DNA bend angle calculation

[Joseph Hussain]

We are trying to calculate DNA bend angle using the output obtained from
X3DNA online software, we use the equation given below to solve the
problem and we were unsuccessful.

acos(dot(a, b)) * 180/pi      as mentioned in the blog of Prof. Xiang-Jan Lu

Can anyone please help us in solving the bend angle for the following vectors

Global linear helical axis defined by equivalent C1' and RN9/YN1 atom pairs
Deviation from regular linear helix: 3.42(0.40)
Helix:    -0.007  -0.076   0.997
HETATM 9998  XS    X X 999      68.227   2.641 -26.513
HETATM 9999  XE    X X 999      67.797  -2.012  34.748
Average and standard deviation of helix radius:
      P: 9.51(0.62), O4': 6.66(0.67),  C1': 6.05(0.65)Helix:    -0.007  -0.076   0.997

Looking for your reply

Regards,
Joseph Hussain
Research scholar, Dept. of Chemistry,
IIT Bombay, Mumbai

P.S Prof. Xiang-Jan Lu, some how I could not post this in the forum, can you please help me in posting this message. Thank you

[xiangjun]

Thanks for posting your question on the forum. I guess you are referring to the FAQ post "How to calculate DNA bending angle?".

we use the equation given below to solve the problem and we were unsuccessful. ...

Could you be specific on how you "were unsuccessful"? What vectors did you use and what result bending angle did you expect?

Xiang-Jun

[Joseph Hussain]

Hi,
Thank you for your reply.

the vectors we used were

HETATM 9998  XS    X X 999      68.227   2.641 -26.513
HETATM 9999  XE    X X 999      67.797  -2.012  34.748

and the output obtained from w3dna is followed

Global linear helical axis defined by equivalent C1' and RN9/YN1 atom pairs
Deviation from regular linear helix: 3.42(0.40)
Helix:    -0.007  -0.076   0.997
HETATM 9998  XS    X X 999      68.227   2.641 -26.513
HETATM 9999  XE    X X 999      67.797  -2.012  34.748
Average and standard deviation of helix radius:
      P: 9.51(0.62), O4': 6.66(0.67),  C1': 6.05(0.65)Helix:    -0.007  -0.076   0.997

we have normalized the vectors and got the dot product of two vectors and applied acos on the result of dot product of two vectors and then multiplied with 180/Pi. Precisely the following equation we have used to calculate the bend angle

acos(dot(a, b)) * 180/pi

Thank you

Joseph Hussain

[xiangjun]

Okay. Now I see where the problem is.

HETATM 9998  XS    X X 999      68.227   2.641 -26.513
HETATM 9999  XE    X X 999      67.797  -2.012  34.748

Those pseudo HETATM records are just the two end points one helix passes through. As shown in the bending angle FAQ, The normalize helical axis is:

Helix:    -0.007  -0.076   0.997

So this section defines only ONE (1) helix. You need another relatively straight helical fragment to define a second helix in a similar fashion, then you can get the bending angle using the simple mathematical formula.

Read carefully the following paragraph from the FAQ on bending angle calculation, and repeat recipe #4 of the 2008 3DNA Nature Protocols should clarify your confusion.

With the two HETATM records, one can easily add them into the original PDB file to display the helical axis using a molecular graphics programs (e.g., RasMol, Jmol or PyMOL). Moreover, the two helix vectors can be used to reorient the original PDB structure into a view so that one helical fragment lies along the x-axis, and the other in the xy-plane. As documented in detail in recipes #4 on "Automatic identification of double-helical regions in a DNA–RNA junction" of the 2008 3DNA Nature Protocols paper, "The chosen view allows for easy visualization and protractor measurement of the overall bending angle between the two relatively straight helices."

Please report back in details how it goes. Based on your feedback, I will consider to refine the FAQ post to make it clearer.

Alternatively, you may want to try Curves+ which provides a more comprehensive bending analysis.

Xiang-Jun