Dependence of the linking deficiency of supercoiled minichromosomes upon nucleosome distortion

The contribution from each nucleosome to the linking number of minichrosome DNA depends on two factors. These are the wrapping number, omega, which is the number of times the DNA wraps about the axis of the nucleosome; and the winding number, phi, which is the number of base pairs on the nucleosome divided by the helical repeat of the DNA. If the nucleosome is distorted with DNA surface contacts being preserved, phi remains unchanged. The wrapping number may still change, however, depending on the extent of the distortion. For example, if the usual cylindrical shape of the nucleosome is deformed into an ellipsoid while preserving the equatorial radius, then the wrapping number will increase. We apply these concepts to minichromosomes torsionally stressed by supercoiling with, for example, DNA gyrase. We analyze the experimental result that the maximum amount of supercoiling obtained by gyrase treatment of minichromosomes is the same as that of naked DNA. In particular, we show that this phenomenon can be explained by a relatively slight distortion of the nucleosome core while maintaining the surface contacts of the DNA on the core.