Over the past couple of weeks, I’ve added two more DSSR options, --symmetry and --nmr, that are closely related to an ensemble of MODEL/ENDMDL-delineated structures in PDB files. However, there exist subtle differences between the two cases, and the usage of the same MODEL/ENDMDL ensemble format can be ambiguous to the uninitiated. This blog post aims to clarify the issues, using concrete examples.

The --symmetry options applies to X-ray crystal structures where an asymmetric unit represents only part of the whole biological assembly. In standard PDB format, the asymmetric unit contains instructions to produce crystallographic symmetry
related molecules.. Nevertheless, the biological assembly are also provided by the PDB (or NDB), with coordinate files ending with .pdb1 or such. For example, the PDB entry 2d94 has the single-stranded sequence GGGCGCCC in its asymmetric unit (2d94.pdb). It is the biological assembly in file 2d94.pdb1 that contains the DNA double helix.

x3dna-dssr -i=2d94.pdb # no pairs found
x3dna-dssr -i=2d94.pdb1 # still no pairs found
x3dna-dssr -i=2d94.pdb1 --symm # 8 pairs found
x3dna-dssr -i=2d94.pdb --symm # no pairs found

As shown by the above examples, DSSR by default reads only the first model even given the biological assemble file 2d94.pdb1. It is with --symmetry (abbreviated to --symm) explicitly specified that DSSR takes all models in the input biological assemble file into consideration. The last case also illustrates that DSSR does not generate crystallographic symmetry related molecules. The --symm simply informs DSSR to take all models, which already exist in the input file, into consideration.

On the other hand, the --nmr option is for auto-processing an ensemble of structures solved by solution NMR method (or trajectories of molecular dynamics simulations). The key point here is that each of the MODEL/ENDMDL-delinated structures is independent and thus can be processed separately, even though they are obviously closely related. Using the PDB entry 2n2d as an example, here are some sample usages:

x3dna-dssr -i=2n2d.pdb -o= 2n2d-first.out # only the first structure is processed
x3dna-dssr -i=2n2d.pdb --nmr -o=2n2d-all.out # all 10 structures are processed
x3dna-dssr -i=2n2d.pdb --nmr --json -o=2n2d-all.json # ibid., with output in JSON

Note that the NMR file is named 2n2d.pdb, and it contains 10 structures.

Interesting mixes show up when an X-ray biological assembly with multiple MODEL/ENDMDL entries is analyzed with --nmr, or an NMR entry is handled with --symmetry. Here are two such examples:

x3dna-dssr -i=2d94.pdb1 --nmr -o=temp # models 1 and 2 are handled sepatately
x3dna-dssr -i=2n2d.pdb --symm -o=temp # wrong -- does not make sense!

In summary, the --symmetry option is intended to treat symmetry-related molecules as a whole, as in a biological assembly of X-ray crystal structures. In contrast, the --nmr option aims to automate the analysis of each structure in a MODEL/ENDMDL-delineated ensemble, as in NMR structures or trajectories of MD simulations. The distinction between the two MODEL/ENDMDL usages is most clearly seen via a molecular visualization program: for example, check the figure below for 2d94.pdb1 (left) and 2n2d.pdb (right) when all frames are selected using Jmol.

2d94 (2 models)	2n2d (10 models)

JSON (JavaScript Object Notation) is a simple human-readable format that expresses data objects in name-value pairs. Over the years, it has surpassed XML to become the preferred data exchange format between applications. As a result, I’ve recently added the --json command-line option to DSSR to make its numerous derived parameters easily accessible.

The DSSR JSON output is contained in a compact one-line text string that may look cryptic to the uninitiated. Yet, with commonly available JSON parsers or libraries, it is straightforward to make sense of the DSSR JSON output. In this blogpost, I am illustrating how to parse DSSR-derived .json file via two command-line tools, jq and Underscore-CLI.

jq — lightweight and flexible command-line JSON processor

According to its website,

jq is like sed for JSON data – you can use it to slice and filter and map and transform structured data with the same ease that sed, awk, grep and friends let you play with text.

Moreover, like DSSR per se, “jq is written in portable C, and it has zero runtime dependencies.” Prebuilt binaries are available for Linux, OS X and Windows. So it is trivial to get jq up and running. The current stable version is 1.5, released on August 15, 2015.

