Trefoil Knotting Revealed by Molecular Dynamics Simulations of Supercoiled
DNA
Computer simulations of the supercoiling of DNA, largely limited to stochastic
search techniques, can offer important information to complement analytical
models and experimental data. Through association of an energy function,
minimum-energy supercoiled conformations, fluctuations about these states,
an interconversions among forms may be sought. In theory, the observation
of such large-scale conformational changes is possible, but modeling
and numerical considerations limit the picture obtained in
practice. A new computational approach is reported that combines an idealized
elastic energy model, a compact B-spline representation of circular duplex
DNA, and deterministic minimization and molecular dynamics algorithms.
A trefoil knotting result, made possible by a large time-step dynamics
scheme, is described. The simulated strand passage supports and details
a supercoiled-directed knotting mechanism. This process may be associated
with collective bending and twisting motions involved in supercoiling
propagation and interwound branching. The results also demonstrate the
potential effectiveness of the Langevin/implicit-Euler dynamics scheme
for studying biomolecular folding and reactions over biologically interesting
time scales.
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