Dimensions of a plectonemic DNA supercoil under fairly general perturbations

A dimensional relation between the superhelical pitch angle and the superhelical radius is derived for plectonemic DNA. A uniform classical Hamiltonian is extracted from the free energy of the supercoil. The DNA superhelix may be perturbed by a variety of sources, but this does not alter the theoretical argumentation. Semiclassical arguments are presented for the validity of the analysis although one may simply appeal to establishing a classical superhelical "trajectory" experimentally. The theory is in good agreement with the microscopic determination of the plectonemic dimensions of closed circular DNA by T.C. Boles et al. (J. Mol. Biol. 213 (1990) 931).