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

James Starlight jmsstarlight at gmail.com
Tue Feb 24 12:32:24 CET 2015

```Hi Tsjerk,

thank you very much for the explanation! So in that case the choosing of
the best method in relation to specified task will depend on the
sensitivity of both methods.  In case of NMA it should be based on the
knowing that initial structure is lied within the deepest minima along all
its possible states from the energy landscape => it means that we start to
looking on the softest transition pathways exactly from this point. On
other hand  in case of PCA the results should be depends on full coverage
of the analyzed trajectory trajectory -> it means that the rolling ball
visit all possible states along its pathway. Does it correct? In any case
It's not quite understand for me why the directions of the first PCs (most
collective dynamics) should be at the same time more softest (less-energy
consuming pathways).

Thanks for suggestions again!

James

2015-02-24 11:42 GMT+01:00 Tsjerk Wassenaar <tsjerkw at gmail.com>:

> Oh, there's a minor correction to NMA. You actually determine the steepest
> gradient first, and then the steepest gradient perpendicular to the first
> direction. That's why the smallest normal modes correspond to the largest
> eigenvectors :)
>
> Cheers,
>
> Tsjerk
>
> On Tue, Feb 24, 2015 at 11:31 AM, Tsjerk Wassenaar <tsjerkw at gmail.com>
> wrote:
>
> > 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.
> >
> >
>
>
> --
> Tsjerk A. Wassenaar, Ph.D.
> --
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