COMPARISON OF ANALYTICAL THEORY WITH BROWNIAN DYNAMICS SIMULATIONS FOR SMALL LINEAR AND CIRCULAR DNAS

An approximate analytical theory is constructed for the optical anisot ropy of a circular weakly bending filament. It is argued that such cir cles exhibit very nearly dynamical mean local cylindrical symmetry, de spite their inherent curvature. This theory and the corresponding appr oximate analytical theory for weakly bending rods are tested by fittin g each theory to the results of Brownian dynamics simulations, in whic h all of the relevant forces are included. A rigorous derivation is pr esented for the force arising from the torsion potential, which couple s torsional strain to writhing and crankshaft motions, and a new more convenient expression is obtained. Simulations of equilibrium trajecto ries performed with and without this force show that it has no signifi cant effect on the optical anisotropy of either circular or linear fil aments with parameters appropriate for DNA. However, when large net to rsional strains are introduced into planar circles, this force enormou sly enhances the rate at which twist is converted into writhe during t he subsequent nonequilibrium trajectories (Chirico, G.; Langowski, J. Biopolymers 1994, 34, 415-433). The analytical theories give good fits to the simulated anisotropies, and the ratios of best-fit torsion con stants to the input values are relatively close to 1.0. These ratios a re tabulated as correction factors to be applied to best-fit torsion c onstants obtained by fitting experimental anisotropy data.