Geometry of the nucleosomal DNA superhelix

Nucleosome stability is largely an indirect measure of DNA sequence based on the material properties of DNA and the ability of a sequence to assume the required left-handed superhelical conformation. Here we focus attention only on the geometry of the superhelix and present two distinct mathematical expressions that rely on the DNA helical parameters (Shift, Slide, Rise, Tilt, Roll, Twist). One representation requires torsion for superhelix formation; the other requires shear. To compare these mathematical expressions to experimental data we develop a strategy for Fourier-filtering the helical parameters that identifies necessary and sufficient conditions to achieve a high-resolution model of the nucleosome superhelix. We apply this filtering strategy to 24 high-resolution structures of the nucleosome and demonstrate that all structures have a highly conserved distribution of Roll, Slide and Twist that involves two length scales. One length scale spans the entire length of nucleosomal DNA. The other is associated with the helix repeat. Our strategy also enables us to identify ground state or simple nucleosomes and altered nucleosome structures. These results form a basis for characterizing structural variations in the emerging family of nucleosome structures and a method for further developing structure-based models of nucleosome stability.