The divergence time of protein structures modelled by Markov matrices and its relation to the divergence of sequences

TL;DR

This paper introduces a Bayesian framework to estimate divergence times of protein structures using Markov matrices, providing more accurate evolutionary insights than sequence-based models, and demonstrates its effectiveness in structure prediction.

Contribution

It develops a novel time-parameterized structural divergence model based on Markov matrices, improving evolutionary analysis and structure prediction accuracy.

Findings

Estimated divergence times from structures outperform sequence-based proxies.

Established a quantitative relationship between structural and sequence divergence.

Achieved competitive secondary structure prediction accuracy.

Abstract

A complete time-parameterized statistical model quantifying the divergent evolution of protein structures in terms of the patterns of conservation of their secondary structures is inferred from a large collection of protein 3D structure alignments. This provides a better alternative to time-parameterized sequence-based models of protein relatedness, that have clear limitations dealing with twilight and midnight zones of sequence relationships. Since protein structures are far more conserved due to the selection pressure directly placed on their function, divergence time estimates can be more accurate when inferred from structures. We use the Bayesian and information-theoretic framework of Minimum Message Length to infer a time-parameterized stochastic matrix (accounting for perturbed structural states of related residues) and associated Dirichlet models (accounting for insertions and deletions during the evolution of protein domains). These are used in concert to estimate the Markov time of divergence of tertiary structures, a task previously only possible using proxies (like RMSD). By analyzing one million pairs of homologous structures, we yield a relationship between the Markov divergence time of structures and of sequences. Using these inferred models and the relationship between the divergence of sequences and structures, we demonstrate a competitive performance in secondary structure prediction against neural network architectures commonly employed for this task. The source code and supplementary information are downloadable from \url{http://lcb.infotech.monash.edu.au/sstsum}.