Structural transitions in DNA driven by external force and torque

Experiments on single DNA molecules have shown that abrupt transitions between states of different extensions can be driven by stretching and twisting. Here we show how a simple statistical-mechanical model can be used to globally fit experimental force-extension data of Léger et al. [Phys. Rev. Lett. 83, 1066 (1999)], over a wide range of DNA molecule twisting. We obtain the mean twists, extensions, and free energies of the five DNA states found experimentally. We also predict global force-torque and force-linking number phase diagrams for DNA. At zero force, the unwinding torque for zero-force structural transition from the double helix to an unwound structure is found to be $\approx -{2k}_{B}T,$ while the right-handed torque needed to drive DNA to a highly overwound state $\approx {7k}_{B}T.\mathrm{}$