X3DNA-DSSR: a resource for structural bioinformatics of nucleic acids
(An NIGMS National Resource supported by NIH grant R24GM153869)

Recently, I came across the so-called Calcutta U-U base pair (bp) [see figure below] while reading articles on C-H…O contacts in nucleic acid structures. Not familiar with this named pair before, I was curious to find out what it’s about. After some searching, I traced the origin of the Calcutta U-U bp to the following two papers published by Sundaralingam’s group during the middle 1990s:

• Wahl et al. (1996). The structure of r(UUCGCG) has a 5’-UU-overhang exhibiting Hoogsteen-like trans UU base pairs. Nat. Struct. Biol., 3(1), 24-31. In Note added in proof, the author wrote:

We have called the novel U•U base pair, where the Hoogsteen face of one of the pyrimidines is involved in a C5-H—O4 hydrogen bond, the ‘Calcutta Base Pair’, since it was announced at the International Seminar-cum-School on Macromolecular Crystallographic Data held in Calcutta, November 16-20, 1995.

• Wahl & Sundaralingam (1997). C-H…O hydrogen bonding in biology. Trends Biochem Sci., 22(3), 97-102. In this review article, the authors noted:

We recently discovered a novel U•U base pair, referred to as the Calcutta base pair, in the crystal structure of an RNA hexamer UUCGCG (Ref. 18). The two uracil bases form a conventional N(3)-H…O(4) and an unconventional C(5)-H…O(2) hydrogen bond (Fig. 3a). The C-H…O interaction is entirely ‘voluntary’ and not ‘forced’, underlining its importance in base mispairing.

3DNA has no problem to identify the Calcutta U-U bps (or any pair for that matter); an example is shown below based on the RNA hexamer UUCGCG structure (PDB entry: 1osu) solved by Sundaralingam and colleagues.

In the new 3DNA component I’ve been working on (and to be released soon), the Calcutta U-U pair is characterized as below:

1/A.U1 3/A.U2 [U-U] Calcutta 00-n/a tHW -MW
  anti C3'-endo 8.9 --- anti C3'-endo 30.3
  dcc=11.18  dnn=8.48  dmm=7.58  tor=-174.1
  H-bonds[2]: "O4(carbonyl)-N3(imino)[2.76]; C5-O4(carbonyl)[3.27]"

  Shear=-3.67   Stretch=-0.52     Stagger=-0.89
  Buckle=-1.41  Propeller=-16.03  Opening=-90.67

The Calcutta pair is explicitly named, along with other named base pairs (e.g., Watson-Crick [WC], Wobble, and Hoogsteen bps). It is classified as type tHW (trans with Hoogsteen/WC interacting edges), following the commonly used Leontis-Westhof nomenclature. It does not belong to any of the 28 bps (00-n/a) with at least two conventional H-bonds, as categorized by Saenger. In 3DNA, the Calcutta U-U pair is of M-N type, designated as -MW.

Among the well-known named base pairs, some are after the scientists who discovered them (e.g., WC and Hoogsteen bps), while others are based on chemical/geometrical features (e.g., Wobble and Sheared G-A bps), or a combination of both (e.g., reversed WC/Hoogsteen bps). The Calcutta U-U pair is unique in that it is named after a place in India:

Kolkata, or Calcutta, is the capital of the Indian state of West Bengal. … While the city’s name has always been pronounced Kolkata or Kolikata in Bengali, the anglicized form Calcutta was the official name until 2001, when it was changed to Kolkata in order to match Bengali pronunciation.

Prior to v2.1, 3DNA does not provide any direct support for the analysis of molecular dynamics (MD) simulations trajectories of nucleic acid structures. Nevertheless, over the years, I noticed some significant applications of 3DNA in the active MD field; see my blog post (December 6, 2009) titled 3DNA in the PCCP nucleic acid simulations themed issue. In January 2011, I released a set of two Ruby scripts specifically aimed to facilitate the analysis of MD simulations trajectories. Thereafter (as of 3DNA v2.1), I have significantly refined and expanded the Ruby scripts, and consolidated the functionality under one umbrella, x3dna_ensemble with multiple sub-commands (analyze, block_image, extract, and reorient). I believe x3dna_ensemble would make it straightforward to analyze ensembles (NMR or MD simulations trajectories) of nucleic acid structures.

