A stochastic model for helix bending in B-DNA.

Bending in double-helical B-DNA apparently occurs only by rolling adjacent base pairs over one another along their long axes. The lifting apart of ends that would be required by tilt or wedge angle contributions is too costly in free energy and does not occur. Roll angles at base steps can be positive (compression of major groove) or negative (compression of minor groove), with the former somewhat easier. Individual steps may advance or oppose the overall direction of bend, or make lateral excursions, but the result of this series of "random roll" steps is the production of a net bending in the helix axis. Because the natural roll points for bending in a given plane occur every 5 base pairs, one would expect that double-helical DNA wrapped around a nucleosome core would exhibit bends with the same periodicity. Alternate bends might be particularly acute where the major groove faced the nucleosome core and was compressed against it. The "annealed kinking" model proposed by Fratini et al. (J. Biol. Chem. 257, 14686 (1982) was suggested from the observation that a major bend at a natural roll point is flanked by decreasing roll angles at the steps to either side, as though local strain was being minimized by somewhat blurring the bend out rather than keeping it localized. The random walk model suggested in this paper would describe this as a decreased roll angle as the helix step rotates toward a direction perpendicular to the overall bend. Bending of DNA is seen to be a more stochastic process than had been suspected. Detailed analysis of every helix step reveals both side excursions and backward or retrograde motion, as in any random walk situation. Yet these isolated steps counteract one another, to leave behind a residuum of overall bending in a specific direction.