We studied a population containing five mutations known to affect mating competence (). Deletions of FUS3
cause mating defects, whereas deletions of BAR1
induce hypersensitivity to pheromone. The STE11-4
allele is a missense mutation that constitutively activates the pheromone signaling response 
. We constructed, genotyped, and analyzed 218 MATa
strains, each containing an independent assortment of the five perturbations (Methods
). This constituted a population of mixed positive and negative effect mutations that are known to exhibit genetic interactions 
, and therefore provided an effective test population for our analysis methods.
Genetic perturbations in this study.
We quantified overall mating efficiency (ME) and molecular pheromone response (PR) for each strain (Methods
). The PR phenotype shares many genetic components with the ME phenotype and therefore ensured a degree of pleiotropy. However, because the PR assay was more narrowly focused on pheromone signaling, PR and ME were not expected to be entirely redundant. For example, strains with moderate defects in pheromone signaling may be mating competent (or hyper-competent) due to compensatory mutations that affect other biological processes. As expected, the ME and PR phenotypes were significantly correlated (Pearson r
). To maximize complementarity between these phenotypes, we performed singular value decomposition (SVD) (Methods
). The two resulting eigentrait vectors were orthogonal, normalized combinations of the sum and difference of ME and PR, respectively. We refer to these composite phenotypes as eigentraits 1 and 2 (ET1 and ET2).
Although all five perturbations have known roles in mating, some of them did not exhibit significant effects when considered individually. For each eigentrait we performed single-locus regression on each of our five genetic perturbations to identify significant variants used as covariates in pair-wise scans (Methods
). Significance was defined as effect coefficients at least 3.55 estimated standard errors from zero (p
). The far1Δ
, and fus3Δ
perturbations were identified as covariates for ET1 and the far1Δ
perturbations were identified as covariates for ET2. These perturbations correspond to genes with very strong known effects (BAR1
) or downstream signaling activators (FAR1
). Any significant effects of the STE11-4
perturbations were masked by the other factors in single-locus scans.
We next computed pair-wise models for each of the ten possible locus pairs to derive a genetic interaction network. One interaction, the inferred fus3Δ
suppression of the STE11-4
allele, is illustrated in . We performed pair-wise linear regression on the eigentraits (; Methods
, Eq. 3
) and then reparametrized the interactions in terms of two variant-to-variant influences between perturbations (Methods
, Eqs. 5
). This procedure reinterprets statistical epistasis in terms of a genetic influences model. shows how the complementary information in our two eigentraits therefore determines that the fus3Δ
perturbation reduces the effect of the STE11-4
allele, ruling out alternative hypotheses such as a STE11-4
enhancement of the fus3Δ
effect that would be consistent with ET1 but not ET2. To determine the allelic effects on the ME and PR phenotypes, we recomposed the phenotype SVD for each pair-wise model and averaged over all models to obtain variant-to-phenotype influence coefficients (; Methods
). This final step does not modify the inferred genetic interaction. Errors were estimated for all coefficients using standard least-squares regression and error propagation formulas for quantities computed from regression coefficients (Methods
, Eq. 8
). Our significance threshold was defined as p
<0.05 based on genotype permutations and adjusted for multiple testing (Methods
). All calculations were performed on a desktop PC using Mathematica software and each locus pair took approximately 30 milliseconds. We obtained a network of 12 significant interactions (), including 6 variant-to-variant influences that fit the observed genetic interactions for both phenotypes. Results for all influence parameters are listed in Table S4
Genetic interactions between fus3Δ and STE11-4 mutations, following .
Combined genetic influence network for mating efficiency (ME) and pheromone response (PR) mapping positive (green) and negative (red) influences between mutations and on the phenotypes.
We combined ME and PR with gene expression data to identify complementary biological processes underlying the genetic interaction analysis. We selected a subset of strains representing the genetic diversity of the population and collected gene expression data after exposure to α-factor (Methods
). To identify the global expression patterns we performed singular value decomposition (SVD) on the gene expression matrix (6208 genes across 92 strains) 
). Because we sought to identify expression patterns that correspond to the ME and PR phenotypes, we included these quantitative phenotypes as additional rows in the gene expression matrix. The phenotypes were expressed relative to the unperturbed strain (wild-type) and normalized to a standard deviation of 2 in order to match the origin and scale of the gene expression data. Because these two rows were added to the expression patterns of thousands of genes, their contribution to the overall SVD patterns is negligible. The first two modes are the most dominant patterns in the data and account for 47% and 17% of the total variation in gene expression, respectively (Figure S3
). By examining the ME and PR weight vectors for correspondence with each gene expression pattern, we found that Modes 1 and 2 capture the similarity and difference of these two phenotypes. The ME phenotype corresponds to both Modes 1 and 2, whereas the PR phenotype only corresponds to Mode 2 (). Mode 3 further reinforces this conclusion. These different expression patterns therefore separate the biological processes shared between ME and PR (Expression Mode 2) and unique to ME (Expression Mode 1).
