[Chimera-users] meaning of the ANISOU PDB parameters

[Eric Pettersen]

On Feb 10, 2012, at 1:55 PM, Julian Chen wrote:

> hi Eric,
>
> First of all, hello, I was in Stroud's lab for many years, until  
> 2003, when I left SF.

Hi Julien!

> I am in a rather interesting situation where we have been dealing  
> with neutron and X-ray refinement, and we have been able to do  
> anisotropic refinement on selected hydrogen atoms, from having high  
> resolution neutron data. I've been using Chimera.
>
> I am still somewhat confused as to the meaning of the six ANISOU  
> terms, I understand that the first three describe the three  
> orthogonal axes of the ellipsoid, and that the last three somehow  
> relate this to the coordinate space.

The six terms actually describe a 3x3 matrix that is symmetric about  
the diagonal.  The eigenvectors and eigenvalues of that matrix are the  
atomic displacement axes and the mean squares of the displacements  
respectively.  The first thing to know is that the values shown in the  
ANISOU records are scaled by 10**4.  The other thing to know is that  
the six numbers correspond to these positions in the matrix:  1,1 2,2  
3,3 1,2 1,3 2,3.  Since the eigenvalues are mean squares, one  
typically works with the square roots of the eigenvalues.

> Specifically, I want to look at the ANISOU for the H/D atoms, and  
> want to try to correlate it to its bonded neighbor (the C or the N  
> or the O). If possible, I'd like to extract some vector for the  
> 'directionality' of the aniso atoms and relate them to one another.  
> I want to see if the vibrational motions of the hydrogen are  
> correlated to the vibrational motions of its bonded neighbor. Is  
> there anything in CHIMERA that could do something like this, or some  
> appropriate mathematical formula that could output the right sort of  
> information? The ellipsoids option in the program gives a  
> qualitative description, but I'd like to get something a bit more  
> quantitative in nature.

Depending on how comfortable you are with programming in Python, you  
could either write your own external code based on the info above, or  
write something that runs in Chimera.  The latter does have the  
advantage of you not having to write PDB-parsing code an so on.

In Chimera, atoms with corresponding ANISOU records have an 'anisoU'  
attribute which is a 3x3 matrix (the matrix is often referred to as  
'U' in the literature, hence ANISOU record).  This code snippet  
(basically copied from the Chimera's Aniso module) will extract the  
eigenvectors/values for an atom and take the root of the values:

from numpy.linalg import svd
ignore, lengths, axes = svd(atom.anisoU)
from numpy import sqrt
lengths2 = sqrt(lengths)

Let me know if you need more info or help with scripting.

--Eric

                         Eric Pettersen
                         UCSF Computer Graphics Lab
                         http://www.cgl.ucsf.edu


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