In their latest submission to bioRxiv, Echave, Jackson, and Wilke present a model to explain site-specific evolutionary rates among amino acids in a protein based on biophysical principles.
Relationship between protein thermodynamic constraints and variation of evolutionary rates among sites Julian Echave, Eleisha L. Jackson, Claus O Wilke http://dx.doi.org/10.1101/009423
They compare two approaches which are based on (1) overall thermodynamic stability changes after mutation and (2) the changes of internal stress due to packing of side chains in the protein interior. The latter is measured by an Elastic Network Model that treats pairwise atomic distances as harmonic springs. Mutations act as perturbations of these springs that are at an energy minimum only for the wild type reference structure.
They find that the two models perform equally well on average in predicting empirical site variations of evolutionary rates, but that their predictive power can vary when compared between individual proteins, suggesting that internal stress plays a larger role in some proteins than in others.
One potential shortcoming of their stability model is the assumption that epistasis is negligible. In other words, mutational effects per site are treated independently and additively. The importance of epistasis has been argued by many, although there is conflicting evidence in the case of stability effects of mutations. Some argue that the stability change of a particular substitution is independent of the genetic background, i.e. the identity of amino acids at non-mutated sites. Others argue for epistasis, finding that compensatory mutations will enable otherwise destabilizing substitutions at other sites.
Interestingly, one lab has published experimental results on the same protein (influenza nucleoprotein) and in one paper find no evidence for stability-based epistasis, while finding it in another study. I think this illustrates that stability-based epistasis needs more attention.
I would like to see a more nuanced discussion of epistasis than just citing one half of the literature. How would epistasis have to be implemented? What are the challenges? Their “neutral” stability model that either accepts or rejects a mutation based on a single stability cut-off would probably need to be extended to allow stability effects of varying magnitudes.
They also compare two force fields commonly used for stability calculations as provided by FoldX and Rosetta’s ddg_monomer, finding only a negligible difference for their model predictions. All stability effect predictors still have the same fundamental flaw of treating a single conformation as the reference native structure. One of the major challenges, however, still is the proper treatment of unfolded conformations. A large proportion of stability effects are likely to manifest in the unfolded ensemble. Simulations of protein folding are still very time consuming and therefore unlikely to be applied to such large scale mutational studies as presented here any time soon.
The advances in combining evolutionary models with structural/biophysical data are very promising and the authors have made very significant contributions (especially in previous publications). The present article suggests that future models will incorporate a combination of different structure-based measures.