Coupled dynamics of sequence selection and compactification in mean-field hetero-polymers

TL;DR

This paper presents an exactly solvable mean-field model that explores how the interplay between folding and genetic selection influences the evolution of hetero-polymer sequences, revealing complex phase behaviors.

Contribution

It introduces a novel coupled dynamics model for sequence selection and folding in hetero-polymers, solved exactly using the replica method, providing new insights into phase transitions.

Findings

Exact solutions for phase transitions in the model

Rich phase diagrams with multiple transition types

Insights into the balance of functionality and reproducibility

Abstract

We study a simple solvable model describing the genesis of monomer sequences for hetero-polymers (such as proteins), as the result of the equilibration of a slow stochastic genetic selection process which is assumed to be driven by the competing demands of functionality and reproducibility of the polymer's folded structure. Since reproducibility is defined in terms of properties of the folding process, one is led to the analysis of the coupled dynamics of (fast) polymer folding and (slow) genetic sequence selection. For the present mean-field model this analysis can be carried out using the finite-dimensional replica method, leading to exact results for (first- and second-order) transitions and to rich phase diagrams.