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 $\Gamma$ 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 $\sigma$. The denaturation free energy $\Delta G$, the phase diagram in the $T,\Gamma$ plane and isotherms in the $\sigma, \Gamma$ plane are calculated. At T=298K and for a Poly(dGdT)-Poly(dAdC)-DNA at $20 mM Na^+$, the critical torque $\Gamma_c \simeq -0.033 eV/rad$ and degree of supercoiling $\sigma_c \simeq -0.01$ are in fair agreement with experimental data.