Elastic stability of DNA configurations. II. Supercoiled plasmids with self-contact

Configurations of protein-free DNA miniplasmids are calculated with the eff ects of impenetrability and self-contact forces taken into account by using exact solutions of Kirchhoff's equations of equilibrium for elastic rods o f circular cross section. Bifurcation diagrams are presented as graphs of e xcess link, Delta L, versus writhe, W, and the stability criteria derived i n paper I of this series are employed in a search for regions of such diagr ams that correspond to configurations that are stable, in the sense that th ey give local minima to elastic energy. Primary bifurcation branches that o riginate at circular configurations are composed of configurations with D-m symmetry (m = 2,3,...). Among the results obtained are the following. (i) There are configurations with C-2 symmetry forming secondary bifurcation br anches which emerge from the primary branch with m = 3, and bifurcation of such secondary branches gives rise to tertiary branches of configurations w ithout symmetry. (ii) Whether or not self;contact occurs, a noncircular con figuration in the primary branch with m = 2, called branch alpha, is stable when for it the derivative d Delta C/dW, computed along that branch, is st rictly positive. (iii) For configurations not in alpha, the condition d Del ta L/dW>O is not sufficient for stability; in fact, each nonplanar contact- free configuration that is in a branch other than alpha is unstable. A rule relating the number of points of self-contact and the occurrence of interv als of such contact to the magnitude of Delta L, which in paper I was found to hold for segments of DNA subject to strong anchoring end conditions, is here observed to hold for computed configurations of protein-free miniplas mids.