3/THP1 complex; at least seven gene products involved in mRNA splicing; approximately half of the gene products annotated to the cytoplasmic mRNA processing (P) body; genes involved in protein transport and degradation, including three members of the Golgi-localized alpha-1,6-mannosyltransferase complex and eight gene products involved in vacuolar acidification; and genes involved in the control of actin (nine genes) and microtubule (12 genes) organization and in bud emergence or selection.

Phenotypic Capacitors Are Likely to Be Network Hubs

Protein–protein interaction (PPI) and synthetic lethal interaction (SLI) networks have a small number of highly connected nodes (hubs) and many more poorly connected nodes [26,27]. In PPI networks, deletion of a hub is more likely to be lethal than deletion of other nodes [26]. This finding suggests that genetic properties are, at least in part, traceable to global network architecture. Our numerical simulations of transcriptional networks implied that robustness is likely to be an emergent property of complex networks, and that in some cases network architecture constrains functional and evolutionary properties [15,16,28]. Others have predicted that SLIs are crucial to understanding buffering [29] or that phenotypic capacitors are likely to be hubs [30,31]. Thus, we asked here if a gene's phenotypic potential is traceable to network position.

First, we used networks derived both from curated literature citations [32] and from the nearly complete set of affinity-capture mass spectrometry interactions [33,34] to determine if the average PPI degree (number of interactions) of capacitors is different than that of other genes. We found that capacitors have more physical interactions than other nonessential gene products but fewer than essential gene products (Figure 3A). Because capacitors are enriched in select GO categories, one potential explanation for the high degree of capacitors is that they fall into GO categories whose members tend to be highly connected. However, in most cases, capacitors have significantly more interactions than GO-matched nonessential genes (Figure S10). Exceptions to this rule appear to occur mostly in GO categories where essential and nonessential genes do not differ in PPI degree.

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Figure 3. Network and Dispensability Characteristics of Phenotypic Capacitors

(A) The average number of physical interactions of high (C1, dark blue), mid (C2, blue), and low (C3, light blue) confidence phenotypic capacitors versus all nonessential (light grey) or essential (dark grey) genes using all physical interactions in the literature-curated network of the BioGRID (solid bars) or only affinity-capture mass spectrometry interactions (diagonal stripes).

(B) The average phenotypic potential of all nonessential genes (blue squares) or nonessential genes that have not been classified as a phenotypic capacitor (black triangles) binned by their number of affinity-capture mass spectrometry PPIs.

(C) The average number of SLIs using all interactions annotated in the literature curated BioGRID network (solid bars), interactions derived only from SGA experiments considering only genes used as bait (diagonal stripes), and interactions derived only from SGA experiments considering only genes not used as bait (horizontal stripes).

(D) The average phenotypic potential of all nonessential (blue squares) or nonessential noncapacitor (black triangles) genes binned by their number of literature-citation SLIs.

(E) The average growth rates for haploid KO (solid bars), heterozygous diploid KO (diagonal stripes), and homozygous diploid KO (horizontal stripes) strains. Values are relative to wild type.

(F) The average phenotypic potential of all nonessential (blue squares) or nonessential noncapacitor (black triangles) genes binned by their haploid growth rates. Error bars represent the standard error of the mean. All p-values are a comparison to nonessential genes, Wilcoxon-Mann-Whitney test: *, p < 0.05; **, p < 0.001; ***, p < 1 × 10⁻⁵; ****, p < 1 × 10⁻¹⁰.

https://doi.org/10.1371/journal.pbio.0060264.g003

A plot of phenotypic potential versus binned PPI degree shows that gene products with a higher connectivity have on average a higher phenotypic potential (Figure 3B); this relationship is almost entirely explainable by an increased proportion of capacitors in the highly connected bins (Figure S11). Interestingly, the proportion of capacitors precipitously drops at PPI degrees above 30, with similar proportions in the highest (>80 PPI) and lowest (<3 PPI) bins. The vast majority of genes in this highest bin have a duplicate in the genome, including 28 ribosomal proteins, three histones, and, of particular note, the homologues of Hsp90: HSP82 and HSC82. While surprising, the finding that Hsp90 homologues do not act as capacitors in S. cerevisiae according to our definition is consistent with a previous study that found that Hsp90 activity, not impairment, allowed new mutations to have immediate phenotypic consequence [35]. However, we do find a homologue of the chaperone Hsp70, SSE1, to be a capacitor in yeast, consistent with studies on other Hsp70 family members [36].

