A solvable model of the genesis of amino-acid sequences via coupled dynamics of folding and slow genetic variation

TL;DR

This paper presents a solvable microscopic model that captures the coupled dynamics of protein folding and genetic sequence evolution, predicting phase transitions and diagrams with physical interpretations supported by simulations.

Contribution

It introduces a novel solvable model combining folding and genetic variation, providing explicit phase transition predictions and physical insights.

Findings

Explicit phase diagrams at genetic equilibrium

Support from numerical simulations

Physical interpretation of folding-genetics coupling

Abstract

We study the coupled dynamics of primary and secondary structure formation (i.e. slow genetic sequence selection and fast folding) in the context of a solvable microscopic model that includes both short-range steric forces and and long-range polarity-driven forces. Our solution is based on the diagonalization of replicated transfer matrices, and leads in the thermodynamic limit to explicit predictions regarding phase transitions and phase diagrams at genetic equilibrium. The predicted phenomenology allows for natural physical interpretations, and finds satisfactory support in numerical simulations.