Under this background, I am glad to read recently an article titled Structure, Stiffness and Substates of the Dickerson-Drew Dodecamer in J. Chem. Theory Comput. where 3DNA was used extensively. This work represents a re-visit of the classic Dickerson−Drew B-DNA dodecamer d-[CGCGAATTCGCG]2 using state-of-the-art MD simulations with different ionic conditions and solvation models, and compares the MD trajectories with modern crystallographic and NMR data. Among the author list (Tomas Drsata, Alberto Perez, Modesto Orozco, Alexandre Morozov, Jiri Sponer, and Filip Lankas) are some well-known figures in the MD field of nucleic acid structures.

Reading through the text, I am not sure if the newly available functionality of x3dna_ensemble was used. From the excerpts of the citations given below, however, it seems obvious that 3DNA is now well-accepted by the MD community.

Snapshots taken in 10 ps intervals were analyzed using the 3DNA program.43 From 3DNA outputs, time series of conformational parameters were extracted. These included the intra-base-pair coordinates (buckle, propeller, opening, shear, stretch, and stagger), inter-base-pair or step coordinates (tilt, roll, twist, shift, slide, and rise) as well as groove widths (based on P−P distances), backbone torsions, and sugar puckers.

Contrary to the original work of Lankas et al.,31 the intra-base-pair and step coordinates used here are those defined by 3DNA.43

Here, we apply this model together with the 3DNA definitions of the intra-base-pair and step coordinates.43

However, important differences remain, and non- negligible differences are in fact observed between individual experimental structures also in the central part of DD, even though the intra-base-pair and step coordinates are computed using the same coordinate definitions64 (we consistently use the 3DNA coordinates in this work).

In the field of nucleic acid structures, especially in the ‘RNA world’, we often hear named base pairs (bp). Among those, the Watson-Crick (WC) A–U and G–C bps (see figure below) are by far the most common.

Reversed WC (rWC) base pairs

Closely related to the WC bps are the so-called reversed WC (rWC) bps, where the relative glycosidic bond are reversed; instead of being on the same side of the bases as in WC bps shown above, they are now on opposite sides in rWC bps as shown below. According to the Leontis-Westhof (LW) bp classification scheme, the rWC bps belong to trans WC/WC. Following Saenger’s numbering, the rWC A+U bp corresponds to XXI, and the rWC G+C bp XXII.

In the figures below, the name of each type of bp and its LW & Saenger designations (separated by ‘;’) are noted under the corresponding image. All images are generated with 3DNA; for easy comparison, each bp is oriented in the reference frame of the leading base.

Reversed WC A+U pair	Reversed WC G+C pair
trans WC/WC; XXI	trans WC/WC; XXII

Hoogsteen and reversed Hoogsteen base pairs

The next most famous one is the Hoogsteen A+U bp, which also has a reverse variant, i.e., the rHoogsteen A–U bp (see figure below). Now the major groove edge of A, termed the Hoogsteen edge by LW, is used for pairing with U.

Hoogsteen A+U pair	Reversed Hoogsteen A–U pair
cis Hoogsteen/WC; XXIII	trans Hoogsteen/WC; XXIV

The G–U Wobble base pair

First proposed by Crick in 1966 to account for the degeneracy in codon–anticodon pairing, the Wobble bp is an essential component (in addition to the WC bps) in forming double helical RNA secondary structures.

Wobble G–U pair

cis WC/WC; XXVIII

The sheared G–A base pair

Sheared G–A is a commonly found non-WC bp in both DNA and RNA structures. Noticeably, tandem sheared G–A bps introduce distinct stacking geometry. Here G uses its minor groove edge, termed the sugar edge by LW, to pair with the Hoogsteen edge of A.

