Dynamics and structures of linear and supercoiled DNAs

Abstract

A normal mode theory is developed for the Brownian dynamics of weakly bending rods with preaveraged hydrodynamic interactions. An expression is given for the mean squared angular displacement $$ of the $m\sp{th}$ bond-vector around the instantaneous x-axis (perpendicular to the end-to-end vector z). The normal mode theory is compared with Brownian dynamics simulations for the same model by examining $3 $ for the central bond vector of rods comprising 10 and 30 subunits with various persistence lengths.Rapidly relaxing components in the decay of the transient electric dichroism of DNA restriction fragments reported by Diekmann et al. (Diekmann et al., 1982) and Porschke (Porschke et al., 1987) are analyzed using the new normal mode theory for weakly bending rods and assigned to bending. The longest bending relaxation times for fragments with 95 to 250 base-pairs coincide with theoretical curve calculated for a dynamic bending rigidity corresponding to a dynamic persistence length $P\sb{d}$ = 2100 A.Autocorrelation functions of the light field scattered by weakly bending rods with various persistence lengths are simulated using the normal mode analysis. $D\sb{app}(K)$ could be extracted from these autocorrelation functions and could be used to fit DLS (Dynamic Light Scattering) experimental data.Samples of pUC8 dimer (5434 base-pairs) with different superhelix densities are prepared by the action of Topoisomerase I in the presence of various amounts of ethidium. The translational diffusion coefficient $(D\sb{0})$ and the plateau diffusion coefficient $(D\sb{plat})$ characterizing internal motions over short distances (225 A) are determined by dynamic light scattering. The torsion constant ($\alpha$) between base-pairs is determined by time-resolved fluorescence polarization anisotropy. Circular dichroism spectra are also measured for each sample. These data are consistent with the hypothesis that supercoiling induces two successive allosteric transitions to alternate global secondary structures.Interactions of supercoiled and linear DNAs with EcoRI endonuclease, and dye molecules have been studied with DLS experiments. Results of these experiments have been useful in understanding the mechanisms of these reactions.