Re: [PyMOL] Rotation/Translation

[Christoph G. <cg...@uc...>]

On 5/29/2010 8:21 AM, J. Fleming wrote:
> Hello,
>
> I've been using 'super' to align the C-alphas within one domain of two
> different models of the same protein while leaving the second domain
> to move freely.  I can do this using:
>
> super (A and resid 1-100 and name ca), (B and resid 1-100 and name ca)
>
> What I would like to do is determine the rotation and translation of
> model B's second domain as it moves away from A's second domain.
>
> I can output a matrix after running super using:
>
> print cmd.get_object_matrix("A")
>
> How do I go from the matrix to an angle and distance?
>
> Thanks for any thoughts,
> Jon
>


To extract Euler rotation angles from the superimposition matrix you can 
use the euler_from_matrix function of the transformations.py module at 
<http://www.lfd.uci.edu/~gohlke/code/transformations.py.html>. If you 
rather have a rotation angle and axis use the rotation_from_matrix 
function. You might have to use the transpose of the matrix returned by 
PyMOL, not sure. The extraction of the translation vector has already 
been explained.

To find how domain #2 is translated and rotated in molecule B relative 
to A when the domains #1 of A and B are superimposed, you can write a 
Python script outside of PyMOL. The following untested (!) script 
assumes that you have (1) the C-alpha coordinates of molecule A and B as 
homogeneous coordinate numpy arrays of shape (4, *), and (2) the C-alpha 
atom indices that belong to domain 1 and 2 as Python sequences or slices:


import numpy
import transformations

# transform B such that domain1 of A and B overlap
S0 = transformations.superimposition_matrix(
          B[:, domain1], A[:, domain1])
B = numpy.dot(S0, B)

# calculate matrix to transform domain2 of A to B
S1 = transformations.superimposition_matrix(
          A[:, domain2], B[:, domain2])

# extract translation vector and Euler rotation angles from S1
translation = S1[:3, 3].copy()
eulerangles = transformations.euler_from_matrix(S1)


--
Christoph