These distinctly different structures give the same base-pair step parameters.

[wolson]

According to their 3DNA output files, all four of the attached structures have the same positive rise (+3.4 A), the PP and MM files have the same positive twist (+36 deg), and the PM and MP files have the same negative twist (-36 deg). The structures should have all four possible combinations of the signs for rise and twist, i.e., (+3.4, +36) for PP, (–3.4, -36) for MM, (+3.4, -36) for PM, and (-3.4, +36) for MP.

The error is related to the implementation of the Cambridge Convention in the computation of base-pair step parameters in 3DNA. Users interested in structures like these are interested in rigid-body parameters that reproduce the input structures rather than adhering to the Convention.

A useful option for such users would be the option NOT to follow the Cambridge Convention.

[xiangjun]

Hi Wilma,

Thanks for bringing up this "issue". As always, the four concrete PDB files helped clarify everything. In short, 3DNA is behaving properly: because PP and MM are IDENTICAL (RMSD=0 Å), so are PM and MP (RMSD=0.0174364 Å). There are only two structures; the PP/MM pair is right-handed with Rise=+3.4Å, and Twist=+36°, whilst the PM/MP pair is left-handed Rise=+3.4Å, and Twist=–36°.

Now let's get into details to see why PP=MM, and PM=MP.

• The PP vs MM case is clear-cut:
  head Srini_PP.pdb Srini_MM.pdb
  ==> Srini_PP.pdb <==
  ATOM      1  P     A A   1      -0.299   9.399  -1.529
  ATOM      2  O1P   A A   1      -0.377  10.734  -2.162
  ATOM      3  O2P   A A   1       0.714   9.245  -0.460
  ATOM      4  O5'   A A   1      -1.738   8.985  -0.968
  ATOM      5  C5'   A A   1      -2.674   8.343  -1.855
  ATOM      6  C4'   A A   1      -3.346   7.182  -1.148
  ATOM      7  O4'   A A   1      -2.596   5.941  -1.284
  ATOM      8  C3'   A A   1      -3.530   7.338   0.361
  ATOM      9  O3'   A A   1      -4.771   6.752   0.737
  
  ==> Srini_MM.pdb <==
  ATOM      1  P     A A   1       0.299   9.399   1.529
  ATOM      2  O1P   A A   1       0.377  10.734   2.162
  ATOM      3  O2P   A A   1      -0.714   9.245   0.460
  ATOM      4  O5'   A A   1       1.738   8.985   0.968
  ATOM      5  C5'   A A   1       2.674   8.343   1.855
  ATOM      6  C4'   A A   1       3.346   7.182   1.148
  ATOM      7  O4'   A A   1       2.596   5.941   1.284
  ATOM      8  C3'   A A   1       3.530   7.338  -0.361
  ATOM      9  O3'   A A   1       4.771   6.752  -0.737
  The simple head Unix command shows clearly PP and MM are related by a rotation about y-axis by 180°. Thus, the two structures have identical y-coordinates, but opposite x- and z-coordinates. Naturally, the RMSD between them is perfectly 0.
• The case for PM vs MP is similar, as shown below.
  head Srini_PM.pdb Srini_MP.pdb
  ==> Srini_PM.pdb <==
  ATOM      2  O5*   A A   1       1.736   9.011  -0.504   1.0   0.0           O
  ATOM      3  C5*   A A   1       2.715   8.816   0.515   1.0   0.0           C
  ATOM      6  C4*   A A   1       3.299   7.393   0.557   1.0   0.0           C
  ATOM      8  O4*   A A   1       2.287   6.447   0.872   1.0   0.0           O
  ATOM      9  C1*   A A   1       2.480   5.346   0.001   1.0   0.0           C
  ATOM     11  N9    A A   1       1.290   4.498   0.000   1.0   0.0           N
  ATOM     12  C8    A A   1      -0.023   4.897   0.000   1.0   0.0           C
  ATOM     14  N7    A A   1      -0.878   3.903   0.000   1.0   0.0           N
  ATOM     15  C5    A A   1      -0.071   2.772   0.000   1.0   0.0           C
  
