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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