# [gmx-users] Overlap between PC motions

Tsjerk Wassenaar tsjerkw at gmail.com
Thu May 30 14:06:18 CEST 2013

```Hi Miguel,

The fitting doesn't play a role; it's the dynamics of the system in the
internal frame. Because the internal frame moves, you fit, so that any
contribution due to the rigid body motion is removed.

For the rest you have to look at it like this: You start out somewhere and
walk (relax) towards some city, several kilometers away. You get there and
get lost in the streets, making random walks. Now, what you do with
covariance analysis is looking at the displacements around the mean
position. Your mean position will lie somewhere between your starting
position and the place where you ended up. The deviations from the mean
will be dominated by vectors pointing from wherever you are in the city
towards your starting point. That will be reflected in the covariance
matrix, which doesn't change much, certainly not in terms of the directions
of the first few eigenvectors.
Probably you're actually more interested in the things you do in the city,
your native configuration energy well. But to analyze that, you have to cut
off the part of the journey that brought you there. So it makes sense to do
the covariance analysis on the last half or quarter of the trajectory. It
would also be interesting to check the convergence from the other side of
the trajectory, varying the starting point of the analysis, rather than the
end point.

Hope it helps,

Tsjerk

On Thu, May 30, 2013 at 1:37 PM, Miguel Ángel Mompeán García <
mig.mompean at gmail.com> wrote:

> Hi Tsjerk,
>
> Thanks for the reply! So, let me see if I am getting the things right. The
> same fitting structure is used for the overlap calculation. Since the
> averaged structure is used for the covariance matrices, this is the reason
> why the relaxation is included. Am I right?
> The overall behavior of the system is that the structure keeps very
> "compact" and one additional hydrogen bond between two residues is formed
> at ~60ns, and stable till the end of the run, as computed with g_hbond.
> That interaction is already present in the average structure. So if I
> understood properly your comment, from the time window 0-70 up to the end,
>  there will not be significant contributions to the covariance matrix.
>
> Thanks for your valuable comments. Highly appreciated!
>
>
> 2013/5/30 Tsjerk Wassenaar <tsjerkw at gmail.com>
>
> > Hi Miguel,
> >
> > Sorry for not responding earlier, but the question isn't really simple :)
> > What you do is determining the covariance matrix from the start up to a
> > certain point and see for different end points what the overlap is with
> the
> > covariance matrix from the whole. This means that in all cases, the
> > relaxation of the system is included, and this is the dominant
> contribution
> > to your covariance matrix. At some point, the system has reached the
> region
> > around B and then stays there. All kinds of things may be happening, but
> > they're overwhelmed by the changes associated with the relaxation. Hence,
> > the part of the trajectory after 70 ns doesn't contribute significantly
> to
> > the covariance matrix anymore.
> >
> > Hope it helps,
> >
> > Tsjerk
> >
> >
> >
> > On Thu, May 30, 2013 at 12:26 PM, Miguel Ángel Mompeán García <
> > mig.mompean at gmail.com> wrote:
> >
> > > Dear all,
> > >
> > > I posted some days ago an issue regarding overlap values. If any of you
> > is
> > > experienced with this I would appreciate some comments. Please find
> below
> > > the mentioned post:
> > >
> > >
> > > I am doing PCA on a 110ns run.
> > > When calculating the subspace overlap from independent PCA performed in
> > > different time windows, I expect the overlap to be 1 only when the time
> > > interval is equal to 110ns, since both covariance matrices are
> identical.
> > > However, I found that from the interval 0-70 forwards (I'm increasing
> > each
> > > window in 10ns) the overlap reaches that value. Is this expected? From
> > the
> > > rmsd, cosine content and visual inspection of the trajectory I expected
> > > small changes from this point till the total time, but not the two
> > matrices
> > > being equal... Am I doing something wrong or this may happen?
> > >
> > > Here is my data set of results:
> > >
> > > Normalized Shape DT
> > > 0.611        0.638    0-10ns
> > > 0.616        0.650    0-20ns
> > > 0.646        0.671    0-30ns
> > > 0.656        0.678    0-40ns
> > > 0.659        0.683    0-50ns
> > > 0.873        0.919    0-60ns
> > > 1.000        1.000    0-70ns
> > > 1.000        1.000    0-80ns
> > > 1.000        1.000    0-90ns
> > > 1.000        1.000    0-100ns
> > > 1.000        1.000    0-110ns = Ttot
> > >
> > >
> > > Regards,
> > > Miguel
> > > --
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> >
> >
> >
> > --
> > Tsjerk A. Wassenaar, Ph.D.
> > --
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--
Tsjerk A. Wassenaar, Ph.D.

```