Evidence for universal scaling behavior of a freely relaxing DNA molecule

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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

Brochard-Wyart "stem-and-flower" model

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>.

Rescaling analysis of the full data set. Inset = Dispersion of the data around the theoretical scaling factor of 1/2.

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