Eur. Phys. J. E 2, 377-402
Elastic rod model of a supercoiled DNA molecule
C. Bouchiat1 - M. Mézard1,2
1 Laboratoire de Physique Théorique de l'Ecole
Normale Supérieure, 24 rue Lhomond 75231 Paris Cedex 05, France
2 Institute for Theoretical Physics, University of California
Santa Barbara, CA 93106-4030, USA
claude.bouchiat@lpt.ens.fr
Received 1 April 1999 and Received in final form 4 January 2000
Abstract
We study the elastic behaviour of a supercoiled DNA molecule.
The simplest model is that of a rod-like chain, involving two
elastic constants, the bending and the twist rigidities. Writing
this model in terms of Euler angles, we show that the corresponding
Hamiltonian is singular and needs a small distance cut-off, which
is a natural length scale giving the limit of validity of the
model, of the order of the double-helix pitch. The rod-like chain
in the presence of the cut-off is able to reproduce quantitatively
the experimentally observed effects of supercoiling on the
elongation-force characteristics, in the small supercoiling regime.
An exact solution of the model, using both transfer matrix
techniques and its mapping to a quantum mechanics problem, allows
to extract, from the experimental data, the value of the twist
rigidity. We also analyse the variation of the torque and the
writhe-to-twist ratio versus supercoiling, showing
analytically the existence of a rather sharp crossover regime which
can be related to the excitation of plectoneme-like structures.
Finally we study the extension fluctuations of a stretched and
supercoiled DNA molecule, both at fixed torque and at fixed
supercoiling angle, and we compare the theoretical predictions to
some preliminary experimental data.
PACS
87.15.By Structure and bonding
- 61.41.+e Polymers, elastomers, and plastics
Copyright EDP Sciences, Società Italiana di Fisica, Springer-Verlag
