[gmx-users] frequence from PCA eigenvalue

[Berk Hess]

>From: pascal.baillod at epfl.ch
>Reply-To: Discussion list for GROMACS users <gmx-users at gromacs.org>
>To: gmx-users at gromacs.org
>Subject: [gmx-users] frequence from PCA eigenvalue
>Date: Mon, 22 Oct 2007 20:37:10 +0200 (MEST)
>
>Dear community,
>
>I have done a principal component analysis on an MD trajectory (g_covar) 
>and
>would like to compute the frequency related to the first principle 
>component.
> >From what I have read in different sources:
>
>1. the unit of an eigenvalue ei in gromacs (non mass weighted) are : 
>(nm)^(-2)
>2. the frequency fi of that principle component (pc) would be : fi = 
>k/sqrt(ei),
>where k is a constant with units of velocity.
>
>Are these correct?
>What would the value of k be? In my case, I get 43.21 for e1 (first 
>eigenvalue)
>and 17 for e2, for a 315 ns trajectory of a 103 residue protein.

In general there is no frequency associated with a principal component,
since the free energy landscape is generally not harmonic and the
motion is often diffusive.

>
>I also read that the first pc of a protein simulation often has a high 
>cosine
>content, close to 1. In my case the first pc has a cosine content of 0.89. 
>This
>pc would thus be related to a diffusive, non-potential related motion, but 
>how
>characteristic would it be of my system?

This cosine content indicates that you first mode is diffusive (and 
determining
a frequency would be nonsence).
You should chop up the trajectory in part, say 4 parts, and determine the
subspace overlap of the first, or the first few, eigenvectors.

Berk.

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