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

[Steve Spronk]

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

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