The Twist, Writhe, and Linking Number Distributions in Closed Circular DNA

We discuss the predictions which follow from the assumption of statistically independent twist and writhe distributions of given variances in circular DNA with single-strand nicks. The nature of the topoisomer distribution produced upon covalent closure of the nicks is described, as well as the nature of the twist and writhe distributions in the fully-closed molecules. In particular, we show how the distributions depend on the magnitudes of the given variances, and how the relative magnitudes of the variances can be deduced from experiment. One additional consequence of the theory is the prediction of a necessary difference between the temperature coefficient of the twist in nicked versus fully-closed circular DNA. The ratio of the two twist coefficients turns out to depend only on the ratio of the twist and writhe variances in nicked DNA.