Historical contingency and entrenchment in protein evolution under purifying selection

Premal Shah, Joshua B. Plotkin
(Submitted on 15 Apr 2014)

The fitness contribution of an allele at one genetic site may depend on the states of other sites, a phenomenon known as epistasis. Epistasis can profoundly influence the process of evolution in populations under selection, and shape the course of protein evolution across divergent species. Whereas epistasis among adaptive substitutions has been the subject of extensive study, relatively little is known about epistasis under purifying selection. Here we use mechanistic models of thermodynamic stability in a ligand-binding protein to explore computationally the structure of epistatic interactions among substitutions that fix in protein sequences under purifying selection. We find that the selection coefficients of mutations that are nearly neutral when they fix are highly conditional on the presence of preceding mutations. In addition, substitutions which are initially neutral become increasingly entrenched over time due to antagonistic epistasis with subsequent substitutions. Our evolutionary model includes insertions and deletions, as well as point mutations, which allows us to quantify epistasis between these classes of mutations, and also to study the evolution of protein length. We find that protein length remains largely constant over time, because indels are more deleterious than point mutations. Our results imply that, even under purifying selection, protein sequence evolution is highly contingent on history and it cannot be predicted by the phenotypic effects of mutations introduced into the wildtype sequence alone.