Statistical epistasis is a generic feature of gene regulatory networks - PubMed (original) (raw)

Statistical epistasis is a generic feature of gene regulatory networks

Arne B Gjuvsland et al. Genetics. 2007 Jan.

Abstract

Functional dependencies between genes are a defining characteristic of gene networks underlying quantitative traits. However, recent studies show that the proportion of the genetic variation that can be attributed to statistical epistasis varies from almost zero to very high. It is thus of fundamental as well as instrumental importance to better understand whether different functional dependency patterns among polymorphic genes give rise to distinct statistical interaction patterns or not. Here we address this issue by combining a quantitative genetic model approach with genotype-phenotype models capable of translating allelic variation and regulatory principles into phenotypic variation at the level of gene expression. We show that gene regulatory networks with and without feedback motifs can exhibit a wide range of possible statistical genetic architectures with regard to both type of effect explaining phenotypic variance and number of apparent loci underlying the observed phenotypic effect. Although all motifs are capable of harboring significant interactions, positive feedback gives rise to higher amounts and more types of statistical epistasis. The results also suggest that the inclusion of statistical interaction terms in genetic models will increase the chance to detect additional QTL as well as functional dependencies between genetic loci over a broad range of regulatory regimes. This article illustrates how statistical genetic methods can fruitfully be combined with nonlinear systems dynamics to elucidate biological issues beyond reach of each methodology in isolation.

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Figures

F<sc>igure</sc> 1.—

Figure 1.—

Connectivity diagrams for the 12 network motifs in the simulation study. Each motif consists of three genes, named _X_1, _X_2, and _X_3 and represented by circles. In the text they are called gene 1, gene 2, and gene 3, respectively. Genes without any arrows pointing at them are constitutively expressed, while an arrow pointing from gene i to gene j means that gene i is regulating the expression of gene j. The sign of the arrow indicates whether the type of regulation is activation (+) or inhibition (−). When a gene has two regulators the individual signals are combined with a logic block, represented by a rectangle, mapping the two signals into one by the continuous analog of the Boolean functions AND or OR.

F<sc>igure</sc> 2.—

Figure 2.—

Curves showing the distribution of the proportion of genetic variance explained by marginal (additive and dominance) effects of the three genes in motifs 1–12. The 1000 F2 populations for each motif are sorted by an increasing amount of epistatic variance. The three different types of motif are represented by different colors, red for no feedback, green for negative feedback, and blue for positive feedback.

F<sc>igure</sc> 3.—

Figure 3.—

The statistical genetic signature of the biological interactions in motifs 1 and 10 as the proportion of genetic variance explained by marginal (additive and dominance) effects, two-way interactions, and three-way interactions between the three genes of (A) motif 1 and (B) motif 10. The 1000 simulated F2 populations are sorted by an increasing amount of epistatic variance. The box plots show the distribution, within bins of 100 populations, of the largest proportion of genetic variance explained by marginal effects of one gene.

F<sc>igure</sc> 3.—

Figure 3.—

The statistical genetic signature of the biological interactions in motifs 1 and 10 as the proportion of genetic variance explained by marginal (additive and dominance) effects, two-way interactions, and three-way interactions between the three genes of (A) motif 1 and (B) motif 10. The 1000 simulated F2 populations are sorted by an increasing amount of epistatic variance. The box plots show the distribution, within bins of 100 populations, of the largest proportion of genetic variance explained by marginal effects of one gene.

F<sc>igure</sc> 4.—

Figure 4.—

The amount of significant two-way interactions between all pairs of genes in the 12 simulated network motifs for the broad-sense heritability _H_2 = 0.2. The color coding indicates the percentage of the 1000 simulated F2 populations for which a full model, including all marginal and two-way interaction parameters of the genes indicated on the _y_-axis, fits significantly better than a reduced model with only the marginal parameters.

F<sc>igure</sc> 5.—

Figure 5.—

The statistical significance of individual two-way interaction parameters for the 12 simulated network motifs. The color coding indicates the percentage of the 1000 simulated F2 populations where the given interaction parameter is significant when a full model, containing all marginal parameters of the gene pair and the single interaction parameter indicated on the _y_-axis, is compared to a reduced model with only the marginal parameters.

F<sc>igure</sc> 6.—

Figure 6.—

The cumulative number of significant QTL for all 12 simulated network motifs at _H_2 = 0.2 after testing for significant marginal effects only, when testing for significant two-way interactions in addition to the marginal effects, and when testing for significant three-way interactions in addition to marginal and two-way interaction effects.

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