Robust detection of specific epistasis using rank statistics

The phenotypic effect of a mutation may depend on the genetic background in which it occurs, a phenomenon referred to as epistasis. One source of epistasis in proteins is direct interactions between residues in close physical proximity to one another. However, epistasis may also occur in the absence of specific interactions between amino acids if the genotype-to-phenotype map is nonlinear. Disentangling the contributions of these two phenomena—specific and global epistasis—from noisy, high-throughput mutagenesis experiments is highly non-trivial: the form of the nonlinearity is generally not known and model misspecification may lead to over- or underestimation of specific epistasis. In contrast to previous approaches, we do not attempt to model the fitness measurements directly. Rather, we begin with the observation that global epistasis, under the assumption of monotonicity, imposes strong constraints on the rank statistics of a combinatorial mutagenesis experiment. Namely, the rank-order of mutant phenotypes should be preserved across genetic backgrounds. We exploit this constraint to devise a simple semi-parametric method to detect specific epistasis in the presence of global epistasis and measurement noise. We apply this method to three high-throughput mutagenesis experiments, uncovering known protein contacts with similar or higher accuracy than existing, more complicated procedures. Moreover, the principles underlying our framework may suggest new ways of understanding the mechanisms which generate epistasis and their consequences for protein evolution.