Composite cylinder models of DNA: application to the electrostatics of the B-Z transition

We develop and test a Poisson-Boltzmann model of the electrostatics of the B-Z transition of DNA. Starting from the detailed geometries of the two forms, we compute at each radius the fractions of DNA matter, of volume forbidden (for nonpoint-like ions), and of volume accessible to the center of ions. These radial distributions are incorporated in a composite cylinder model; availability to ions (porosity) and the dielectric constant at each radial distance are then obtained. The phosphate charge is distributed with cylindrical symmetry on two layers at the appropriate radial distances. The porous sheath, between the axis and the charge distribution, provides much more room for ions in B-DNA than in Z-DNA. By using previously developed methods, the Poisson-Boltzmann problem of such cylinders is easily solved. The computational load is small, so that results can be obtained for a large set of salt concentrations and for a number of ionic radii. The variation of the electrostatic free energy difference with salt concentration compares favorably with the experimental value (it is half as large). There is also qualitative agreement with experiments on supercoiled DNA, including a maximum of the free energy difference at submolar salt concentrations. The results for this cylinder with porous sheath are in line with those of the earlier simple planar model and of a plain cylinder with sheath, which is also presented here. They are thus insensitive to details of the model. They support the proposition that the main electrostatic feature of the B-Z transition is the better immersion of the B-DNA phosphates into the solution. They also give confidence in the validity of the Poisson-Boltzmann approach, despite the large salt concentrations involved. Prior studies using an approach based on the potential of mean force are discussed.