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. 2017 Apr 13;13(4):e1005496.
doi: 10.1371/journal.pcbi.1005496. eCollection 2017 Apr.

Inferring Modulators of Genetic Interactions With Epistatic Nested Effects Models

Free PMC article

Inferring Modulators of Genetic Interactions With Epistatic Nested Effects Models

Martin Pirkl et al. PLoS Comput Biol. .
Free PMC article


Maps of genetic interactions can dissect functional redundancies in cellular networks. Gene expression profiles as high-dimensional molecular readouts of combinatorial perturbations provide a detailed view of genetic interactions, but can be hard to interpret if different gene sets respond in different ways (called mixed epistasis). Here we test the hypothesis that mixed epistasis between a gene pair can be explained by the action of a third gene that modulates the interaction. We have extended the framework of Nested Effects Models (NEMs), a type of graphical model specifically tailored to analyze high-dimensional gene perturbation data, to incorporate logical functions that describe interactions between regulators on downstream genes and proteins. We benchmark our approach in the controlled setting of a simulation study and show high accuracy in inferring the correct model. In an application to data from deletion mutants of kinases and phosphatases in S. cerevisiae we show that epistatic NEMs can point to modulators of genetic interactions. Our approach is implemented in the R-package 'epiNEM' available from and

Conflict of interest statement

The authors have declared that no competing interests exist.


Fig 1
Fig 1. Schematic representation of different buffering relationships.
Left: Complete redundancy is explained by an effect only being visible when both genes A and B are knocked out simultaneously. Right: Mixed epistasis is characterized by a mixed behaviour of two genes. Their interaction differs for different gene sets.
Fig 2
Fig 2. epiNEMs versus NEMs.
(A) Nested Effect Models model how perturbations on signaling genes/proteins (A, B, C, D) affect downstream sets of effect reporters (EA, EB, EC, ED). Effects of perturbing D (=ED) are nested in the effects of perturbing A (= {EA, EC, ED}) and B (={EB, ED}). The matrices show the expected behaviour under the model. In real data, each gene in a set of effect reporters E. can be independently influenced by noise. (B) epiNEMs introduce logical functions for every node that has two parents (in this case D). The choice of logical function determines the effects observed in a combinatorial perturbation. The only difference to the NEM without logical functions is the expected perturbation effect on ED if A or B are perturbed individually or in combination (indicated by question marks). (C) Five of the 23 = 8 possible logical functions are AND, OR, XOR, not-A and not-B. The NEM in (A) is the special case of epiNEM with an OR logic. (D) The three other logical functions can be expressed by simpler graph structures, which remove an edge from A, or B or both.
Fig 3
Fig 3. Result of 100 simulation runs on 4 node networks.
(A) Time in seconds. (B) Accuracy of inferred edges. Accuracy of logic gates (C) and expected data (D), which is similar to the truth table. epiNEM is faster than B-NEM and slower than the other methods, while correctly identifying the logic gate for the median of all networks for up to 20% of false negative rate.
Fig 4
Fig 4. Identification of signal modulators.
(A) The identified modulators for ark1 and prk1 confirm the complete redundancy. (B) The identified modulators for ptc1 and ptc2 exhibit masking of ptc1 by ptc2 and some lower ranking modulators complete redundancy. (C) The modulators of the snf1 and rim11 knock-out signal are identified as complete redundancy and the masking of rim11 by snf1.
Fig 5
Fig 5. Interplay of gln3, gzf3 and gat1.
Gzf3 masks the effect of gln3 (A), which confirms the result of Sameith et al. Gat1 masks both the effects of gln3 and gzf3 (B-C). Additionally, we identify gln3 as a high scoring modulator of the signaling between gzf3 and gat1 (C, red arrow).
Fig 6
Fig 6. The distribution of the logic gates for each double knock-out of the data from van Wageningen et al. (A) and Sameith et al. (B).
In both cases the AND logic (blue) is the most dominant. The absence of OR gates can be explained by the selection of regulators. Only a few modulators are identified as related to the regulators, but not via any logic (purple). False negatives in the data and equivalences can be responsible for the absence of XOR gates and the large amount of masking logics.
Fig 7
Fig 7. String-db interaction score distributions.
The distributions for the string-db interaction scores for the top 30 modulators with their respective regulators (red) and the distributions for the interaction scores of all possible modulators and regulators in the data (blue) for the Van Wageningen et al. (A) and the Sameith et al. (B) data sets. The Mann-Whitney test with alternative “greater” produces p-values which indicate that the modulators identified by epiNEMs have higher interaction scores with their regulators than explained by random drawing.

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