# [Chimera-users] Define Plane

Catherine Jenifer Rajam Rajendran catrajen at umail.iu.edu
Sat Jul 1 10:05:57 PDT 2017

```Hi Eric,

Thank you so much for the links and the explanation!

- Catherine

On Fri, Jun 30, 2017 at 7:13 PM, Eric Pettersen <pett at cgl.ucsf.edu> wrote:

> Chimera simply calls numpy.linalg.svd (singular value decomposition) on an
> array of the xyz coordinate (after the centroid position has been
> subtracted from them).  The documentation for numpy.linalg.svd is here:
>
> https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.svd.html
>
> It looks like it in turn calls LAPACK routine_gesdd, which is documented,
> in general, here:
>
> https://software.intel.com/en-us/mkl-developer-reference-c-
> singular-value-decomposition-lapack-computational-routines?language=es
>
> It’s an implementation of singular value decomposition, described in
> general terms here:
>
> https://en.wikipedia.org/wiki/Singular_value_decomposition#
> Relation_to_eigenvalue_decomposition
>
> The math is pretty complicated.
>
> —Eric
>
> Eric Pettersen
> UCSF Computer Graphics Lab
>
>
>
>
> On Jun 30, 2017, at 10:09 AM, Catherine Jenifer Rajam Rajendran <
> catrajen at umail.iu.edu> wrote:
>
> Hi Elaine,
>
> Thank you for helping me understand it. Can you give me more details about
> how PDB file is decomposed to find the plane and normal. Like, how the
> eigenvectors are calculated from the atomic coordinates.
>
> Thanks,
> Catherine
>
> On Thu, Jun 29, 2017 at 7:23 PM, Elaine Meng <meng at cgl.ucsf.edu> wrote:
>
>>
>>
>> > On Jun 29, 2017, at 2:14 PM, Catherine Jenifer Rajam Rajendran <
>> catrajen at umail.iu.edu> wrote:
>> >
>> > Hi,
>> >
>> Hi Catherine,
>>
>> > I am trying to understand how the plane is defined in chimera. Can you
>> >
>> > "Define a plane for the specified atoms. Eigenvectors/values are
>> calculated from the atomic coordinates after subtracting the position of
>> their non-mass-weighted centroid. The plane is anchored at the centroid and
>> aligned with the first two eigenvectors (the third eigenvector is normal to
>> the plane)."
>> >
>> > Define a plane for the specified atoms.
>> > - specified atoms, i use 'sel protein’
>>
>> OK, so if using the graphical tool (Axes/Planes/Centroids) it uses the
>> selected atoms, meaning all the protein atoms if you had used “sel
>> protein.”  If using the “define” command, you can just specify “protein”
>> directly in the command to use all the protein atoms, without making a
>> selection.
>> >
>> > Eigenvectors/values are calculated from the atomic coordinates
>> > - atomic coordinates, so x,y,z coordinates of all atoms. (Can you
>> please explain a bit more like how and what you read from PDB file to
>> define plane).
>>
>> For the atoms you specified, there are ATOM lines in the PDB file with
>> X,Y,Z coordinates.  Each atom is a point in 3D (X,Y,Z).
>>
>> >
>> > after subtracting the position of their non-mass-weighted centroid
>> > - how is non-mass-weighted centroid is calculated
>>
>> It is the centroid of the points (atomic positions), not sure how else to
>> say it.  The average position of all the atomic points is the centroid.
>> Non-mass-weighted just means all the atomic points are treated equally,
>> instead of heavier atoms being treated as more important than lighter atoms.
>> >
>> > The plane is anchored at the centroid
>> > - which centroid is this? Is the protein moved to the origin(0,0,0)
>> position?
>> >
>> The centroid is the same centroid as in your previous question. Nothing
>> is moved.
>> >
>> > Thanks,
>> > Catherine
>>
>> You’re welcome.  I hope this helps,
>> Elaine
>> ----------
>> Elaine C. Meng, Ph.D.
>> UCSF Chimera(X) team
>> Department of Pharmaceutical Chemistry
>> University of California, San Francisco
>>
>>
>>
>>
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