Phenotype data and genetic interaction
A genetic interaction is the interaction of two genetic perturbations in the determination of a phenotype. Genetic interaction is observed in the relation among the phenotypes of four genotypes: a reference genotype, the 'wild type'; a perturbed genotype, A, with a single genetic perturbation; a perturbed genotype, B, with a perturbation of a different gene; and a doubly perturbed genotype, AB. Gene perturbations may be of any form (such as null, loss-of-function, gain-of-function, and dominant-negative). Also, two perturbations can interact in different ways for different phenotypes or under different environmental conditions.
Geneticists recognize biologically informative modes of genetic interaction, for example, epistasis and synthesis. These two modes can illustrate the general properties of genetic interactions. An epistatic interaction occurs when two single mutants have different deviant (different from wild-type) phenotypes, and the double mutant shows the phenotype of one of the single mutants. Analysis of epistatic interactions can reveal direction of information flow in molecular pathways [8
]. If we represent a phenotype of a given genotype, X
, as ΦX
, then we can write a phenotype inequality representing a specific example of epistatic genetic interaction, for example, ΦA
. Likewise, a synthetic interaction occurs when two single mutants have a wild-type phenotype and the double mutant shows a deviant phenotype, for example, ΦWT
. Synthetic interactions reveal mechanisms of genetic 'buffering' [1
Some modes of genetic interaction are symmetric; other modes are asymmetric. This symmetry or asymmetry is evident in phenotype inequalities, and is biologically informative. Epistasis illustrates genetic-interaction asymmetry. If mutation A
is epistatic to B
, then B
is hypostatic to A
. The asymmetry of epistasis, and the form of the mutant alleles (gain or loss of function), indicates the direction of biological information flow [8
]. Conversely, synthetic interactions are symmetric. If mutation A
is synthetic with B
, then B
is synthetic with A
. The symmetry of genetic synthesis reflects the mutual requirement for phenotype buffering [1
The representation of genetic interactions as phenotype inequalities accommodates all possibilities without assumptions about how genetic perturbations interact. In addition, it demands quantitative (or at least ordered) phenotypes. In principle, all phenotypes are measurable; complex phenotypes (for example, different cell-type identities) are amalgamations of multiple underlying phenotypes. There is a total of 75 possible phenotype inequalities for WT, A, B, and AB. Using a hybrid approach combining the mathematical properties of phenotype inequalities and familiar genetic-interaction concepts and nomenclature, the 75 phenotype inequalities were grouped into nine exclusive modes of genetic interaction, some of which are genetically asymmetric (Additional data file 1). This approach can be extended to the interactions of more than two perturbations as well. The nine interaction modes include familiar ones: noninteractive, epistatic, synthetic, conditional, suppressive, and additive; and modes that certainly occur but, to our knowledge, have not been previously defined: asynthetic, single-nonmonotonic, and double-nonmonotonic. All interaction modes are defined in the Materials and methods; brief descriptions follow for the unfamiliar (previously undefined) modes. In asynthetic interaction, A, B, and AB all have the same deviant phenotype. In single-nonmonotonic interaction, a mutant gene shows opposite effects in the WT background and the other mutant background (for example, ΦWT < ΦA and ΦAB < ΦB). In double-nonmonotonic interaction, both mutant genes show opposite effects.
Implementation of the foregoing principles renders genetic-interaction-network derivation fully computable from data on any measured cell property with any interacting perturbations. We developed an open-source cross-platform software implementation called PhenotypeGenetics, available at [10
], a plug-in for the Cytoscape general-purpose network visualization and analysis platform [11
]. PhenotypeGenetics supports an XML specification for loading any dataset, allows user-defined genetic-interaction modes, and supports all of the analyses described in this paper. It was used to derive and analyze a genetic-interaction network from yeast invasion phenotype data.
