The sugar puckers in DNA/RNA structures are predominately in either C3′-endo (A-DNA or RNA) or C2′-endo (B-DNA; see Figure below, left), corresponding to the A- or B-form conformation in a duplex. In these two sugar conformations, the distance between neighboring phosphorus (P) atoms and the orientation of P relative to the sugar/bases are also dramatically different (figure below, right).

Recently, I carefully re-read some articles on RNA backbone conformation by Richardson *et al.*, including:

- RNA backbone is rotameric (
*PNAS*2003) - RNA backbone: consensus all-angle conformers and modular string nomenclature (
*RNA*2008) - MolProbity: all-atom structure validation for macromolecular crystallography (
*Acta Crystallogr D Biol Crystallogr.*2010) - PHENIX: a comprehensive Python-based system for macromolecular structure solution (
*Acta Crystallogr D Biol Crystallogr.*2010)

I became intrigued by one of their observations: i.e., the correlation between the sugar pucker and a simple distance parameter:

C3′-endo and C2′-endo sugar puckers are highly correlated to the perpendicular distance between the C1′–N1/9 glycosidic bond vector and the following phosphate: > 2.9 Å for C3′-endo and < 2.9 Å for C2′-endo. (p.16 from the MolProbity paper).

Out of curiosity and for a better understanding of this correlation, I played around with some sample cases both visually and numerically. Overall, this involves a simple geometric calculation, i.e., the shortest distance from a point to a line in three-dimensional space. Given below is the Octave/Matlab script for calculating the distances for G175 and U176 of PDB entry 1jj2 (the large ribosomal subunit of *Haloarcula marismortui*):

`function d = get_p3_nc_dist(P3, C1, N) C1_N = N - C1; # vector from C1′ to N nv_C1_N = C1_N / norm(C1_N); # normalized vector C1_P3 = P3 - C1; # vector from C1′ to P3 proj = dot(C1_P3, nv_C1_N); d = norm(C1_P3 - proj * nv_C1_N); end`

`## G175 P3 = [70.104 112.366 44.586]; C1 = [73.017 109.666 45.304]; N9 = [74.445 109.380 45.288]; d1 = get_p3_nc_dist(P3, C1, N9) # 2.2 Å -- C2′-endo`

`## U176 P3 = [66.871 116.402 46.804]; C1 = [68.213 112.454 49.279]; N1 = [69.678 112.480 49.438]; d2 = get_p3_nc_dist(P3, C1, N1) # 4.6 Å -- C3′-endo`

The GpU dinucleotide used in the above example forms a platform (see figure below), where the sugar of G175 adopts a C2′-endo conformation, and that of U176 C3′-endo. Indeed, the distance for G175 is 2.2 Å (< 2.9 Å); whilst the value for U176 is 4.6 Å (> 2.9 Å).

Note that the Richardson *et al.* articles focus on the RNA backbone, *without* paying attention to the base (pair) geometry. The 3DNA Zp parameter, which is the mean *z*-coordinate of the two P atoms in the mean reference frame of a dinucleotide step (see figure below), has been readily adapted to single-stranded RNA structures. For example, the vertical distances of the 3′ P atoms to the G175 and U176 base planes are 1.9 Å and 4.4 Å, respectively. Since *base plane*s and the *P* atoms are the two most accurately located entities in a given nucleic acid structure, the nucleotide-based Zp variant is presumably more robust and discriminative than the distance from P to the glycosidic bond.

This new single-stranded based “Zp” parameter is available as of 3DNA v2.1.