Torsional and bending rigidity of the double helix from data on small DNA rings

We have calculated the variance of equilibrium distribution of a circular wormlike polymer chain over the writhing number, Wr)2), as a function of the number of Kuhn statistical segments, n. For large n these data splice well with our earlier results obtained for a circular freely jointed polymer chain. Assuming that delta Lk)2) = delta Tw)2) we have compared our results with experimental data on the chain length dependence of the delta Lk)2) value recently obtained by Horowitz and Wang for small DNA rings. This comparison has shown an excellent agreement between theory and experiment and yielded a reliable estimate of the torsional and bending rigidity parameters. Namely, the torsional rigidity constant is C = 3.0.10(-19) erg cm, and the bending rigidity as expressed in terms of the DNA persistence length is a = 500 A. The obtained value of C agrees well with earlier estimates by Shore and Baldwin as well as by Horowitz and Wang whereas the a value is in accord with the data of Hagerman. We have found the data of Shore and Baldwin on the chain length dependence of the delta Lk)2) value to be entirely inconsistent with our theorectical results.