DNA loop statistics and torsional modulus

The modelling of DNA mechanics under external constraints is discussed. Two analytical models are widely known, but disagree for instance on the value of the torsional modulus. The origin of this embarassing situation is located in the concept of writhe. This letter presents a unified model for DNA establishing a relation between the different approaches. I show that the writhe created by the loops of DNA is at the origin of the discrepancy. To take this into account, I propose a new treatment of loop statistics based on numerical simulations using the most general formula for the writhe, and on analytic calculations with only one fit parameter. One can then compute the value of the torsional modulus of DNA without the need of any cut-off. 1 General motivations New experimental techniques in single molecule manipulation of DNA and supercoiling control have stimulated improvements in the understanding of DNA mechanics [1, 2, 3, 4]. Surprisingly, the measurements have to be interpreted through a rather sophisticated model in order to extract physical constants [5, 6, 7]. Different approaches lead to disagreeing values of, in particular, the torsional modulus C of the molecule along its axis. The method used by Moroz and Nelson [6] leads to the value C/kBT = 109 nm, while using the same experimental data the model provided by Mézard and Bouchiat [7] gives 84±10 nm. Recently, another experiment performed two direct measurements [1] with a weighted average of 102± 6 nm. In this letter, I will establish the domains of validity of the two mentioned theoretical approaches, clarify the origin of their disagreement and compute a value of the torsional constant C with a new model. This letter is organized as follows: It starts with a short introduction to two widely used models for elasticity of a polymer. In order to take into account Present address: Max Planck Institut für Physik Komplexer Systeme Nöthnitzer Straße 38, D-01187 Dresden, Germany. E-mail: [email protected]