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

Mark Moll mmoll at cs.rice.edu
Thu Dec 11 17:21:35 PST 2008

```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},
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
> 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
>> http://www.cgl.ucsf.edu/mailman/listinfo/chimera-users
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>

--
Mark

```