In response to growth on low-ammonium agar, Saccharomyces cerevisiae MATa
diploid yeast cells differentiate from the familiar ovoid single-cell growth form to a filamentous form able to invade the agar substrate [12
]. Invasive filamentous-form growth is regulated by a mitogen-activated protein kinase (MAPK) kinase cascade, the Ras/cAMP pathway, and multiple other pathways [13
]. We investigated genetic interaction among genes in these pathways and processes. Quadruplicate sets of homozygous diploid single-mutant and double-mutant yeast strains were constructed (Materials and methods). Two purposes guided the selection of genes and mutant combinations to study: to represent key pathways and processes regulating invasion; and to ensure a diversity of invasion phenotypes (non-invasive, hypo-invasive, wild type, and hyper-invasive) to permit the detection of diverse genetic interactions. A set of 19 mutant alleles of genes in key pathways controlling invasive growth, including 13 plasmid-borne dominant or multicopy wild-type alleles and 6 gene deletions, was crossed against a panel of 119 gene deletions. All mutant alleles used in this study are listed in Additional data file 2.
We developed a quantitative invasion-phenotype assay. Yeast agar-substrate invasion can be assessed by growing colonies on low-ammonium agar, removing cells on the agar surface by washing, and observing the remaining growth of cells inside the agar. Replicate quantitative invasion-phenotype data with error ranges were extracted from images of pre-wash and post-wash colonies. Each tested interaction was recorded as an inequality, and assigned a genetic-interaction mode. This process is detailed in the Materials and methods and illustrated in Figures and , using the example of the epistasis of a deletion of the FLO11
gene, a major determinant of invasiveness, to a deletion of the SFL1
gene, encoding a repressor of FLO11
. Note that the error-bounded intervals (black bars) for the genotypes in Figure are representative of the entire dataset. These errors are: flo11
, 0.02; flo11 sfl1
, 0.01; WT
, 0.05; sfl1
, 0.06. Additional data file 3
shows a plot of error values for all genotypes sorted by error magnitude. The median error is 0.04.
Figure 1 Application of the method to yeast agar invasion data to derive a genetic-interaction network. (a) Pre-wash and post-wash images of example genotypes in a yeast agar-invasion assay. (b) The invasion data shown on a phenotype axis with replicate-measurement (more ...)
Graphical visualization of the genetic interactions revealed a dense complex network. For clarity, a small part of this network (interactions among transcription factors) is shown in Figure , illustrating the diversity of the observed genetic interactions. Perturbed genes are nodes in the network. Each tested allele combination generates an edge representing a genetic interaction. Edge colors and arrow heads (where appropriate) indicate interaction mode and asymmetry as indicated in Figure . The entire network of 127 nodes and 1,808 edges is shown in Additional data file 4. All of the underlying data, including tested interactions, genotypes, and quantitative phenotype data with error values, are listed in Additional data file 5. All nine genetic-interaction modes were observed among the 1808 interactions. Other than the noninteractive mode (with 443 occurrences), the most frequent modes were additive (347), epistatic (271), conditional (245), and suppressive (202) interaction. Lower frequencies of asynthetic (111), single-nonmonotonic (74), synthetic (62), and double-nonmonotonic (52) interaction were observed. Note that though the asynthetic, single-nonmonotonic, and double-nonmonotonic modes are not recognized by common genetic nomenclature, they occurred at substantial frequencies.
Genetic perturbations interacting with a specific biological process
Because genetic interactions reflect functional interactions, a genetic perturbation may interact in a specific mode with more than one gene in a specific biological process. This conjecture is supported by the finding of 'monochromatic' interaction among biological-process modules [15
]. Table lists 23 interactions in a specific mode between a mutant allele and a biological process. The statistical validation of these interactions is detailed in the Materials and methods. Figure shows three examples. In Figure , a PBS2
gene deletion is additive with mutations of small-GTPase-mediated signal transduction genes (P
= 0.001). These include genes in the Rho signal transduction/cell polarity pathway (BNI1
) and the Ras/cAMP signaling pathway (RAS2, BMH1
). These signaling pathways contribute to invasive growth phenotype in concert with the stress response regulated by the Pbs2 MAPK kinase [16
]. In Figure , deletions of invasive-growth genes DFG16
, and DIA2
are epistatic to overexpression of the invasion-activating Phd1 transcription factor (P
= 0.002). The combination of this epistasis with the forms of the interacting alleles (PHD1
overexpression is a gain of function, whereas the others are null alleles) leads to the suggestion that DFG16
, and DIA2
may be regulated by Phd1. In Figure , a deletion of the ISW1
gene suppresses the effects of perturbations of small-GTPase-mediated signal transduction genes CDC42
, and IRA2
= 0.005). ISW1
encodes an ATP-dependent chromatin-remodeling factor [17
]. Halme et al
] have shown that invasiveness of yeast cells is controlled epigenetically. High-frequency spontaneous mutations of IRA1
relieve epigenetic silencing of invasion genes. The suppression of an IRA2
mutation by ISW1
mutation suggests the possibility that ISW1
-dependent chromatin remodeling mediates effects of IRA2
mutation. Table and Figure illustrate local interaction patterns among mutant genes and biological processes.
