How shear affects twist angle of a dinucleotide step?

A recent post in the 3DNA forum, titled "NUPARM vs X3DNA twist values", made me to rethink the issue of how or why shear affects twist angle of a dinucleotide step.

To me, this problem has long been solved as demonstrated by the following two well-cited publications:

1. The Tsukuba report, a.k.a., "A Standard Reference Frame for the Description of Nucleic Acid Base-pair Geometry". When Dr. Olson and I were drafting this report, I felt clearly the need to caution the community of the intrinsic correlations between base-pair parameters and the associated step parameters (Figure 3 there) to avoid possible mis-interpretations in structural analysis. This is specially the case for the effect of shear on twist, since the G–U wobble base-pair is common in RNA and it has a ~2.0 A shear.


2. The 3DNA 2003 NAR paper. There is a subsection on the "Treatment of non-Watson–Crick base pairing motifs", and Figure 3 addressed specially on the issue:

   "Large Shear of the G–U wobble base pair influences the calculated but not the ‘observed’ Twist. The 3DNA numerical values of Twist, 20° (top) and 43° (bottom), differ from the visualization of nearly equivalent Twist suggested by the angle between successive C1'···C1' vectors (finely dotted lines)."

It was thus a bit surprising that such question still popping up. On second thought, however, it is quite understandable: one cannot expect everyone to read that two papers; not to mention remembering such details. So I am glad that this question was brought up to my attention, and it made me thinking possible ways to document more thoroughly the many 3DNA-related "technical details" that are crucial for better understanding of nucleic acid structures.

Coming back to the shear on twist angle issue, the figure at the left shows a G–U wobble pair example (top), and a simple rationale: the base-pair is approximately of 10Å-by-5Å (as defined in SCHNArP/3DNA), so a 2Å shift will lead to an angle:

atan2(2, 10) * 180 / pi = 11.3 degrees

(i.e., the red dotted line relative to the bottom horizontal line).

To a first order approximation, that is the difference between RC8–YC6 (or C1'–C1') vs. the base-centered mean y-axis of the pair for calculating twist angle. So whenever one has a G–U wobble pair next to a normal Watson-Crick pair, there would be ~11 degrees difference in "calculated" twist angle between the two approaches (NewHelix/CEHS/SCHNAaP/NUPARM vs 3DNA/Curve+). Moreover, when a G–U wobble is next to a U–G wobble pair, the difference would be doubled to ~23 degrees!

It is worth mentioning that the issue here (as in other similar cases) is not which number is "correct" or which is "wrong": a number is a number. It is its interpretation that matters, and it is here that "details" do count.