Strong evidence for protein epistasis, weak evidence against it

A recent paper by Ashenberg et al. (1) reports protein stability measurements and computational simulations that they claim contradict the results of our previous paper describing a “Stokes shift” in protein evolution (2). They make strong assertions that coevolutionary interactions among amino acids due to effects on stability do not significantly modify amino acid preferences or evolutionary patterns and thus are unimportant for phylogenetics. However, on review, we find their experimental results are highly compatible with epistasis and Stokes shift theory. The apparent contradiction arises from their making sparse measurements on closely related strains of influenza, an inappropriate model system, and from ignoring most of our results.

The evolutionary Stokes shift describes how, subsequent to fixation of an amino acid variant, epistatic interactions cause shifts in amino acid preferences, tending to make the newly resident amino acid more favorable. Ashenberg et al.’s study measured the melting temperature changes of only six different mutations (compared with the 300 × 19 in our work), none of which came close to fixation. The idiosyncratic nature of influenza population biology leads to frequent selective sweeps, inducing bottlenecks and partial fixation of deleterious mutations, whereas high mutation rates promote frequent back mutation. Furthermore, their studies considered mutations in closely related influenza strains in proteins that have evolved to buffer deleterious mutations (3), a situation with limited opportunities for epistasis. Predisposing fluctuations leading to Stokes shifts would be modest under these conditions; correspondingly, Ashenberg et al. observe fluctuations in melting temperatures up to 3 °C. Contrary to their claims, this is epistasis and is highly compatible with our expectations when the resident amino acid is mostly constant. Ashenberg et al. claim that much of the discrepancy between their results and ours is that we force fixation of deleterious mutations and prevent back mutations. In contrast, we show in numerous simulations (ignored by Ashenberg et al.) that no such requirements are necessary; random fluctuations in the evolving sequence will occasionally predispose the protein toward a particular replacement.

Neither their simulations nor our simulations are sufficiently accurate to make specific predictions about stabilities over moderate- to long-term evolution. An appropriate test of Stokes predictions of epistatic change after amino acid replacements is to calculate distributions of expected energetic differences in complementary mutations at sites with long-term fixed replacements. The changes in such free energies in moderately and highly diverged real proteins, presented in Pollock et al. (2), support our predictions, but were again ignored by Ashenberg et al. Also neglected was exciting recent work that extracted detailed structural information from epistatic interactions (4). The small differences between simulation results may be due to differences in protein length, stability, and structure and because Ashenberg et al. consider many fewer substitutions and (contrary to their assertions) much shorter evolutionary times than did our simulations of more than 120,000 substitutions each.

We support Ashenberg et al.’s call for greater focus on site-specific selective constraints in molecular evolution, but it is clear that temporal heterogeneity is also important. We need a better understanding of both.