On Higher Buckling Transitions in Supercoiled DNA
A combination of detailed energy minimization and molecular dynamics studies
of closed circular DNA offers here new information that may be relevant
to the dynamics of short DNA chains and/or low superhelical densities.
We find a complex dependence of supercoiled DNA energies and geometries
on the linking number difference Lk
as physiological superhelical densities (||
~ 0.06) are approached. The energy minimization results confirm and extend
predictions of classical elasticity theory for the equilibria of elastic
rods. The molecular dynamics results suggest how these findings may affect
the dynamics of supercoiled DNA.
The minimization reveals sudden higher order configurational transitions
in addition to the well known catastrophic buckling from the circle to
the figure-8. The competition among the bending, twisting, and self-contact
forces leads to different families of supercoiled forms. Some of those
families begin with configurations of near zero-twist. This offers the
intriguing possibility that nicked DNA may relax to low twist forms other
than the circle, as generally assumed. Furthermore, for certain values
of Lk, more than one interwound
DNA minimum exists. The writhing number as a function of Lk
is discontinuous in some ranges; it exhibits pronounced jumps as Lk
is increased from zero, and it appears to level off to a characteristic
slope only at higher values of Lk,
These findings suggest that supercoiled DNA may undergo systematic rapid
interconversions between different minima that are both close in energy
and geometry.
Our molecular dynamics simulations reveal such transitional behavior. We
observe the macroscopic bending and twisting fluctuations of interwound
forms about the global helix axis as well as the end-over-end tumbling
of the DNA as a rigid body. The overall mobility can be related to ||
and to the bending, twisting and van der Waals energy fluctuations. The
general character of molecular motions is thus determined by the
types of energy minima found at a given Lk.
Different time scales may be attributed to each type of motion:
the overall chain folding occurs on a time scale almost an order of magnitude
faster than the end-over-end tumbling. The local bending and twisting of
individual chain residues occur at an even faster rate. which in turn correspond
to several cycles of local variations for each large-scale bending and
straightening motion of the DNA.
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