Scaling regimes for wormlike chains confined to cylindrical surfaces under tension

TL;DR

This paper develops a theoretical framework to analyze the free energy and extension behavior of wormlike chains confined to cylindrical surfaces under tension, revealing different scaling regimes and applying results to DNA unwrapping forces.

Contribution

It introduces a mean field variational approach to study the confinement and tension effects on wormlike chains, deriving analytical scaling laws for various regimes.

Findings

Reproduces Odijk scaling for strongly confined chains at zero tension.

Identifies regimes where Odijk scaling is observable at moderate tension.

Estimates unwrapping forces for DNA from nucleosomes.

Abstract

We compute the free energy of confinement ${\cal{F}}$ for a wormlike chain (WLC), with persistence length $l_p$, that is confined to the surface of a cylinder of radius $R$ under an external tension $f$ using a mean field variational approach. For long chains, we analytically determine the behavior of the chain in a variety of regimes, which are demarcated by the interplay of $l_p$, the Odijk deflection length ($l_d=(R^2l_p)^{1/3}$), and the Pincus length ($l_f = {k_BT}/{f}$, with $k_BT$ being the thermal energy). The theory accurately reproduces the Odijk scaling for strongly confined chains at $f=0$, with ${\cal{F}}\sim Ll_p^{-1/3}R^{-2/3}$. For moderate values of $f$, the Odijk scaling is discernible only when ${l_p}\gg R$ for strongly confined chains. Confinement does not significantly alter the scaling of the mean extension for sufficiently high tension. The theory is used to estimate unwrapping forces for DNA from nucleosomes.