Glycosidic torsion angle ($\chi$)

In a nucleoside or nucleotide, the 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: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.^[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.^[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 asusing 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.^[ref]

An anti glycosidic conformation is a base–sugar orientation in the anti region of the glycosidic torsion angle $\chi$. Under the IUPAC-IUB atom convention, this region is centered at $180^{\circ }$ and extends90degrees on either side. Equivalently, for an angle reported in $[0^{\circ },360^{\circ })$, the broad anti region lies between90 and270degrees.^[ref]

For a purine nucleoside, $\chi$ uses O4′–C1′–N9–C4; for a pyrimidine, it uses O4′–C1′–N1–C2. The ordered atoms specify the dihedral angle. An angle reported using different outer atoms cannot be assigned to this region by its numerical value alone.^[ref]

For an original example, $\chi =-160^{\circ }$ and $\chi =200^{\circ }$ describe the same orientation modulo one full turn, and both are anti. Moving to $\chi =60^{\circ }$ changes the orientation into the syn glycosidic conformation region while retaining the base–sugar bond connectivity. Conformational change and a change in covalent constitution are different descriptions.

The word anti here does not describe how two bases pair with one another. RNA base-pair geometry can separately classify the relative orientations of two glycosidic bonds. Nor does a single anti torsion determine the entire nucleotide or RNA structure: sugar geometry and the other backbone angles remain to be specified.

A syn glycosidic conformation is a base–sugar orientation in the syn region of the glycosidic torsion angle $\chi$. In the IUPAC-IUB convention the region is centered at $0^{\circ }$ and spans90degrees on either side. In a nonnegative360degree reporting interval, this region crosses the boundary: angles near both0 and360degrees belong to it.^[ref]

For an original example, $\chi =30^{\circ }$ and $\chi =330^{\circ }$ are both syn, because330degrees is equivalent to−30degrees. Their shortest angular separation is60degrees. Their ordinary arithmetic mean,180degrees, falls in the anti glycosidic conformation region and is therefore misleading as a mean orientation. Averaging their unit-circle vectors instead giveswhich points toward $\chi =0^{\circ }$.

The numerical convention is essential. Older choices using the base atom C8 for purines or C6 for pyrimidines can differ from the recommended glycosidic torsion angle by approximately180degrees. Comparing the same number under those two definitions could therefore appear to reverse a syn/anti assignment without any molecular motion.^[ref]

Syn is a local conformational descriptor. It is neither a statement that two bases are paired nor a label for the overall handedness of a nucleic-acid helix. Structural comparisons should retain the defining atoms and angle convention alongside the syn/anti label.