Learning the pattern of epistasis linking genotype and phenotype in a protein

Understanding the pattern of epistasis – the non-independence of mutations – is critical for relating genotype and phenotype in biological systems. However, the complexity of potential epistatic interactions has limited approaches to this problem at any level. To develop practical strategies, we carried out a comprehensive experimental study of epistasis between all mutations that link two phenotypically distinct variants of the Entacmaea quadricolor fluorescent protein. The data demonstrate significant high-order epistatic interactions between mutations, but also reveals extraordinary sparsity, enabling novel experimental strategies and sequence-based statistical methods for learning the relevant epistasis. The sequence space linking the parental fluorescent proteins is functionally connected through paths of single mutations; thus, high-order epistasis in proteins is consistent with evolution through stepwise variation and selection. This work initiates a path towards characterizing epistasis in proteins in general.