Melting of persistent double-stranded polymers

TL;DR

This paper develops an advanced transfer matrix method to analyze the melting behavior of double-stranded polymers, incorporating bending stiffness and branch point effects, with applications to DNA and collagen.

Contribution

It introduces a generalized transfer matrix approach for branched, persistent polymers with bending rigidity, extending the Poland-Scheraga model to include complex structural features.

Findings

Reentrant melting transition predicted for stiff double strands

Efficient computation of phase diagrams and force-extension curves

Method applicable to polymers with multiple strand bubbles

Abstract

Motivated by recent DNA-pulling experiments, we revisit the Poland-Scheraga model of melting a double-stranded polymer. We include distinct bending rigidities for both the double-stranded segments, and the single-stranded segments forming a bubble. There is also bending stiffness at the branch points between the two segment types. The transfer matrix technique for single persistent chains is generalized to describe the branching bubbles. Properties of spherical harmonics are then exploited in truncating and numerically solving the resulting transfer matrix. This allows efficient computation of phase diagrams and force-extension curves (isotherms). While the main focus is on exposition of the transfer matrix technique, we provide general arguments for a reentrant melting transition in stiff double strands. Our theoretical approach can also be extended to study polymers with bubbles of any number of strands, with potential applications to molecules such as collagen.