Supplementary Methods

DNA curvature, base pair and base-pair-step parameters, and backbone geometry were calculated with the program Curves1,2. The resulting values are consistent with standard definitions3,4. The program uses two coordinate frames at each base pair to obtain the values reported here. 1) A fixed coordinate frame is rigidly attached to each base pair. 2) A helix coordinate frame is associated with each fixed frame and defines the double helix axis locally. The position and orientation of each helix frame is determined by least squares minimization of two sets of translational and orientational differences: a) the difference in the relationship of a fixed frame and associated helix frame for two successive base pairs, and b) the difference between two successive helix frames. Importantly, this latter restraint favors axis linearity. The DNA form parameters tip, inclination, x-displacement and y-displacement are found from the relationship between fixed and helix frames for a base pair. The base-pair-step parameters roll, tilt, slide and shift are found from the difference in the values of tip, inclination, x-displacement and y- displacement, respectively for the two base pairs in the step plus the appropriate component of the difference in orientation or translation of the two related helix frames. The base-pair-step parameters twist and rise are determined directly from the two succesive helix frames. The twist values reported and labelled “global” by Curves correspond to the laboratory frame of reference5. The twist values reported and labelled “local” by Curves do not correspond to the local frame of reference used in this work.

1. Lavery, R. & Sklenar, H. The Definition of Generalised Helicoidal Parameters and of Axis Curvature for Irregular Nucleic Acids. J. Biomol. Struct. Dynam. 6, 63-91 (1988). 2. Lavery, R. & Sklenar, H. Defining the structure of irregular nucleic acids: conventions and principles. J Biomol Struct Dyn 6, 655-67 (1989). 3. Dickerson, R. E. et al. Definitions and nomenclature of nucleic acid structure parameters. EMBO J. 8, 1-4 (1989). 4. Saenger, W. Principles of Nucleic Acid Structure (Springer Verlag, New York, 1984). 5. Travers, A. A. & Klug, A. The bending of DNA in nucleosomes and its wider implications. Philos Trans R Soc Lond B Biol Sci 317, 537-61 (1987).

1