Using the crystal structure of yeast phenylalanine tRNA (1ehz) as an example, here are some sample usages with DSSR-derived JSON output:

    # Pretty print JSON
x3dna-dssr -i=1ehz.pdb --json | jq .
    # Extract the top-level keys, in insertion order 
x3dna-dssr -i=1ehz.pdb --json | jq keys_unsorted
    # Extract parameters for nucleotides
x3dna-dssr -i=1ehz.pdb --json | jq .nts
    # Extract nucleotide id and its base reference frame
x3dna-dssr -i=1ehz.pdb --json | jq '.nts[] | (.nt_id, .frame)'

Underscore-CLI — command-line utility-belt for hacking JSON and Javascript.

Underscore-CLI is built upon Node.js, and can be installed using the npm package manager. It is claimed as ‘the “swiss-army-knife” tool for processing JSON data – can be used as a simple pretty-printer, or as a full-powered Javascript command-line.’

Following the above examples illustrating jq, here are the corresponding commands for Underscore-CLI:

x3dna-dssr -i=1ehz.pdb --json | underscore print --color
x3dna-dssr -i=1ehz.pdb --json | underscore keys --color
x3dna-dssr -i=1ehz.pdb --json | underscore select .nts --color
x3dna-dssr -i=1ehz.pdb --json | underscore select .nts | underscore select '.nt_id, .frame' --color

jq or Underscore-CLI — which one to use?

As always, it depends. While jq feels more like a standard Unix utility (as sed, awk, grep etc), Underscore-CLI is better integrated into the Javascript language. For simple applications such as parsing DSSR output, either jq or Underscore-CLI is more than sufficient.

I use jq most of the time, but resort to Underscore-CLI for its “smart whitespace”. Here is an example to illustrate the difference between the two:

# z-axis of A.G1 (1ehz) base reference frame
# jq output, split in 5 lines
    "z_axis": [
      0.799,
      0.488,
      -0.352
    ]
# Underscore-CLI, in a more-readable one line
    "z_axis": [0.799, 0.488, -0.352]

Recently, I read with great interest an article titled A context-sensitive guide to RNA & DNA base-pair & base-stack geometry by Dr. Jane Richardson, published in CCN (Computational Crystallography Newsletter, 2015, 5, 42—49). Highlighted in the article are Buckle and Propeller twist (see bottom left of the figure below), two of the angular parameters that characterize base-pair (bp) non-planarity. Particularly, I was intrigued by the “Notes on measures and figures” at the end:

Base normals were constructed in Mage (Richardson 2001) and twist torsions and buckle angles were measured from them; propeller-twists were measured as dihedral angles around an axis between N1/9 atoms.

The Richardson CCN article prompted me to think more on intuitive description of bp geometry that can be easily grasped by experimentalist, especially X-ray crystallographers or cryo-EM practitioners. Without worrying about model building as with the six rigid-body parameters, it is straightforward to come up with a new set of four ‘simple’ parameters (Shear, Stretch, Buckle and Propeller) with the following characteristics:

• Each parameter can be positive or negative. For type M–N pairs (as in the canonical cases), Shear and Buckle reverse their signs when the two bases are swapped (i.e. counted as N–M instead of M–N). In all other cases, the signs of the parameters remain unchanged. See the DSSR paper for the definition of M+N vs M–N type of pairs.
• Intuitive results for non-canonical pairs, even when Opening is ~180º.
• Consistent definition between Shear/Buckle (_x_-axis) vs Stretch/Propeller (_y_-axis).
• As in 3DNA and DSSR, Buckle^2 + Propeller^2 = interBase_angle^2. Either Buckle or Propeller can render the two base planes of a pair non-parallel. Combined together, they introduce a non-zero inter-base angle. By definition, each parameter should not be larger than the overall inter-base angle.

With the cartoon-block representation introduced in DSSR, base-stacking interactions and bp deformations (especially Buckle and Propeller) are immediately obvious. Two example are illustrated in the figure below: one is the classic Dickerson B-DNA dodecamer (355d, DSSR output), and the other is the parallel double-stranded helix of poly(A) RNA (4jrd, DSSR output).

