KINETICS OF DNA SUPERCOILING STUDIED BY BROWNIAN DYNAMICS SIMULATION

We have developed a model for the simulation of the structure and dynamics of covalently closed circular DNA. It is based on the generalization of the original Brownian dynamics algorithm [D. L. Ermak & J. A. McCammon (1978) Journal of Chemical Physics, Vol. 69, pp. 1352-1359; M. Fixman (1978) Journal of Chemical Physics, Vol. 69, pp. 1527-1537] developed for bead-chain models of linear DNA to a second order numerical integration [A. Iniesta & J. Garcia de la Torre (1990) Journal of Chemical Physics, Vol. 92, pp. 2015-2018], which we extended here to accommodate the torsional potential. The topological constraints and torsional-bending coupling in superhelical DNA are explicitly taken into account in this work by adapting a model for torsional-bending motion of linear DNA developed by Allison et al. [S. A. Allison, R. Austin, & M. Hogan (1989) Journal of Chemical Physics, Vol. 90, pp. 3843-3854]. The dynamics of closed DNAs of 1124 base pairs (380 nm in length) were simulated up to congruent to 40 mu s for linking number differences Delta Lk between 0 and -6. Each bead in the model corresponded to 37 base pairs. For -2 congruent to Delta Lk congruent to -6, the writhing number appears to decay to a limiting negative value with a single exponential law, and the relaxation time of this decay, starting from a planar closed molecule, is 3-6 mu s. For the trajectories studied here, the formation of the superhelix proceeds through an initial phase of 1-2 mu s where a toroidal-iike structure is formed, which then converts into an interwound structure starting from a random nucleation site. For one simulation at Delta LK = -6, a branched structure was observed that did not convert into the linear interwound form for the time course of the simulation (31 mu s). A verification of the simulation was performed by computing the diffusion coefficient of the 1124 base pair circle through known hydrodynamic formulas or through the center of mass displacement, and comparing these theoretical values with diffusion coefficients previously measured by dynamic light scattering. (C) 1994 John Wiley & Sons, Inc.