How to draw a helical axis

[xiangjun]

While experimentally-determined DNA/RNA double helices (as deposited in the PDB) are never strictly linear, oligonucleotides or fragments of large nucleic acid molecules may be approximately straight. In such cases, it is informative to draw a helical axis to visualize them in a 3D molecular viewer (such as PyMOL or Jmol). Moreover, helical axes from two different fragments can be used to determine the "bending angle" between them. 3DNA and DSSR provide this info, as illustrated below using PDB id 355d as an example.

• Running 3DNA (v2.3) find_pair 355d.pdb | analyze, the output file 355d.out contains the following segment:
  

  Global linear helical axis defined by equivalent C1' and RN9/YN1 atom pairs
  Deviation from regular linear helix: 3.30(0.52)
  Helix:    -0.1269   -0.2753   -0.9530
  HETATM 9998  XS    X X 999      17.536  25.713  25.665
  HETATM 9999  XE    X X 999      12.911  15.677  -9.080
  Average and standard deviation of helix radius:
        P: 9.42(0.82), O4': 6.37(0.85),  C1': 5.85(0.86)

  The two HETATM records can be copy-and-pasted into the original PDB file. The line can be easily drawn between them, which is the helical axis.
  
  
• Running DSSR: x3dna-dssr -i=355d.pdb --more, the output contains the following segment:
  

    helix#1[1] bps=12
        strand-1 5'-CGCGAATTCGCG-3'
         bp-type    ||||||||||||
        strand-2 3'-GCGCTTAAGCGC-5'
        helix-form  BBBBBBBBBBB
      helical-rise:   3.30(0.52)
      helical-radius: 9.42(0.82)
      helical-axis:   -0.127    -0.275    -0.953
         point-one:   17.536    25.713    25.665
         point-two:   12.911    15.677    -9.080

  With the --helical-axis option, as in x3dna-dssr -i=355d.pdb --more --helical-axis, DSSR also generates a file named dssr-helicalAxes.pdb with the following content:
  

  REMARK-DSSR: helix#1
  ATOM      1  P1   DC A   1      17.536  25.713  25.665  1.00 10.97      H1   P
  REMARK-DSSR: helix#1
  ATOM      2  P2   DG A  12      12.911  15.677  -9.080  1.00 18.40      H1   P
  CONECT    1    2
  CONECT    2    1

  Loading both 355d.pdb and dssr-helicalAxes.pdb into PyMOL, one can get an image as attached.