Internal Motion of Supercolied DNA: Brownian Dynamics Simulations of Site
Juxtaposition
Thermal motions in supercoiled DNA are studied by Brownian dynamics (BD)
simulations with a focus on the site juxtaposition process. It had been
shown in the last decade that BD approach is capable of describing actual
times of large scale DNA motion. The bead model of DNA used here accounts
for bending and torsional elasticity as well as the electrostatic repulsion
among DNA segments. The hydrodynamic interaction among the beads of the
model chain and the aqueous solution is incorporated through the Rotne-Prager
tensor. All simulations were performed for the sodium ion concentration
of 0.01 M. We first showed, to test our BD procedure, that the same distributions
of equilibrium conformational properties are obtained as by Monte Carlo
simulations for the corresponding DNA model. The BD simulations also predict
with accuracy published experimental values of the diffusion coefficients
of supercoiled DNA. To describe the rate of conformational changes, we
also calculated the autocorrelation functions for the writhe and radius
of gyration for the supercoiled molecules. The rate of site juxtaposition
was then studied for DNA molecules up to 3000 bp in length. We find that
site juxtaposition is a very slow process: although accelerated by a factor
of more than 100 by DNA supercoiling, the times of juxtaposition are in
the range of ms even for highly supercoiled DNA, about two orders of magnitude
higher than the relaxation times of writhe and the radius of gyration for
the same molecules. By inspecting successive simulated conformations of
supercoiled DNA, we conclude that slithering of opposing segments of the
interwound superhelix is not an efficient mechanism to accomplish site
juxtaposition, at least for conditions of low salt concentration. Instead,
transient distortions of the interwound superhelix, followed by continuous
reshaping of the molecule, contribute more significantly to site juxtaposition
kinetics.
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