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Soft Matter and Biological Physics

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

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