Secondary Structures in Long Compact Polymers

TL;DR

This paper introduces an efficient Monte-Carlo algorithm for sampling long compact polymers, enabling analysis of secondary structures and revealing their prevalence compared to open chains.

Contribution

A novel Monte-Carlo method for uniformly sampling long compact polymer configurations, facilitating statistical analysis of secondary structures.

Findings

Secondary structure participation is self-averaging in long chains.

Fraction of monomers in secondary structures is less than one.

Compact chains are more prone to form secondary structures than open chains.

Abstract

Compact polymers are self-avoiding random walks which visit every site on a lattice. This polymer model is used widely for studying statistical problems inspired by protein folding. One difficulty with using compact polymers to perform numerical calculations is generating a sufficiently large number of randomly sampled configurations. We present a Monte-Carlo algorithm which uniformly samples compact polymer configurations in an efficient manner allowing investigations of chains much longer than previously studied. Chain configurations generated by the algorithm are used to compute statistics of secondary structures in compact polymers. We determine the fraction of monomers participating in secondary structures, and show that it is self averaging in the long chain limit and strictly less than one. Comparison with results for lattice models of open polymer chains shows that compact chains are significantly more likely to form secondary structure.