Minimum epistasis interpolation for sequence-function relationships

Abstract

Massively parallel phenotyping assays have provided unprecedented insight into how multiple mutations combine to determine biological function. While these assays can measure phenotypes for thousands to millions of genotypes in a single experiment, in practice these measurements are not exhaustive, so that there is a need for techniques to impute values for genotypes whose phenotypes are not directly assayed. Here we present a method based on the idea of inferring the least epistatic possible sequence-function relationship compatible with the data. In particular, we infer the reconstruction in which mutational effects change as little as possible across adjacent genetic backgrounds. Although this method is highly conservative and has no tunable parameters, it also makes no assumptions about the form that genetic interactions take, resulting in predictions that can behave in a very complicated manner where the data require it but which are nearly additive where data is sparse or absent. We apply this method to analyze a fitness landscape for protein G, showing that our technique can provide a substantially less epistatic fit to the landscape than standard methods with little loss in predictive power. Moreover, our analysis reveals that the complex structure of epistasis observed in this dataset can be well-understood in terms of a simple qualitative model consisting of three fitness peaks where the landscape is locally additive in the vicinity of each peak.