Semiflexible Chains under Tension

TL;DR

This paper develops a theoretical framework using functional integrals and meanfield approximation to analyze the extension behavior of semiflexible chains like DNA under tension and in nematic fields, matching experimental data in some regimes.

Contribution

It introduces a meanfield approach to model semiflexible chains under tension and in nematic fields, providing quantitative agreement with experiments and insights into different field regimes.

Findings

Reproduces experimental force-extension curves for DNA.

Accurately describes chain expansion in weak nematic fields.

Fails to predict persistence length dependence in strong nematic fields.

Abstract

A functional integral formalism is used to derive the extension of a stiff chain subject to an external force. The force versus extension curves are calculated using a meanfield approach in which the hard constraint $u^2(s)=1$ is replaced by a global constraint $ < u^2(s) > = 1$ where $ u(s)$ is the tangent vector describing the chain and $s$ is the arc length. The theory ``quantitatively'' reproduces the experimental results for DNA that is subject to a constant force. We also treat the problems of a semiflexible chain in a nematic field. In the limit of weak nematic field strength our treatment reproduces the exact results for chain expansion parallel to the director. When the strength of nematic field is large, a situation in which there are two equivalent minima in the free energy, the intrinsically meanfield approach yields incorrect results for the dependence of the persistence length on the nematic field.