Prediction of site-specific amino acid distributions and limits of divergent evolutionary changes in protein sequences

摘要

We derive an analytic expression for site-specific stationary distributionsof amino acids from the Structurally Constrained Neutral (SCN) model of proteinevolution with conservation of folding stability. The stationary distributionsthat we obtain have a Boltzmann-like shape, and their effective temperatureparameter, measuring the limit of divergent evolutionary changes at a givensite, can be predicted from a site-specific topological property, the principaleigenvector of the contact matrix of the native conformation of the protein.These analytic results, obtained without free parameters, are compared withsimulations of the SCN model and with the site-specific amino aciddistributions obtained from the Protein Data Bank. These results also providenew insights into how the topology of a protein fold influences itsdesignability, i.e. the number of sequences compatible with that fold. Thedependence of the effective temperature on the principal eigenvector decreasesfor longer proteins, a possible consequence of the fact that selection forthermodynamic stability becomes weaker in this case.