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

[Mark Moll]

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
>> _______________________________________________
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>> Chimera-users at cgl.ucsf.edu
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-- 
Mark