Green function of correlated genes in a minimal mechanical model of protein evolution

TL;DR

This paper presents a simplified mechanical model of protein evolution using Green functions to relate gene sequence correlations to physical interactions, revealing how mutations influence protein function and epistasis through force transmission and topological transitions.

Contribution

It introduces a novel framework linking genetic correlations to mechanical properties of proteins via Green functions, highlighting the role of force scattering and topological changes in evolution.

Findings

Mutations act as localized perturbations scattering the force field.

A topological transition divides the protein into functional subdomains.

Long-range epistasis facilitates collective functional modes.

Abstract

The function of proteins arises from cooperative interactions and rearrangements of their amino acids, which exhibit large-scale dynamical modes. Long-range correlations have also been revealed in protein sequences, and this has motivated the search for physical links between the observed genetic and dynamic cooperativity. We outline here a simplified theory of protein, which relates sequence correlations to physical interactions and to the emergence of mechanical function. Our protein is modeled as a strongly-coupled amino acid network whose interactions and motions are captured by the mechanical propagator, the Green function. The propagator describes how the gene determines the connectivity of the amino acids, and thereby the transmission of forces. Mutations introduce localized perturbations to the propagator which scatter the force field. The emergence of function is manifested by a topological transition when a band of such perturbations divides the protein into subdomains. We find that epistasis -- the interaction among mutations in the gene -- is related to the nonlinearity of the Green function, which can be interpreted as a sum over multiple scattering paths. We apply this mechanical framework to simulations of protein evolution, and observe long-range epistasis which facilitates collective functional modes.