DSSR Output for 355d	DSSR Output for 4jrd

A portion of DSSR output for the B-DNA duplex 355d is shown below. Note that the first bp (at the bottom left in the figure above) has a Propeller of –17º (and a Buckle of +7º). As beautifully explained by Calladine et al. in their book Understanding DNA,
The Molecule & How It Works, Watson-Crick pairs prefer to have negative Propeller in right-handed DNA double helices to improve same-strand base-stacking interactions. The average value of Propeller in A- and B-DNA crystal structures is around –11º (see Table 3 of the Olson et al. standard base reference frame paper).

     nt1            nt2           bp  name        Saenger    LW  DSSR
   1 A.DC1          B.DG24         C-G WC          19-XIX    cWW  cW-W
       [-105.9(anti) ~C2'-endo lambda=53.5] [-141.3(anti) ~C3'-endo lambda=52.7]
       d(C1'-C1')=10.71 d(N1-N9)=8.96 d(C6-C8)=9.88 tor(C1'-N1-N9-C1')=-21.4
       H-bonds[3]: "O2(carbonyl)-N2(amino)[2.83],N3-N1(imino)[2.90],N4(amino)-O6(carbonyl)[2.98]"
       interBase-angle=19  Simple-bpParams: Shear=0.28 Stretch=-0.13 Buckle=7.3 Propeller=-17.2
       bp-pars: [0.28    -0.14   0.07    6.93    -17.31  -0.61]
   2 A.DG2          B.DC23         G-C WC          19-XIX    cWW  cW-W
       [-85.4(anti) ~C2'-endo lambda=53.4] [-150.3(anti) ~C3'-endo lambda=55.4]
       d(C1'-C1')=10.61 d(N1-N9)=8.92 d(C6-C8)=9.83 tor(C1'-N1-N9-C1')=-21.7
       H-bonds[3]: "O6(carbonyl)-N4(amino)[2.91],N1(imino)-N3[2.88],N2(amino)-O2(carbonyl)[2.88]"
       interBase-angle=17  Simple-bpParams: Shear=-0.24 Stretch=-0.18 Buckle=9.0 Propeller=-14.5
       bp-pars: [-0.24   -0.18   0.49    9.34    -14.30  -2.08]

A portion of DSSR output for the parallel A-DNA duplex 4jrd is shown below. Note that the values of ‘simple’ Propeller are positive for both bps #7 and #8. In contrast, the rigid-body bp parameters have their signs flipped over when Opening is switched from –179.56º for bp#7 to +179.23º for bp#8. This sign ‘ambiguity’ around 180º Opening could be confusing. Yet, all the six bp parameters must be kept as they are for rigorous rebuilding, especially within a larger context than a bp per se. From the very beginning, 3DNA has adopted the convention of keeping angular parameters in the range of [–180º, +180º] instead of [0, 360º], allowing left-handed Z-DNA to have negative twist.

   7 A.A8           B.A7           A+A --          02-II     tHH  tM+M
       [-175.8(anti) ~C3'-endo lambda=10.2] [-172.7(anti) ~C3'-endo lambda=12.6]
       d(C1'-C1')=11.15 d(N1-N9)=8.29 d(C6-C8)=6.31 tor(C1'-N1-N9-C1')=160.1
       H-bonds[4]: "OP2-N6(amino)[2.97],N7-N6(amino)[2.97],N6(amino)-OP2[2.92],N6(amino)-N7[2.91]"
       interBase-angle=14  Simple-bpParams: Shear=-7.88 Stretch=0.66 Buckle=-7.8 Propeller=11.9
       bp-pars: [-6.00   5.15    -0.02   0.63    14.22   -179.56]
   8 A.A9           B.A8           A+A --          02-II     tHH  tM+M
       [-177.4(anti) ~C3'-endo lambda=12.4] [-175.8(anti) ~C3'-endo lambda=10.3]
       d(C1'-C1')=11.01 d(N1-N9)=8.15 d(C6-C8)=6.18 tor(C1'-N1-N9-C1')=158.5
       H-bonds[4]: "OP2-N6(amino)[2.93],N7-N6(amino)[2.88],N6(amino)-OP2[2.97],N6(amino)-N7[2.92]"
       interBase-angle=15  Simple-bpParams: Shear=-7.91 Stretch=0.56 Buckle=-7.0 Propeller=13.7
       bp-pars: [6.11    -5.06   -0.05   -2.26   -15.22  179.23]

From early on, the x3dna.org domain and its related sub-domains (e.g., for the forum and the web-interface to DSSR) has been served via shared hosting. By and large, this simple arrangement has worked quite well. Over the years, though, I’ve gradually realized some of its inherent limitations. One is the limited resources available to the 3DNA-related websites. Another is the accessibility issue from countries like China.