Sheared G–A pair

trans Suger/Hoogsteen; XI

Dinucleotide platforms

Dinucleotide platforms are formed via side-by-side pairing of adjacent bases; the most common of which are GpU and ApA. Here the sugar (minor-groove) edge of the 5′ base interacts with the Hoogsteen (major-groove) edge of the 3′ base. Since there is only one base-base H-bond in dinucleotide platforms, no Saenger classification is available. In 3DNA output, the GpU dinucleotide platform is designated as G+U, and ApA as A+A.

GpU dinucleotide platform	ApA dinucleotide platform
cis Sugar/Hoogsteen; n/a	cis Sugar/Hoogsteen; n/a

Other named base pairs

There exist other named bps in RNA literature, e.g., G⋅A imino, A⋅C reverse Hoogsteen, G⋅U reverse Wobble etc. In the my experience, they are (much) less commonly used than the ones illustrated above.

Glycosidic bond “is a type of covalent bond that joins a carbohydrate (sugar) molecule to another group, which may or may not be another carbohydrate.” In nucleic acid structures, the other group is a nucleobase, and the predominated type is the N-glycosidic bond where the purine (A/G) N9 or pyrimidine (C/T/U) N1 atom connects to the C1′ atom of the five-membered (deoxy) ribose sugar ring. Another well-known type is the C-glycosidic bond in pseudouridine, the most common modified base in RNA structures where the C5 atom instead of N1 is linked to the C1′ atom of the sugar ring.

Recently, I performed a survey of all nucleic-acid-containing structures in the PDB/NDB database to see how many types of glycosidic bond are there. As always, I noticed some inconsistencies in the data: nucleotides with disconnected base/sugar, a base labeled as U but with pseudoU-type C-glycosidic bond. Shown below are a few unusual types of glycosidic bond in otherwise seemingly “normal” structures:

• The residue GN7 (number 28 on chain A) in PDB entry 1gn7 contains a N7-glycosylated guanine.

• The residue UPG (number 501 on chain A) in PDB entry 1y6f has sugar C1C (instead of C1′) atom connects to N1 of U.

• The residue XAE (number 11 on chain B) in PDB entry 2icz contains a benzo-homologous adenine.

• The residue F5H (number 206 on chain B) in PDB entry 3v06 has N1 of U connects to C2′ of a six-membered sugar ring.

The unusual glycosidic bond has implications in 3DNA calculated parameters, for example the chi torsion angle. Identifying such cases would help refine 3DNA to provide sensible parameters and to avoid possible misinterpretations.

As of today (2012-09-16), the number of 3DNA forum registrations has reached 500! A quick browse of the ‘Statistics Center’ shows that over 80% of the registrations (400+) are after March 2012, when the new 3DNA homepage/forum were launched.

The sharp increase in registration is mostly due to the streamlined, web-based way to distribute the 3DNA software package. As far as I know, the number of 3DNA registrations/downloads in the past six months is significantly higher than that of 3DNA v2.0 for over three years. Equally importantly, I have been able to fixed every reported bug, addressed each feature request, and updated the 3DNA v2.1 distribution promptly.

I also feel confident to declare that up to now, the 3DNA Forum is spam free (at least to the extent I am aware). To this end, I’ve taken the following three measures:

• Installation of the SMF “Mod Stop Spammer”; as of this writing, it shows “3920 Spammers blocked up until today”.
• By using 3DNA-related verification questions. At its current setting, a user must answer correctly three of the ‘simple’ yet effective verification questions. Early on, I decided deliberately not to use CAPTCHA as an anti-spam means, based on my past experience.
• I’ve continuously monitored (new) registrations, and taken immediate actions against any suspicious registration. Due to the effectiveness of above two steps, so far I only have to manually handle just a few spam registrations. Nevertheless, it does illustrate the fact that no automatic method is perfect, and expert inspection is required to ensure desired results.

