Abstract
Recently described stochastic models of protein evolution have demonstrated that the inclusion of structural information in addition to amino acid sequences leads to a more reliable estimation of evolutionary parameters. We present a generative, evolutionary model of protein structure and sequence that is valid on a local length scale. The model concerns the local dependencies between sequence and structure evolution in a pair of homologous proteins. The evolutionary trajectory between the two structures in the protein pair is treated as a random walk in dihedral angle space, which is modeled using a novel angular diffusion process on the two-dimensional torus. Coupling sequence and structure evolution in our model allows for modeling both “smooth” conformational changes and “catastrophic” conformational jumps, conditioned on the amino acid changes. The model has interpretable parameters and is comparatively more realistic than previous stochastic models, providing new insights into the relationship between sequence and structure evolution. For example, using the trained model we were able to identify an apparent sequence–structure evolutionary motif present in a large number of homologous protein pairs. The generative nature of our model enables us to evaluate its validity and its ability to simulate aspects of protein evolution conditioned on an amino acid sequence, a related amino acid sequence, a related structure or any combination thereof.
Highlights
Several studies (Challis and Schmidler 2012; Herman et al 2014) have proposed joint stochastic models of evolution which take into account simultaneous alignment of protein sequence and structure
We present a generative evolutionary model, ETDBN (Evolutionary Torus Dynamic Bayesian Network) for pairs of homologous proteins
The Relationship between Evolutionary Time and Angular Distance Is Adequately Modeled We investigated the relationship between evolutionary time and angular distance between real protein pairs and protein pairs where the dihedral angles of pb (Xb) were treated as missing and sampled
Summary
Several studies (Challis and Schmidler 2012; Herman et al 2014) have proposed joint stochastic models of evolution which take into account simultaneous alignment of protein sequence and structure. These studies point out the limitations of earlier non-probabilistic methods, which often rely on heuristic procedures to infer parameters of interest. A major disadvantage of using heuristic procedures is that they typically fail to account for sources of uncertainty. ETDBN captures dependencies between sequence and structure evolution, accounts for alignment uncertainty, and models the local dependencies between aligned sites
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