Freezing Transition of Random Heteropolymers Consisting of an Arbitrary Set of Monomers

TL;DR

This paper uses mean field replica theory to analyze the freezing transition in random heteropolymers with arbitrary monomer types, revealing a transition from a diverse globule to a few dominant conformations.

Contribution

It introduces a formalism for studying the freezing transition in heteropolymers with arbitrary interaction matrices, expanding understanding of their phase behavior.

Findings

Existence of a freezing transition from a random to a frozen globule.

Transition depends on the interaction matrix structure.

Special cases reveal relationship between interactions and transition nature.

Abstract

Mean field replica theory is employed to analyze the freezing transition of random heteropolymers comprised of an arbitrary number ($q$) of types of monomers. Our formalism assumes that interactions are short range and heterogeneity comes only from pairwise interactions, which are defined by an arbitrary $q \times q$ matrix. We show that, in general, there exists a freezing transition from a random globule, in which the thermodynamic equilibrium is comprised of an essentially infinite number polymer conformations, to a frozen globule, in which equilibrium ensemble is dominated by one or very few conformations. We also examine some special cases of interaction matrices to analyze the relationship between the freezing transition and the nature of interactions involved.