Here, we propose a new probabilistic model, Coev, to identify coevolving positions and their associated profile in DNA sequences while incorporating the underlying phylogenetic relationships. The process of coevolution is modeled by a 16 × 16 instantaneous rate matrix that includes rates of transition as well as a profile of coevolution. We used simulated, empirical and illustrative data to evaluate our model and to compare it with a model of 'independent' evolution using Akaike Information Criterion. We showed that the Coev model is able to discriminate between coevolving and non-coevolving positions and provides better specificity and specificity than other available approaches. We further demonstrate that the identification of the profile of coevolution can shed new light on the process of dependent substitution during lineage evolution.

Small protein fragments, and not just residues, can be used as basic building blocks to reconstruct networks of coevolved amino acids in proteins. Fragments often enter in physical contact one with the other and play a major biological role in the protein. The nature of these interactions might be multiple and spans beyond binding specificity, allosteric regulation and folding constraints. Indeed, coevolving fragments are indicators of important information explaining folding intermediates, peptide assembly, key mutations with known roles in genetic diseases, distinguished subfamily-dependent motifs and differentiated evolutionary pressures on protein regions. Coevolution analysis detects networks of fragments interaction and highlights a high order organization of fragments demonstrating the importance of studying at a deeper level this structure. We demonstrate that it can be applied to protein families that are highly conserved or represented by few sequences, enlarging in this manner, the class of proteins where coevolution analysis can be performed and making large-scale coevolution studies a feasible goal.

Models of codon evolution have attracted particular interest because of their unique capabilities to detect selection forces and their high fit when applied to sequence evolution. We described here a novel approach for modeling codon evolution, which is based on Kronecker product of matrices. The 61 × 61 codon substitution rate matrix is created using Kronecker product of three 4 × 4 nucleotide substitution matrices, the equilibrium frequency of codons, and the selection rate parameter. The entities of the nucleotide substitution matrices and selection rate are considered as parameters of the model, which are optimized by maximum likelihood. Our fully mechanistic model allows the instantaneous substitution matrix between codons to be fully estimated with only 19 parameters instead of 3,721, by using the biological interdependence existing between positions within codons. We illustrate the properties of our models using computer simulations and assessed its relevance by comparing the AICc measures of our model and other models of codon evolution on simulations and a large range of empirical data sets. We show that our model fits most biological data better compared with the current codon models. Furthermore, the parameters in our model can be interpreted in a similar way as the exchangeability rates found in empirical codon models.