{title2=$\chi$}

In a <nucleoside> or <nucleotide>, the \b[glycosidic torsion angle] $\chi$ describes rotation of the <nucleobase> relative to the sugar about their N-glycosidic bond. It is a signed <dihedral angle> defined by four ordered atoms:
$$
\begin{aligned}
\chi_{\mathrm{purine}}&=\operatorname{dih}(\mathrm{O4'},\mathrm{C1'},\mathrm{N9},\mathrm{C4}),\\
\chi_{\mathrm{pyrimidine}}&=\operatorname{dih}(\mathrm{O4'},\mathrm{C1'},\mathrm{N1},\mathrm{C2}).
\end{aligned}
$$
The middle two atoms specify the <glycosidic bond>; the outer atoms define the two reference planes. Thus the atom sequence, not the symbol $\chi$ alone, fixes the angle convention.<Abbreviations and Symbols for the Description of Conformations of Polynucleotide Chains>[Section2.3, N-Glycosidic Bond]{ref}

The recommended broad regions are <syn glycosidic conformation>, centered at $0^\circ$ with a90degree range on either side, and <anti glycosidic conformation>, centered at $180^\circ$ with the corresponding range. For example, $\chi=60^\circ$ lies in the syn region and $\chi=-160^\circ$ in the anti region. These describe base–sugar orientation; they do not by themselves specify sugar-ring shape or the complete <RNA> conformation.<Abbreviations and Symbols for the Description of Conformations of Polynucleotide Chains>[Section2.3, notes(a)–(c), syn and anti conventions]{ref}

An original angular comparison illustrates periodicity. Measurements of $179^\circ$ and $-179^\circ$ differ by only2degrees around the circle, not358degrees. A signed shortest difference can be calculated as
$$
\Delta\chi=\operatorname{atan2}\!\bigl(\sin(\chi_2-\chi_1),\cos(\chi_2-\chi_1)\bigr),
$$
using radians inside the trigonometric functions. Interpreting the two near-boundary values as distant conformations would be an artifact of the angle's reporting interval.

The convention is important when comparing structural models or older literature. Alternative choices using C8 for a <purine> or C6 for a <pyrimidine> can shift the numerical angle by approximately180degrees. Numerical torsions should therefore be compared only after checking their defining atoms.<Abbreviations and Symbols for the Description of Conformations of Polynucleotide Chains>[Section2.3, note(b), old and new chi definitions]{ref}


 Glycosidic torsion angle (source code)