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   Nucleic acid backbone parameters
   1. Backbone torsion angles
   2. Sugar pucker
   3. Glycosidic bond
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Helix and bending analysis of nucleic acid double helix structures

Nucleic acid backbone parameters


1. Backbone torsion angles

Figure 1. Backbone torsion angles in nucleic acid structures. (Saenger W. 1984. Principles of Nucleic Acid Structure. Springer, New York.)

The torsion angles in the backbone of nucleic acid chains are designated with greek letters (alpha to zeta). Because the torsion angles are correlated, we list only a subset of the torsion angles in the table. The angles selected are most informative for describing the conformation of double helices.

alpha, beta

Alpha is the torsion angle about the P-O5' bond, and beta is about the O5'-C5' bond. Beta is found almost always in the antiperiplanar range (+150° ... +210°).


Gamma is the torsion angle about the C5'-C4' bond. The +synclinal range (+30° ... +90°) is preferred in most duplex structures. In Z-DNA however, syn guanines show gamma in the antiperiplanar range (+150° ... +210°).


Delta is the torsion angle about the C4'-C3' bond. Delta is correlated with the sugar pucker phase angle (see 2. Sugar pucker).

epsilon-zeta (BI/BII conformation of phosphate)

Epsilon is the torsion angle about the C3'-O3' bond, and zeta is about the O3'-P bond. Both angles determine the position of the phosphate with respect to the sugar of the preceding residue. A phosphate can adopt either the BI or the BII conformation. The BI conformation is most often found in double helices. Nevertheless, some phosphate groups swap temporarily into the BII conformation. These residues show a dynamic equilibrium between BI and BII conformation. Sometimes such residues are caught in the BII conformation in time averaged structures as obtained from X-ray crystallography or NMR. The difference (epsilon-zeta) is commonly used to characterize the conformation of the phosphate group. Here we use the following assignment:

 BI:     (epsilon-zeta) = -160° ... +20°
BII:     (epsilon-zeta) =  +20° ... +200°

A phosphate in the BII conformation forces its neighboring phosphates into the BI conformation. Having two neighboring phosphates in the BII conformation at the same time is an extremely rare event.


2. Sugar pucker

Figure 2. Structures for the C2'-endo and C3'-endo conformations of ribose. (Blackburn GM, Gait MJ. 1996. Nucleic acids in chemistry and biology. Oxford University Press.)

The conformation of the ribose ring can be described by only two quantities, sugar pucker phase angle and sugar pucker amplitude. Pucker phase angle and pucker amplitude are calculated from the torsion angles about the five bonds in the ribose ring. The torsion angles in a closed ring are highly correlated.

The differing conformations of the ribose have been named with respect to that ring atom which puckers out of the plane given by the other ring atoms. The most prominent conformations are C2'-endo in B-helices and C3'-endo in A-helices. At room temperature both conformers are in a dynamic equilibrium. Transitions occur via the O4'-endo state. Intermediates between C2'-endo and C3'-endo are found in several (time-averaged) structures obtained from X-ray crystallography or NMR. When changing the pucker phase angle from 0° to 360° we step through all possible conformations of the ribose ring. This pseudo-rotation cycle can be depicted as a conformational wheel (Figure 3).

Table 1. Ranges of the sugar pucker phase angle for all conformations of ribose.

Angle range Name Occurrence
-36° ...
324° ... 360°
... 36°
  C3'-endo  ideal A-helix 
36° ... 72°
72° ... 108°
108° ... 144°
144° ... 180°
  C2'-endo  ideal B-helix 
180° ... 216°
-180° ... -144°
216° ... 252°
-144° ... -108°
252° ... 288°
-108° ... -72°
288° ... 324°
-72° ... -36°
324° ... 360°
-36° ...

Figure 3. Conformational wheel of the sugar pucker pseudo-rotation cycle (Saenger W. 1984. Principles of Nucleic Acid Structure. Springer, New York.)


3. Glycosidic bond

chi  (syn and anti conformation)

Chi is the torsion angle about the N-glycosidic bond between the ribose and purine or pyrimidine base. Rotamers with chi values between -90° and +90° are called syn whereas anti refers to chi values from +90° to +270°. In Watson-Crick double helixes both bases of a base pairs are in anti conformation. Bases in syn conformation indicate a distortion of the double helix due to base pair opening or mismatched base pairs. The syn conformation is also found with guanines in left-handed Z-DNA (zig-zag helix). Calculation of the helical axis with Curves 5.3 fails for technical reasons, if a right-handed double helix contains bases in syn conformation.

Figure 4. Torsional energy profile for rotation about the glycosidic bond in desoxyribocytosine. Energies were calculated with a molecular mechanics force field (Cornell et al. 1995. J Am Chem Soc, 117: 5179-5197.) applying vacuum conditions.

The typical energy profile for rotation about the glycosidic bond of a desoxyribonucleotide in Figure 4. It turns out that the energy minimum of the anti conformation is located at -140° and the minimum of the syn conformation at +30°. In addition, there is a third minimum at -60°. The range between -110° and -60° is termed high anti. The high anti range is often populated in duplex structures.

The glycosidic torsion angle chi is correlated with sugar puckering. High anti is often found with C2'-endo sugars (B-helix), while C3'-endo sugars (A-helix) are associated with more canonical anti values in the range from -150° to -180°.


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Perl script:  (22 Mar 1999)
Author:    Peter Slickers  (,  IMB Jena,  Germany