Next, we used all SLIs from curated literature citations [32] and, again, find that capacitors have a higher degree than other nonessential genes (Figure 3C, solid bars). Because genome-scale SLI assays have only been completed for a subset of genes (∼267 used as bait in synthetic genetic array [SGA] experiments), one potential explanation for the high SLI degree of capacitors is that they were more likely to be used as bait. To control for this possibility, we generated a subnetwork derived only from SGA experiments and divide genes in this network into those that had been used as bait and those that had not. For each class, we found that capacitors have higher SLI degree than other nonessential genes (Figure 3C, striped bars). The higher SLI degree of capacitors is maintained even when the number of physical interactions of a gene is controlled for (Figure S12) or when capacitors are compared to other nonessential genes within GO categories (Figure S13). A plot of phenotypic potential versus binned SLI degree (Figure 3D) shows that genes with a higher connectivity have on average a higher phenotypic potential; this relationship is almost entirely explainable by an increased proportion of capacitors in the highly connected bins (Figure S11).

Effects of Phenotypic Capacitor Knockouts on Growth Rate

We have shown that capacitors are likely to be PPI and/or SLI hubs, that they might be less likely to be completely functionally redundant, and that they are involved in a number of central processes in the cell. At this point, one might ask if disruption of capacitor function has too drastic of an effect on fitness to play a role in adaptation. To investigate this possibility, we asked if capacitors are less dispensable than other nonessential genes by comparing the growth rates of haploid [37] or diploid [38] mutants. Whereas capacitors appear to have no effect on growth rate in the heterozygous diploid, they are less dispensable in haploid and homozygous diploid knockouts, with a larger rate decrease seen in the haploid (Figure 3E). This effect is maintained even when we controlled for the PPI degree (Figure S12) or when capacitors were compared to other nonessential genes within GO categories (Figure S14). Gene knockouts that result in drastically reduced growth rates (less than 70% of wild-type) on average have higher phenotypic potentials (Figure 3F); this relationship is entirely explainable by an increased proportion of capacitors that cause low growth rates (Figure S11). However, in most cases, capacitors cause decreases in growth rate that are not as severe, with 79% and 95% of capacitor YKOs having a growth rate exceeding 0.80 of wild-type in the haploid and homozygous diploid, respectively. Indeed, 124 capacitor YKOs have an increased growth rate over the wild type.

Duplicate and Singleton Capacitors Have Different Modes of Functional Redundancy

The finding that many of the most highly connected PPI hubs are duplicates but not capacitors (Figure 3B) suggests a relationship between functional redundancy and buffering. We investigated this further by asking how capacitor genes distribute among the 1,425 unambiguous duplicates and 2,375 unambiguous singletons that have been identified in the yeast genome [39–41]. We found that capacitor genes are more likely to be singletons than other nonessential genes (Table 1, p < 0.026, G-test). Capacitor singletons and capacitor duplicates tend to be enriched in different GO process categories. Capacitor singletons are enriched in the categories of DNA maintenance and organization, response to stimuli, and RNA transcription and localization (Table S3). Capacitor duplicates, while more heterogeneous overall, tend to be most enriched in the categories of protein metabolism and endocytosis. We next investigated if capacitor singletons differ from capacitor duplicates in any network or dispensability properties. Both duplicate and singleton capacitor genes tend to have a high number of SLIs and to cause decreases in growth rate when knocked out in the haploid or homozygous diploid (Figure S15). However, only capacitor duplicates tend to be PPI hubs (Figure 4A).

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Table 1.

