From Collapse to Freezing in Random Heteropolymers

TL;DR

This paper investigates the phase transition behaviors of a two-letter lattice heteropolymer model, revealing collapse and freezing phenomena, and discusses implications for protein folding.

Contribution

It introduces a detailed analysis of collapse and freezing transitions in a lattice heteropolymer model with implications for understanding protein folding.

Findings

Collapse structures form at zero temperature for any fraction of attracting sites.

Average chain size scales with a function of site fraction, showing different regimes.

Entropy drops abruptly at the phase boundary between swollen and collapsed states.

Abstract

We consider a two-letter self-avoiding (square) lattice heteropolymer model of N_H (out ofN) attracting sites. At zero temperature, permanent links are formed leading to collapse structures for any fraction rho_H=N_H/N. The average chain size scales as R = N^{1/d}F(rho_H) (d is space dimension). As rho_H --> 0, F(rho_H) ~ rho_H^z with z={1/d-nu}=-1/4 for d=2. Moreover, for 0 < rho_H < 1, entropy approaches zero as N --> infty (being finite for a homopolymer). An abrupt decrease in entropy occurs at the phase boundary between the swollen (R ~ N^nu) and collapsed region. Scaling arguments predict different regimes depending on the ensemble of crosslinks. Some implications to the protein folding problem are discussed.