Overall, the new simplified way to distribute the 3DNA software package is working as intended; now users can easily access all distributed versions of 3DNA, and I can focus on support and further development of the software.

From v1.5 or even earlier on, 3DNA provides an automatic classification of a dinucleotide step into A-, B- or TA-DNA conformation. Figure 5 of the 2003 3DNA Nucleic Acids Research paper (NAR03) shows three sets of scatter plots — helical inclination and x‐displacement, dimer step Roll and Slide, and the projected phosphorus z coordinates Zp and Zp(h) — to differentiate the A-, B- and TA-DNA dinucleotide steps.

Among the criteria tested, the most discriminative ones are the projected phosphorus z coordinates, Zp in the middle step frame (see figure below), and Zp(h) defined similarly but in the middle helical frame.

Over the years, I have received many questions regarding the datasets used in generating Figure 5 of NAR03. Back in August 2006, a user asked for IDs of the TA-DNA structures — see DNA standards/statistics using 3DNA. In April 2007, another user requested the same TA-DNA dataset. Early this year, a user asked for 3DNA’s A-DNA definition. More recently, yet another user would like to ask about the DNA set used for the analysis that is presented in Fig 5. in the NAR 2003 paper.

I am glad to see that after nearly a decade of the NAR03 publication, the user community is still interested in knowing details in the work. So I decided to dig into my archive for the original data files and scripts used to generate Figure 5 of NAR03. It was not an easy journey; just releasing the data files and scripts is not enough, I’d like to verify that they work together as intended in today’s computing environment. Luckily, I am finally able to get to the bottom of the issues. The details are in the post Datasets and scripts for reproducing Figure 5 of the 3DNA NAR03 paper. The tarball file named 3DNA-NAR03-Fig5.tar.gz is available by clicking the link.

As noted in post Rectangular block expressed in MDL molfile format, I added the -mol option (in v2.1) to convert 3DNA’s native alchemy to the better-supported MDL molfile format, to make the characteristic schematic representations more widely accessible. Along the line, I have recently further augmented alc2img with the -pdb option to transform alchemy to the PDB format.

While the macromolecular PDB format is certainly not convenient for specifying linkage details of small molecules, it’s nevertheless the best-documented and by far the most widely supported than molfile or alchemy in currently available molecular viewers. For example, the PDB format is consistently supported in Jmol, PyMOL, RasMol, DeepView, and UCSF Chimera. Moreover, the PDB format does have the CONECT section to provide information on atomic connectivity:

The CONECT records specify connectivity between atoms for which coordinates are supplied. The connectivity is described using the atom serial number as shown in the entry. CONECT records are mandatory for HET groups (excluding water) and for other bonds not specified in the standard residue connectivity table.

The alc2img -pdb option takes advantage of the CONECT records and specifies all ‘bond’ linkages explicitly. The usage is very simple — take the standard base-pair rectangular block file (‘Block_BP.alc’) as an example, the conversion can be performed as below:

alc2img -pdb Block_BP.alc Block_BP.pdb

Content of ‘Block_BP.alc’

   12 ATOMS,    12 BONDS
    1 N      -2.2500   5.0000   0.2500
    2 N      -2.2500  -5.0000   0.2500
    3 N      -2.2500  -5.0000  -0.2500
    4 N      -2.2500   5.0000  -0.2500
    5 C       2.2500   5.0000   0.2500
    6 C       2.2500  -5.0000   0.2500
    7 C       2.2500  -5.0000  -0.2500
    8 C       2.2500   5.0000  -0.2500
    9 C      -2.2500   5.0000   0.2500
   10 C      -2.2500  -5.0000   0.2500
   11 C      -2.2500  -5.0000  -0.2500
   12 C      -2.2500   5.0000  -0.2500
    1     1     2
    2     2     3
    3     3     4
    4     4     1
    5     5     6
    6     6     7
    7     7     8
    8     5     8
    9     9     5
   10    10     6
   11    11     7
   12    12     8

Content of ‘Block_BP.pdb’

