[chimera-dev] [Chimera-users] drawing a symmetry axis

[Tom Goddard]

Hi Mark, Dan, Mili,

  There are two common cases where we want to know the symmetry axes.  
In one case we have an assembly of multiple proteins with coordinates 
for the positions of all atoms.  In the other case we have a 
3-dimensional density map (a 3-d array of numbers) for example from 
electron microscopy.  In the molecule case the main difficulty is 
establishing a correspondence between symmetrically equivalent atoms.  
All the atoms have names and are part of amino acid sequences and the 
main method to address this is sequence alignment, not a any geometric 
criteria.  In the second case with density maps we don't have a very 
good solution.  We don't know the center of rotation and the data can be 
very noisy -- tomography of virus spikes or nuclear pores.  This is 
generally tackled by a 6 degree-of-freedom search calculating the 
correlation of the density map with a rotated and translated copy of 
itself.  This can be slow (minutes).  We generally work on interactive 
methods taking at most a few seconds to compute.  I'll be working on 
this problem in the next few months and am open to ideas.  I'll have to 
look at more than the abstract of the paper you mention to know if that 
could help.  We are always looking for collaborators.

Thanks,

    Tom



Mark Moll wrote:
> Tom (and other Chimera developers),
>
> You might be interested in the paper below. It describes a method for  
> computing the best axis of symmetry and computing a `symmetrized'  
> version of a symmetric complex (i.e. with deviations from symmetry  
> removed). They have extended the analysis since this paper appeared to  
> other forms of symmetry, but this hasn't appeared yet, AFAIK. (The  
> authors are cc-ed in case they want to follow up.) The first author  
> may have a reference matlab implementation that could probably without  
> too much trouble be converted into python using numpy.
>
> @article{shah2006a-symmetry-preserving-singular-value,
> 	Abstract = {A reduced order representation of a large data set is  
> often realized through a principal component analysis based upon a  
> singular value decomposition (SVD) of the data. The left singular  
> vectors of a truncated SVD provide the reduced basis. In several  
> applications such as facial analysis and protein dynamics, structural  
> symmetry is inherent in the data. Typically, reflective or rotational  
> symmetry is expected to be present in these applications. In protein  
> dynamics, determining this symmetry allows one to provide SVD major  
> modes of motion that best describe the symmetric movements of the  
> protein. In face detection, symmetry in the SVD allows for more  
> efficient compression algorithms. Here we present a method to compute  
> the plane of reflective symmetry or the axis of rotational symmetry of  
> a large set of points. Moreover, we develop a symmetry preserving  
> singular value decomposition (SPSVD) that best approximates the given  
> set while respecting the symmetry. Interesting subproblems arise in  
> the presence of noisy data or in situations where most, but not all,  
> of the structure is symmetric. An important part of the determination  
> of the axis of rotational symmetry or the plane of reflective symmetry  
> is an iterative reweighting scheme. This scheme is rapidly convergent  
> in practice and seems to be very effective in ignoring outliers  
> (points that do not respect the symmetry).
> },
> 	Author = {Mili I. Shah and Danny C. Sorensen},
> 	Doi = {10.1137/050646676},
> 	Journal = {{SIAM} Journal on Matrix Analysis and Applications},
> 	Number = {3},
> 	Pages = {749--769},
> 	Title = {A Symmetry Preserving Singular Value Decomposition},
> 	Url = {http://link.aip.org/link/?SML/28/749/1},
> 	Volume = {28},
> 	Year = {2006}
> }
>
>
> On Dec 11, 2008, at 6:49 PM, Thomas Goddard wrote:
>
>   
>> Hi Philip,
>>
>>   I don't know an easy way to show the symmetry axis of your dimer  
>> as a
>> line or rod using the normal Chimera commands.  But you could do  
>> this by
>> modifying the keyboard shortcut ai Python code.
>>
>>   You would edit the file
>>
>> 	chimera/share/MatchDomains/__init__.py
>>
>> or on the Mac it would be
>>
>> 	Chimera.app/Contents/Resources/share/MatchDomains/__init__.py
>>
>> (and on the Mac you'd need to click the Chimera icon and choose "Show
>> package contents" to see in the Chimera.app folder).
>>
>>   You would change the transform_schematic() routine (line 171) code  
>> from
>>
>> #    tarray = ((0,1,2),(0,2,3))
>>     tarray = ((0,1,2),(0,2,3),(0,1,5),(0,5,4),(1,2,6),(1,6,5),
>>               (2,3,7),(2,7,6),(3,0,4),(3,4,7),(4,5,6),(4,6,7))
>>     g1 = sm.addPiece(varray, tarray, from_rgba)
>> #    g1.displayStyle = g1.Mesh
>>
>>     from Matrix import xform_matrix, apply_matrix
>>     tf = xform_matrix(xform)
>>     corners2 = [apply_matrix(tf, p) for p in corners]
>>     varray2 = corners2
>>     g2 = sm.addPiece(varray2, tarray, to_rgba)
>> #    g2.displayStyle = g2.Mesh
>>
>>
>> to
>>
>> #    tarray = ((0,1,2),(0,2,3))
>>     tarray = ((0,1,1),)
>> #    tarray = ((0,1,2),(0,2,3),(0,1,5),(0,5,4),(1,2,6),(1,6,5),
>> #              (2,3,7),(2,7,6),(3,0,4),(3,4,7),(4,5,6),(4,6,7))
>>     g1 = sm.addPiece(varray, tarray, from_rgba)
>>     g1.displayStyle = g1.Mesh
>>     g1.lineThickness = 3
>>
>>     from Matrix import xform_matrix, apply_matrix
>>     tf = xform_matrix(xform)
>>     corners2 = [apply_matrix(tf, p) for p in corners]
>>     varray2 = corners2
>> #    g2 = sm.addPiece(varray2, tarray, to_rgba)
>> #    g2.displayStyle = g2.Mesh
>>
>> Then restart Chimera and use the script you referred to.  It will  
>> draw a
>> line for the axis with width 3 pixels.  In the future we will try to  
>> add
>> some simpler capability to find and show symmetry axes.
>>
>> 	Tom
>>
>>
>> Philip Wurm wrote:
>>     
>>> Hi,
>>> i have a protein dimer and i would like to show the symmetry axis. I
>>> found a script in this mailing list:
>>>
>>> http://www.cgl.ucsf.edu/pipermail/chimera-users/2008-October/003140.html
>>>
>>> which works quite nice. But i would like to have a nicer  
>>> representation
>>> of my symmetry axis, not this two slabs. Just a line or thin rod  
>>> would
>>> be nice.
>>>
>>> Does anyone know how to do this?
>>>
>>> Thanks,
>>> Philip
>>> _______________________________________________
>>> Chimera-users mailing list
>>> Chimera-users at cgl.ucsf.edu
>>> http://www.cgl.ucsf.edu/mailman/listinfo/chimera-users
>>>       
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>
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