BUCKLING TRANSITIONS IN SUPERHELICAL DNA - DEPENDENCE ON THE ELASTIC-CONSTANTS AND DNA SIZE

Buckling transitions in superhelical DNA are sudden changes in shape t hat accompany a smooth variation in a key parameter, such as superheli cal density. Here we explore the dependence of these transitions on th e elastic constants for bending and twisting, A and C, important chara cteristics of DNA's bending and twisting persistence lengths. The larg e range we explore extends to other elastic materials with self-contac t interactions, modeled here by a Debye-Huckel electrostatic potential . Our collective description of DNA shapes and energies over a wide ra nge of rho = A/C reveals a dramatic dependence of DNA shape and associ ated configurational transitions on rho: transitions are sharp for lar ge rho but masked for small rho. In particular, at small rho, a nonpla nar circular family emerges, in agreement with Julicher's recent analy tical predictions; a continuum of forms (and associated writhing numbe rs) is also observed. The relevance of these buckling transitions to D NA in solution is examined through studies of size dependence and ther mal effects. Buckling transitions smooth considerably as size increase s, and this can be explained in part by the lower curvature in larger plasmids. This trend suggests that buckling transitions should not be detectable for isolated (i.e., unbound) DNA plasmids of biological int erest, except possibly for very large rho. Buckling phenomena would no netheless be relevant for small DNA loops, particularly for higher val ues of rho, and might have a role in regulatory mechanisms: a small ch ange in superhelical stress could lead to a large configurational chan ge. Writhe distributions as a function of rho, generated by Langevin d ynamics simulations, reveal the importance of thermal fluctuations. Ea ch distribution range (and multipeaked shape) can be interpreted by ou r buckling profiles. Significantly, the distributions for moderate to high superhelical densities are most sensitive to rho, isolating diffe rent distribution patterns. If this effect could be captured experimen tally for small plasmids by currently available imaging techniques, su ch results suggest a slightly different experimental procedure for est imating the torsional stiffness of supercoiled DNA than considered to date. (C) 1997 John Wiley & Sons, Inc.