Elastic stability of DNA configurations. I. General theory

Results are presented in the theory of the elastic rod model for DNA, among which are criteria enabling one to determine whether a calculated equilibrium configuration of a DNA segment is stable in the sense that it gives a local minimum to the sum of the segment's elastic energy and the potential of forces acting on it. The derived stability criteria are applicable to plasmids and to linear segments subject to strong anchoring end conditions. Their utility is illustrated with an example from the theory of configurations of the extranucleosomal loop of a DNA miniplasmid in a mononucleosome, with emphasis placed on the influence that nicking and ligation on one hand, and changes in the ratio of elastic coefficients on the other, have on the stability of equilibrium configurations. In that example, the configurations studied are calculated using an extension of the method of explicit solutions to cases in which the elastic rod modeling a DNA segment is considered impenetrable, and hence excluded volume effects and forces arising from self-contact are taken into account.