REMARK    3DNA v2.1 (c) 2012 Dr. Xiang-Jun Lu (http://x3dna.org)
HETATM    1  N   ALC A   1      -2.250   5.000   0.250  1.00  1.00           N  
HETATM    2  N   ALC A   1      -2.250  -5.000   0.250  1.00  1.00           N  
HETATM    3  N   ALC A   1      -2.250  -5.000  -0.250  1.00  1.00           N  
HETATM    4  N   ALC A   1      -2.250   5.000  -0.250  1.00  1.00           N  
HETATM    5  C   ALC A   1       2.250   5.000   0.250  1.00  1.00           C  
HETATM    6  C   ALC A   1       2.250  -5.000   0.250  1.00  1.00           C  
HETATM    7  C   ALC A   1       2.250  -5.000  -0.250  1.00  1.00           C  
HETATM    8  C   ALC A   1       2.250   5.000  -0.250  1.00  1.00           C  
HETATM    9  C   ALC A   1      -2.250   5.000   0.250  1.00  1.00           C  
HETATM   10  C   ALC A   1      -2.250  -5.000   0.250  1.00  1.00           C  
HETATM   11  C   ALC A   1      -2.250  -5.000  -0.250  1.00  1.00           C  
HETATM   12  C   ALC A   1      -2.250   5.000  -0.250  1.00  1.00           C  
CONECT    1    2    4                                                  
CONECT    2    1    3                                                  
CONECT    3    2    4                                                  
CONECT    4    1    3                                                  
CONECT    5    6    8    9                                             
CONECT    6    5    7   10                                             
CONECT    7    6    8   11                                             
CONECT    8    5    7   12                                             
CONECT    9    5                                                       
CONECT   10    6                                                       
CONECT   11    7                                                       
CONECT   12    8                                                       
END

From a pure structural perspective, the designation of the two strands in an anti-parallel DNA duplex is sort of arbitrary. Thus, for a given PDB file, let’s assume that the atomic coordinates of chain A (strand I) come before those of chain B (strand II). We can swap the order of the two chains as they appear in the PDB file, i.e., list first the atomic coordinates of chain B and then those of chain A.

Structurally, the two settings corresponding to exactly the same DNA molecule. As far as 3DNA goes, however, the different orderings do make a different in calculated parameters. Using the Dickerson B-DNA dodecamer CGCGAATTCGCG solved at high resolution (PDB entry 355d) as an example, running 3DNA find_pair and analyze on ‘355d.pdb’ gives the results (abbreviated) below:

find_pair 355d.pdb 355d.bps
    # contents of file '355d.bps':
------------------------------------------------------------------
355d.pdb
355d.out
    2         # duplex
   12         # number of base-pairs
    1    1    # explicit bp numbering/hetero atoms
    1   24  0 #    1 | ....>A:...1_:[.DC]C-----G[.DG]:..24_:B<....
    2   23  0 #    2 | ....>A:...2_:[.DG]G-----C[.DC]:..23_:B<....
    3   22  0 #    3 | ....>A:...3_:[.DC]C-----G[.DG]:..22_:B<....
    4   21  0 #    4 | ....>A:...4_:[.DG]G-----C[.DC]:..21_:B<....
    5   20  0 #    5 | ....>A:...5_:[.DA]A-----T[.DT]:..20_:B<....
    6   19  0 #    6 | ....>A:...6_:[.DA]A-----T[.DT]:..19_:B<....
    7   18  0 #    7 | ....>A:...7_:[.DT]T-----A[.DA]:..18_:B<....
    8   17  0 #    8 | ....>A:...8_:[.DT]T-----A[.DA]:..17_:B<....
    9   16  0 #    9 | ....>A:...9_:[.DC]C-----G[.DG]:..16_:B<....
   10   15  0 #   10 | ....>A:..10_:[.DG]G-----C[.DC]:..15_:B<....
   11   14  0 #   11 | ....>A:..11_:[.DC]C-----G[.DG]:..14_:B<....
   12   13  0 #   12 | ....>A:..12_:[.DG]G-----C[.DC]:..13_:B<....
------------------------------------------------------------------

