[gmx-users] Extracting C-alpha component from all-atom Hessian matrix

[Lei Zhou]

Dear GMX-users,

I have been working on extracting the C-alpha component from the all-atom
Hessian matrix, according to the
equation proposed initially by Berk, H'=Hxx-HxyHyy-1Hyx. It worked quite
nice in my hand and for

a test protein, there is almost no visual difference in the confromational
changes described by the eigenvectors
between two methods (all-atom normal mode or C-alpha only).

I am wondering whether there is a reference for this equation? Is it based
on Gram-Schmidt formula for deriving a
new set of vectors? There was a old paper by Brooks and Karplus (J. Comp.
Chem., 1995) gave a detailed description
of the normal mode analysis and prosposed a methods for extracting dihedral
angle normal modes. So is there any
difference between the method they proposed and equation mentioned above?

Thank you for the help.

Lei Zhou
Columbia University

[gmx-users] Normal Mode Analysis on Calphas only ??
*Berk Hess* gmx3 at hotmail.com
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*Wed May 18 08:42:23 CEST 2005*

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------------------------------

Here is the formula (thanks to Herman Berendsen).
I was slightly wrong. You first need to reduce the Hessian
and then diagonalize the C-alpha only Hessian.

definitions:
Interesting particle coordinates: x
Uninsteresting particle coordinates y
full hessian in terms of (x, y): H

Split H into four blocks:

     Hxx    Hxy
H =
     Hyx    Hyy

Then the hessian H' in the subspace of x coordinates, under the condition
that the y coordinates are in a minimum, is

H' = Hxx - Hxy Hyy^-1 Hyx

This is a simple transformation, requiring only one inversion and two matrix
multiplications.

Berk.
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