[gmx-users] Re: PCA eigenvalue normalization

[Tsjerk Wassenaar]

Hi Tyler,

First, what question are you trying to answer? You're different peptides
have completely different conformational spaces, simply because of the
differences in degrees of freedom, so you can't compare the PCA results from
one system with the other. That is, unless you pick a subset from each
system, consisting of comparable particles, for which you can safely make
the assumption that under equal circumstances should give the same
eigenvectors and -values. From that assumption, you could try to make an
assessment whether the behaviour between the systems is different.

Also, since you're using only the first three residues for fitting, you
generate a non-central covariance matrix. That would be useful if you would
like to exaggerate certain motional features, right, but it makes the
interpretation of PCA results difficult. If it's for the purpose of
comparing things, I wouldn't go there if I were you. The non-centrality is
also the reason that your standard deviations end up high. You're not
subtracting the mean so your standard deviations is sqrt( sum(x^2)/N )
rather than sqrt( sum((x-average)^2))/N ). Is this really what you want to
do? What are you expecting to get from this? I'd like to know the question
your trying to answer and your assumptions on the nature of the data...

Cheers,

Tsjerk

On 4/7/06, Tyler Luchko <tluchko at ualberta.ca> wrote:
>
> Hello,
>
> Thank you for the previous responses.  I still have some questions
> about the eigenvalues however.
>
> I should note that the frames of my trajectory have been fit to a
> reference structure using the backbone atoms of the first three
> residues.  This is because the peptide is a fragment of a much larger
> protein.
>
> 1) If I wish to compare the eigenvalues of several peptides of
> different lengths how would I normalize the eigenvalues?  Do I simply
> divide by the number of atoms used in the calculation?
>
> 2) If the eigenvalue represents the sum of the variances for each
> particle along the eigenvector then dividing the eigenvector by the
> number of atoms used in the calculation should be the average
> variance. Likewise, the square root of this should be the average
> standard deviation per atom.  In my case, the first eigenvector is a
> stretching in the length of the peptide.  Shouldn't the average
> standard deviation per atom along this stretching motion be smaller
> that the standard deviation in the length of the entire peptide, or
> at least smaller than the extended length of the peptide?
>
> Thank you,
>
> Tyler
>
> > Hi Tyler,
> >
> > Note that the eigenvalue represents the sum of the variances for each
> > particle along the associated eigenvector. That seems quite
> > reasonable to
> > me.
> >
> > Tsjerk
> >
> > On 4/6/06, Tyler Luchko <tluchko at ualberta.ca> wrote:
> >>
> >> Hello,
> >>
> >> I have performed PCA analysis, without mass weighting, on a peptide
> >> using g_covar and g_anaeig.  The first principal component generally
> >> corresponds to the stretching of the peptide.  I understand that each
> >> eigenvalue represents the variance in the motion along the associated
> >> eigenvector.  However, the square root of the variance for the first
> >> eigenvalue is ~20 nm while the maximum extended length of any peptide
> >> is ~3 nm.  I have tried normalizing the eigenvalues by the number of
> >> atoms used for the analysis (73) but this gives the standard
> >> deviation of the motion to be ~2.2 nm, still much too large.  I would
> >> like to know how to normalize the eigenvalues to obtain reasonable
> >> standard deviations from the eigenvalues.
> >>
> >> Thank you,
> >>
> >> Tyler
> >>
> >>
> >>   ________________________________________________________________
> >> (_    Tyler Luchko                           Ph.D. Candidate    _)
> >>   _)   Department of Physics            University of Alberta   (_
> >> (_    Edmonton, Alberta, Canada                                 _)
> >>   _)   780-492-1063                       tluchko at ualberta.ca   (_
> >> (________________________________________________________________)
> >>
> >>
> >>
> >> _______________________________________________
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> >
> >
> >
> > --
> >
> > Tsjerk A. Wassenaar, M.Sc.
> > Groningen Biomolecular Sciences and Biotechnology Institute (GBB)
> > Dept. of Biophysical Chemistry
> > University of Groningen
> > Nijenborgh 4
> > 9747AG Groningen, The Netherlands
> > +31 50 363 4336
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--

Tsjerk A. Wassenaar, M.Sc.
Groningen Biomolecular Sciences and Biotechnology Institute (GBB)
Dept. of Biophysical Chemistry
University of Groningen
Nijenborgh 4
9747AG Groningen, The Netherlands
+31 50 363 4336
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