# Evidence for universal scaling behavior of a freely relaxing DNA molecule

## Contents

## Reference

**Evidence for the universal scaling behaviour of a freely relaxing DNA molecule**

S. Manneville, Ph. Cluzel, J.-L. Viovy, D. Chatenay, F. Caron

Europhysics Letters **36**: 413-418 (1996)

## Key Results

The Brochard-Wyart "stem-and-flower" model posits that the relaxation of a tethered polymer under flow at intermediate velocities is described by

<math> L(t)-L_0 \propto \sqrt{\frac{kT}{\eta a} t} </math>

Where L(t) is the length at time t, <math>L_0</math> is the initial length, k is the Boltzmann constant, T is the absolute temperature, <math>\eta</math> is the viscosity of the solvent, and a is the persistence length. The experiments showed that:

- <math>L(t)-L_0</math> obeys a power law
- Changing <math>\eta</math> does not change the scaling exponent

All of the experiments can be plotted at the same time if we plot <math> \frac{L(t)-L_0}{L_0 /2} </math> versus <math> \frac{t}{\tau_{1/2}} </math>, where <math> L(\tau_{1/2}) = L_0/2 </math>.

The data above follows a power law with a scaling exponent of 0.51. Analyzing data generated by another set of experiments (Science 264:822) generated scaling exponents which ranged between 0.43-0.52.

## Why Care

There have been previous studies which looked at the kinetics of DNA relaxation, but they relied on either optical tweezers or magnetic beads. This is the first work in which the molecule was stretched purely by flow, presumably providing a cleaner measurement of the phenomenon.

## Methods

48.5 kb <math>\lambda</math>-phage DNA was kept 0.1 M phosphate buffer with a pH of 7.4. Shorter (38.4 kb and 24.5 kB) molecules were obtained by restriction enzyme digest. The DNA was stained with the double-stranded nucleic acid stain YOYO-1, 2-mercaptoethanol was added to reduce photobleaching, and the resulting solution was mixed with glyceral to get one of the desired <math>\eta</math> (30-180 cP). The DNA solution was added to a 50 x 500 <math>\mu</math>m chamber, and it was visualized under Poiseuille flow conditions created by a syringe pump. Relaxation kinetics were measured by rapidly stopping flow using another syringe pump.