ON HIGHER BUCKLING TRANSITIONS IN SUPERCOILED DNA

A combination of detailed energy minimization and molecular dynamics s tudies of closed circular DNA offers here new information that may be relevant to the dynamics of short DNA chains and/or low superhelical d ensities. We find a complex dependence of supercoiled DNA energies and geometries on the linking number difference Delta Lk as physiological superhelical densities (\sigma\ similar to 0.06) are approached. The energy minimization results confirm and extend predictions of classica l elasticity theory for the equilibria of elastic rods. The molecular dynamics results suggest how these findings may affect the dynamics of super-coiled DNA. The minimization reveals sudden higher order config urational transitions in addition to the well-known catastrophic buckl ing from the circle to the figure-8. The competition among the bending , twisting, and self-contact forces leads to different families of sup ercoiled forms. Some of those families begin with configurations of ne ar-zero twist. This offers the intriguing possibility that nicked DNA may relax to low-twist forms other than the circle, as generally assum ed. Furthermore, for certain values of Delta Lk, more than one interwo und DNA minimum exists. The writhing number as a function of Delta Lk is discontinuous in some ranges; it exhibits pronounced jumps as Delta Lk is increased from zero, and it appears to level off to a character istic slope only at higher values of Delta Lk. These findings suggest that supercoiled DNA may undergo systematic rapid interconversions bet ween different minima that are both close in energy and geometry. Our molecular dynamics simulations reveal such transitional behavior. We o bserve the macroscopic bending and twisting fluctuations of interwound forms about the global helix axis as well as the end-over-end tumblin g of the DNA as a rigid body. The overall mobility can be related to \ sigma\ and to the bending, twisting, and van der Waals energy fluctuat ions. The general character of molecular motions is thus determined by the types of energy minima found at a given Delta Lk. Different time scales may be attributed to each type of motion: The overall chain fol ding occurs on a time scale almost an order of magnitude faster than t he 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 an d straightening motion of the DNA. (C) 1994 John Wiley and Sons, Inc.