[gmx-users] Re: PCA eigenvalue normalization

[Tyler Luchko]

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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