analyze 355d.bps
    # generate output file '355d.out', with base-pair step parameters:
****************************************************************************
    step       Shift     Slide      Rise      Tilt      Roll     Twist
   1 CG/CG      0.09      0.04      3.20     -3.22      8.52     32.73
   2 GC/GC      0.50      0.67      3.69      2.85     -9.06     43.88
   3 CG/CG     -0.14      0.59      3.00      0.97     11.30     25.11
   4 GA/TC     -0.45     -0.14      3.39     -1.59      1.37     37.50
   5 AA/TT      0.17     -0.33      3.30     -0.33      0.46     37.52
   6 AT/AT     -0.01     -0.60      3.22     -0.31     -2.67     32.40
   7 TT/AA     -0.08     -0.40      3.22      1.68     -0.97     33.74
   8 TC/GA     -0.27     -0.23      3.47      0.68     -1.69     42.14
   9 CG/CG      0.70      0.78      3.07     -3.66      4.18     26.58
  10 GC/GC     -1.31      0.36      3.37     -2.85     -9.37     41.60
  11 CG/CG     -0.31      0.21      3.17     -0.68      6.69     33.31
****************************************************************************

Reversing the order of chains A and B in ‘355d.pdb’ as ‘355d-reversed.pdb’ and repeating the above procedure, we have the following results:

find_pair 355d-reversed.pdb 355d-reversed.bps
    # contents of file '355d-reversed.bps':
------------------------------------------------------------------
355d-reversed.pdb
355d-reversed.out
    2         # duplex
   12         # number of base-pairs
    1    1    # explicit bp numbering/hetero atoms
    1   24  0 #    1 | ....>B:..13_:[.DC]C-----G[.DG]:..12_:A<....
    2   23  0 #    2 | ....>B:..14_:[.DG]G-----C[.DC]:..11_:A<....
    3   22  0 #    3 | ....>B:..15_:[.DC]C-----G[.DG]:..10_:A<....
    4   21  0 #    4 | ....>B:..16_:[.DG]G-----C[.DC]:...9_:A<....
    5   20  0 #    5 | ....>B:..17_:[.DA]A-----T[.DT]:...8_:A<....
    6   19  0 #    6 | ....>B:..18_:[.DA]A-----T[.DT]:...7_:A<....
    7   18  0 #    7 | ....>B:..19_:[.DT]T-----A[.DA]:...6_:A<....
    8   17  0 #    8 | ....>B:..20_:[.DT]T-----A[.DA]:...5_:A<....
    9   16  0 #    9 | ....>B:..21_:[.DC]C-----G[.DG]:...4_:A<....
   10   15  0 #   10 | ....>B:..22_:[.DG]G-----C[.DC]:...3_:A<....
   11   14  0 #   11 | ....>B:..23_:[.DC]C-----G[.DG]:...2_:A<....
   12   13  0 #   12 | ....>B:..24_:[.DG]G-----C[.DC]:...1_:A<....
------------------------------------------------------------------

analyze 355d-reversed.bps
    # generate output file '355d-reversed.out', with base-pair step parameters:
****************************************************************************
    step       Shift     Slide      Rise      Tilt      Roll     Twist
   1 CG/CG      0.31      0.21      3.17      0.68      6.69     33.31
   2 GC/GC      1.31      0.36      3.37      2.85     -9.37     41.60
   3 CG/CG     -0.70      0.78      3.07      3.66      4.18     26.58
   4 GA/TC      0.27     -0.23      3.47     -0.68     -1.69     42.14
   5 AA/TT      0.08     -0.40      3.22     -1.68     -0.97     33.74
   6 AT/AT      0.01     -0.60      3.22      0.31     -2.67     32.40
   7 TT/AA     -0.17     -0.33      3.30      0.33      0.46     37.52
   8 TC/GA      0.45     -0.14      3.39      1.59      1.37     37.50
   9 CG/CG      0.14      0.59      3.00     -0.97     11.30     25.11
  10 GC/GC     -0.50      0.67      3.69     -2.85     -9.06     43.88
  11 CG/CG     -0.09      0.04      3.20      3.22      8.52     32.73
****************************************************************************

