Finite-size corrections for confined polymers in the extended de Gennes regime

TL;DR

This paper derives finite-size corrections for the extension of confined polymers in the extended de Gennes regime, providing more accurate predictions for experimental and simulation conditions where polymer length is finite.

Contribution

It introduces a mapping to a one-dimensional weakly self-avoiding random walk to calculate finite-size effects, improving upon the infinite-length theoretical models.

Findings

Finite-size corrections match well with PERM simulation results.

Results are relevant for interpreting experiments on DNA in nanochannels.

Provides insights for high ionic strength experimental conditions.

Abstract

Theoretical results for the extension of a polymer confined to a channel are usually derived in the limit of infinite contour length. But experimental studies and simulations of DNA molecules confined to nanochannels are not necessarily in this asymptotic limit. We calculate the statistics of the span and the end-to-end distance of a semiflexible polymer of finite length in the extended de Gennes regime, exploiting the fact that the problem can be mapped to a one-dimensional weakly self-avoiding random walk. The results thus obtained compare favourably with pruned-enriched Rosenbluth method (PERM) simulations of a three-dimensional discrete wormlike chain model of DNA confined in a nanochannel. We discuss the implications for experimental studies of linear $\lambda$-DNA confined to nanochannels at the high ionic strengths used in many experiments.