Sign epistasis caused by hierarchy within signalling cascades.

Sign epistasis is a central evolutionary constraint, but its causal factors remain difficult to predict. Here we use the notion of parameterised optima to explain epistasis within a signalling cascade, and test these predictions in Escherichia coli. We show that sign epistasis arises from the benefit of tuning phenotypic parameters of cascade genes with respect to each other, rather than from their complex and incompletely known genetic bases. Specifically, sign epistasis requires only that the optimal phenotypic parameters of one gene depend on the phenotypic parameters of another, independent of other details, such as activating or repressing nature, position within the cascade, intra-genic pleiotropy or genotype. Mutational effects change sign more readily in downstream genes, indicating that optimising downstream genes is more constrained. The findings show that sign epistasis results from the inherent upstream-downstream hierarchy between signalling cascade genes, and can be addressed without exhaustive genotypic mapping.