Number of Singletons or Duplicates in Different Gene Classes

https://doi.org/10.1371/journal.pbio.0060264.t001

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Figure 4. Characteristics of Capacitor Duplicates

(A) The average number of affinity-capture mass spectrometry interactions of all nonessential genes (grey), all nonessential singletons (light green), capacitor singletons (light blue), all nonessential duplicates (dark green), and capacitor duplicates (dark blue).

(B) Ks (left) and the expression similarity (right) between duplicate pairs that contain at least one essential gene (dark grey), at least one capacitor (solid dark blue), only nonessential noncapacitor genes (solid light grey), at least one gene product with over 19 PPIs annotated in the literature-curated BioGRID network and at least one capacitor (dark blue stripes), and at least one gene product with over 19 PPIs and no capacitors or essential genes (light grey stripes).

(C) The mRNA abundance (left), protein abundance (middle), and SLI degree (right) of capacitors with only one paralog in the genome (blue) and their paralogs (green).

(D) The phenotypic potential of capacitors with only one paralog in the genome (blue), their paralogs (green), and all nonessential genes (grey). Error bars represent the standard error of the mean. Unless otherwise marked, p-values are a comparison to duplicate capacitors, Wilcoxon-Mann-Whitney test: *, p < 0.05; **, p < 0.001; ***, p < 1 × 10⁻⁵; ****, p < 1 × 10⁻¹⁰.

https://doi.org/10.1371/journal.pbio.0060264.g004

The above finding presents an apparent contradiction: high PPI degree is strongly associated with capacitor identity in duplicates (Figure 4A) yet many highly connected duplicates are not capacitors (Figure 3B). The resolution of this contradiction appears to be that capacitor duplicate pairs are older and have less functional redundancy than other hub duplicate pairs. Using the synonymous substitution rate (Ks) between members of a duplicate pair as a rough estimate of age of the duplication event [39,42], we found that duplicate pairs that contain at least one capacitor are on average less ancient than duplicate pairs that contain at least one essential gene and appear to be more ancient than duplicate pairs that contain only nonessential noncapacitor genes (Figure 4B). Because substitution rates correlate negatively with expression level of a gene [43,44], one explanation for the differences in Ks is that duplicates that contain at least one capacitor have a different distribution of expression levels than other duplicate pairs. However, we found the pattern persists even when we control for mRNA expression level (Figure S16). The average age difference between capacitor duplicate pairs and nonessential duplicate pairs appears to be due to recent duplicates (Ks < 1), of which there are fewer capacitor duplicate pairs than nonessential noncapacitor duplicate pairs (p < 0.002, G-test, Figure S17). The same relation holds when comparing only hub duplicate pairs, which we defined as duplicate pairs where at least one paralog has a PPI degree ≥ 20. To calculate this difference, we separated hub duplicate pairs into those that contain at least one capacitor and those that do not. The average PPI degree of gene products in these two categories is approximately the same (p = 0.53, Wilcoxon-Mann-Whitney test). Comparing these two categories, we found that hub capacitor duplicates appear to be older on average due to an absence of recent duplication events. The greater average age of capacitor duplicate pairs raises the possibility that they are predominantly ohnologs, tracing their origin to the whole genome duplication in yeast ∼100 million years ago [45]. However, we did not find ohnologs to be overrepresented among capacitor duplicates relative to noncapacitor duplicates (p = 0.47, G-test). The greater synonymous-site divergence of capacitor duplicate pairs does not appear to be matched by greater divergence, as measured by the nonsynonymous substitution rate (Ka). For this comparison, we restricted our analysis to ohnologs to control for differences in duplication time that might introduce errors in Ka/Ks. Capacitor ohnologs have Ka values that are not significantly different from nonessential ohnologs, whereas essential ohnologs show marginally greater divergence (Figure S18).

