From classical genetics to quantitative genetics to systems biology: modeling epistasis

Abstract

Gene expression data has been used in lieu of phenotype in both classical and quantitative genetic settings. These two disciplines have separate approaches to measuring and interpreting epistasis, which is the interaction between alleles at different loci. We propose a framework for estimating and interpreting epistasis from a classical experiment that combines the strengths of each approach. A regression analysis step accommodates the quantitative nature of expression measurements by estimating the effect of gene deletions plus any interaction. Effects are selected by significance such that a reduced model describes each expression trait. We show how the resulting models correspond to specific hierarchical relationships between two regulator genes and a target gene. These relationships are the basic units of genetic pathways and genomic system diagrams. Our approach can be extended to analyze data from a variety of experiments, multiple loci, and multiple environments.

Figure 1. Modeling the Relationship A Is an Upstream Repressor of B.

B in Turn Enhances a Target Gene X. In this example, deleting A will change the state of the target gene from off to on. Therefore, we include A's effect in the corresponding regression model. Deleting B leaves the target gene in the same state as the wild type and its effect is not included. The AB double mutant is also not expected to deviate from the wild type despite the significance of the A deletion. Since A's effect is already included in the model for this contrast, it must be offset by the interaction term. We conclude that if A is enhanced by the signal, A represses B, and B enhances X, the corresponding best-fit regression model will include coefficients for A and an interaction term. Similar logic applies to the case in which the signal represses A. The signal represses A, thus deleting A has no downstream effects. We expect only the coefficient corresponding to the downstream gene in the best-fit model.

Figure 2. Post-Aggregation Distribution of Best-Fit Models at p<0.01 Significance Threshold.

The frequency distribution of best-fit regression models can be interpreted as hierarchical relationships between genes. Model 8 corresponds to no deletion effects and is supported by a large number of traits in each contrast; these genes are likely not downstream of the deletions. The model supported by the majority of remaining traits is assumed to represent the true relationship.