# [gmx-users] combined ED analysis

bgroot at gwdg.de bgroot at gwdg.de
Tue Dec 14 22:25:02 CET 2004

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> On Tue, 2004-12-14 at 17:56 +0100, vincenzo venditti wrote:
>
> > >I don't understand what you want to do.
> > >What do you mean with "fluctuations along eigenvectors"
> > >and with "show different averaged projections"?
> >
> > >
> >
> > If I've for example for the 4 sistems under analysis differnt averaged
> > projection along the second eigenvector:
> >
> >                         sistem 1                  sistem 2
> > sistem 3               sistem 4
> >
> > vector 2             3.378                    2.547
> > -3.375                  -2.540
> >
> > And I've for the same sistems along the same eigenvector different
> > rmsf value:
> >
> >                         sistem 1                  sistem 2
> > sistem 3               sistem 4
> >
> > vector 2             1.2                           0.8
> > 0.5                      0.3
> >
> > Could I say that sistem 1 is more flexible than the other sistem along
> > this direction of motion?
> Yes, since the covariance analysis is done on the combined trajectories.

agreed.

> However you need to consider whether, say, the first 10 eigenvectors are
> equally important in all simulations, by computing the projections and
> the combined volume. If, e.g. in system 3 your eigen vector 11 has the
> largest msf you have to reconsider your analysis.

I don't think this is likely, since in a combined covariance analysis
the largest fluctuations will be represented by the first couple of
eigenvectors, irrespective of their origin. So it doesn't matter in this case
if all 4 sub-trajectories sampled such a motion or if it was only sampled in
one. If the amplitude is large enough it will be among the first couple of
eigenvectors of the combined analysis (as the eigenvectors are sorted by
eigenvalue). This is actually the main advantage of such a combined analysis:
all large amplitude fluctuations are automatically included, whereas if one
would have cross-projected simulations on eigenvectors of another trajectory,
then indeed the effect you mentioned (overlooking lare-amplitude motions
present in one trajectory but not in the other) may become relevant.

The problem (of e.g. eigenvector 11 corresponding to the largest ampitude
motion in system 3) can only occur when the fluctuations are *very* unevenly
distributed among the 4 systems, such that in this case the first ten
eigenvectors would be dominated by ev's 1,2 and 4 and only in the 11th ev
system 3 would become relevant. First, this is not particularly likely (as one
generally would combine "similar" molecular systems into such an analysis),
second, one would notice this (by the extremely low fluctuations for system 3
along the first ten eigenvectors), and third, it would question the relevance
of this motion anyway as it only represents the 11th-largest amplitude overall
motions.

Bert

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