To remedy such issues, I’ve recently moved the 3DNA Forum and the web-interface to DSSR to a dedicated web server at Columbia University. Moreover, a duplicate copy of the 3DNA homepage is made available via http://home.x3dna.org hosted at Columbia. The three new websites have been verified to be accessible directly from China.

These updates on x3dna.org not only ensure global accessibility to 3DNA/DSSR, but also allow for more web services to be made available.

As of v1.3.3-2015sep03, DSSR outputs the reference frame of any base or base-pair (bp). With an explicit list of such reference frames, one can better understand how the 3DNA/DSSR bp parameters are calculated. Moreover, third-party bioinformatics tools can take advantage of the frames for further exploration of nucleic acid structures, including visualization.

Let’s use the G1–C72 bp (detailed below) in the yeast phenylalanine tRNA (1ehz) as an example:

1 A.G1           A.C72          G-C WC          19-XIX    cWW  cW-W

The standard base reference frame for A.G1 is:

{
  rsmd: 0.008,
  origin: [53.757, 41.868, 52.93],
  x_axis: [-0.259, -0.25, -0.933],
  y_axis: [-0.543, 0.837, -0.073],
  z_axis: [0.799, 0.488, -0.352]
}

And the one for A.C72 is:

{
  rsmd: 0.006,
  origin: [53.779, 42.132, 52.224],
  x_axis: [-0.402, -0.311, -0.861],
  y_axis: [0.451, -0.886, 0.109],
  z_axis: [-0.797, -0.345, 0.497]
}

The G1–C72 bp reference frame is:

{
  rsmd: null,
  origin: [53.768, 42, 52.577],
  x_axis: [-0.331, -0.283, -0.9],
  y_axis: [-0.497, 0.863, -0.089],
  z_axis: [0.802, 0.418, -0.427]
}

The beauty of the DSSR JSON output is that the above information can be extracted on the fly. For example, the following commands extract the above frames:

x3dna-dssr -i=1ehz.pdb --json | jq '.ntParams[] | select(.nt_id=="A.G1") | .frame'
x3dna-dssr -i=1ehz.pdb --json | jq '.ntParams[] | select(.nt_id=="A.C72") | .frame'
x3dna-dssr -i=1ehz.pdb --json --more | jq .pairs[0].frame

Note that in JSON, the array is 0-indexed, so the first bp (G1–C72) has an index of 0. In addition to jq, I also used underscore to pretty-print the frames.

Standard nitrogenous bases in DNA and RNA (A, C, G, T, and U) are aromatic compounds, each with a planar geometry. In the analyses of three-dimensional (3D) nucleic acid structures, the planar bases are normally taken as rigid bodies. The relative geometry of the two bases in base pair (bp) can then be rigorously quantified by six rigid-body parameters (see figure below). The three translations along the _x_-, _y_- and _z_-axes are termed Shear, Stretch, and Stagger, respectively. The three corresponding rotations are called Buckle, Propeller (twist), and Opening.

3DNA is unique with its coupled analyze and rebuild programs. The former calculates six bp parameters given 3D atomic coordinates (in PDB or PDBx/mmCIF format), while the later takes a set of such parameters to generate the corresponding structure. The rigor of the description can be easily verified in two equivalent ways: the close to zero root-mean-square deviation (RMSD) between the rebuilt structure and the original coordinates, after a least-squares superposition; or the identical six bp parameters when the rebuilt structure is analyzed.

