# Re: [AMBER] similarity of quasi-harmonic modes dependent on reference conformation

From: Jason Swails <jason.swails.gmail.com>
Date: Tue, 29 Jun 2010 23:37:57 -0400

Hello,

Why do you expect identical eigenvectors? I'd agree that the eigenvalues
should all be nearly identical (though the RMS fit may be different based on
the frame you fit to). However, wouldn't the cartesian representation of
the eigenvectors depend on the orientation of the reference frame? I can
imagine you'd get better agreement if you could find out how to rotate the
first frame to fit the last frame, then apply those transformations to the
one of the sets of eigenvectors.

For the metric you're using: suppose in the extreme case that the last
frame has undergone a 90 degree rotation in the X-Y plane (and Z has stayed
the same). Then the same mode will be perpendicular in the two matrices you
construct using each frame as a reference, and their similarity will
*appear* to be 0 according to your criteria (I think it's basically just an
inner product). However, they're really identical since they describe
exactly the same motion.

You or others may correct me here if I'm missing something obvious.

Good luck!
Jason

On Tue, Jun 29, 2010 at 10:34 PM, Jose Borreguero <borreguero.gmail.com>wrote:

> Dear Amber users,
>
> In ptraj, using *matrix mwcovar* produces very different set of modes if
> one
> uses different reference conformations to remove translations and
> rotations.
> Does anyone know why is this the case? I had assume that being the same
> trajectory, the modes would be very similar. If the modes are to be a
> property of the protein, they should be quite independent of the reference
> conformation.
>
> This is the ptraj input file. Here I used the first conformation as
> reference:
> *trajin mdcrd
> reference first.rst
> rms reference :.CA
> matrix mwcovar name pca :.CA out evecs_first.dat
> *
> I also have another input file using the last conformation as reference (*
> last.rst* produces *evecs_last.dat*)
>
> As it turns out, modes in *evecs_first.dat *and *evecs_last.dat *are very
> different! I compare the modes using the Hess metric:
> *similarity = 1/N * Sum_i Sum_j (v_i w_j)^2,*
> where *v_i* are the first *N* modes from *evecs_first.dat *and *w_j* are
> the
> first *N *modes from *evecs_last.dat*. There is a dot product between the
> modes.
>
> Has anybody encountered such situation?
>
> Best regards,
> -Jose M. Borreguero
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>

```--
Jason M. Swails
Quantum Theory Project,
University of Florida