Comparing the base-pair step parameters between ‘355d.out’ and ’355d-reversed.out’, one would notice that while slide/rise/roll/twist simply switch orders, shift/tilt (the x-axis parameters) also flip their signs. On the other hand, the nucleotide serial numbers specifying base pairs (the left two columns) are identical in ‘355d.bps’ and ’355d-reversed.bps’.

Apart from explicitly swapping the two strands in PDB data file, one can simply switch around the nucleotide serial numbers generated with find_pair in order to analyze a DNA duplex based on its complementary sequence instead of the primary one. For example, starting from the same PDB file ‘355d.pdb’, we change ‘355d.bps’ to ’355d-cs.bps’ as below,

------------------------------------------------------------------
355d.pdb
355d-cs.out
    2         # duplex
   12         # number of base-pairs
    1    1    # explicit bp numbering/hetero atoms
   13   12
   14   11
   15   10
   16    9
   17    8
   18    7
   19    6
   20    5
   21    4
   22    3
   23    2
   24    1
------------------------------------------------------------------

Run analyze 355d-cs.bps, one would get exactly the same parameters in output file ’355d-cs.out’ as in ’355d-reversed.out’.

Ever since the 2003 publication of the initial 3DNA Nucleic Acids Research paper (NAR03), the schematic diagrams of base-pair parameters (see figure below) has become quite popular. Over the years, we have received numerous requests for permission to use the figure, or a portion thereof; as an example, the figure has been adopted into a structural biology textbook. In the 2008 3DNA Nature Protocols paper (NP08), we devoted the very first protocol to “create a schematic image for propeller of 45°”.

Figure legend taken from Figure 1 of NAR03: Pictorial definitions of rigid body parameters used to describe the geometry of complementary (or non‐complementary) base pairs and sequential base pair steps (19). The base pair reference frame (lower left) is constructed such that the x‐axis points away from the (shaded) minor groove edge of a base or base pair and the y‐axis points toward the sequence strand (I). The relative position and orientation of successive base pair planes are described with respect to both a dimer reference frame (upper right) and a local helical frame (lower right). Images illustrate positive values of the designated parameters. For illustration purposes, helical twist (Ωh) is the same as Twist (ω), formerly denoted by Ω (19,20) and helical rise (h) is the same as Rise (Dz).

I recall spending around two weeks to produce the above figure. Content-wise, the figure was constructed in only a short while; it was the little details that took me most of the time.

Over time, I’ve witnessed numerous versions of such schematic images in publications related to DNA/RNA structures. While looking similar, the schematics differ subtly in the magnitude, orientation and relative scale of illustrated parameters. To the best of my knowledge, only 3DNA provides a pragmatic approach to generate the base-pair schematic diagrams consistently.

To make the schematics more readily accessible, I’ve reproduced a high resolution image (in png format) for each of the 14 parameters shown above. You are welcome to pick and match the diagrams as necessary. If you use any of them in your publications, please cite the 3DNA NAR03 and/or NP08 paper(s).

Note that in the schematic diagrams below, the shaded edge (facing the viewer) denotes the minor-groove side of a base or base pair.

Shear (Sx)	Stretch (Sy)	Stagger (Sz)
Buckle (κ)	Propeller (π)	Opening (σ)
Shift (Dx)	Slide (Dy)	Rise (Dz)
Tilt (τ)	Roll (ρ)	Twist (ω)
x-displacement (dx)	y-displacement (dy)	Helical Rise (h)
		As for Rise above (for illustration purpose)
Inclination (η)	Tip (θ)	Helical Twist (Ωh)
		As for Twist above (for illustration purpose)