Bending angle of internal loops

[cigdem]

Hi Xiang-Jun,

When I use json option, I see that you also calculate bending angle.

For 1e7k:

"bending_angle": 66.74

Since I am also interested in bending (and torsion) angles, could you please give me details on how you calculate the bending angle of internal loops? I wasn't able to find information on that.

Thank you.
Cigdem

[xiangjun]

Hi Cigdem,

Using 1e7k as an example, with the --more option, you will see the following output,

  stem#3[#2] bps=3
      strand-1 5'-GCC-3'
       bp-type    |||
      strand-2 3'-CGG-5'
      helix-form  AA
    helical-rise:   2.50(0.10)
    helical-radius: 9.58(0.87)
    helical-axis:    0.603     0.693    -0.394
       point-one:   13.025    22.254    97.826
       point-two:   15.968    25.639    95.900
...
  stem#4[#3] bps=2
      strand-1 5'-GG-3'
       bp-type    ||
      strand-2 3'-CC-5'
      helix-form  .
    helical-rise:   3.25(0.11)
    helical-radius: 9.79(0.24)
    helical-axis:    0.474    -0.849     0.234
       point-one:   31.349    15.331    89.586
       point-two:   32.889    12.574    90.346

The bending angle you referred to (66.74 degrees) is calculated based on the two helical axes. See FAQ entry "How to calculate DNA bending angle?" for more info.

The helical axis info is also available in --json output for each helix/stem when --more is specified. Please read the "DSSR User Manual", specifically Section 3.5 on "The --more option". To get a real feeling of what DSSR has to offer, it helps to reproduce the "results reported in the NAR paper".

HTH,

Xiang-Jun

[cigdem]

Hi Xiang-Jun,

Thank you for the explanation. I ran DSSR for a set of RNA structures and checked the bend angles. I see that the bend angle of the internal loops is always less than 90 degrees.

Could you please explain me how exactly do you calculate the bend angle after determining the helical axes? How do you choose the directions?

In my opinion, since the bend angle is the angle between two stems, it should be in 0-180 degrees range.

Best regards,
Cigdem

[xiangjun]

Hi Cigdem,

Yes, the bending angle as currently output from DSSR is defined to be within the range of [0, 90].

Xiang-Jun

[cigdem]

Hi Xiang-Jun,

In that case, if two stems making 130 degree between them will be calculated as having a 50 degree bend angle. Do you consider it as a possible kink-turn? For example look at 2JTP.

Cigdem

[xiangjun]

Hi Cigdem,

In that case, if two stems making 130 degree between them will be calculated as having a 50 degree bend angle.

Yes. The C function is as below:

Code: [Select]

double angle90_normalized_vectors(double *va, double *vb)
{
    double dval = dot_xyz_angle(dot_xyz(va, vb));

    return 90.0 - fabs(dval - 90.0);  /* absolute value */
}


Do you consider it as a possible kink-turn? For example look at 2JTP.

As shown below, DSSR detects a bending angle of 48 degrees in the internal loop in 2jtp, and a sheared G-A pair. However, the iloop misses some features required for a proper K-turn, and that's why it is marked as an "Undecided case". To be on the safe side, I'd suggest you not to take it as a K-turn.

Code: [Select]

# x3dna-dssr -i=2jtp.pdb --json | jq .Kturns

[
  {
    "index": 1,
    "type": "Undecided case with GA on helix#1 (same as C- and NC-helix)",
    "iloop_index": 1,
    "Cstem_index": 1,
    "NCstem_index": 2,
    "Cstem_pair": "A-U (1:A.A11,1:A.U24) WC",
    "NCstem_pair": "C-G (1:A.C21,1:A.G15) WC",
    "GA_pair": "G-A (1:A.G12,1:A.A23) Sheared",
    "bending_angle": 48.2,
    "strand1": {
      "num_nts": 16,
      "nts_short": "GGAUGGGGAAAGAAGC",
      "nts_long": "1:A.G1,1:A.G2,1:A.A3,1:A.U4,1:A.G5,1:A.G6,1:A.G7,1:A.G8,1:A.A9,1:A.A10,1:A.A11,1:A.G12,1:A.A13,1:A.A14,1:A.G15,1:A.C16"
    },
    "strand2": {
      "num_nts": 15,
      "nts_short": "GCAAUUUCCCCAUCC",
      "nts_long": "1:A.G20,1:A.C21,1:A.A22,1:A.A23,1:A.U24,1:A.U25,1:A.U26,1:A.C27,1:A.C28,1:A.C29,1:A.C30,1:A.A31,1:A.U32,1:A.C33,1:A.C34"
    }
  }
]
HTH,

Xiang-Jun