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| - | <a href=" #modeling"><img src="https://static.igem.org/mediawiki/2008/5/5b/Model1a.jpg" border="0" /></a> <a href=" #parameters"><img src="https://static.igem.org/mediawiki/2008/ 4/ 43/ Model2.jpg" border="0" /></a> <a href=" #simulation"><img src="https://static.igem.org/mediawiki/2008/7/7f/Model3.jpg" border="0" /></a><br> | + | <a href=" https://2008.igem.org/Team:LCG-UNAM-Mexico/Modeling"><img src="https://static.igem.org/mediawiki/2008/5/5b/Model1a.jpg" border="0" /></a> <a href=" https://2008.igem.org/Team:LCG-UNAM-Mexico/Parameters"><img src="https://static.igem.org/mediawiki/2008/ f/ fd/ Model2ae.jpg " width="190" height="31" border="0" /></a> <a href=" https://2008.igem.org/Team:LCG-UNAM-Mexico/Simulation"><img src="https://static.igem.org/mediawiki/2008/7/7f/Model3.jpg" border="0" /></a><br> |
| | <a name="modeling"></a><img src="https://static.igem.org/mediawiki/2008/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /><br /> | | <a name="modeling"></a><img src="https://static.igem.org/mediawiki/2008/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /><br /> |
| | </div> | | </div> |
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| | <tr> | | <tr> |
| | <td class="pageName"><div align="center"> | | <td class="pageName"><div align="center"> |
| - | <p>Modeling the system </p> | + | <p><br> |
| | + | Modeling the system </p> |
| | </div></td> | | </div></td> |
| | </tr> | | </tr> |
| | <tr> | | <tr> |
| - | <td class="bodyText"><p align="justify">The objective of our modeling is to accurately describe and predict the behavior of the system and its response given an inducing signal. Also, we aim to better know and understand the system through the identification of critical parameters and species, and thus be able to obtain the desired dynamics.<br /> | + | <td class="bodyText"><p align="center"><a href="#metabolites">Metabolites & Enzymes</a> | <a href="#reactions">Reactions</a> | <a href="#odes">Ordinary Differential Equations</a> | <a href="#assumptions">Assumptions of the Model</a> </p> |
| - | Our system is composed of 13 <a href="#metabolites">species</a> and 11 coupled <a href="#reactions">biochemical reactions</a> that completely describe it. This can be represented through a set of <a href="#odes">ordinary differential equations</a> (ODEs). The <a href="#simulation">simulations</a> were done using Simbiology, a package from Matlab.</p> | + | <p align="justify">The objective of our modeling is to accurately describe and predict the behavior of the system and its response given an inducing signal. Also, we aim to better know and understand the system through the identification of critical parameters and species, and thus be able to obtain the desired dynamics.<br /> |
| | + | Our system is composed of 13 <a href="#metabolites">species</a> and 11 coupled <a href="#reactions">biochemical reactions</a> that completely describe it. This can be represented through a set of <a href="#odes">ordinary differential equations</a> (ODEs). The <a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Simulation">simulations</a> were done using Simbiology, a package from Matlab.</p> |
| | <p align="center"> <img alt="Iwig 2006" src="https://static.igem.org/mediawiki/2008/4/47/Diagrama3.jpg"> </p> | | <p align="center"> <img alt="Iwig 2006" src="https://static.igem.org/mediawiki/2008/4/47/Diagrama3.jpg"> </p> |
| - | <p align="justify" class="style1"><strong><em>FIG 1</em>:</strong> Our system is conformed by two regulation mechanisms. The first mechanism is the one controlled by us through <a href="#metabolites">AHL</a>. <a href="#metabolites">LuxR</a> and <a href="#metabolites">AiiA</a> compete to bind AHL when it enters the cell. AiiA efficiently degrades AHL, while LuxR and AHL form a dimer. This dimer serves as an activator of <a href="#metabolites">CI</a>*, which represses <a href="#metabolites">RcnA</a>. The second of these mechanisms is the natural regulation of RcnA in response to the intracellular <a href="#metabolites">nickel</a> concentration. When there is no nickel inside the cell, RcnR represses RcnA. However, when nickel enters the cell, it forms a dimer with RcnR and changes its conformation so it no longer represses RcnA. RcnA is then free to start pumping Ni out of the cell. We are keeping this because it is damaging to the bacteria to have the pump always on, and otherwise it would need a constant supply of AHL.