Hi Tim, thanks for the reference! There is a number of instances where this approach is useful. In Phenix this is also used to determine density map peak sphericity (see cctbx/maptbx/sphericity.h) and to get initial values for refinement of anisotropic ADPs from map peaks. Sure I will play with this and visit as many corner cases as I could think of! All the best, Pavel On 1/21/14, 1:25 AM, Tim Gruene wrote:
Hi Pavel,
that's the method described in http://journals.iucr.org/a/issues/2011/01/00/sc5036/index.html ;-) based on the moments of inertia (a computer scientist might name it differently). I am not sure, though, you would get the desired result for short helices. E.g. a helix defined by three atoms the eigenvalue would point roughly in the direction of the external phosphates, which is far from parallel with the helix axis.
Best, Tim
On 01/21/2014 04:20 AM, Pavel Afonine wrote:
Hi Ed,
interesting idea! Although I was thinking to have a tool that is a little more general and a little less context dependent. Say you have two clouds of points that are (thinking in terms of macromolecules) two alpha helices (for instance), and you want to know the angle between the axes of the two helices. How would I approach this?..
First, for each helix I would compute a 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 atom, the sum is taken over all atoms, and (xc,yc,zc) is the coordinate of the center of mass.
Second, for each of the two matrices I would find its eigen-values and eigen-vectors, and select eigen-vectors corresponding to largest eigenvalues.
Finally, the desired angle is the angle between the two eigen-vectors found above, which is computed trivially. I think this a little simpler than finding the best fit for a 3D line.
What you think?
Pavel
On 1/20/14, 2:14 PM, Edward A. Berry wrote:
Pavel Afonine wrote: . .
The underlying procedure would do the following: - extract two sets of coordinates of atoms corresponding to two provided atom selections; - draw two optimal lines (LS fit) passing through the above sets of coordinates; - compute and report angle between those two lines?
This could be innacurate for very short helices (admittedly not the case one usually would be looking for angles), or determining the axis of a short portion of a curved helix. A more accurate way to determine the axis- have a long canonical duplex constructed with its axis along Z (0,0,1). Superimpose as many residues of that as required on the duplex being tested, using only backbone atoms or even only phosphates. Operate on (0,0,1) with the resulting operator (i.e. take the third column of the rotation matrix) and use that as a vector parallel to the axis of the duplex being tested. _______________________________________________ phenixbb mailing list [email protected] http://phenix-online.org/mailman/listinfo/phenixbb
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