Disentangling contact and ensemble epistasis in a riboswitch.

Mutations introduced into macromolecules often exhibit epistasis, where the effect of one mutation alters the effect of another. Knowing the mechanisms that lead to epistasis is important for understanding how macromolecules work and evolve, as well as for effective macromolecular engineering. Here, we investigate the interplay between "contact epistasis" (epistasis arising from physical interactions between mutated residues) and "ensemble epistasis" (epistasis that occurs when a mutation redistributes the conformational ensemble of a macromolecule, thus changing the effect of the second mutation). We argue that the two mechanisms can be distinguished in allosteric macromolecules by measuring epistasis at differing allosteric effector concentrations. Contact epistasis manifests as nonadditivity in the microscopic equilibrium constants describing the conformational ensemble. This epistatic effect is independent of allosteric effector concentration. Ensemble epistasis manifests as nonadditivity in thermodynamic observables-such as ligand binding-that are determined by the distribution of ensemble conformations. This epistatic effect strongly depends on allosteric effector concentration. Using this framework, we experimentally investigated the origins of epistasis in three pairwise mutant cycles introduced into the adenine riboswitch aptamer domain by measuring ligand binding as a function of allosteric effector concentration. We found evidence for both contact and ensemble epistasis in all cycles. Furthermore, we found that the two mechanisms of epistasis could interact with each other. For example, in one mutant cycle we observed 6 kcal/mol of contact epistasis in a microscopic equilibrium constant. In that same cycle, the maximum epistasis in ligand binding was only 1.5 kcal/mol: shifts in the ensemble masked the contribution of contact epistasis. Finally, our work yields simple heuristics for identifying contact and ensemble epistasis based on measurements of a biochemical observable as a function of allosteric effector concentration.