Re: [PyMOL] Rotation/Translation

[Martin Hoefling]

Quoting J. Fleming moloch...@gmail.com:

Hello Jon  ML,

 print cmd.get_object_matrix(A)

 How do I go from the matrix to an angle and distance?

according to

http://www.pymolwiki.org/index.php/Get_object_matrix

you should recieve a 4x4 matrix which contains the inital and target  
translation as lower and right vector. Their difference should be the  
translation. The 3x3 top-left ist the rotation matrix.

The angular extraction depends on which angle(s) you're interested in.  
If you e.g. have a vector, that describes you inital orientation  
(along a helix), you can transform it via the rotation matrix and then  
determine the angle between both.

If youre interested in the rotation axis and the angle, have a look  
into Finding the rotation matrix

http://en.wikipedia.org/wiki/Rotation_matrix


Hope this helps.

Best

Martin

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Re: [PyMOL] Rotation/Translation

[Christoph Gohlke]

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

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[PyMOL] Rotation/Translation

[J. Fleming]

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

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