Free Energy of Twisted Semiflexible Polymers

TL;DR

This paper analyzes the free energy differences in twisted semiflexible polymers under different measurement ensembles, providing analytical expressions and predictions that can be tested in single-molecule experiments.

Contribution

It introduces a theoretical framework for understanding free energy differences in torque-link measurements of semiflexible polymers, highlighting ensemble inequivalence and providing explicit formulas.

Findings

Distinct torque-link relations in different ensembles.

Analytical expressions for free energy differences.

Predictions testable in single-molecule experiments.

Abstract

We investigate the role of fluctuations in single molecule measurements of torque-link ($t-lk$) curves. For semiflexible polymers of finite persistence length (i.e. polymers with contour length $L$ comparable to the persistence length $L_P$), the torque versus link curve in the constant torque (isotorque) ensemble is distinct from the one in the constant link (isolink) ensemble. Thus, one encounters the conceptually interesting issue of a ``free energy of transition'' in switching ensembles while making torque-link measurements. We predict the dependence on the semiflexibility parameter $\beta = L/L_P$ of this extra contribution to the free energy which shows up as an area in the torque-link plane. This can be tested against future torque-link experiments with single biopolymers. We bring out the inequivalence of torque-link curves for a stiff polymer and present explicit analytical expressions for the {\it distinct} torque-link relations in the two ensembles and the free energy difference in switching ensembles in this context. The predictions of our work can be tested against single molecule experiments on torsionally constrained biopolymers.