As is often the case, a concrete example would make the point clear. Here I am using the reverse Hoogsteen (rHoogsteen) bp between U8 and A14 (see image below) in the yeast phenylalanine tRNA (1ehz) as an example. The PDB atomic coordinates of the U8–A14 rHoogsteen pair, excluding backbone atoms except for C1′, is stored in file 1ehz-U8-A14.pdb.

find_pair 1ehz-U8-A14.pdb stdout | analyze stdin
    # bp parameters in file '1ehz-U8-A14.out'
    # also generated 'bp_step.par' for rebuilding below
rebuild -atomic bp_step.par 1ehz-U8-A14-3DNA.pdb
    # rmsd is 0.044 Å between '1ehz-U8-A14.pdb' and '1ehz-U8-A14-3DNA.pdb'
find_pair 1ehz-U8-A14-3DNA.pdb stdout | analyze stdin
    # bp parameters of the rebuilt structure in '1ehz-U8-A14-3DNA.out'
rebuild -atomic bp_step.par 1ehz-U8-A14-3DNA-new.pdb
    # rmsd is 0 Å between '1ehz-U8-A14-3DNA.pdb' and '1ehz-U8-A14-3DNA-new.pdb'

Note that the above commands should be performed in order, since the file bp_step.par is overwritten after each analyze run. For your verification, here are the links to the five files:

• 1ehz-U8-A14.pdb
• 1ehz-U8-A14.out
• 1ehz-U8-A14-3DNA.pdb
• 1ehz-U8-A14-3DNA.out
• 1ehz-U8-A14-3DNA-new.pdb

The 0.044 Å rmsd between the original PDB coordinates in 1ehz-U8-A14.pdb and the 3DNA rebuilt structure in 1ehz-U8-A14-3DNA.pdb is due to the slight non-planarity of experimental bases. The rmsd is 0 between the two rounds of 3DNA rebuilt structures, 1ehz-U8-A14-3DNA.pdb and 1ehz-U8-A14-3DNA-new.pdb, as expected.

The bp parameters in 1ehz-U8-A14.out and 1ehz-U8-A14-3DNA.out are identical, as expected, and they are shown below.

Local base-pair parameters
     bp        Shear    Stretch   Stagger    Buckle  Propeller  Opening
    1 U-A       4.14     -1.91      0.77     -4.62     12.12   -103.09 

Running DSSR on 1ehz-U8-A14.pdb gives the following results. Note that the six bp parameters (last row prefixed with bp-pars) are the exactly same as in 3DNA — we are consistent.

# x3dna-dssr -i=1ehz-U8-A14.pdb --more
List of 1 base pair
      nt1            nt2           bp  name        Saenger    LW  DSSR
   1 A.U8           A.A14          U-A rHoogsteen  24-XXIV   tWH  tW-M
       [n/a(n/a) ---- lambda=28.3] [n/a(n/a) ---- lambda=21.5]
       d(C1'-C1')=9.63 d(N1-N9)=7.06 d(C6-C8)=6.00 tor(C1'-N1-N9-C1')=174.4
       H-bonds[2]: "O2(carbonyl)-N6(amino)[3.00],N3(imino)-N7[2.74]"
       interBase-angle=12.97  Simple-bpParams: Shear=4.28 Stretch=1.55 Buckle=-11.8 Propeller=5.4
       bp-pars: [4.14    -1.91   0.77    -4.62   12.12   -103.09]

As mentioned in the recent DSSR paper:

As in 3DNA (6,7), DSSR takes advantage of the six standard base-pair parameters––three translations (Shear, Stretch, Stagger) and three rotations (Buckle, Propeller, Opening)––to quantify the relative spatial position and orientation of any two interacting bases rigorously. Among the six parameters, only Shear, Stretch, and Opening are critical for characterizing different types of pairs. Buckle, Propeller and Stagger, on the other hand, describe the nonplanarity of a given pair (6). By virtue of the definition of the standard base reference frame, Shear, Stretch, and Opening are all close to zero for Watson-Crick pairs. Moreover, every other type of pair has a set of characteristic parameters. For example, the wobble G–U pair is characterized by an average Shear of –2.2 Å, and the Hoogsteen A+U pair is distinguished by a Stretch of approximately –3.5 Å and an Opening of near 66º.

In a follow-up post, I will talk about the “simple” bp parameters (Simple-bpParams in the above DSSR output list) recently introduced into DSSR — stay tuned!

As of DSSR v1.3.0-2015aug27, the --json option is available for producing analysis results that is strictly compliant with the JSON data exchange format. The JSON file contains numerous DSSR-derived structural features, including those in the default main output, backbone torsions in dssr-torsions.txt, and a detailed list of hydrogen bonds.

