[phenixbb] measuring the angle between two DNA duplexes

Pavel Afonine pafonine at lbl.gov
Tue Jan 21 18:06:29 PST 2014


next nightly build of Phenix should have this available in the command 
line (It's up to Nat when (and if) it's going to be available in the GUI).

   Given PDB file and two atom selections that allow to define two lines 
   the angle between these two lines. If atom selection defines two 
points then
   the line is defined uniquely and passes through these points. If atom
   selection defines more than two points then line coincides with the 
   axis of the cloud of points.

*Example 1:* two pairs of points are given to define two axes:

phenix.angle model.pdb "chain A and (resseq 1 and name CA or resseq 2 
and name CA)" "chain B and (resseq 1 and name CA or resseq 2 and name CA)"

Above, selection "chain A and (resseq 1 and name CA or resseq 2 and name 
CA)" selects two C-alpha atoms in residues 1 and 2 in chain A.
Analogously, "chain B and (resseq 1 and name CA or resseq 2 and name 
CA)" selects two C-alpha atoms in residues 1 and 2 in chain B.
Both atom selections define two lines, and the angle between these lines 
is output.

*Example 2:*

phenix.angle model.pdb "chain A" "chain B"

Here "chain A" selects all atoms in chain A, similarly second selection 
does for chain B.

*More Phenix atom selection syntax and examples:*

*Under the hood:*

If provided atom selections specify four points - two for each axis, 
then the angle is computed trivially.

If provided atom selections specify more than two points to define axis, 
then the following is done:

1) Select atoms corresponding to two selections;

2) Assign selected atoms occupancy=1 and B=20, and move atoms into an 
orthorhombic box;

3) Compute two Fourier maps of 4A resolution (perhaps 6A is even 
better!) corresponding to two sets of selected atoms;

4) Sigma-scale each synthesis, and truncate {m=0, if m<1, else m=m};

5) For each of the two maps compute symmetric 3x3 matrix like this:

sum(xn-xc)**2 sum(xn-xc)*(yn-xc)   sum(xn-xc)*(zn-zc)
sum(xn-xc)*(yn-xc)     sum(yn-yc)**2        sum(yn-yc)*(yz-zc)
sum(xn-xc)*(zn-zc)     sum(yn-yc)*(yz-zc)   sum(zn-zc)**2

where (xn,yn,zn) is the coordinate of nth grid point, the sum is taken 
over all grid points in within the radius that is equal to the half of 
max length of the selected set of atoms, and (xc,yc,zc) is the 
coordinate of the center of mass. Each some above is weighted by map value.

6) For each of the two matrices I would find its eigen-values and 
eigen-vectors, and select eigen-vectors corresponding to largest 

7) The desired angle is the angle between the two eigen-vectors found in 
step 6.

This may seem a bit convoluted but actual calculations take a fraction 
of a second, and the underlying code is just about 130 lines (including 
i/o and documentation page).

For those liking to dig in the code, the tests that exercise 
phenix.angle can be found here:
which basically define the scope of problems that I used so far to 
exercise the tool.

I notices that a minimal fraction of a helix need to contain at least 
5-6 residues: this typically provides 5% accuracy (of calculated angle 
using the above procedure compared to the known answer).

Please let me know of any problems, bugs, feature requests and 
suggestions etc *off-list*.


On 1/20/14, 5:48 AM, ?? wrote:
> Hi,
> I have a DNA model which is composed of two DNA duplexes. I want to 
> measure the angle between the two duplexes and if there a way to do it 
> in PHENIX or in other software?
> Thanks you very much for your help!
> Sincerely,
> Xiang
> -- 
> Li Xiang
> Department of chemistry,
> Purdue University
> Email:lixiang1642 at gmail.com <mailto:lixiang1642 at gmail.com>

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