A more striking difference between capacitor duplicate pairs and other duplicate pairs was evident in the correlations in expression between paralogs across many experimental conditions [39]. Duplicate pairs that contain at least one capacitor have a lower expression similarity on average than duplicate pairs that contain an essential gene or noncapacitor nonessential duplicate pairs (Figure 4B). Hub duplicate pairs that contain at least one capacitor also have a lower expression similarity than other nonessential hub duplicate pairs. These findings suggest that capacitor duplicate pairs are less functionally redundant than other duplicate pairs. To further dissect this difference in correlated expression, we examined the 64 capacitor-containing duplicate pairs in which both members of the pair have only one paralog in the genome. From these pairs, we excluded two pairs where both copies encode capacitors (the ribosomal proteins RPL8A and RPL8B and the mannotransferases HOC1 and OCH1) and two pairs where a capacitor gene is paired with an essential gene (the cyclins CDH1 and CDC20 and the UDP-glucose phosphorylases YHL012W and UGP1), yielding 60 capacitor genes paired with a nonessential noncapacitor gene. Comparing only these 60 capacitors to their paralogs, we found that the capacitor is likely to have a higher mRNA and protein abundance than its noncapacitor duplicate (Figure 4C).

Perhaps because of these expression profile differences, the capacitor gene has on average approximately three times as many SLIs as its paralog (Figure 4C). The higher expression of the capacitor in the pair suggests that perhaps the noncapacitor paralog also has an effect on robustness but a smaller one that did not surpass our threshold for capacitor identification. However, the noncapacitor paralogs do not have elevated phenotypic potentials when compared to all nonessential genes (Figure 4D, p = 0.38, Wilcoxon-Mann-Whitney test). Indeed, analysis of noise in protein abundance [46] suggests that the noncapacitor paralogs might be the targets rather than the sources of buffering: nonessential duplicates have on average greater variability in protein abundance than nonessential singletons (p < 2.2 × 10⁻³, Wilcoxon-Mann-Whitney test; Figure S15). A partially redundant duplicate (the capacitor gene) might buffer this variability, whereas its deletion might expose this variability at the level of the phenotype.

If one assumes that incomplete functional redundancy is also causing high phenotypic variability in the case of deleted singleton capacitors, understanding the mechanism of this process poses a greater challenge because there are no obvious candidate genes that overlap with singleton function. One hypothesis is that redundancy is achieved not at the level of the single gene as is the case for duplicates, but rather at the level of the protein module. Indeed, many singleton capacitors are part of functionally overlapping modules in the DNA integrity network [25]. To test the hypothesis that this is a more general property of singleton capacitors, we examined further their network characteristics. The clustering coefficient is a measure of local network interconnectivity. Singleton capacitors have on average higher clustering coefficients in the PPI network than all nonessential singletons, suggesting that they are interacting with more tightly knit groups of proteins that might represent functional modules (Figure 5A). Despite their high local connectivity, capacitor singletons occupy less central positions in the overall PPI network than do other nonessential singletons, as measured by betweenness centrality (Figure 5A). This is in stark contrast to capacitor duplicates, which tend to be more central when compared to other nonessential duplicates (Figure S15).

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Figure 5. Network characteristics of capacitor singletons

(A) The clustering coefficient (left) and betweenness centrality (right) of all nonessential singletons (light green) and capacitor singletons (light blue).

(B) Properties of the immediate PPI neighbors of a gene controlled for the degree of that gene (FDN score, see methods) for all nonessential singletons (light green) and capacitor singletons (light blue). From left to right: the phenotypic potential, the number of essential genes, the fraction of SLIs in the literature-curated BioGRID network, the haploid growth rate when deleted, the diploid growth rate when both copies are deleted. Error bars represent the standard error of the mean. Wilcoxon-Mann-Whitney test: *, p < 0.05; **, p < 0.01.

https://doi.org/10.1371/journal.pbio.0060264.g005

The clustering of singleton capacitors into modules suggests that their other immediate PPI partners, or first-degree neighbors (FDN), might have special network and dispensability characteristics. Because neighbor parameters are not likely to be independent of PPI degree, we first generated FDN scores for each gene product that describe the properties of a gene product's neighbors while controlling for the PPI degree of that gene product (see Materials and Methods). Using these measures, we found that the FDNs of singleton capacitors are more likely to be capacitors, essential genes, or genes with a high SLI degree when compared to all nonessential singletons (Figures 5B and S19). We also found that FDNs of singleton capacitors are more likely to cause decreases in growth rate in haploid or homozygous diploid knockouts. Taken together, these results suggest that singleton capacitors are acting in highly interconnected modules whose other members are likely to disrupt robustness or be deleterious when knocked out.