Weights of mating efficiency (ME) and pheromone response (PR) phenotypes for global expression patterns Mode 1 and Mode 2.
Gene set analysis revealed the biological functions of the genes associated with ME and PR. We identified sets of genes positively and negatively associated with each mode (Methods
; Table S2
). We queried each set of genes for enriched Gene Ontology (GO) annotations and transcription factor targets (Methods
; and Table S3
). Expression Mode 1, the pattern associated with ME but not PR, was positively shown by a set of 169 genes that was most enriched in organic acid metabolic processes genes and transcriptional targets of Gcn4. The negative pattern, driven by 109 genes that were downregulated when mating efficiency is high, was shown by genes enriched in cell cycle and transcriptional targets of the SBF complex. Expression Mode 2, the pattern positively shown by 179 genes that were upregulated when both ME and PR are high, was enriched in mating genes and transcriptional targets of mating regulators. Many of the Mode 2 positive mating genes were also enriched in the Mode 1 positive gene set, but the Mode 1 negative metabolism and cell cycle genes were not present in Mode 2. This demonstrates that both ME and PR were reporting the changes in cellular morphology associated with mating. In contrast, the metabolic upregulation and cell-cycle downregulation were primarily associated with ME but not PR. We conclude that this difference constituted the complementary biological processes that allowed us to infer the genetic interaction network for mating efficiency and pheromone response ().
Summary of enriched functions and transcription factor binding targets for expression gene sets.
The network model () was readily interpreted in terms how the perturbed genes affect the phenotypes and associated expression patterns. The expected bar1Δ
, and STE11-4
single-perturbation effects on ME and/or PR were resolved. The strongest direct effects were from perturbations of canonical downstream pathway elements Far1 and Fus3. The far1Δ
effect on ME was stronger than its effect on PR. Our gene expression analysis provides evidence that this was due to the role of Far1 in cell cycle regulation, a biological process that contributed to our ME phenotype but not PR (Results
). The bar1Δ
mutation had a very strong effect on PR but did not have a significant effect on ME. This was likely due to the fact that Bar1 degrades the alpha pheromone and thus its knockout leads to enhanced MAPK pathway activity 
.This Bar1 activity also enhances escape from pheromone-induced cell-cycle arrest to reinitiate proliferation 
The six variant-to-variant influences comprised a network view of how the perturbations affect one another and, in turn, the downstream phenotypes. The Msg5 phosphatase is known to affect mating by dephosphorylating the MAP kinase Fus3 
, which is consistent with the suppression of msg5Δ
effects by the fus3Δ
allele. The fus3Δ
allele also suppresses the effects of bar1Δ
, two genes that are upstream of Fus3 in the canonical MAPK pathway. The moderate suppression of far1Δ
by the STE11-4
allele was consistent with the previous finding that MAPK pathway activation can provide compensatory cell cycle arrest in the absence of Far1 
Our gene expression data set provided additional data for genetic interaction modeling. SVD modes have been demonstrated to be a suitable basis for statistical genetic analysis of gene expression 
and we extended this concept to our pair-scan method. We modeled the first three SVD modes, comprising 73% of the global variation (Methods
), which captured multiple biological processes ( and Table S3
) and was suitable for the analysis of a relatively small sample size. Although there were substantially fewer samples than the phenotype data (92 versus 218 strains), the samples were selected for genetic diversity and the SVD modes provide more precise summary phenotypes because they are averaged over hundreds of genes. Therefore, the analysis was sufficiently powered to identify significant interactions and map a network model with five variant-to-variant influences (Figure S4
and Table S5
). Three of these were identical in direction and sign to the ME/PR model (), with two additional interactions that did not qualify as significant in the ME/PR model. The two independently-analyzed data sets thus uncover generally similar interaction networks with different details. We added additional SVD modes to the analysis on an exploratory basis and derived similar interactions but, as expected, found decreasing significance as signals were added. For example, the fus3Δ
suppression of msg5Δ
obtained in the ME/PR model (p
0.006) was derived at similar interaction strength when taking three, four, or five SVD modes but with decreasing significance (p
0.030, and p
0.076, respectively). This reduction in significance was due to adding additional signals without increasing population size.