Genetic interactions of mutant genes with biological processes
Figure 2 Gene perturbations show specific modes of genetic interaction with biological processes. (a) PBS2 deletion interacts additively with mutations of small-GTPase-mediated signal transduction genes. (b) PHD1 overexpression is hypostatic to deletions of invasive-growth (more ...)
Mutually informative patterns of genetic interaction
The phenotypic consequences of combinatorial genetic perturbations are complex, in a strict sense; knowing the phenotypes of two single perturbations, there are no simple rules to know the combinatorial phenotype. Counteracting this complexity, large sets of genetic-interaction data may contain large-scale patterns. We examined the possibility that there are pairs of perturbations with mutually informative patterns of genetic interaction with their common interaction partners. In other words, knowing the interactions of one perturbation may allow one to know, to some quantifiable extent, the interactions of another perturbation, and vice versa. Mutual information, and significance thereof, was calculated for all pairs of perturbations sharing tested interactions with other genes. For all 171 pairs of the 19 mutant alleles of genes in key pathways, mutual information was based on their interactions with the panel of 119 gene deletions. Similarly, among all 7,021 pairs of the 119 gene deletions, mutual information was based on their interactions with the 19 mutant alleles of genes in key pathways. Among all possible pairs, 23 showed significant (P < 0.001) mutual information (Materials and methods and Additional data file 6).
The results suggest that the most mutually informative genetic-interaction patterns occur among gene perturbations with similar effects on biological processes. For example, three of the six mutant gene pairs with the most significant mutual information are overexpressers of STE12
, and STE20
(Additional data file 6). These three genes encode central components of the MAPK signaling pathway promoting invasive filamentous-form growth [14
], and they show similar patterns of genetic interaction, as exemplified by STE12
in Figure . The dominant pattern is one of uniform interaction (A and B interact in the same mode with C), suggesting similar effects of the gene perturbations on the underlying molecular network. In addition, there are frequent occurrences of repeated mixed-mode interaction (A interacts in some mode with C, and B interacts in a different mode with C), suggesting that the molecular effects of gene perturbations may differ yet show consistent differences. Both uniform interaction and consistent mixed-mode interaction contribute to mutual information.
Mutually informative genes show large-scale patterns of genetic interaction. Genetic interactions of STE12 and STE20 overexpressers. Key to interactions as in Figure 1d.
Genetic interactions are ultimately a property of a network of biological information flows. The mutual information among pathway co-member genes like STE12 and STE20 supports this. Figure shows a mutual-information network of perturbed genes. Each edge indicates significant mutual information (Additional data file 6). Some of these edges connect genes in different cellular processes. For example, an edge connects the GLN3 gene, encoding a transcriptional regulator of nitrogen metabolism, and the CDC42 gene, encoding a GTPase involved in cell polarity. Such cases of mutual information suggest that in the underlying molecular network, there are important information flows between the different pathways and processes.
Figure 4 Networks of mutual information in patterns of genetic interaction show cliques. Nodes represent perturbed genes (see Additional data file 2). gf indicates a gain-of-function allele; lf indicates a loss-of-function allele. Edges connect gene pairs with (more ...)
In addition to pairwise mutual information, there is the possibility that multiple genes may exhibit significant mutual information. The network in Figure contains multiple n-cliques, subnetworks of n completely connected nodes. There is a 3-clique, including two main components (PBS2 and HOG1) of the HOG MAP-kinase pathway, and three overlapping 4-cliques (with many subcliques) containing filamentation MAPK pathway components. The STE12-STE20-CDC42 3-clique is in this cluster of cliques. The cliques and clusters suggest ternary and higher orders of mutual information, reflecting similarities in the global effects of perturbations on molecular information flows.