# [gmx-users] Formula for cosine content in essential dynamics

Steve Spronk spronk at umich.edu
Mon Aug 27 15:18:30 CEST 2007

```Thank you, Berk, for clearing it up for me.  I thought that maybe I didn't
understand something fundamental to the method.  The formula lacking the 1/T
is in quite a few papers as well as the Gromacs manual.  It has escaped
attention so far probably because g_analyze takes care of the calculation
automatically.

-Steve

-----Original Message-----
From: gmx-users-bounces at gromacs.org [mailto:gmx-users-bounces at gromacs.org]
On Behalf Of Berk Hess
Sent: Monday, August 27, 2007 9:11 AM
To: gmx-users at gromacs.org
Subject: RE: [gmx-users] Formula for cosine content in essential dynamics

>From: "Steve Spronk" <spronk at umich.edu>
>Reply-To: Discussion list for GROMACS users <gmx-users at gromacs.org>
>To: <gmx-users at gromacs.org>
>Subject: [gmx-users] Formula for cosine content in essential dynamics
>Date: Fri, 24 Aug 2007 17:04:04 -0400
>
>Hi,
>
>
>
>I am working on essential dynamics analysis of my protein, and I have a
>basic question on the calculation of the cosine content of the principal
>components.
>
>
>
>The way that I understand it, the first few principal components may
>resemble cosine functions, with the period equal to half the principal
>component index i.  However, in the formula for cosine component listed in
>Hess's papers, the Gromacs manual, and all other sources I've checked, the
>cosine function is
>
>
>
>cos(i*pi*t)
>
>
>
>which is not actually a cosine that has a period of half the index.  I must
>be misunderstanding something, because if you want to compare to a cos
>function that passes through half a period over the whole time of the
>simulation, shouldn't the formula include this instead:
>
>
>
>cos(i*pi*t/T)
>
>
>
>where T is the length of the simulation?  This way, it also appears to me
>that the units work out correctly.
>
>
>
>I'm confused.  Can you help me understand the formula better?
>
>
>
>Thanks,
>
>Steve
>

I probably forgot to add a factor of 1/T in the manual.
I'll fix it.

Thanks,

Berk.

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