For many traits, including susceptibility to common diseases in humans, causal loci uncovered by genetic mapping studies explain only a minority of the heritable contribution to trait variation. Multiple explanations for this “missing heritability” have been proposed1. Here we use a large cross between two yeast strains to accurately estimate different sources of heritable variation for 46 quantitative traits and to detect underlying loci with high statistical power. We find that the detected loci explain nearly the entire additive contribution to heritable variation for the traits studied. We also show that the contribution to heritability of gene-gene interactions varies among traits, from near zero to approximately 50%. Detected two-locus interactions explain only a minority of this contribution. These results substantially advance our understanding of the missing heritability problem and have important implications for future studies of complex and quantitative traits.

Protein-protein interaction specificity is often encoded at the primary sequence level. However, the contributions of individual residues to specificity are usually poorly understood and often obscured by mutational robustness, sequence degeneracy, and epistasis. Using bacterial toxin-antitoxin systems as a model, we screened a combinatorially complete library of antitoxin variants at three key positions against two toxins. This library enabled us to measure the effect of individual substitutions on specificity in hundreds of genetic backgrounds. These distributions allow inferences about the general nature of interface residues in promoting specificity. We find that positive and negative contributions to specificity are neither inherently coupled nor mutually exclusive. Further, a wild-type antitoxin appears optimized for specificity as no substitutions improve discrimination between cognate and non-cognate partners. By comparing crystal structures of paralogous complexes, we provide a rationale for our observations. Collectively, this work provides a generalizable approach to understanding the logic of molecular recognition.

Summary Proteins often accumulate neutral mutations that do not affect current functions but can profoundly influence future mutational possibilities and functions. Understanding such hidden potential has major implications for protein design and evolutionary forecasting, but has been limited by a lack of systematic efforts to identify potentiating mutations. Here, through the comprehensive analysis of a bacterial toxin-antitoxin system, we identified all possible single substitutions in the toxin that enable it to tolerate otherwise interface-disrupting mutations in its antitoxin. Strikingly, the majority of enabling mutations in the toxin do not contact, and promote tolerance non-specifically to, many different antitoxin mutations, despite covariation in homologs occurring primarily between specific pairs of contacting residues across the interface. In addition, the enabling mutations we identified expand future mutational paths that both maintain old toxin-antitoxin interactions and form new ones. These non-specific mutations are missed by widely used covariation and machine learning methods. Identifying such enabling mutations will be critical for ensuring continued binding of therapeutically relevant proteins, such as antibodies, aimed at evolving targets.