Hi Tsjerk,
The system I am working on is the C-terminal tails of tubulin. The
structure of the tails is missing in all of the crystal structures of
tubulin, likely due to the flexibility of the tails. Since tubulin
is quite large, a heterodimer of almost 900 residues, it is not
really possible for us to adequately sample the tails' configuration
space by simulating the whole protein. What we have done is to
simulate nine different isotypes of the c-terminal tail fragment
(9-26 residues) using constant pressure REMD.
Among the properties we are interested in is quantifying and
comparing the flexibility of tails from the different isotypes. I
have performed PCA twice on this; fitting the all the C-alphas and
then the backbone atoms of the first three residues to a reference
structure. The motivation for the later fitting procedure is that
the fragments would be anchored to tubulin at the fragments N-
terminus. This is to look at how the fragments behave in the absence
of tubulin's potential but as if they are still anchored. When
performing the PCA we are fitting to a reference structure but still
using the deviations from the mean and not from the reference
structure. To compare the flexibility between the isotypes we had
hoped to normalize the eigenvalues.
I did note that I was inadvertently using the deviation from the
reference structure rather than from the mean (-ref). Is this what
you meant by a non-central covariance matrix? Using the deviation
from the mean I obtained standard deviations more inline with what I
originally expected. These are 0.8 nm at most if I normalize the
variance by the number of atoms.
My two questions are then:
1) does it make sense to fit the last three residues, as I described
above, for the purposes of PCA?
2) is it possible to compare the relative flexibilities of the
fragments using PCA?
Thank you,
Tyler
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 <[EMAIL PROTECTED]> 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 <[EMAIL PROTECTED]> 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 [EMAIL PROTECTED] (_
(________________________________________________________________)
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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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