Electrostatic-undulatory theory of plectonemically superooiled DNA

We present an analytical calculation of the electrostatic interaction in a pletonemic supercoil within the Poisson-Boltzmann approximation. Undulation s of the supercoil strands arising from thermal motion couple nonlinearly w ith the electrostatic interaction, giving rise to a strong enhancement of t he bare interaction. In the limit of fairly tight winding, the free energy of a plectonemic supercoil may be split into an elastic contribution contai ning the bending and torsional energies and an electrostatic-undulatory fre e energy. The total free energy of the supercoil is minimized according to an iterative scheme, which utilizes the special symmetry inherent in the us ual elastic free energy of the plectoneme. The superhelical radius, opening angle, and undulation amplitudes in the radius and pitch are obtained as a function of the specific linking difference and the concentration of monov alent salt. Our results compare favorably with the experimental values for these parameters of Boles et al. (1990. J. Mol. Biol. 213:931-951). In part icular, we confirm the experimental observation that the writhe is a virtua lly constant fraction of the excess linking number over a wide range of sup erhelical densities. Another important prediction is the ionic strength dep endence of the plectonemic parameters, which is in reasonable agreement wit h the results from computer simulations.