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

Tue Feb 24 15:20:21 CET 2015

Hi James,

Well, with NMA you need to go to the minimum first, using extensive energy
minimization. ENM/GNM/ANM avoids this by defining the structure as the
minimum, using only interactions derived from distances in that structure.
In any case, NMA methods only provide informations about THAT POINT in
conformational space. The normal modes are the tangents of the energy
minimum, which show how the gradients run. The softest mode shows in which
direction the system can move easiest.

In a simulation, the system will move easiest in the direction in which it
can move easiest. That's not a suprise, of course, but put like this
stresses the link with the result from NMA. But, what MD can do, and NMA
not: make a transition to another well. Often such other wells lie grossly
in the direction of the soft modes, because the transition is linked to the
function of, e.g., the protein, and the protein evolved to support that
function. But the transition and the sampling of other regions will cause
divergence between the normal modes and the principal components. Do note
that most likely the 'principal subspaces' will remain pretty much the
same. Only if the simulation samples the energy well around one minimum
will the PCA results and the NMA results be really the same.

Now, what about incomplete sampling? Let's say that you let go of the ball
somewhat away from the minimum. Since it has fixed kinetic energy, it rolls
off, and maybe even goes a bit up a steep end if you kicked it in that
direction. Yet if it has any momentum along the shallowest direction, it
will make it's biggest strides there. And even if you only see it going
halfway from one end to the other, you will be able to see what the
direction of least energy is, which matches up with the lowest energy mode.
So full sampling is not necessary to find correspondence between PCA and
NMA. Moreover, if full sampling implies multiple energy wells, than it will
actually cause the two to correspond less, as explained above.

NMA only gives local information.
PCA only gives information about the wells sampled.

Hope it helps,

Tsjerk

On Tue, Feb 24, 2015 at 12:32 PM, James Starlight <jmsstarlight at gmail.com>
wrote:

> 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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-- 
Tsjerk A. Wassenaar, Ph.D.