Variance of Writhe for Wormlike DNA Rings with Excluded Volume

We have calculated the variance of the equilibrium distribution of a circular wormlike polymer chain over the writhing number, less than (Wr)2 greater than, with allowance for the excluded volume effects. Within this model the less than (Wr)2 greater than value is a function of the number of Kuhn statistical segments, n, and the chain diameter, d measured in Kuhn statistical lengths, b. Simulated DNA chains varied from 200 to 10,000 base pairs and the d value varied from 0.02 to 0.2. Theory predicts a considerable ionic strength dependence of the DNA superhelix energy as a consequence of the change in the DNA diameter. A comparison with the available experimental data has yielded an estimate of the DNA torsional rigidity, the Kuhn statistical length, and the effective diameter of the double helix under conditions of the complete screening of the DNA electrostatic potential.