Team:TU Darmstadt/Labjournal/Simulation/GNM

<html>
<link rel="stylesheet" href="https://2012.igem.org/wiki/index.php?title=Team:TU_Darmstadt/css&amp;action=raw&amp;ctype=text/css" type="text/css" />
<div id="TUD">
<div id="top">
	<ul>
		<li><a href="http://www.igem.tu-darmstadt.de/igem/projekt/index.en.jsp" title="iGEM">iGEM@TUD</a></li>
		<li><a href="/Team:TU_Darmstadt" title="Home">Home</a></li>
		<li><a href="/Team:TU_Darmstadt/Project" title="Project">Project</a><ul>
	        <li><a href="/Team:TU_Darmstadt/Project" title="Team:Overview">Overview</a></li>
	        <li><a href="/Team:TU_Darmstadt/Project/Degradation" title="Degradation">1. Degradation</a></li>
	        <li><a href="/Team:TU_Darmstadt/Project/Transport" title="Transport">2. Transport</a></li>
	        <li><a href="/Team:TU_Darmstadt/Project/Metabolism" title="Metabolism">3. Metabolism</a></li>
	        <li><a href="/Team:TU_Darmstadt/Project/Material_Science" title="Material Science">4. Material Science</a></li>
	        <li><a href="/Team:TU_Darmstadt/Project/Simulation" title="Simulation">5. Simulation</a></li>
	        <li><a href="/Team:TU_Darmstadt/Project/Ecology" title="Ecology">Ecology</a></li>
	        <li><a href="/Team:TU_Darmstadt/Project/Philosophy" title="Philosophy">Philosophy</a></li></ul></li>
		<li><a href="/Team:TU_Darmstadt/Team" title="Team:TU_Darmstadt/Team">Team</a><ul>
	        <li><a href="/Team:TU_Darmstadt/Team" title="Team:TU_Darmstadt/Team">Members</a></li>
	        <li><a href="/Team:TU_Darmstadt/Supporters" title="Team:TU_Darmstadt/Supporters">Supporters</a></li></ul></li>
		<li><a href="/Team:TU_Darmstadt/Parts" title="BioBricks">BioBricks</a></li>
		<li><a href="/Team:TU_Darmstadt/Documentation" title="Documentation">Documentation</a><ul>
			<li><a href="/Team:TU_Darmstadt/Documentation" title="Documentation">Overview</a></li>
		    <li><a href="/Team:TU_Darmstadt/Labjournal" title="Labjournal">Labjournal</a></li>
		    <li><a href="/Team:TU_Darmstadt/Protocols" title="Protocols">Protocols</a></li>
		    <li><a href="/Team:TU_Darmstadt/Safety" title="Safety">Safety</a></li>
		    <li><a href="/Team:TU_Darmstadt/Downloads" title="Downloads">Downloads</a></li></ul></li>
		<li><a href="/Team:TU_Darmstadt/Human_Practice" title="Human Practice">Human Practice</a><ul>
		    <li><a href="/Team:TU_Darmstadt/Human_Practice/Panel_Discussion " title="Panel Discussion">Panel Discussion</a></li>
		    <li><a href="/Team:TU_Darmstadt/Human_Practice/Symposia" title="Symposia">Symposia</a></li>
		    <li><a href="/Team:TU_Darmstadt/Human_Practice/Classes" title="Classes">Classes</a></li></ul></li>  
		<li><a href="/Team:TU_Darmstadt/Sponsors" title="Sponsors">Sponsors</a><ul>
		    <li><a href="/Team:TU_Darmstadt/Sponsors" title="Sponsors">Overview</a></li>
		    <li><a href="/Team:TU_Darmstadt/Contact" title="Contact">Benefits</a></li></ul></li>  		
	</ul>
</div>
<!-- end #menu -->
</html>

== Gaussian network model ==
Nearly all biologically important processes such as enzyme catalysis,ligand binding and allosteric regulation occur on a large time-scale (micro- to millisecond). A Gaussian network model (GNM) is  a coarse-grained  representation of a protein as an network consisting of  balls and springs. In our approach, proteins are represented by balls corresponding to the CA –atom of each residue[1]⁠ . While Molecular Dynamics (MD) simulations  are computational expensive,  a GNM calculation only needs a few seconds.

===Computation===
The dynamics of the structure in the GNM is described by the topology of contacts within the Kirchhoff matrix G. Thus in this  network of N interacting sites, the elements of G are computed as:

<math>
\Gamma_{ij} = \left\{\begin{matrix} 
-1, & \mbox{if } i \ne j & \mbox{and }R_{ij} \le r_c  \\ 
0, & \mbox{if } i \ne j & \mbox{and }R_{ij} > r_c  \\
-\sum_{j,j \ne i}^{N} \Gamma_{ij}, & \mbox{if } i = j \end{matrix}\right.   
<math>

where Rij is the distance between point i and j. We used Gamma as  the intra CA-contact matrix. The inverse of it describes correlations between ﬂuctuations within the proteins native state. The diagonal of the matrix is replaced by the sum of contacts of one CA-atom within the whole protein. After a singular value decomposition (SVD) we have calculated the normal modes of the protein. Slow modes describe functionally relevant residues within a biomolecule[2]⁠. The opposite,  Fast modes, represent an uncorrelated motion without significant changes in the structure.


[[File:Ali2MI.png|700px]]

A recent examination of the X-ray crystallographic B-factors of over 100 proteins showed that the GNM closely reproduces the experimental data [3]⁠.
===Application to our Proteins===
We computed the GNM in [https://2012.igem.org/Team:TU_Darmstadt/Protocols/R_Programming R] [4]⁠ by using the BioPhysConnectoR [5]⁠ library.

* pnB-Esterase
* Fusarium solani cutinase

===References===

[1] A. R. Atilgan, S. R. Durell, R. L. Jernigan, M. C. Demirel, O. Keskin, and I. Bahar, “Anisotropy of fluctuation dynamics of proteins with an elastic network model.,” Biophys J, vol. 80, no. 1, pp. 505–515, Jan. 2001.

[2] C. Chennubhotla, A. J. Rader, L.-W. Yang, and I. Bahar, “Elastic network models for understanding biomolecular machinery: from enzymes to supramolecular assemblies.,” Physical Biology, vol. 2, no. 4, pp. S173–S180, 2005.

[3] I. Bahar and A. J. Rader, “Coarse-grained normal mode analysis in structural biology.,” Current Opinion in Structural Biology, vol. 15, no. 5, pp. 586–592, 2005.

[4] R. D. C. Team, “R: A Language and Environment for Statistical Computing.” Vienna, Austria, 2008.

[5] F. Hoffgaard, P. Weil, and K. Hamacher, “BioPhysConnectoR: Connecting sequence information and biophysical models.,” BMC Bioinformatics, vol. 11, p. 199, 2010.