Site-specific structure and stability constrained substitution models improve phylogenetic inference.

In previous studies, we presented our site-specific Stability Constrained substitution models of Protein Evolution (Stab-CPE) that define fitness as the probability of finding a protein folded in its native state but ignore changes in the native structure. Stab-CPE models can be used to predict a more realistic evolutionary variability across protein sites, nevertheless they still qualitatively differ from observed data and appear too tolerant to mutations. Here we present novel structurally constrained substitution models (Str-CPE) that define fitness based on the structural deformation produced by a mutation, which we predict adopting an extension of Juli'an Echaveás linearly forced elastic network model. Compared to our previous Stab-CPE models, the novel Str-CPE models are more stringent (they predict lower sequence entropy and substitution rate), provide higher likelihood to multiple sequence alignments (MSAs) that include one or more known structures, and better predict the observed conservation across sites. The models that combine Str-CPE and Stab-CPE models are even more stringent and fit the empirical MSAs better. We collectively refer to our models as Structure and Stability Constrained substitution models of Protein Evolution (SSCPE). When using distantly-related proteins, we find that more similar phylogenies are inferred under the SSCPE models than under traditional empirical substitution models if compared to the corresponding reference phylogenies inferred using structural distances. Therefore, SSCPE models seem to be much better-fitting substitution models for deep phylogeny inference. The SSCPE models have been implemented in the PERL-based program SSCPE.pl, which uses RAxML-NG to infer phylogenies under the SSCPE model given a concatenated MSA and a list of protein structures that match the sequences in the MSA.