Pseudoknots in a Homopolymer

TL;DR

This paper investigates the behavior of pseudoknots in homopolymers, analyzing their scaling and phase transitions across different temperature regimes in two and three dimensions.

Contribution

It introduces a detailed analysis of pseudoknot scaling in homopolymers and proposes a simple model to study phase transitions involving pseudoknot formation.

Findings

Number of pseudoknots is extensive at all temperatures.

Pseudoknots between chain halves diverge logarithmically at certain temperatures.

Phase diagram includes swollen, branched, and collapsed phases.

Abstract

After a discussion of the definition and number of pseudoknots, we reconsider the self-attracting homopolymer paying particular attention to the scaling of the number of pseudoknots at different temperature regimes in two and three dimensions. Although the total number of pseudoknots is extensive at all temperatures, we find that the number of pseudoknots forming between the two halves of the chain diverges logarithmically at (in both dimensions) and below (in 2d only) the theta-temparature. We later introduce a simple model that is sensitive to pseudoknot formation during collapse. The resulting phase diagram involves swollen, branched and collapsed homopolymer phases with transitions between each pair.