Physical Constraints on Epistatic Interactions

Epistasis, or the context-dependence of mutations, makes evolutionary trajectories difficult to predict. Here, we argue that knowledge of the physics of a system can tame its apparent evolutionary complexity. We focus on proteins, inspired by recent work on low-energy mechanical modes of bio-inspired, functional mechanical networks. Mutations in the sequence of a protein affect its shape, thereby modulating the effect of subsequent mutations; we find epistatic interactions at all probed orders. However, the structure of deformations limits the number of independent epistatic parameters. We find that such constrained epistasis is reflected in the topology of the fitness landscape. In addition to providing a mechanistic basis for experimentally observed epistatic couplings in proteins, we demonstrate how similar considerations may constrain epistasis in other complex systems.