According to the official JSON website:

JSON (JavaScript Object Notation) is a lightweight data-interchange format. It is easy for humans to read and write. It is easy for machines to parse and generate. It is based on a subset of the JavaScript Programming Language… JSON is a text format that is completely language independent… These properties make JSON an ideal data-interchange language.

Indeed, the JSON output file makes DSSR readily accessible for integration with other bioinformatics tools or normal usages from the command line. Using the classic yeast phenylalanine tRNA 1ehz as an example (1ehz.pdb), let’s go over some simple use-cases. Note that the following examples take advantage of jq, a lightweight and flexible command-line JSON processor.

x3dna-dssr -i=1ehz.pdb --json -o=1ehz-dssr.json
jq . 1ehz-dssr.json  # reformatted for pretty output
x3dna-dssr -i=1ehz.pdb --json | jq .  # the above 2 steps combined

With 1ehz-dssr.json in hand, we can easily extract DSSR-derived structural features of interest:

jq .pairs 1ehz-dssr.json   # list of 34 pairs
jq .multiplets 1ehz-dssr.json  # list of 4 base triplets
jq .hbonds 1ehz-dssr.json  # list of hydrogen bonds
jq .helices 1ehz-dssr.json
jq .stems 1ehz-dssr.json
  # list of nucleotide parameters, including torsion angles and suites
jq .ntParams 1ehz-dssr.json
  # list of 14 modified nucleotides
jq '.ntParams[] | select(.is_modified)' 1ehz-dssr.json
  # select nucleotide id, delta torsion, sugar puckering and cluster of suite name
jq '.ntParams[] | {nt_id, delta, puckering, cluster}' 1ehz-dssr.json
  # same selection as above, but in 'Comma Separated Values' format
jq -r '.ntParams[] | [.nt_id, .delta, .puckering, .cluster] | @csv' 1ehz-dssr.json

Here is the result of running jq (v1.5) to select multiplets:

# jq .multiplets 1ehz-dssr.json
[
  {
    "index": 1,
    "num_nts": 3,
    "nts_short": "UAA",
    "nts_long": "A.U8,A.A14,A.A21"
  },
  {
    "index": 2,
    "num_nts": 3,
    "nts_short": "AUA",
    "nts_long": "A.A9,A.U12,A.A23"
  },
  {
    "index": 3,
    "num_nts": 3,
    "nts_short": "gCG",
    "nts_long": "A.2MG10,A.C25,A.G45"
  },
  {
    "index": 4,
    "num_nts": 3,
    "nts_short": "CGg",
    "nts_long": "A.C13,A.G22,A.7MG46"
  }
]

With the JSON file, DSSR can now be connected with the bioinformatics community in a ‘structured’ way, with a clearly delineated boundary. Now I can enjoy the freedom of refining the default main output format, without worrying too much about breaking third-party parsers. Moreover, I no longer need to write an adapter for each integration of DSSR with other tools. So nice!

For your reference, here is the output file 1ehz-dssr.json. It may be possible that the identifiers (names) of the JSON output will be refined in the next few iterations. I welcome your comments to make the DSSR-derived JSON better suite your needs.

It is a great pleasure to note that a paper titled DSSR, an integrated software tool for dissecting the spatial structure of RNA has recently been published in Nucleic Acids Research (NAR). Co-authored by Harmen Bussemaker, Wilma Olson and me (a team with a unique combination of complementary expertise), this DSSR paper represents another solid piece of work that I feel proud of. In contrast to our previous GpU dinucleotide platform paper focusing on results, and the two major 3DNA papers concentrating on methods, the current NAR article describes significant scientific findings that are enabled by the novel analysis algorithms implemented in the program. Moreover, DSSR introduces an appealing and highly informative “cartoon-block” representation of RNA structures that combines PyMOL cartoon schematics with 3DNA base color-coded rectangular blocks.

