[chimera-dev] [Chimera-users] drawing a symmetry axis
Mili Shah
mishah at loyola.edu
Sat Dec 13 06:35:09 PST 2008
Hi Tom--
How do you get your initial guess to the rotation axis? One way of doing
this is to look at the principal axis (eigenvector of the covariance
matrix) associated with the most distinct eigenvalue. Using this method
you do not need to know the correspondence of symmetric pairs. However,
there are drawbacks to this method. First you have to have a 'distinct'
eigenvalue. We have shown that there may not be one in the case of noisy
data.
There may be a way to use this idea as an initial guess for
correspondence...
M
On Fri, 12 Dec 2008, Tom Goddard wrote:
> 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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>>> Chimera-users at cgl.ucsf.edu
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>>>
>>>
>>
>>
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