A generative angular model of protein structure evolution

TL;DR

This paper introduces a novel probabilistic model that captures local dependencies between amino acid sequence changes and structural conformations in protein evolution, allowing for realistic simulation and analysis of structural evolution patterns.

Contribution

It presents a generative angular diffusion model that jointly models sequence and structure evolution, incorporating both smooth and abrupt conformational changes with interpretable parameters.

Findings

Model captures both gradual and sudden conformational changes.

Identifies a conserved sequence-structure evolutionary motif.

Validates the model's ability to simulate realistic protein evolution scenarios.

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 modelled using a novel angular diffusion process on the two-dimensional torus. Coupling sequence and structure evolution in our model allows for modelling 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.