  ==> Srini_MP.pdb <==
  ATOM      2  O5*   A A   1      -1.747   9.015   0.517   1.0   0.0           O
  ATOM      3  C5*   A A   1      -2.723   8.818  -0.506   1.0   0.0           C
  ATOM      6  C4*   A A   1      -3.301   7.393  -0.552   1.0   0.0           C
  ATOM      8  O4*   A A   1      -2.286   6.450  -0.867   1.0   0.0           O
  ATOM      9  C1*   A A   1      -2.480   5.346  -0.001   1.0   0.0           C
  ATOM     11  N9    A A   1      -1.290   4.498   0.000   1.0   0.0           N
  ATOM     12  C8    A A   1       0.023   4.897   0.000   1.0   0.0           C
  ATOM     14  N7    A A   1       0.878   3.903   0.000   1.0   0.0           N
  ATOM     15  C5    A A   1       0.071   2.772   0.000   1.0   0.0           C
  The two structures have an RMSD of only 0.0174364 Å, which can be taken as zero in practical sense. For verification purpose, please download the superimposed PDB coordinates of PM onto MP (Srini-PM2MP.pdb), and its combination with the original MP in a MODEL/ENDMDL delineated PDB file (Srini-MP-PM-aligned.pdb).
  
  You can use Jmol or PyMOL to easily view the aligned structure file Srini-MP-PM-aligned.pdb to see for yourself how they overlap. Given below is the "nmr_ensemble" generated image based on Srini-MP-PM-aligned.pdb. Obviously, the two structures align virtually perfectly, in agreement with an RMSD of less than 0.02 Å.
  
  

I do not quite understand how Srini and you come to the conclusion that 3DNA is in error here. Unless I am missing something obvious, it is hard for me to imagine that simply rotate a DNA structure by 180 degrees about the y-axis should reverse its Rise and Twist. Maybe Srini can shed more light on his thought?

Xiang-Jun

[wolson]

Hi, Xiang-Jun.

While the structures may appear to be identical at the level of successive base pairs, the backbone connections/directions differ. The direction is clear from the color-coding of bases and strands in the attached images. Look, for example, at the different pathways of the red, blue, yellow, green base sequence on the red strand.

Best,
w
 

[xiangjun]

Then we may have different understanding as to what it means to be of the same structure: to me, since PP and MM have an RMSD of 0, they are IDENTICAL. Naturally, 3DNA should output the SAME parameters, as it does. As mentioned in my previous post, the case of PM vs MP follows the same argument.

Ask Sriri to show here in details most possible, how and why PP and MM are different.

Xiang-Jun

[xiangjun]

Hurrying for a meeting this morning, I did not notice the new set of 4 structures you attached when I posted my previous reply. Now things are becoming quite interesting. My arguments with regard to the first set of four structures you provided (Srini_PP.pdb, Srini_MM.pdb, Srini_PM.pdb and Srini_MP.pdb) still hold, i.e., PP=MM, and PM≈MP. There is no such things as "four distinctly different structures" there.

The new set of four structures (Srini_pp1.pdb, Srini_mm1.pdb, Srini_pm1.pdb, Srini_mp1.pdb), hereafter referred as PP1, MM1, PM1 and MP1, are completely different from the first set. 3DNA has no problem in identifying the four distinct forms, based on exactly the same algorithm as described in the 1997 JMB SCHNAaP paper. For example, for MM1, the output from 3DNA is as below:

Code: [Select]

****************************************************************************
Structure classification:

This is a right-handed unknown R-form structure
****************************************************************************
More specifically, Figure 7 of the SCHNAaP paper answers this question:

Figure 7. A representation of four possible arrangements for antiparallel nucleic acid duplexes. Left-handed W and Z-DNA are shown on the left (the characteristic zig-zag backbone pattern is not represented for simplicity). Right-handed A/B and hypothetical R-DNA are shown on the right. The Twist free ladder forms are shown in the middle column. In the top row, the minor groove faces the viewer, while in the bottom row, the major groove faces the viewer. The SCHNAaP coordinate system is also shown. These structures were generated using SCHNArP (see accompanying paper) with Twist= ±36° (0° for the ladder forms), Rise=3.34 Å, and all other step parameters are set to zero. Color scheme: the minor groove side, dark green; the major groove side, light green; and the backbone, red.

In connection with the new set of 4 structures, they correspond to the four forms classified in 3DNA (SCHNAaP) as below:

• PM1: W-form, left-handed
• MP1: Z-form, left-handed
• PP1: A/B-form, right-handed
• MM1: R-form, right-handed

Also as in SCHNAaP, right-handed structures (PP1/MM1) have positive Twist, and left-handed structures (PM1/MP1) have negative Twist. Moreover, they all have positive Rise.

I am really pleased to see the model structures representing the 4 possible distinct forms of double helices. I will consider to include them in future releases of the 3DNA distribution.

Xiang-Jun