In 3DNA, analyze and rebuild are two sides of the same coin

Recently, I noticed the following two papers:

• "A measure of bending in nucleic acids structures applied to A-tract DNA" by Lankas et al. (2010), Nucleic Acids Res.,38(10), 3414–3422.
• "The chirality of DNA: elasticity cross-terms at base-pair level including A-tracts and the influence of ionic strength" by Noy and Golestanian (2010), J. Phys. Chem. B, 114, 8022–8031.

They both cite 3DNA, where the combined usage of its analyze/rebuild components has played a significant role.

When I first had access to the CEHS scheme, I was immediately attracted by its mathematical rigor which allows for complete reversibility in DNA structural analysis and model rebuilding. Historically, CEHS was the initial seed of the SCHNAaP/SCHNArP programs, and analyze/rebuild in 3DNA were directly derived from them.

Frequently, I think of analyze/rebuild as two sides of the same coin: starting from a nucleic acid structure (e.g., a DNA double helix), the analyze program gives a set of base-pair (propeller, buckle etc) and step (roll, slide etc) parameters. The structural parameters can be used to rebuild the structure, which is virtually identical in base geometry (i.e., without taking consideration of the sugar-phosphate backbone) to the original structure. Conversely, analyzing the rebuilt structure again gives exactly the same set of structural parameters describing the relative base geometry.

Reversibility is essentially a simple concept, nevertheless a very powerful one. Over the years, I am glad to see more people are taking advantage of this 3DNA unique feature in addressing real-world problems related to nucleic acid structures. I am confident to see more such applications.

Get all torsion angles in a nucleic acid structure

In the field of nucleic acid structure analysis, a commonly calculated set of parameters is the torsion angles. Specifically, they include the main chain and chi (χ) torsion angles defined as follows:

• α: O3'(i-1)-P-O5'-C5'
• β: P-O5'-C5'-C4'
• γ: O5'-C5'-C4'-C3'
• δ: C5'-C4'-C3'-O3'
• ε: C4'-C3'-O3'-P(i+1)
• ζ: C3'-O3'-P(i+1)-O5'(i+1)
• χ: for pyrimidines (Y, i.e., T, U, C): O4'-C1'-N1-C2; for purines (R, i.e., A, G): O4'-C1'-N9-C4

A related set of parameters characterizes the sugar conformation:

• ν0: C4'-O4'-C1'-C2'
• ν1: O4'-C1'-C2'-C3'
• ν2: C1'-C2'-C3'-C4'
• ν3: C2'-C3'-C4'-O4'
• ν4: C3'-C4'-O4'-C1'
• tm: amplitude of pseudorotation of the sugar ring
• P: phase angle of pseudorotation of the sugar ring

These torsion angles are clearly defined and are readily available from various informatics programs. Not surprisingly, 3DNA also provides a complete set of DNA/RNA backbone torsions, calculated robustly and efficiently. The key is the "-s" option of find_pair" program, which is nevertheless little used, mostly because it is not the default.

Using the Haloarcula marismortui 50S large ribosomal subunit as an example (1jj2), the output file 1jj2.outs from the following command contains all the above mentioned main chain and sugar conformational parameters:

find_pair -s 1jj2.pdb stdout | analyze

Please see the Jena "Nucleic acid backbone parameters" website for a diagram (based on Saenger's book) defining the various backbone torsion angles.