Ensemble epistasis: thermodynamic origins of non-additivity between mutations

Non-additivity between mutations—epistasis—profoundly shapes evolution. It can be difficult to understand its mechanistic origins. Here we show that “ensemble epistasis” is likely a universal feature of macromolecules. Using a simple analytical model, we found that epistasis arises when two conditions are met: 1) a macro-molecule populates at least three structures and 2) mutations have differential effects on a least two of the inactive structures. To explore the relative magnitude of ensemble epistasis, we performed a virtual deep-mutational scan of the allosteric Ca2+ signaling protein S100A4. We found that 27% of mutation pairs gave ensemble epistasis with a magnitude on the order of thermal fluctuations, 1 kT. We observed many forms of epistasis: magnitude, sign, and reciprocal sign epistasis. Depending on the effector concentration, the same mutation pair could even exhibit different forms of epistasis. The ubiquity of ensembles in biology and its pervasiveness in our dataset suggests that ensemble epistasis may be a universal mechanism of epistasis.Significance statementAddressing the mechanistic origins of evolutionary unpredictability is critical to understanding how mutations combine to determine phenotype. Here we lay the theoretical foundations and investigate the plausibility of a potentially universal mechanism of unpredictability in macromolecules. Macromolecules often adopt a set of interchanging structures, called a thermodynamic ensemble. Mutations can change the relative population of each structure, introducing unpredictability in the mapping between genotype and phenotype. The conditions under which we expect this to arise are common in macromolecules, suggesting that this form of unpredictability may be pervasive in evolution. We conclude that the thermodynamic ensemble bakes unpredictability into biology and that future attempts to address it might incorporate this mechanistic insight.