[gmx-users] Essential dynamics and cosine content

Berk Hess gmx3 at hotmail.com
Wed Jun 30 10:04:21 CEST 2004

>From: Leonardo Giantini Trabuco <ltrabuco at cecm.usp.br>
>Reply-To: Discussion list for GROMACS users <gmx-users at gromacs.org>
>To: gmx-users <gmx-users at gromacs.org>
>Subject: [gmx-users] Essential dynamics and cosine content
>Date: Tue, 29 Jun 2004 16:50:11 -0300
>Dear gmx-users,
>I'm performing some essential dynamics analysis. My first principal
>component happened to have a large cosine content (0.807317), which
>indicates it is related with random diffusion.
>I'd like to ask you if there is some threshold of cosine content, above
>which we consider de principal component to be related with random
>So now I'm not very sure of what principal components I should take
>into account. Is it ok to simply ignore the first principal component
>and analyze, for instance, the second and the third?
>And how do I know that I'm analyzing a sufficient ammount of principal
>components? That should have something to do with the relative
>positional fluctuation but, again, I dont't know which threshold I
>should use.

It all depends on what is the purpose of your simulation.
Usually one does PCA to determine the large global motions.
If your first principal component has a large cosine content
(very roughly one could say above 0.5, but in a reasonably
converged simulation it should be below 0.1), all global
motions are for sure not fully sampled.
At this point the extent of sampling (e.g. the eigenvalues)
at well as the ordering of the first few principal components
is unreliable. Usually the space defined by the first few
eigenvector will not change much as the simulation
is extended, but the eigenvalues will increase and
the eigenvectors within this space will rotate.

But you can not just skip the first few, as these are still
the most important for global motions.
The only solution is to extend your simulation.


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