Capacitors and Chromosome Stability

Approximately one-fourth of identified capacitors are annotated to be involved in maintaining chromosome stability. While this class of genes still meets all of the criteria for singleton capacitors discussed above, one alternative mechanism to explain the increased phenotypic variability in these YKOs is that they are causing mutations or chromosomal aberrations [47]. Because YKOs that cause drastic increases in the spontaneous mutation rate are relatively well defined and rare (see Protocol S1), we concerned ourselves with YKOs that may be causing chromosomal aberrations, most easily measured by rates of gross chromosomal rearrangements (GCRs) [48]. We found that a high rate of GCRs is neither necessary nor sufficient for high phenotypic potential. For example, focusing on the eight genes in the homologous recombination module [25], we found YKOs that cause both high phenotypic potentials and high GCR rates (RAD50, RAD52, RAD57, XRS2), high phenotypic potentials but relatively low GCR rates (RAD51, RAD54), and low phenotypic potentials but high GCR rates (MRE11) [48]. Additionally, we estimated that measured GCR rates are likely to be too low to explain the phenotypic heterogeneity observed in the haploid-converted strains (see Protocol S1). Thus it is unlikely that GCR events alone explain high phenotypic variance. Another source of genetic variation in these lines could be caused by increased insertion rates of transposable elements such as Ty1 [49,50]. However, we again found that increased Ty1 insertion rates are neither necessary nor sufficient for high phenotypic potential (see Protocol S1). It is also possible that these same disrupted processes are changing the mutational spectrum at microsatellites [51,52]. Although not related to environmental buffering, this last possible mechanism is of great evolutionary interest, given recent findings in yeast [53] and dogs [54] of phenotypic variation driven by tandem-repeat length changes. Another possibility is that DNA stability knockouts are causing changes at the telomere [55,56] or elsewhere that heterogeneously activate cell cycle checkpoints [51,57]. Thus, the mechanism by which this subset of capacitors produces phenotypic variability warrants further study. If, however, mutational mechanisms can be excluded, our findings might provide new insight into human malignancies. Many cancers are associated with mutations in genes involved in DNA stability, including orthologs of the capacitors RAD50 [58], RAD54 [59,60], and YAF9 [61], or with genes with a large number of interactions, such as the transcription factor p53 [62]. Our results suggest that the first advantage mutations in these genes might provide to developing malignancies is phenotypic heterogeneity by way of network-associated loss of robustness.

Yeast strains.

Haploid convertible diploid BY4743 YKO magic marker deletion strains (MATa/α ura3Δ0/ ura3Δ0 leu2Δ0/leu2Δ0 his3Δ1/ his3Δ1 lys2Δ0/LYS+ met15Δ0/MET15+ can1Δ::LEU2+-MFA1pr-HIS3/CAN1+ xxx::kanMX/XXX+) were purchased from Open Biosystems.

General statistics and programming.

All data analysis was performed using the open-source R statistical computing package (http://www.r-project.org/). Lowess regression was performed using the “lowess” function with a smoother span of 0.2 (944 YKOs) and three iterations for the genome-wide analysis (Figure 1C), and with a smoother span of 0.4 (40 YKOs) and five iterations for the repeated analysis (Figure 2). PAM and silhouette plots were performed using the “pam” and “silhouette” functions from the cluster library.

Dimensional reduction and calculation of phenotypic potential.

A major problem we faced in dealing with a dataset of 220 phenotypes is removing those phenotypes that might be biologically or physically redundant. Principal components analysis, a common means by which to reduce the dimensionality in a matrix (remove redundant phenotypes), transforms the data to a new coordinate system such that the greatest variance of any projection of the data lies on the first coordinate or principal component, the second greatest variance on the second coordinate, etc. This transformation, however, does not preserve the directionality or syntax of the initial dataset because the coordinates are drawn to maximize the overall variance ignoring whether these values are positive or negative. In other words, loadings of the initial data into a principal component may be negative. Thus, a high value in a principal component may represent a high or low variance in the underlying phenotypes. Because we are interested in identifying genes that only result in high variance, principal components analysis was not appropriate, and so we used a strategy based on clustering instead.