The abstract of the paper is quoted below:

Insight into the three-dimensional architecture of RNA is essential for understanding its cellular functions. However, even the classic transfer RNA structure contains features that are overlooked by existing bioinformatics tools. Here we present DSSR (Dissecting the Spatial Structure of RNA), an integrated and automated tool for analyzing and annotating RNA tertiary structures. The software identifies canonical and noncanonical base pairs, including those with modified nucleotides, in any tautomeric or protonation state. DSSR detects higher-order coplanar base associations, termed multiplets. It finds arrays of stacked pairs, classifies them by base-pair identity and backbone connectivity, and distinguishes a stem of covalently connected canonical pairs from a helix of stacked pairs of arbitrary type/linkage. DSSR identifies coaxial stacking of multiple stems within a single helix and lists isolated canonical pairs that lie outside of a stem. The program characterizes ‘closed’ loops of various types (hairpin, bulge, internal, and junction loops) and pseudoknots of arbitrary complexity. Notably, DSSR employs isolated pairs and the ends of stems, whether pseudoknotted or not, to define junction loops. This new, inclusive definition provides a novel perspective on the spatial organization of RNA. Tests on all nucleic acid structures in the Protein Data Bank confirm the efficiency and robustness of the software, and applications to representative RNA molecules illustrate its unique features. DSSR and related materials are freely available at http://x3dna.org/.

During the review process, we are delighted that the referees confirmed the claim that we made in the cover letter: “We would also like to emphasize that our reported results are easily verifiable, and we assure rigorous reproducibility of the data and figures described in this article.” Now that the paper has been published, as a follow-up, I’ve made available all the scripts and data files associated with the paper in a new section DSSR-NAR paper on the 3DNA Forum. The DSSR User Manual has also been updated with additional, previously undocumented, auxiliary options.

Overall, it took me more than ten days to create the 19 posts in the DSSR-NAR paper section and to revise the DSSR User Manual, along with other minor refinements for consistency. During the process, I’ve tried to make the scripts and data files self-contained for wide accessibility and easy understanding.

Any interested party should now be able to reproduce the table and figures (including the supplementary data) reported in the article. Moreover, with the additional details given in the post RNA cartoon-block representations with PyMOL and DSSR, one can easily generate similar schematic images as shown below:

I feel confident to claim that the results reported in our DSSR paper are reproducible. If you have issues related to the paper, please post them on the 3DNA Forum. I strive to respond promptly to any questions asked there.

In summary, DSSR is an integrated computational tool, designed from the bottom up to streamline the analysis of RNA three-dimensional structures. It is built upon my extensive experience in supporting 3DNA, growing knowledge of RNA structures, and refined programming skills. DSSR has a combined set of functionalities well beyond the scope of any known specialized resources. The program may well serve as a cornerstone for RNA structural bioinformatics and will benefit a broad range of possible applications.

The conformation of the five-membered sugar ring in DNA/RNA structures can be characterized using the five corresponding endocyclic torsion angles (shown below).

v0: C4'-O4'-C1'-C2'
v1: O4'-C1'-C2'-C3'
v2: C1'-C2'-C3'-C4'
v3: C2'-C3'-C4'-O4'
v4: C3'-C4'-O4'-C1'

On account of the five-member ring constraint, the conformation can be characterized approximately by 5 - 3 = 2 parameters. Using the concept of pseudorotation of the sugar ring, the two parameters are the amplitude (τ_m) and phase angle (P, in the range of 0° to 360°).

One set of widely used formula to convert the five torsion angles to the pseudorotation parameters is due to Altona & Sundaralingam (1972): “Conformational Analysis of the Sugar Ring in Nucleosides and Nucleotides. A New Description Using the Concept of Pseudorotation” [J. Am. Chem. Soc., 94(23), pp 8205–8212]. As always, the concept is best illustrated with an example. Here I use the sugar ring of G4 (chain A) of the Dickerson-Drew dodecamer (1bna), with Matlab/Octave code:

# xyz coordinates of the sugar ring: G4 (chain A), 1bna
ATOM     63  C4'  DG A   4      21.393  16.960  18.505  1.00 53.00
ATOM     64  O4'  DG A   4      20.353  17.952  18.496  1.00 38.79
ATOM     65  C3'  DG A   4      21.264  16.229  17.176  1.00 56.72
ATOM     67  C2'  DG A   4      20.793  17.368  16.288  1.00 40.81
ATOM     68  C1'  DG A   4      19.716  17.901  17.218  1.00 30.52

