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How complicated is the relationship between a protein’s sequence and its 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 prior studies, however, used methods that misinterpret measurement errors, small local idiosyncracies around a designated wild-type sequence, and global nonlinearity in the sequence-function relationship as rampant high-order interactions. Here we present a simple new method to jointly estimate global nonlinearity and specific epistatic interactions across a protein’s genotype-phenotype map. Our reference-free approach calculates the effect of each amino acid state or combination by averaging over all genotypes that contain it relative to the global average. We show that this method is more accurate than any alternative approach and is robust to measurement error and partial sampling. We reanalyze 20 combinatorial mutagenesis experiments and find that main and pairwise effects, together with a simple form of global nonlinearity, account for a median of 96% of total variance in the measured phenotype (and > 92% in every case), and only a tiny fraction of genotypes are strongly affected by epistasis at third or higher orders. The genetic architecture is also sparse: the number of model terms required to explain the vast majority of phenotypic 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, and new, more tractable experimental approaches, combined with reference-free analysis, may be sufficient to explain it in most cases.
It is widely thought that a protein’s function depends on complex interactions among amino acids. If so, it would be virtually impossible to predict the function of new variants, and understanding how proteins work genetically and biochemically would require huge combinatorial experiments. We show that prior studies overestimated complexity because they analyzed sequence-function relationships from the perspective of a single reference genotype and/or misinterpreted global phenotypic nonlinearities as complex amino acid interactions. By developing a new reference-free approach and using it to reanalyze 20 experimental datasets, we show that additive effects and pairwise interactions alone, along with a simple global nonlinearity, explain the vast majority of functional variation. Higher-order interactions are weak or rare, and a minuscule fraction of possible interactions shape each protein’s function. Our work reveals that protein sequence-function relationships are surprisingly simple and suggests new strategies that are far more tractable than the massive experiments currently used.