Thermal fluctuations of small rings of intrinsically helical DNA treated like an elastic rod.

It is shown that the writhe distribution in a collection of thermally fluctuating rings formed from intrinsically helical DNA treated like an elastic rod can be determined completely from a knowledge of the dependence of the configuration integral on the intrinsic geometric torsion of the rods. When the length of the rods is of the order of the persistence length or less, the configuration integral can be expressed in terms of the frequencies of the normal modes of the rings, and so these torsion-dependent frequencies then become the quantities of interest. The nature of the normal modes of rings formed from intrinsically helical elastic rods, as deduced from the equations of motion in the Kirchhoff-Clebsch theory of the dynamics of elastic rods, is described. Examples of computed writhe distributions are given. The observed broadening of the writhe distribution as the intrinsic curvature of the rods is increased is shown to be related to the stability properties of the circular equilibrium configuration of the elastic rods. These results thus imply that thermal fluctuations in small rings of intrinsically curved DNA will be more pronounced than in rings of the same size formed from intrinsically straight DNA.