Supercoiled pseudocircular domains in single-twisted DNAs under tension: Elastic constants and unwinding dynamics in...

Extension versus twist data of Koster et al. (Nature 2005, 434, 671-674) are analyzed to obtain C for the main-chain segments and the twist energy parameter (ET ) for the supercoiled pseudocircular (sp) domain(s) from which C is estimated via simulations. The torsional rigidity in the tension-free sp domain(s) (C = 163 fJ fm) is typical of the unstrained DNA and is less than half the value in the main-chain segments under tension (C = 350-410 fJ fm). Tension is suggested to induce a structural transition to a torsionally stiffer state. Data of Koster et al. for the rate of extension owing to unwinding of a covalent complex of DNA with human Topoisomerase Ib (H Topo I) are analyzed to determine the torque and rate of rotation from which an effective friction coefficient is obtained. A Langevin equation for the unwinding motion in a supercoiled DNA:H Topo I complex is solved to obtain the temporal trajectory of the average winding angle and the time-dependent distribution of winding angles. The mean rate constant for the religation reaction is estimated from the measured probability of reaction per turn. We predict that unwinding proceeds rather far during a single-cleavage and religation cycle, and is effectively completely equilibrated during the 3.2 cleavage and religation cycles that occur during each noncovalent binding and dissociation event. H Topo I is predicted to be completely processive as in accord with observations on calf-thymus Topo I (Brewood et al., Biochemistry 2010, 49, 3367-3380).