Torsional Directed Walks, Entropic Elasticity, and DNA Twist Stiffness

TL;DR

This paper introduces the concept of torsional directed walks to model DNA's torsional stiffness, providing an analytical solution that fits experimental data and enables direct measurement of microscopic twist parameters.

Contribution

It formulates and solves the torsional directed walk problem analytically, linking microscopic twist stiffness to observable DNA conformational behavior under tension.

Findings

Quantitative fit to experimental DNA extension data over a range of forces

Determined microscopic twist stiffness C=120nm and D=50nm from data

Predicted reduction of effective twist stiffness due to bend fluctuations

Abstract

DNA and other biopolymers differ from classical polymers due to their torsional stiffness. This property changes the statistical character of their conformations under tension from a classical random walk to a problem we call the `torsional directed walk'. Motivated by a recent experiment on single lambda-DNA molecules [Strick et al., Science 271 (1996) 1835], we formulate the torsional directed walk problem and solve it analytically in the appropriate force regime. Our technique affords a direct physical determination of the microscopic twist stiffness C and twist-stretch coupling D relevant for DNA functionality. The theory quantitatively fits existing experimental data for relative extension as a function of overtwist over a wide range of applied force; fitting to the experimental data yields the numerical values C=120nm and D=50nm. Future experiments will refine these values. We also predict that the phenomenon of reduction of effective twist stiffness by bend fluctuations should be testable in future single-molecule experiments, and we give its analytic form.