# endocyclic torsion angles:
v0 = -26.7; v1 = 46.3; v2 = -47.1; v3 = 33.4; v4 = -4.4
Pconst = sin(pi/5) + sin(pi/2.5)  # 1.5388
P0 = atan2(v4 + v1 - v3 - v0, 2.0 * v2 * Pconst);  # 2.9034
tm = v2 / cos(P0);  # amplitude: 48.469
P = 180/pi * P0;  # phase angle: 166.35 [P + 360 if P0 < 0]

The Altona & Sundaralingam (1972) pseudorotation parameters are what have been adopted in 3DNA, following the NewHelix program of Dr. Dickerson. The Curves+ program, on the other hand, uses another (newer) set of formula due to Westhof & Sundaralingam (1983): “A Method for the Analysis of Puckering Disorder in Five-Membered Rings: The Relative Mobilities of Furanose and Proline Rings and Their Effects on Polynucleotide and Polypeptide Backbone Flexibility” [J. Am. Chem. Soc., 105(4), pp 970–976]. The two sets of formula, by Altona & Sundaralingam (1972) and Westhof & Sundaralingam (1983), give slightly different numerical values for the two pseudorotation parameters (τ_m and P).

Since 3DNA and Curves+ are currently two of the most widely used programs for conformational analysis of nucleic acid structures, the subtle differences in pseudorotation parameters may cause confusions for users who use (or are familiar with) both programs. Over the past few years, I have indeed received such questions via email.

With the same G4 (chain A, 1bna) sugar ring, here is the Matlab/Octave script showing how Curve+ calculates the pseudorotation parameters:

# xyz coordinates of sugar ring G4 (chain A, 1bna)

# endocyclic torsion angles, same as above
v0 = -26.7; v1 = 46.3; v2 = -47.1; v3 = 33.4; v4 = -4.4

v = [v2, v3, v4, v0, v1]; # reorder them into vector v[]
A = 0; B = 0;
for i = 1:5
    t = 0.8 * pi * (i - 1);
    A += v(i) * cos(t);
    B += v(i) * sin(t);
end
A *= 0.4;   # -48.476
B *= -0.4;  # 11.516

tm = sqrt(A * A + B * B);  # 49.825

c = A/tm; s = B/tm;
P = atan2(s, c) * 180 / pi;  # 166.64

For this specific example, i.e., the sugar ring of G4 (chain A, 1bna), the pseudorotation parameters as calculated by 3DNA per Altona & Sundaralingam (1972) and Curves+ per Westhof & Sundaralingam (1983) are as follows:

           amplitude        phase angle
3DNA        48.469             166.35
Curves+     49.825             166.64

Needless to say, the differences are subtle, and few people will notice/bother at all. For those who do care about such little details, however, hopefully this post will help you understand where the differences actually come from.

For consistency with the 3DNA output, DSSR (by default) also follows the Altona & Sundaralingam (1972) definitions of sugar pseudorotation. Nevertheless, DSSR also contains an undocumented option, --sugar-pucker=westhof83, to output τ_m and P according to the Westhof & Sundaralingam (1983) definitions.

Each sugar is assigned into one of the following ten puckering modes, by dividing the phase angle (P, in the range of 0° to 360°) into 36° ranges reach.

C3'-endo, C4'-exo,   O4'-endo, C1'-exo,  C2'-endo,
C3'-exo,  C4'-endo,  O4'-exo,  C1'-endo, C2'-exo

For sugars in nucleic acid structures, C3’-endo [0°, 36°) and C2’-endo [144°, 180°) are predominant. The former corresponds to sugars in ‘canonical’ RNA or A-form DNA, and the latter in sugars of standard B-form DNA. In reality, RNA structures as deposited in the PDB could also contain C2′-endo sugars. One significant example is the GpU dinucleotide platforms, where the 5′-ribose sugar (G) is in the C2′-endo form and the 3′-sugar (U) in the C3′-endo form — see my blog post, titled ‘Is the O2′(G)…O2P H-bond in GpU platforms real?’.

Notes:

• This post is based on my 2011-06-11 blog post with the same title.
• While visiting Lyon in July 2014, I had the opportunity to hear Dr. Lavery’s opinion on adopting the Westhof & Sundaralingam (1983) sugar-pucker definitions in Curves+. I learned that the new formula are more robust in rare, extreme cases of sugar conformation than the 1972 variants. After all, Dr. Sundaralingam is a co-author on both papers. It is possible that in future releases of DSSR, the new 1983 formula for sugar pucker would become the default.