<pre>Dear GMX-users,<br><br>I have been working on extracting the C-alpha component from the all-atom Hessian matrix, according to the <br>equation proposed initially by Berk, H'=Hxx-HxyHyy-1Hyx. It worked quite nice in my hand and for
<br>a test protein, there is almost no visual difference in the confromational changes described by the eigenvectors <br>between two methods (all-atom normal mode or C-alpha only). <br><br>I am wondering whether there is a reference for this equation? Is it based on Gram-Schmidt formula for deriving a
<br>new set of vectors? There was a old paper by Brooks and Karplus (J. Comp. Chem., 1995) gave a detailed description <br>of the normal mode analysis and prosposed a methods for extracting dihedral angle normal modes. So is there any
<br>difference between the method they proposed and equation mentioned above?<br><br>Thank you for the help.<br><br>Lei Zhou<br>Columbia University<br><br><br></pre>
<h1><br>
</h1>
<h1><br>
</h1>
<h1><br>
</h1>
<h1>[gmx-users] Normal Mode Analysis on Calphas only ??</h1>
<b>Berk Hess</b>
<a href="mailto:gmx-users%40gromacs.org?Subject=%5Bgmx-users%5D%20Normal%20Mode%20Analysis%20on%20Calphas%20only%20%3F%3F&In-Reply-To=BAY16-F91A6180D2B0CD90A41E108E160%40phx.gbl" title="[gmx-users] Normal Mode Analysis on Calphas only ??">
gmx3 at hotmail.com
</a><br>
<i>Wed May 18 08:42:23 CEST 2005</i>
<ul>
<li>Previous message: <a href="http://www.gromacs.org/pipermail/gmx-users/2005-May/015251.html">[gmx-users] Normal Mode Analysis on Calphas only ??
</a></li><li>Next message: <a href="http://www.gromacs.org/pipermail/gmx-users/2005-May/015259.html">[gmx-users] Normal Mode Analysis on Calphas only ??
</a></li><li> <b>Messages sorted by:</b>
<a href="http://www.gromacs.org/pipermail/gmx-users/2005-May/date.html#15256">[ date ]</a>
<a href="http://www.gromacs.org/pipermail/gmx-users/2005-May/thread.html#15256">[ thread ]</a>
<a href="http://www.gromacs.org/pipermail/gmx-users/2005-May/subject.html#15256">[ subject ]</a>
<a href="http://www.gromacs.org/pipermail/gmx-users/2005-May/author.html#15256">[ author ]</a>
</li>
</ul>
<hr>
<pre>Here is the formula (thanks to Herman Berendsen).<br>I was slightly wrong. You first need to reduce the Hessian<br>and then diagonalize the C-alpha only Hessian.<br><br>definitions:<br>Interesting particle coordinates: x
<br>Uninsteresting particle coordinates y<br>full hessian in terms of (x, y): H<br><br>Split H into four blocks:<br><br> Hxx Hxy<br>H =<br> Hyx Hyy<br><br>Then the hessian H' in the subspace of x coordinates, under the condition
<br>that the y coordinates are in a minimum, is<br><br>H' = Hxx - Hxy Hyy^-1 Hyx<br><br>This is a simple transformation, requiring only one inversion and two matrix <br>multiplications.<br><br>Berk.<br><br>_________________________________________________________________
<br>FREE pop-up blocking with the new MSN Toolbar - get it now! <br><a href="http://toolbar.msn.click-url.com/go/onm00200415ave/direct/01/">http://toolbar.msn.click-url.com/go/onm00200415ave/direct/01/</a><br><br></pre>