Moments for DNA topoisomers: the helical wormlike chain.

Abstract

AbstractThe mean‐square radius 〈S2〉N of gyration of the DNA topoisomer with the linking number N is evaluated as a function of N and chain length L on the basis of a (circular) twisted wormlike chain, i.e., a special case of the helical wormlike chain. Evaluation of 〈S2〉N and also of the moment 〈Wr2〉 of the writhe Wr is carried out over a wide range of L, following the Monte Carlo procedure of Frank‐Kamenetskii et al. It is found that the present Monte Carlo values of 〈Wr2〉 for large L are appreciably larger than the known Monte Carlo values for freely jointed chains. Thus, the empirical interpolation formula for 〈Wr2〉 previously constructed on the basis of the theoretical values for small L along with the latter Monte Carlo values for large L is revised with the present Monte Carlo values. By the use of the revised formula, a reanalysis of the experimental data for the distribution of topoisomers is made, and it is found that the present estimates of the torsional constant and the stiffness parameter are equal to and somewhat larger than the previous ones, respectively. It is shown that 〈S2〉N decreases with increasing |ΔN|, where ΔN = N − N, with N the number of helix turns in the linear DNA chain in its undeformed state. The mean‐square radii of gyration 〈S2〉Wr and 〈S2〉 of the original circular Kratky–Porod wormlike chain with and without Wr fixed are also evaluated.