Dear Sir,<br><br>Thanks sir. I will go through them. However I have referred -<br>"A Tutorial on Principle component Analysis" by Lindsay I Smith.<br>Which gave a good understanding about the concepts. Still I<br>
have some doubts regarding eigen values, as you have told <br>I will think over them again. <br><br>But one statement I was not clear from your previous mail that - <br>"An eigenvalue is an RMSF of the collective motion."<br>
<br>These eigenvalues are the solutions for an Nth order equation <br>arising from N X N covar (sorry for using this term again) matrix <br>(considering only x component). If we consider this covar matrix <br>as a transformation matrix, eigen value would give the magnitude<br>
and direction by which the eigenvector is transformed linearly. <br>Is it correct?<br><br>I will try to think over it again. But I would be glad if you can clarify<br>the doubt. (may be tomorrow). Or if you can provide some reference?<br>
<br>Thank you Sir,<br>With Regards<br>M. Kavyashree<br><br><div class="gmail_quote">On Mon, Jun 6, 2011 at 7:16 PM, Tsjerk Wassenaar <span dir="ltr"><<a href="mailto:tsjerkw@gmail.com">tsjerkw@gmail.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">Hi Kavya,<br>
<div class="im"><br>
> Its g_covar contributed by Dr. Rossen apostolov if I am right. Here it<br>
> states that those which are having correlation coefficient better than 0.5<br>
> will be reported, so covariance gives those which have correlation<br>
> coefficient<br>
> less than 0.5?<br>
<br>
</div>I don't know the modified version. But I presume that the components<br>
with eigenvalues higher than 0.5 are written out, which is not quite<br>
the same as having a correlation coefficient of 0.5.<br>
<div class="im"><br>
> So here the criteria for ill-convergence is the disagreement in<br>
> the principle<br>
> components of the 3 simulations, while random diffusion is the inherent<br>
> property of PCA and its only the extent to which it can be fitted to a<br>
> cosine<br>
> that distinguishes if from a true random motion and any meaningful<br>
> correlations.<br>
<br>
</div>Please get the random diffusion out of your head! :p<br>
Also, do some more background reading on PCA as a<br>
mathematical/statistical technique, not in relation to molecular<br>
simulations. It helps to form a better view on the matter.<br>
<div class="im"><br>
> I understand here that time depends on the system under consideration. But<br>
> my doubt was - for example if we consider a situation where time required<br>
> for<br>
> a conformational change of a protein from native to an active state is<br>
> 100ps,<br>
> then we run a simulation for some 5ns, so theoretically this change of<br>
> conformations<br>
> should have taken place 50 times in that 5ns time span. So if we take any<br>
> 100ps<br>
> (or to be on the safer side 500ps) time for the covariance analysis, after<br>
> the system<br>
> has equilibrated ie., leaving first few hundred ps, then we will be able to<br>
> capture<br>
> this feature of correlated movement in the covariance analysis, is that<br>
> right?<br>
<br>
</div>Most proteins will take quite a bit longer than 100ps to go from one<br>
to the other state. But besides that, if on average a process takes a<br>
certain time, it is not said that an interval of that length (or twice<br>
that length) will also contain the transition. You should have<br>
additional measures for the state of the protein and can then use PCA<br>
to understand which collective motions are related to the transition.<br>
<div class="im"><br>
> In this case should we merge all the .xtc files and superpose all the<br>
> conformations<br>
> with a single pdb file. and then do a covar analysis? Will the difference in<br>
> the amino acid<br>
> and the length of the sequences matter during covariance analysis when we<br>
> deal<br>
> with structures with different sequence but with high degree of structural<br>
> similarity?<br>
<br>
</div>You can merge them. It's not the only way though, but I think it goes<br>
to far to try and explain the ins and outs here :p Do mind that any<br>
systems you want to compare have to have the same conformational<br>
space! In casu, that means that you have to extract trajectories of<br>
those parts of the system that are common to all variants.<br>
<div class="im"><br>
> Any numerical measure of the value of cosine content beyond which the<br>
> analysis is said<br>
> to be more of a random nature than being meaningful?<br>
<br>
</div>It's not about randomness!<br>
<div class="im"><br>
> So in the paper, Berk Hess (Physical reviews E, 62, 8428-8448, 2000), an<br>
> experiment<br>
> conducted on Ompf porin, why is there a cosine nature in first four PC's,<br>
> indicative of<br>
> randomness, even when they have least-square fitted the structures before<br>
> covariance<br>
> analysis?<br>
> Its quite unclear for me Sir as to what physically it means to say that<br>
> there is random<br>
> diffusion even after least-square fitting?<br>
<br>
</div>If the scores (the projection of the trajectory) on the first<br>
principal component fit a cosine, it is indicative of a unidirectional<br>
process. Random diffusion of an atomic system is a unidirectional<br>
process.<br>
<br>
Note I'm not going to reply on covariance analysis more today :) Just<br>
be sure to take some time to think things over. Read a bit more from<br>
alternative sources, and let it all diffuse randomly into your head...<br>
:p<br>
<br>
Cheers,<br>
<div><div></div><div class="h5"><br>
Tsjerk<br>
<br>
<br>
--<br>
Tsjerk A. Wassenaar, Ph.D.<br>
<br>
post-doctoral researcher<br>
Molecular Dynamics Group<br>
* Groningen Institute for Biomolecular Research and Biotechnology<br>
* Zernike Institute for Advanced Materials<br>
University of Groningen<br>
The Netherlands<br>
--<br>
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