[gmx-users] Essential dynamics - concepts

[Kavyashree M]

Dear Sir,

Thanks sir. I will go through them. However I have referred -
"A Tutorial on Principle component Analysis" by  Lindsay I Smith.
Which gave a good understanding about the concepts. Still I
have some doubts regarding eigen values, as you have told
I will think over them again.

But one statement I was not clear from your previous mail  that -
"An eigenvalue is an RMSF of the collective motion."

These eigenvalues are the solutions for an Nth order equation
arising from N X N covar (sorry for using this term again) matrix
(considering only x component). If we consider this covar matrix
as a transformation matrix, eigen value would give the magnitude
and direction by which the eigenvector is transformed linearly.
Is it correct?

I will try to think over it again. But I would be glad if you can clarify
the doubt. (may be tomorrow). Or if you can provide some reference?

Thank you Sir,
With Regards
M. Kavyashree

On Mon, Jun 6, 2011 at 7:16 PM, Tsjerk Wassenaar <tsjerkw at gmail.com> wrote:

> Hi Kavya,
>
> > Its g_covar contributed by Dr. Rossen apostolov if I am right.  Here it
> > states that those which are having correlation coefficient better than
> 0.5
> > will be reported, so covariance gives those which have correlation
> > coefficient
> > less than 0.5?
>
> I don't know the modified version. But I presume that the components
> with eigenvalues higher than 0.5 are written out, which is not quite
> the same as having a correlation coefficient of 0.5.
>
> > So here the criteria for ill-convergence is the disagreement in
> > the principle
> > components of the 3 simulations, while random diffusion is the inherent
> > property of PCA and its only the extent to which it can be fitted to a
> > cosine
> > that distinguishes if from a true random motion and any meaningful
> > correlations.
>
> Please get the random diffusion out of your head! :p
> Also, do some more background reading on PCA as a
> mathematical/statistical technique, not in relation to molecular
> simulations. It helps to form a better view on the matter.
>
> > I understand here that time depends on the system under consideration.
> But
> > my doubt was - for example if we consider a situation where time required
> > for
> > a conformational change of a protein from native to an active state is
> > 100ps,
> > then we run a simulation for some 5ns, so theoretically this change of
> > conformations
> > should have taken place 50 times in that 5ns time span. So if we take any
> > 100ps
> > (or to be on the safer side 500ps) time for the covariance analysis,
> after
> > the system
> > has equilibrated ie., leaving first few hundred ps, then we will be able
> to
> > capture
> > this feature of correlated movement in the covariance analysis, is that
> > right?
>
> Most proteins will take quite a bit longer than 100ps to go from one
> to the other state. But besides that, if on average a process takes a
> certain time, it is not said that an interval of that length (or twice
> that length) will also contain the transition. You should have
> additional measures for the state of the protein and can then use PCA
> to understand which collective motions are related to the transition.
>
> > In this case should we merge all the .xtc files and superpose all the
> > conformations
> > with a single pdb file. and then do a covar analysis? Will the difference
> in
> > the amino acid
> > and the length of the sequences matter during covariance analysis when we
> > deal
> > with structures with different sequence but with high degree of
> structural
> > similarity?
>
> You can merge them. It's not the only way though, but I think it goes
> to far to try and explain the ins and outs here :p Do mind that any
> systems you want to compare have to have the same conformational
> space! In casu, that means that you have to extract trajectories of
> those parts of the system that are common to all variants.
>
> > Any numerical measure of the value of cosine content beyond which the
> > analysis is said
> > to be more of a random nature than being meaningful?
>
> It's not about randomness!
>
> > So in the paper, Berk Hess (Physical reviews E, 62, 8428-8448, 2000), an
> > experiment
> > conducted on Ompf porin, why is there a cosine nature in first four PC's,
> > indicative of
> > randomness, even when they have least-square fitted the structures before
> > covariance
> > analysis?
> > Its quite unclear for me Sir as to what physically it means to say that
> > there is random
> > diffusion even after least-square fitting?
>
> If the scores (the projection of the trajectory) on the first
> principal component fit a cosine, it is indicative of a unidirectional
> process. Random diffusion of an atomic system is a unidirectional
> process.
>
> Note I'm not going to reply on covariance analysis more today :) Just
> be sure to take some time to think things over. Read a bit more from
> alternative sources, and let it all diffuse randomly into your head...
> :p
>
> Cheers,
>
> Tsjerk
>
>
> --
> Tsjerk A. Wassenaar, Ph.D.
>
> post-doctoral researcher
> Molecular Dynamics Group
> * Groningen Institute for Biomolecular Research and Biotechnology
> * Zernike Institute for Advanced Materials
> University of Groningen
> The Netherlands
> --
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