Calculation of the chi (χ) torsion angle of pseudouridines in RNA structures

In RNA structures, chi (χ) is defined as the torsion angle about the N-glycosidic bond between the ribose sugar and the canonical A/C/G/U bases or their modified variants. Specifically, for pyrimidines (C and U), χ is defined by O4'-C1'-N1-C2; and for purines (A and G) by O4'-C1'-N9-C4. See the following figure from the IMB Jena Image Library:



Pseudouridine (5-ribosyluracil, PSU) was the first identified modified nucleoside in RNA and is the most abundant. PSU is unique in that it has a C-glycosidic bond instead of the N-glycosidic bond common to all other nucleosides, canonical or modified. It thus poses a problem as to how to calculate the χ torsion angle: should it be O4'-C1'-C5-C4 reflecting the actual glycosidic bond connection, or should the conventional definition O4'-C1'-N1-C2 still be applied literally? As a concrete example, the figure below shows the (slightly) different numerical values, as given by the two definitions, for PSU 6 on chain A of PDB/NDB entry 3cgp/ar0093.


Needless to say, definition of the χ torsion angle of PSU in RNA structures is a very subtle/minor point, and I am not aware of any discussion on this issue in literature (I'd appreciate your sharing of related information in the comment). In 3DNA, PSU is identified explicitly, and χ is defined by O4'-C1'-C5-C4. In NDB and a couple of other tools (I've played with), χ for PSU is defined by O4'-C1'-N1-C2. Again using 3cgp/ar0093 (figure above) as an example, 3DNA gives -162.7°, whilst NDB gives -163.9°. Hopefully, this post will help clarify a confusion for those who care about such little details.