PAM [77] was selected for dimensional reduction because it has several advantages to k-means clustering with respect to our question: (1) resultant medoid cluster centers are real phenotypes from our residuals of standard deviation matrix (rather than difficult-to-interpret linear combinations of residuals of many phenotypes as in k-means); (2) using medoids as cluster centers rather than average cluster centers makes the procedure more robust to outliers; and (3) an “average silhouette” strategy [78] utilized here allows for estimation of the appropriate number of distinct clusters.

To estimate the number of nonredundant clusters, the average silhouette strategy [78] was used: we performed PAM over a range of 20 to 100 clusters and generated silhouette plots for each. We then plotted the average silhouette width versus the number of clusters chosen (Figure S2). Although the average silhouette width peaks around 80 clusters, significant gaps (silhouette widths close to 0) are more likely to appear in silhouette plots when greater than 70 clusters were chosen, suggesting that noninformative clusters are added beyond 70. Thus, we estimated 70 nonredundant clusters. However, using a range of 50 to 80 clusters for PAM to identify phenotypic capacitors results in an extremely similar set of genes (Figure S3).

Using the reduced matrix of 4,718 YKOs by 70 phenotype medoids, we next calculated a single measure of the overall phenotypic variance resulting from a gene's deletion, which we term the phenotypic potential. We generate this score for each YKO by averaging the top 35 (of 70) residuals of standard deviation. The rationale for using 35 of 70 medoids is as follows: (1) A gene deletion that results in a high variance in only one or a few phenotypes does not meet the pleiotropy requirement of our definition of a phenotypic capacitor. Thus, we sought YKOs that have both a large number of high variance phenotypic medoids and high magnitudes in those medoids (i.e., as many medoids should be averaged as possible to capture the overall phenotypic potential). (2) Only 24 YKOs result in high variance (>1 SD) in greater than 35 phenotype medoids, all of which were subsequently identified as phenotypic capacitors. Thus, phenotypic potential scores that rely on greater than 35 medoids are likely to increase noise in the scoring procedure. Although we chose to score 35 phenotype medoids to identify phenotypic capacitors, alternative procedures result in an extremely similar set of genes over a broad range of number of medoids scored (Figure S4).

Estimation of the number of phenotypic capacitors using the FDR.

First, we generated 100 randomized phenotypic medoid by YKO matrices by permuting elements within each phenotype column of the original matrix. These 100 matrices are then used to calculate phenotypic potentials. We then generated a reference distribution by averaging the top ranking phenotypic potential for each of the 100 trials, the second top ranking phenotypic potential, etc. This reference distribution was used to estimate the expected false positive rate under the null hypothesis. At a given expected false positive rate, the number of true positives was estimated by subtracting the number of false positives (i.e., expected false positive rate × 4,718) from the number of genes in the actual distribution that have a higher phenotypic potential than the reference distribution (all positives). The maximum number of true positives occurs at an expected false positive rate of 0.036 with 333 true positives estimated for 502 positives (a FDR of 34%).

Cell staining and visualization.

YKO magic marker deletion haploid convertible diploid strains (Open Biosystems) were grown on YPD agar for ∼48 h, spread on GNA (5% D-glucose, 3% Difco nutrient broth, 1% Difco yeast extract, 2% bacto agar) plates and grown for 24 h. A single medium-sized colony was added to 5 ml of sporulation medium (10% potassium acetate, 0.005% zinc acetate + Ura + His + Leu) and incubated at 30 °C for 5–7 d. One to 10 μl of the sporulated cells were spread onto magic media plates (SC-Leu-His-Arg + canavanine + G418) and grown until medium sized colonies appeared (∼20 generations and for no more than 72 h when possible). Single colonies were frozen at this point for later processing. Cell stocks were streaked out on YEPD agar and grown at 30 °C for a maximum of ∼48 h when possible (∼20 additional generations). Cells were subsequently grown overnight in 3 ml YEPD at 30 °C with shaking. Because many of the haploid YKO strains were expected to include heterogeneous morphologies, direct cell counts using a hemocytometer were relied upon rather than optical density readings. Cells were counted, then 1 × 10⁸ cells were added to 20 ml YEPD and grown for 3–3.5 hrs at 30 °C (early logarithmic phase).

