bending angle of DNA

[jauchr]

Dear all,

We are working on Sox proteins that bind the minor groove of DNA and induce a rather drastic bend. 3DNA is of fantastic help to analyze base-pair and base step parameters. However, it's common standard to report an actual overall bending angle. It's surely possible to estimate such a bending angle from structural models and report a rough value - we have done so in the past. But I am wondering whether there is a more accurate way of defining this angle (i.e. by defining a kink point and helical axis extending from there).

Regards,

Ralf

[xiangjun]

Dear Ralf,

Thanks for posting a question which should be of general interest. Overall, a (bending) angle is defined by two vectors. For DNA bending angle, the question then becomes how the two (helical) axes are calculated. In 3DNA, if the input structure is not heavily curved, the following section is produced (using [mono:330yz4f2]355d/bdl084[/mono:330yz4f2] as an example):

[pre:330yz4f2]Global linear helical axis defined by equivalent C1' and RN9/YN1 atom pairs                                        
Deviation from regular linear helix: 3.30(0.52)
Helix:    -0.127  -0.275  -0.953
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)[/pre:330yz4f2]

If your structure is curved overall, but with two relatively straight fragments (via a kink), you will need to analyze the two segments separately to get the above information. With the two unit vectors (defined in Helix: line), it is straight forward to calculate the angle between them. Of course, another way to think of the issue is to fit a perfectly straight B-DNA fiber model onto each of the two relatively straight fragments, and calculate the angle between them. The two approaches should give comparable (but usually not identical results).

Several ago while at Rutgers, I helped Chen et al. (in Dr. Berman's group) analyzed some CAP-DNA complexes to quantify bending angles. I sense your case is similar to his. Please see: http://www.ncbi.nlm.nih.gov/pubmed/11724532 and http://www.ncbi.nlm.nih.gov/pubmed/11724533.

The DNA bending question has appeared quite a few times in the forum; you may find it helpful to check "Calculating the angle of DNA curvature".

Specifically, you may want to repeat 3DNA NP2008 paper, protocol (recipe) no. 4 on "Automatic identification of double-helical regions in a DNA–RNA junction", which provides detailed steps on calculating the angle between helices #1 and #3. Note also:

The chosen view allows for easy visualization and protractor measurement of the overall bending angle between the two relatively straight helices (the red horizontal helix h1 and the green vertical helix h3). This intuitive approach, initially developed to quantify the bending angles of a series of catabolic activator protein–DNA complexes67, yields sensible results when other methods fail.

HTH,

Xiang-Jun

[jauchr]

Dear Xiang-Jun,

Thanks for fast and helpful response!

Works a treat.

For R users: you should be able to get the angle with this short calculation:
(180/pi)*acos(sum(vector1*vector2))
Vector 1 and 2 you will obtain following the recipe posted by Xiang-Jun above.  
We get an angle of 72 degree for 3f27 (close to the guesstimated 80deg reported).

Cheers,

Ralf