Scaling regimes of a semi-flexible polymer in a rectangular channel

TL;DR

This paper develops scaling relations for the extension and free energy of semi-flexible polymers in rectangular channels, addressing differences from square channels and aiding interpretation of DNA confinement experiments.

Contribution

It introduces new scaling relations specifically for semi-flexible polymers in rectangular channels, extending previous work focused on square geometries.

Findings

Extension fluctuations differ significantly in rectangular versus square channels.

Results are directly applicable to interpreting DNA nano-channel experiments.

Provides theoretical framework for experimental analysis of confined polymers.

Abstract

We derive scaling relations for the extension statistics and the confinement free energy for a semi-flexible polymer confined to a channel with a rectangular cross-section. Our motivation are recent numerical results [Gupta {\em et al.}, JCP {\bf 140} (2014) 214901] indicating that extensional fluctuations are quite different in rectangular channels compared to square channels. Our results are of direct relevance for interpreting current experiments on DNA molecules confined to nano-channels, as many experiments are performed for rectangular channels with large aspect ratios while theoretical and simulation results are usually obtained for square channels.