[gmx-users] Essential dynamics - concepts

[Tsjerk Wassenaar]

Hi Kavya,

On Sat, Jun 4, 2011 at 8:18 AM, Kavyashree M <hmkvsri at gmail.com> wrote:
> Dear Gromacs users,
>
>  I am new to essential dynamics, I have gone through
> some fundamentals in PCS, the mailing list related to ED
> and few publications by -
> Amadei (Proteins, 17, 412-425, 1993),
> a. Amadei (journal of biomolecular structure and dynamics, 13, 615, 1996)
> b. Berk Hess (Physical reviews E, 62, 8428-8448, 2000)
> c. Berk Hess (Physical reviews E, 63, 031910, 2002)
> d. Caterina (Biophysical chemistry, 92, 183-199, 2001)
>
> I have made a short note of what I understand. Please correct.
> the mistakes.
> 1. ED is principally used to study the anharmonic motions, ie those
>    which are not equilibrated unlike equlibrated motions like bond
>    vibrations, bending etc.. (Equilibrated in the time scale of study)

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.

> 2. So one has to run a simulation long enough so that it is more than
>    or equal to the time scale required for the specific motion (for eg.
>    closing of loop takes place in few ps, one has to run MD for atleast
>    a ns to investigate it)

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.

> 3. After MD for long enough time, when covariance matrix would indicate
>    whether two atoms move in same direction, or opposite over the time
>    of simulation based on positive or negative value. Extracting Eigenvalues
>    and Eigenvectors from the matix gives the directions in which the highly
>    correlated motions occur.

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.

> 4. Analysing all the data values projected over the first few eigen vectors
>     is the priciple component analysis.

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.

> 5. if this experiment is done on same structure more than once (say 3), and
> the first few priciple components of all 3 simulations coincide, then it
> could be
>     the most possible direction of motion in the protein otherwise the
> patern
>     of PC's is most likely due to random motion.

No, if they do not agree, then probably your system is ill-converged.
But that is not the same as being random.

> 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.

> 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.

> 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.

> 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 :)

> 6. I am working on a enzyme whcih upon binding to substrate shows a marginal
>     deviation from the native unbound structure. I have onlt the unbound
> form, but
>      the two forms are available in other organisms whose structures are
> very similar
>      to the one I am working. So would you think doing the ED on this
> protein is
>      logical?

It might make sense. But it's not trivial.

> I was not recieving replies form the forum for my rescent queries (which I
> had to obtain
> from my senior, SO kindly check if there is any problem)
>
> I AM EXTREMELY SORRY FOR VERY BIG MAIL.!!

That's okay. I think these were quite good questions and other people
may benefit from them. If only more people had such doubts raising in
their heads before diving into PCA :)

Cheer,

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