# [gmx-users] On the collective dynamics in terms of NMA and PCA

Tsjerk Wassenaar tsjerkw at gmail.com
Tue Feb 24 11:31:05 CET 2015

```Hi James,

Imagine you have a landscape with a long valley, longer than it's broad.
Now you go to the deepest point and determine the shallowest direction.
Then you take the shallowest direction perpendicular to the first. That's
NMA.

Now you stand before the valley, and you roll a big ball down, which has
the property of maintaining its kinetic energy. It goes down, and past the
lowest point and rolls up the other end, comes back, and so forth. After
some time you take all the positions of the ball, determine the mean and
then determine the axis of the largest spread in the points. Then you
determine the axis of the largest spread perpendicular to the first. That's
PCA.

You see that both give the same result, which is because they both reflect
the same underlying landscape.

I hope this is clear. Otherwise, let me know.

Cheers,

Tsjerk

On Tue, Feb 24, 2015 at 11:20 AM, James Starlight <jmsstarlight at gmail.com>
wrote:

> Dear Gromacs Users!
>
> I have a question regarding calculation of the collective dynamics using
> normal mode analysis and principal components analysis made in case when 1)
> NMA was performed just  based on one reference structure and 2) PCA was
> performed for the md trajectory where each frame has been superimposed
> against that reference structure. Eventually I've found good correlations
> (which means that it has the same directions) in the lowest-frequency modes
> from 1) and first PCs made for 2)  as was obtained by means of dot product
> of both eigenvectors sets. Could someone explain me briefly why such
> correlation is exist? I just know that cov.matrix is correspond to the
> inverse of the hessian but I don't understand physical meaning of that
> fact.
>
> Thanks for help,
>
> James
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--
Tsjerk A. Wassenaar, Ph.D.
```