The equilibrium statistical mechanics of the helix-coil transition in torsionally stressed DNA

A theory of helix-coil transitions in torsionally stressed heteropolymeric DNA is developed. Specifically, the polymer is constrained to have a fixed value of total twist in all accessible states, which may differ from its unstressed total twist. This imposed deformation is partitioned between twisting of the helical portions and melting with subsequent twisting in the coil regions. Quadratic free energy densities are associated to torsion in both types of regions. In this theory two parameters influence helix stability-temperature and the magnitude of the imposed twist. Consequently the predicted transition behavior is considerably more intricate than that arising from thermal transitions in unconstrained molecules. In particular, sufficient untwisting can significantly destabilize the helix, even at low temperatures. In this case melting occurs predominantly in AT-rich regions, although the transition behavior of such regions is complicated. For example, if the imposed twist is altered to decrease helix stability at fixed temperature, the probability of melting of a given monomer unit need not increase monotonically. The predictions of this theory compare favorably with a previous thermodynamic analysis of the same problem.