Multiple peaks and reciprocal sign epistasis in an empirically determined genotype-phenotype landscape

Insight into the ruggedness of adaptive landscapes is central to understanding the mechanisms and constraints that shape the course of evolution. While empirical data on adaptive landscapes remain scarce, a handful of recent investigations have revealed genotype-phenotype and genotype-fitness landscapes that appeared smooth and single peaked. Here, we used existing in vivo measurements on lac repressor and operator mutants in Escherichia coli to reconstruct the genotype-phenotype map that details the repression value of this regulatory system as a function of two key repressor residues and four key operator base pairs. We found that this landscape is multipeaked, harboring in total 19 distinct optima. Analysis showed that all direct evolutionary pathways between peaks involve significant dips in the repression value. Consistent with earlier predictions, we found reciprocal sign epistatic interactions at the repression minimum of the most favorable paths between two peaks. These results suggest that the occurrence of multiple peaks and reciprocal epistatic interactions may be a general feature in coevolving systems like the repressor-operator pair studied here.