[gmx-users] Cosine content of an eigenvector in PCA after 100ns still 0.9

[Tsjerk Wassenaar]

Hi Max,

The diffusion of liquids and gases gives rise to principal components that
form a cosine series, in which the period of the cosine is equal to half
the pc index.

Well, it doesn't actually say "the protein system is not equilibrated yet".
It really says "in the time window you're looking at there is a net
unidirectional motion in conformational space". So you're system may
undergo a conformational change, or it (un)splits over periodic boundaries.
That event may be part of equilibrium behaviour (or may be an artefact in
the PBC case), but you don't observe it going back, so you can't really
tell whether it's a one time event (delayed relaxation, depending on a
stochastic event?) or part of a recurrent motion. So you haven't sampled
enough (or chose a too narrow window) to observe all of the motion, which
is usually translated as 'the system is not in equilibrium".

Hope it helps,

Tsjerk

On Thu, Jan 15, 2015 at 4:26 PM, Ebert Maximilian <m.ebert at umontreal.ca>
wrote:

> Hi Tsjerk,
>
> thanks for your reply. Can you explain this sentence again please:
>
> Not having a full set of cosines with periods equal to half the pc index
> just means you're not simulating gas or liquid.
>
> The simulation runs already for 500ns and I analyzed 100ns from 400 to
> 500ns. How can a simple protein system not be equilibrated yet?
>
> Max
>
> > On Jan 15, 2015, at 3:52 PM, Tsjerk Wassenaar <tsjerkw at gmail.com> wrote:
> >
> > Hi Max,
> >
> > The cosine content is a rather nonsensical parameter.
> > HOWEVER, having a cosine content with 1/2 period that high one ANY
> > eigenvector is indicative of unidirectional motion (a.k.a. conformational
> > change/drift). That cosine contents with other periods on other
> > eigenvectors is low is meaningless. Not having a full set of cosines with
> > periods equal to half the pc index just means you're not simulating gas
> or
> > liquid.
> >
> > In short, your system is not equilibrated.
> >
> > Cheers,
> >
> > Tsjerk
> >
> > On Thu, Jan 15, 2015 at 3:43 PM, Ebert Maximilian <m.ebert at umontreal.ca>
> > wrote:
> >
> >> Hi there,
> >>
> >> I have one question regarding the cosine content of an eigenvector. I
> did
> >> a PCA and calculated the cosine content of the 10 main eigenvectors.
> Except
> >> for the first all are really low. However, the main eigenvector is still
> >> around 0.9 after 100ns simulation. I am pretty sure my system is
> >> equilibrated. Do you have any idea what might happen?
> >>
> >> Thank you very much,
> >>
> >> Max
> >> --
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> >
> >
> > --
> > Tsjerk A. Wassenaar, Ph.D.
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-- 
Tsjerk A. Wassenaar, Ph.D.