Fixation and straining was performed as described in the CalMorph manual with modifications (http://scmd.gi.k.u-tokyo.ac.jp/datamine/calmorph/). Briefly, cells were fixed in 3.7% formaldehyde, 100 mM potassium phosphate, and triply stained for cell-surface manno-protein, actin cytoskeleton, and nuclear DNA using fluorescein isothiocyanate-Con A (Sigma), rhodamine-phalloidin (Molecular Probes), and 4′, 6-diamidino-2-phenylindole (Sigma), respectively. Cells were mounted in vectashield (Vector Laboratories), and visualized by epifluorescent microscopy on a Nikon Eclipse 90i automated microscope using a 100× objective and a Roper 1K CCD camera. For each YKO, a minimum of 40 micrographs was captured to yield a minimum of 200 (and usually in excess of 300) phenotyped cells that are not classified as “complex.” Captured micrographs were analyzed for quantitative morphological traits using the CalMorph software package. For all YKOs processed, ∼50 generations is estimated to have passed from sporulation to fixation and phenotyping: ∼40 generations on agar plates and ∼10 generations in liquid media. Control strains are defined as those knockouts with a phenotypic potential that ranked below 1,000 in the original analysis of the haploid knockout library.

GO enrichment.

The full GO term hierarchy was downloaded from the GO website on May 11, 2007 (http://www.geneontology.org/). To determine GO process term enrichment, the hierarchy was first trimmed by removing GO terms that did not annotate three or more yeast ORFs. Additionally, the highly annotated process GO terms “physiological process,” “cellular process,” “biological process,” and “cellular physiological process” were removed because they are too general to be meaningful. Trimmed hierarchies resulted in 775 process terms. Significance of GO term enrichment of the 502 putative phenotypic capacitors was calculated using the hypergeometric distribution and Bonferroni corrected using the trimmed hierarchy.

Network parameters.

The May 1, 2007 release of interaction data (BIOGRID-ORGANISM-Saccharomyces_cerevisiae-2.0.27.tab.txt) was downloaded from the BioGRID (http://www.thebiogrid.org/) [32].

For analysis of physical interactions, two networks were constructed from the BioGRID: (1) every physical interaction from the hand-curated literature citation interaction database was included (including affinity capture-mass spectrometry, affinity capture-western, affinity capture-RNA, cofractionation, colocalization, copurification, fluorescence resonance energy transfer (FRET), two-hybrid, biochemical activity, cocrystal structure, far western, protein–peptide, protein–RNA, reconstituted complex; 5,192 nodes, 70,900 edges); or (2) only interactions from the higher confidence affinity capture-mass spectrometry (3,686 nodes, 47,774 edges). Because nearly every gene has been used as bait for the affinity capture-mass spectrometry network [33,34] and because of the higher consistency and lower rate of false positives compared to other methods, this network might represent the most unbiased view of the PPI network. Thus, this smaller network was used to calculate network properties of genes such as betweenness and clustering coefficient, to control for PPIs when estimating other gene properties such as synthetic lethality and dispensibility, and to estimate the properties of immediate neighbors in the physical interaction network.

