The simplicity of protein sequence-function relationships.

How complicated is the genetic architecture of proteins - the set of causal effects by which sequence determines function? High-order epistatic interactions among residues are thought to be pervasive, making a protein's function difficult to predict or understand from its sequence. Most studies, however, used methods that overestimate epistasis, because they analyze genetic architecture relative to a designated reference sequence - causing measurement noise and small local idiosyncrasies to propagate into pervasive high-order interactions - or have not effectively accounted for global nonlinearity in the sequence-function relationship. Here we present a new reference-free method that jointly estimates global nonlinearity and specific epistatic interactions across a protein's entire genotype-phenotype map. This method yields a maximally efficient explanation of a protein's genetic architecture and is more robust than existing methods to measurement noise, partial sampling, and model misspecification. We reanalyze 20 combinatorial mutagenesis experiments from a diverse set of proteins and find that additive and pairwise effects, along with a simple nonlinearity to account for limited dynamic range, explain a median of 96% of total variance in measured phenotypes (and >92% in every case). Only a tiny fraction of genotypes are strongly affected by third- or higher-order epistasis. Genetic architecture is also sparse: the number of terms required to explain the vast majority of variance is smaller than the number of genotypes by many orders of magnitude. The sequence-function relationship in most proteins is therefore far simpler than previously thought, opening the way for new and tractable approaches to characterize it.