<div><font face="" size="2">Dear GMX-users,<br></font></div>
<div><font face="" size="2"><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
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<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
<div><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</div>
<div><br><font face="" size="2">[gmx-users] Normal Mode Analysis on Calphas only ??</font></div><font face=""><font size="2"><b>Berk Hess</b> </font></font><a title="[gmx-users] Normal Mode Analysis on Calphas only ??" onclick="return top.js.OpenExtLink(window,event,this)" 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" target="_blank">
<font face="" size="2">gmx3 at hotmail.com </font></a><br><font face=""><font size="2"><i>Wed May 18 08:42:23 CEST 2005</i> </font></font>
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</font><pre><font face="" size="2">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.</font></pre>