All interactions in the BioGRID annotated with “Synthetic Lethality” were used to generate the SLI network (2330 nodes, 18,550 edges). Because the SLI network is incomplete, we hand curated synthetic-lethal entries to create a subset of this network that only includes interactions derived from SGAs where both genes are completely functionally compromised and where the experiment contains ten or more total interactions (1,326 nodes, 11,934 edges). The subset of genes involved in SLIs discovered in SGA experiments was further separated into those genes that have been used as “bait” and those that have not, “prey.” Double knockouts for the 267 bait genes and all other nonessential genes have been performed and thus the complete SLIs for bait genes have likely been discovered; however, double knockouts for the 1,060 prey genes have only been performed with the 267 genes used as bait and thus represent an incomplete, although likely representative, interaction set. Genes without any interactions were excluded from the interaction networks. Betweenness [79] was calculated using the “betweenness” function from the “sna” library in R. The clustering coefficient for each gene was calculated, as described [80].

Essential genes are those genes that were determined to be essential in the systematic deletion project [81] except for the following genes which were deemed nonessential based on subsequent synthetic-lethal analysis: YJL174W, YJR057W, YLR103C, YOR326W, YPL153C, YBR234C, YDL102W, YDL029W, YDL017W, YDL003W, YDR052C [19,82]. Unless otherwise noted, nonessential genes refers to the 4,718 genes that were knocked-out and phenotyped in the high-dimensional quantitative morphological phenotyping experiment including any identified phenotypic capacitors [17].

Significance calculation of PPI degree comparison between capacitors and essential genes.

All putative phenotypic capacitors (those with the top 502 phenotypic potential scores) were compared to all essential genes by Wilcoxon-Mann-Whitney test using PPI degrees derived from both the literature citation and mass spectrometry networks (p < 2.2 × 10⁻¹⁶ and p < 5.2 × 10⁻¹³, respectively). A similar comparison was made using only capacitors in the C1 and C2 classes (p < 2.0 × 10⁻⁶ for the literature citation network, and p < 7.8 × 10⁻⁷ for the mass spectrometry network).

Genome-wide datasets.

Genome-wide datasets were acquired from the following sources: PPIs and SLIs [32], haploid growth rates [37], heterozygous and homozygous diploid growth rates [38], duplicate and singleton identity [39], ohnolog identity [45], Ks of duplicate pairs [39], mRNA length [43], mRNA abundance [83], protein abundance [84], noise in protein expression in permissive (YEPD) and restrictive (SD) media [46], Ka/Ks [43,85]. The expression similarity between duplicate pairs was acquired from Kafri et al. [39] and was determined using correlations of expression over several reported expression array experiments (Ran Kafri, personal communication). The Ka for duplicates resulting from the whole genome duplication (ohnologs) was calculated as follows: alignments of the S. cerevisiae ohnologs and an ortholog from Kluyveromyces waltii, a related species whose divergence precedes the whole genome duplication event, have been previously performed [86]. Ka was calculated from these alignments in PAML [87] using the Yang and Nielsen method [88] with all settings set to default except for “icode,” which was set to 2 to reflect the yeast genome.

Analysis of covariance to control for the effect of expression level on Ks and Ka.

Because Ks and Ka are correlated with the expression level [43], we performed analyses of covariance (ANCOVAs) to estimate evolution rate differences. ANCOVAs were performed as described with modifications [43]. In one case we used Ks instead of dN, and we used the average mRNA expression level of the two paralogs as the continuous variable. Only duplicate pairs for which the expression level of each paralog has been measured were used for the analysis (Figures S16 and S18).

FDN score.

Parameters (such as phenotypic potential, dispensability, physical, or synthetic-lethal degree) for the immediate PPI neighbors of a given gene were calculated as follows: first, each gene is given a neighbor score in the parameter by averaging the scores of all of its neighbors. For example, a gene with three neighbors with haploid growth rate scores of 0.5, 0.9, and 1.0 will get a neighbor haploid growth rate score of 0.8. Second, the effect of PPI degree on the neighbor parameter score is removed by plotting the neighbor parameter score for each gene versus its PPI degree, fitting a lowess regression to this plot, and taking residuals of the curve fit as a measure of the neighbor parameter controlled for the number of PPIs. Thus, the gene described above with three neighbors and a neighbor haploid growth rate score of 0.8 will only have a low neighbor growth rate (and a negative residual) if it is low relative to other genes with a similar number of PPIs.