[gmx-users] Re: questions about Principal Component Analysis

[Tsjerk Wassenaar]

Hi Thomas,

First of all, proteins in solution don't suddenly stop with Brownian
motion at some point. It's just the way things move at the microscopic
level. Second, the cosine content has nothing to do with randomness.
Really. Nothing. On the contrary. The cosine content indicates
unidirectional motion. I repeat, the cosine content has NOTHING to do
with RANDOM motion! Really really. High cosine content?
U-ni-di-rec-tio-nal motion; movement from one point to another point.
The trick is realizing that the best reaction coordinate for random
motion from point A to point B is the straight line between A and B.

Unfortunately, the RMSIP is no help where it comes to convergence. It
only tells you whether the directions in conformational space along
which most of the motion takes place is similar between two (parts of)
simulations. For convergence, you want to check the projections, and
the cosine content thereof. The cosine content should indeed be low.
Your case, with relatively high cosine content in every window,
suggests that there is still motion, c.q. conformational
rearrangement, on route to another state of the system. I fear there
is no other way of looking at it that will suggest it has converged
already. Actually, 20 ns is very little for equilibration, especially
if convergence requires rearrangement of protein-protein interactions.

Cheers,

Tsjerk


On Thu, Apr 5, 2012 at 2:38 PM, Thomas Evangelidis <tevang3 at gmail.com> wrote:
> Dear Tserk and the rest of GROMACS users,
>
> Last time I measured the cosine content of different time intervals from the
> PCs of the whole trajectory. This time I did PCA for each time interval and
> measured the cc which is the right way I suppose. Maisuradze et al., 2009
> claim that a CC value below 0.5 indicates that the protein-water system
> stops behaving as one with Brownian motions. Yet in none of my time
> intervals the CC dropped below 0.6. Can this happen for an equilibrated
> system?
>
> It is known that RMSIP can be used to measure the overlap between essential
> subspaces. My question is can RMSIP
> help me decide at which point to consider a system equilibrated from a
> thermodynamical point of view, namely the point at which the system stops
> doing Brownian motion? Does this point necessarily coincide with that where
> the RMSD is stabilized?
>
> Our protein is co-complexed in another one in the crystal structure, which
> is believed to hold it in an "inactive state". However, we simulate the
> monomer state, hence we expect a large domain motion to occur in the first
> few nanosecond. Provided that the first 20ns are considered the time for
> equilibration, does it make sense to do PCA in this time interval?
>
>
> Thanks in advance for your help.
>
>
> Thomas
>
>
>
>
> On 12 March 2012 15:44, Tsjerk Wassenaar <tsjerkw at gmail.com> wrote:
>>
>> Hi Thomas,
>>
>> Whether or not it makes sense to do PCA on the domain only depends on
>> the question you ask. It may well make sense if you aim at
>> characterizing the intra-domain motions. But be aware that you will
>> view those motions within the context of the rest of the protein. It
>> is quite likely that the internal motions depend on the interaction
>> with the surroundings.
>>
>> Concerning the cosine content, there indeed seems to ba a transition.
>> But that is already evident from your RMSD plot. A lot of stuff is
>> still happening in the second half of the simulation. To see if the
>> last part of your simulation is in a (local) equilibrium, you can
>> calculate the average structure from that part, say the alst 10 or 20
>> ns, and determine the RMSD against the average. The RMSD should then
>> decrease towards the average and level off or oscillate around it to
>> assure you've reached some sort of equilibrium. On the basis of that
>> you could then decide whether it's worthwhile performing PCA on that
>> part only.
>>
>> Cheers,
>>
>> Tsjerk
>>
>
> --
>
> ======================================================================
>
> Thomas Evangelidis
>
> PhD student
>
> Biomedical Research Foundation, Academy of Athens
>
> 4 Soranou Ephessiou , 115 27 Athens, Greece
>
> email: tevang at bioacademy.gr
>
>           tevang3 at gmail.com
>
>
> website: https://sites.google.com/site/thomasevangelidishomepage/
>
>
>
>
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-- 
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