Mutational paths with sequence-based models of proteins: from sampling to mean-field characterisation

TL;DR

This paper introduces a framework for analyzing mutational paths in proteins using sequence-based models, combining sampling algorithms and mean-field theory to understand evolutionary dynamics and extend distance estimates.

Contribution

It presents a novel algorithm for sampling mutational paths and applies mean-field theory to characterize their properties in sequence-based protein models.

Findings

Validated sampling algorithm on solvable protein models

Applied models to natural protein data using Restricted Boltzmann Machines

Extended Kimura's evolutionary distance estimate to epistatic models

Abstract

Identifying and characterizing mutational paths is an important issue in evolutionary biology and in bioengineering. We here introduce a generic description of mutational paths in terms of the goodness of sequences and of the mutational dynamics (how sequences change) along the path. We first propose an algorithm to sample mutational paths, which we benchmark on exactly solvable models of proteins in silico, and apply to data-driven models of natural proteins learned from sequence data with Restricted Boltzmann Machines. We then use mean-field theory to characterize the properties of mutational paths for different mutational dynamics of interest, and show how it can be used to extend Kimura's estimate of evolutionary distances to sequence-based epistatic models of selection.