Statistical Mechanics of Torque Induced Denaturation of DNA

A unifying theory of the denaturation transition of DNA, driven by temperature T or induced by an external mechanical torque Γ is presented. Our model couples in a geometrical way the hydrogen-bond opening and the untwisting of the helicoidal molecular structure. Using the transfer matrix method, we show that denaturation corresponds to a first-order phase transition from BDNA to dDNA phases and that the coexistence region is naturally parametrized by the degree of supercoiling σ. The denaturation free energy ∆G, the phase diagram in the T,Γ plane and isotherms in the σ,Γ plane are calculated. At T = 298K and for a Poly(dGdT)-Poly(dAdC)-DNA at 20mM Na+, the critical torque Γc ≃ −0.033eV/rad and degree of supercoiling σc ≃ −0.01 are in fair agreement with experimental data. PACS Numbers : 87.14.Gg, 05.20.-y, 64.10.+h Denaturation of the DNA, due to its essential relevance to transcription processes has been the object of intensive works in the last decades. Experiments on dilute DNA solutions have provided evidence for the existence of a thermally driven melting transition corresponding to the sudden opening of base pairs at a critical temperature Tm [1]. Recently, following the work of Smith et al. [2], micromanipulation techniques have been developed to study single-molecule behaviour under stress conditions and how structural transitions of DNA can be mechanically induced. While most single-molecule experiments have focused on stretching properties so far, the response of a DNA molecule to an external torsional stress has been studied very recently [3,4], sheding some new light on denaturation [3]. From a biological point of view, torsional stress is indeed not unusual in the living cell. Supercoiling and topological problems are present not only in DNA spatial organization in the cell but also in its functioning [5,6]. Locally unwound DNA is necessary for transcriptional activation, moreover transcription and replication generate supercoiling that is relaxed by the action of topoisomerases [7]. For a straight DNA molecule with fixed ends the topological constant called linking number Lk reduces to the number of twist Tw, i.e. the number of times the two strands of the DNA double-helix are intertwined [8]. The degree of supercoiling σ = (Lk − Lk0)/Lk0 characterizes the relative linking number with respect to its counterpart Lk0 for an unconstrained linear molecule. In Strick et al. experiment [3], a λ DNA molecule, in 10 mM PB, is