[gmx-users] Essential dynamics - concepts

[Kavyashree M]

Dear Sir,

    Thanks for giving a clearer picture about essential dynamics. I was very
eagerly  awaiting for a reply. Thanks you very much :).

No, ED does not make any assumptions on the nature of motions. It does
> not distinguish anharmonic from harmonic motions. It also does not
> distinguish between equilibrated and non-equilibrated motions. It will
> give insight in correlated (global) and non-correlated (local)
> motions. Note that it will only give linearly correlated motions, and
> neglects non-linear correlations. Also note that it will not give the
> motions that are most strongly correlated, btu those which have the
> largest extent of motion, collectivelye. (There is a modification on
> the gromacs contribution page to give the motions of highest
> correlation.
>

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?


> PCA/ED only allows one to make statements about the time scales
> simulated, so to describe a certain motion, the simulation has to be
> long enough to encompass the motion.
>
> The eigenvectors give the direction of the motion in conformational
> space, and the the eigenvalues the associated extents of the motions.
> An eigenvalue is an RMSF of the collective motion.
>
> No, 'Principal component analysis' is rewriting the original data with
> many variables as a set of new variables that are linear combinations
> of the original ones but describe the underlying structure better.
> These new variables, the principal components or latent variables,
> presumably reflect the true degrees of freedom better.
>
> No, if they do not agree, then probably your system is ill-converged.
> But that is not the same as being random.
>

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.


>
> > My questions -
>
> > 1. While chosing the period for covariance analysis, what is the
> criteria?
> > in the
> >     paper b, author mention that a certain peroid was chosen because the
> > peptide
> >     free enegry minimum. Not clear about this, because when the protein
> > resides in
> >     an energy minimum how can there be transition to another
> configuration
> > (eg a loop
> >     movement) without crossing the barrier. should we not consider the
> time
> > which
> >     spans a native conformation to say an active conformation during the
> > simulation?
>
> It depends on the time required for equilibration and the time scale
> of the process you're interested in. There's no golden standard there.
>
>
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?



> > 2. If we have done a long enough simulation of say 100ns for 4 proteins
> with
> > similar
> >    structure but with sequence id of 40-60% (different chain lengths
> > 230-260aa), Can
> >    we do a covar analysis of these 4 simulations?
>
> You can always do covariance analysis. Whether it makes sense is the
> real question ;) But it may certainly make sense to do covariance
> analysis on related systems.
>

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?


>
> > 3. How much should be the socine content to tell that it is not a random
> > diffusion?
>
> All cows are animals, but not all animals are cows. Likewise, the
> principal components of random diffusion are characterised by their
> fit to a cosine series, but if you're projections yield a perfect fit
> to a cosine series... In most cases such a fit is obtained when the
> system is still equilibrating.
>

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?


>
> > 4. Is ED analysis itself is not enough to establish a important movement
> in
> > the
> >     protein.. further ED sampling is required to prove it?
>
> Whether it's important is up to the researcher :)
>
> > 5. Concept doubt - When all the structures at least square fitted before
> > building a
> >     covariance matrix, where is the random diffusion comming into
> picture? I
> > am
> >     sorry I was not clear about this consept qualitatively.
>
> Right.. No random diffusion :)
>

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?

Thanks for the patiently going through my queries and for clear explanations
Sir.

Thank you
With Regards
M. Kavyashree
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