Global force-torque phase diagram for the DNA double helix: structural transitions, triple points, and collapsed plectonemes.

We present a free energy model for structural transitions of the DNA double helix driven by tensile and torsional stress. Our model is coarse grained and is based on semiflexible polymer descriptions of B-DNA, underwound L-DNA, and highly overwound P-DNA. The statistical-mechanical model of plectonemic supercoiling previously developed for B-DNA is applied to semiflexible polymer models of P- and L-DNA to obtain a model of DNA structural transitions in quantitative accord with experiment. We identify two distinct plectonemic states, one "inflated" by electrostatic repulsion and thermal fluctuations and the other "collapsed," with the two double helices inside the supercoils driven to close contact. We find that supercoiled B and L are stable only in the inflated form, while supercoiled P is always collapsed. We also predict the behavior and experimental signatures of highly underwound "Q"-DNA, the left-handed analog of P-DNA; as for P, supercoiled Q is always collapsed. Overstretched "S"-DNA and strand-separated "stress-melted" DNA are also included in our model, allowing prediction of a global phase diagram for forces up to 1000 pN and torques between ±60 pN nm, or, in terms of linking number density, from σ=-5 to +3.