A mutation’s effect on its carrier is often contingent on other mutations already in the genome, and geneticists call such mutational interactions epistasis. Colloquially, we can think of epistasis as measuring our surprise at the effect some set of mutations have on an organism, given information on the effects of subsets of those same mutations (Weinreich et al. 2013). Past results include

• The theoretical significance of sign epistasis (Weinreich et al. 2005).
• The empirical significance of sign epistasis in TEM-1 β-lactamase, an enzyme that confers bacterial resistance to penicillin and related compounds (Weinreich et al. 2006).
• Inferring the dimensionality of RA Fisher's phenotypic space from data on pairwise epistasis (Weinreich and Knies 2013).
• The mechanistic basis of sign epistasis in TEM-1 β-lactamase (Knies et al. 2017).
• The theoretical and empirical consequences of higher-order epistatic interactions (Weinreich 2011,Weinreich et al 2013; Weinreich et al 2018).

Current work on epistasis is funded by NSF EPSCoR award 1736253 and includes:

• A survey of epistatic interactions and mechanistic determinants among deleterious mutations. Some time ago Wylie and Shakhnovich 2011 demonstrated that a model in which missense mutations outside an enzyme's active site only perturb folding stability were entirely consistent with data from a bulk survey in TEM-1 β-lactamase from Berstein et al 2006. We are testing that model using individual randomly chosen missense mutations in TEM-1 β-lactamase in collaboration with Mandar Naik (Brown MPPB) and Brenda Rubenstein (Brown Chemistry).
• Deep mutational scanning (DMS) and the detection of epistasis. Most current DMS datasets exhaustively examine single mutations around some wild-type and are thus mute on the question of epistasis. In collaboration with Lorin Crawford (Brown SPH), we are now exploring computational approaches to detect epistasis from slightly larger DMS datasets. We are also building a DMS dataset on SHV-1 β-lactamase , another enzyme that confers bacterial resistance to penicillin and related compounds. SHV-1 is roughly 30% diverged from TEM-1.