Theory of the influence of changes in salt concentration on the configuration of intrinsically curved, impenetrable, rod-like structures modeling DNA minicircles

DNA molecules in the familiar double helical B form are treated here as though they have rod-like structures obtained by stacking the nearly planar base pairs comprising them one on top of another with each rotated by approximately one-tenth of a full turn with respect to its immediate predecessor in the stack. As each base in a base pair is attached to the sugar–phosphate backbone chain of one of the two DNA strands that have come together to form the Watson–Crick structure, and each phosphate group in a backbone chain bears one electronic charge, two such charges are associated with each base pair. Thus, each base pair is subject to not only the elastic forces and moments exerted on it by its neighboring base pairs but also to electrostatic forces, of sequentially remote origin, that, because they are only partially screened out by positively charged counter ions, can render the molecule's equilibrium configurations sensitive to changes in the concentration of salt in the medium. As there are cases in which, even though the intramolecular electrostatic forces of repulsion are strong, the distance of closest approach has value equal to that of the impenetrable diameter of the molecule, the theory presented here takes into account self-contact. Examples are given of cases in which the theory predicts that the radius of gyration of the minimum energy configuration of a small (549 base pair) circularized DNA molecule (called a “DNA minicircle”) has a remarkably strong dependence on the salt concentration.