# [gmx-users] Eigenvector and eigenvalues

Ankita naithani ankitanaithani at gmail.com
Sun Jun 9 17:28:13 CEST 2013

```Hi Tsjerk,

Thank you so much for the helpful insight. It will surely help in clearing
some basic concepts about eigenvectors and the projections.
Also, since in the end you mentioned about my matrix being derived only
from C-alpha atoms which proves a limitation, would you reckon a backbone
analysis would be better suited to gain some helpful insight into protein
motions (Allosteric transitions, effector signalling??). It would however
be intensively complicated to derive for the whole protein considering mine
is a tetramer and a huge system.

Kind regards,

Ankita

On Sat, Jun 8, 2013 at 9:18 PM, Tsjerk Wassenaar <tsjerkw at gmail.com> wrote:

> Hi Ankita,
>
> It is important to use the correct names for things. The projection is the
> (scalar) inner product of the configuration (coordinates) with the
> eigenvector. This is also named the score of the configuration on the
> selected eigenvector. With g_anaeig -proj you get the projection. Each
> configuration of a trajectory has a projection, and you can plot them over
> time, or plot the projection on one eigenvector against another (-2d). You
> can also make a 3D plot of three selected eigenvectors (-3d), which is
> written out as a PDB file. The projection is not a structure, and you can't
> have a movie of structures. What you can do is extract the structures
> corresponding to the extreme projections (-extr). Those are always written
> per eigenvector. Since the eigenvectors are uncorrelated, the extremes are
> not defined for combinations of them. It is also possible to filter a
> trajectory on a set of eigenvectors. That will give a trajectory of
> (unphysical) structures, in which the projections on the non-selected
> eigenvectors are set to zero. This filtering is a matrix operation, using
> the matrix of selected eigenvectors and the corresponding atoms of the
> trajectory. Because the matrix of eigenvectors is derived from C-alpha
> atoms only in your case, it is not possible to get anything else out of it.
>
> Hope it helps,
>
> Tsjerk
>
>
>
> On Sat, Jun 8, 2013 at 1:06 PM, Ankita naithani <ankitanaithani at gmail.com
> >wrote:
>
> > Hi Tsjerk,
> >
> > [I am reposting it since my previous attachment was unable to proceed I
> > guess]
> >
> > Thank you for the reply. I am sorry but I don't have the snapshots with
> me
> > as my system was formatted and I lost that information. However, I
> > performed PCA again on Calpha atoms and this time my matrix is 5976X5976
> > wherein 1992 are my total number of calpha atoms. So, yes indeed I did
> > something foolish in the previous case to have got that result. However,
> I
> > will try to look at it and find my mistake so as to not repeat it again.
> >
> > I would be really grateful if you could help me with my another naive
> > query. I wanted to see the movie of first few eigenvectors as individual
> > and also separately. I know I can extract that with the help of g_anaeig
> > but as I did PCA on only calpha atoms, all I get in the projection of
> first
> > eigenvector is the calpha dots. Is there any way, I can visualise the
> > projection of whole protein on that particular eigenvector?
> >
> > Secondly, if I want to see the projection along first 10 eigenvectors and
> > last 10 eigenvectors (slow modes and fast modes), how could I proceed
> > because when I choose -first 1 -last 10, it gives me individual pdb files
> > corresponding to the eigenvectors.
> >
> > Third, as can be judged by my absolute naivety, I did a 2d projection on
> PC
> > 1 and PC 2. I can visualise that plot in grace as a 2d plot. An example
> > file is appended herein. I know each dot might correspond to a particular
> > conformation in the trajectory but I really have no idea as to how to
> > interpret the results and draw conclusions from these 2d plots and also
> 3d
> > pdb projections. Could you please guide me in the right direction to
> > understand these 2d plots and infer the significant results?
> >
> >
> > Kind regards,
> >
> > Ankita
> >
> >
> > On Thu, Jun 6, 2013 at 2:49 PM, Tsjerk Wassenaar <tsjerkw at gmail.com>
> > wrote:
> > >
> > >> Hi Ankita,
> > >>
> > >> Please provide the commands you've run and the screen output from
> > g_covar.
> > >>
> > >> Cheers,
> > >>
> > >> Tsjerk
> > >>
> > >>
> > >>
> > >> On Thu, Jun 6, 2013 at 3:44 PM, Ankita naithani <
> > ankitanaithani at gmail.com
> > >> >wrote:
> > >>
> > >> > Hi,
> > >> >
> > >> > I wanted to know about the eigenvectors and eigenvalues. I recently
> > >> > performed the principal component analysis (only the backbone into
> > >> > consideration) on a trajectory of 2000 residues. I obtained 15641
> > >> > eigenvectors and 17928 eigenvalues. There is a difference in the
> > number,
> > >> > which I am not quite sure off (perhaps that has to do with
> eigenvalue
> > >> for
> > >> > each eigenvector, and the eigenvector has 3 co-ordinates x,y,z. I
> > know I
> > >> > may be wrong completely but since there are 15641 eigenvectors, then
> > >> > shouldn't there by only 15641 eigenvalues for those eigenvectors)
> > >> >
> > >> > My second problem lies that I am trying to extract information or
> say
> > >> RMSF
> > >> > values for the first 10 eigenvectors (10 slowest modes) and the last
> > 10
> > >> > eigenvectors (fastest modes) and there I face segmentation fault. I
> > can
> > >> get
> > >> > information on the first 10 but when I try last 10 with the command
> as
> > >> > follows:
> > >> >
> > >> > g_anaeig -v eigenvec.trr -eig eigenval.xvg -rmsf eig_rmsf.xvg -first
> > >> 15631
> > >> >
> > >> > [where -first should have the starting eigenvector ]
> > >> >
> > >> > (I choose, 15631 since I want the plot for last 10 but I get
> > >> segmentation
> > >> > fault, which is also to do with the fact that the eigenval.xvg has
> > 17928
> > >> > values. This number doesn't match and so, maybe the plot is from
> > >> > 15631-17928). This has further confused me about the slowest and
> > fastest
> > >> > modes (and somehow I do need information on the first 10 slowest
> modes
> > >> and
> > >> > 10 fastest modes). In a broad way, the slowest modes would be the
> ones
> > >> with
> > >> > high eigenvalues say, first 10 eigenvectors in eigenval.xvg would
> give
> > >> the
> > >> > slowest 10 modes and the last 10 in eigenval.xvg should give the
> > >> fastest 10
> > >> > modes.
> > >> >
> > >> > Here, again I feel quite confused because eigenval.xvg has 17928
> > entries
> > >> > and in the legend, it says that x axis is the eigenvector index and
> y
> > >> axis
> > >> > is eigenvalue index so it leaves me quite perplexed about the
> problem.
> > >> >
> > >> > I am sorry for this extremely long and confusing post, but any help
> in
> > >> this
> > >> > regard would be really beneficial.
> > >> >
> > >> >
> > >> > Kind regards,
> > >> >
> > >> > Ankita
> > >> >
> > >> > --
> > >> > Ankita Naithani
> > >> > --
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> > >>
> > >>
> > >>
> > >> --
> > >> Tsjerk A. Wassenaar, Ph.D.
> > >> --
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> > >
> > >
> > >
> > > --
> > > Ankita Naithani
> > >
> >
> >
> >
> > --
> > Ankita Naithani
> >
> >
> >
> > --
> > Ankita Naithani
> > --
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>
>
>
> --
> Tsjerk A. Wassenaar, Ph.D.
> --
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--
Ankita Naithani

```