Based on preliminary recommendations made at the Tsukuba Workshop on Nucleic Acid Structure and Interactions held on January 13-14, 1999 at the AIST-NIBHT Structural Biology Centre in Tsukuba, Japan.

1. Cartesian coordinates for A, C, G, T, and U in the optimized reference frame
   Adenine,   Cytosine,   Guanine,   Thymine,   Uracil

   Standard chemical structures taken from Clowney et al. (1996), J. Am. Chem. Soc., 118, 509-518). These data do not include C1' atoms, which are placed here in the least-squares plane of the base atoms, with the purine C1'-N9 bond length and C1'-N9-C4 valence angle set respectively to 1.46 Å and 126.5° and the pyrimidine C1'-N1 bond and C1-N1-C2 angle to 1.47 Å and 118.1°. These distances and angles are based on the average glycosyl geometries of purines and pyrimidines in high resolution crystal structures of nucleic acid analogs from the Cambridge Structure Database (John Westbrook and Helen M. Berman, unpublished data).

2. Schematic representation of base-pair, dimer step and helical parameters

   If a base or base-pair is taken as a rigid block, six parameters are required to describe rigorously the position and orientation of one base-pair relative to another. There are two sets of local parameters commonly in use in nucleic acid conformational analysis: step parameters (Shift, Slide, Rise, Tilt, Roll and Twist) which show the stacking geometry between neighboring base-pairs, and helical parameters (x-displacement, y-displacement, helical rise, inclination, tip, and helical twist) which demonstrate the position and orientation of a base-pair relative to the helical axis, defined here by the repetitive of a two-base-pair unit. These two sets of parameters are obviously interrelated: from one set, the other can be deduced and vice versa. The values of local vs. helical rise and twist from these two sets of parameters can be quite different in DNAs which deviate significantly from B-DNA.

3. Comparative analysis of DNA base-pair parameters in the TATA-box protein-DNA crystal structure (pdt012, Y. Kim, J. H. Geiger, S. Hahn & P. B. Sigler (1993) ``Crystal structure of a yeast TBP/TATA-box complex,'' Nature 365, 512-520.)
   • Starting from the same base reference frame, all methods of analysis give similar numerical values, and show the same sequence-dependent patterns. This similarity holds more for base-pair parameters than for dimer step or helical parameters, since the base-pair reference frame is derived differently by the various methods.
     • List of detailed output from 3DNA (Lu & Olson, in preparation)

     • List of parameters based on seven other analysis schemes as calculated within 3DNA

   • Slight variations in the imposed configurational constraints have a limited and systematic influence on the base reference frame, and thus affect base-pair parameters but do not affect step and helical parameters. More specifically, changing the O^…H-N distance (dO-N) from 3.0 Å to 2.9 Å increases stretch by about 0.1 Å, and changing lambda₀ from 54.5° to 55.5° decreases Opening by about 2°. This is illustrated using the kinked AA/TT (base-pairs 8 and 9) from pdt012 as an example.

4. Average values and dispersion (in parentheses) of base-pair, dimer step, and helical parameters in high resolution A-DNA and B-DNA structures surveyed in this study. These parameters are calculated for different analysis schemes with 3DNA using the newly recommended base reference frame.

5. Intrinsic correlations

   By definition, there are four sets of intrinsic correlations between base-pair parameters and dimer step parameters associated with the current reference frame (illustrated here using pdt012 as an example):

   • Negative correlation between Rise and the difference of Buckle. Since base-pair distortion by buckling is both large and frequent, this correlation is strong and has been known for many years.

   • Negative correlation between Tilt and the difference of Stagger.

   • Positive correlation between Shift and the difference of Opening.

   • Positive correlation between Twist and the difference of Shear.

   Since the variations in Shear, Stagger, Opening, Tilt and Shift are normally small, they are often ignored in DNA conformational analysis. Not surprisingly, the last three correlations have never been previously uncovered. These correlations, however, exist in the original Curves, CompDNA and RNA programs, but not in the original FREEHELIX, CEHS and NUPARM programs, where the base-pair reference frame is defined by the RC8-YC6 line and the base-pair normal vector rather than the "middle-frame" of the two complementary bases. The discrepancy in Twist between heavily sheared base-pairs has been reported in the literature.

   By contrast, Slide and Roll, two of the most important parameters, are much less sensitive to base-pair distortions, and are thus more reliably defined in a comparable way among the currently available analysis programs.