<br> | + | <p align="justify" class="style1"><strong><em>FIG 1</em>:</strong> Our system is conformed by two regulation mechanisms. The first mechanism is the one controlled by us through <a href="#metabolites">AHL</a>. <a href="#metabolites">LuxR</a> and <a href="#metabolites">AiiA</a> compete to bind AHL when it enters the cell. AiiA efficiently degrades AHL, while LuxR and AHL form a dimer. This dimer serves as an activator of <a href="#metabolites">CI</a>*, which represses <a href="#metabolites">RcnA</a>. The second of these mechanisms is the natural regulation of RcnA in response to the intracellular <a href="#metabolites">nickel</a> concentration. When there is no nickel inside the cell, RcnR represses RcnA. However, when nickel enters the cell, it forms a dimer with RcnR and changes its conformation so it no longer represses RcnA. RcnA is then free to start pumping Ni out of the cell. We are keeping this because it is damaging to the bacteria to have the pump always on, and otherwise it would need a constant supply of AHL.</p> |
| | + | <p align="center" class="style1"><a href="#top"><img src="https://static.igem.org/mediawiki/2008/c/cd/Boton_back.jpg" alt="Back to top" border="0"></a><br> |
| | <br> | | <br> |
| - | </p>
| + | <img src="https://static.igem.org/mediawiki/2008/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /></p> |
| | <p class="style3"><strong><a name="metabolites"></a>Metabolites and enzymes relevant to the model </strong></p> | | <p class="style3"><strong><a name="metabolites"></a>Metabolites and enzymes relevant to the model </strong></p> |
| | <table width="585" border="0" bordercolor="#75923C"> | | <table width="585" border="0" bordercolor="#75923C"> |
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| | </tr> | | </tr> |
| | </table> | | </table> |
| - | <br> | + | <p align="center"> </p> |
| - | <br> | + | <p><img src="https://static.igem.org/mediawiki/2008/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /></p> |
| | <p><strong><span class="style3"><a name="reactions"></a>Reactions</span><br> | | <p><strong><span class="style3"><a name="reactions"></a>Reactions</span><br> |
| | </strong><br> | | </strong><br> |
| | You can click on the next image to see a table of our reactions with their kinetics.</p> | | You can click on the next image to see a table of our reactions with their kinetics.</p> |
| | <p><a href="https://static.igem.org/mediawiki/2008/7/77/Tabla_ecuaciones.pdf" target="_blank"><img src="https://static.igem.org/mediawiki/2008/1/12/Bichem_react_table.PNG" alt="Table of biochemical reactions" width="581" height="279" border="0"></a><span class="style1"><br> | | <p><a href="https://static.igem.org/mediawiki/2008/7/77/Tabla_ecuaciones.pdf" target="_blank"><img src="https://static.igem.org/mediawiki/2008/1/12/Bichem_react_table.PNG" alt="Table of biochemical reactions" width="581" height="279" border="0"></a><span class="style1"><br> |
| - | <strong>* </strong>The equations are numbered like this because those we had initially defined evolved into this final list throughout the summer. We didn't want to change all references made to these equations so we just adjusted the numbering.<br>
| + | <strong>* </strong>The equations are numbered like this because those we had initially defined evolved into this final list throughout the summer. We didn't want to change all references made to these equations so we just adjusted the numbering.</span></p> |
| - | </span><br> | + | <p align="center"><span class="style1"><a href="#top"><img src="https://static.igem.org/mediawiki/2008/c/cd/Boton_back.jpg" alt="Back to top" border="0"></a><br> |
| - | </p>
| + | </span><br> |
| | + | <img src="https://static.igem.org/mediawiki/2008/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /></p> |
| | <p class="style2"><a name="odes"></a>Ordinary Differential Equations</p> | | <p class="style2"><a name="odes"></a>Ordinary Differential Equations</p> |
| | <p align="justify">We are taking into account the following set of ODEs, based on the biochemical reactions above. This set accurately and completely describes our model. Please click on the image to see a higher resolution.</p> | | <p align="justify">We are taking into account the following set of ODEs, based on the biochemical reactions above. This set accurately and completely describes our model. Please click on the image to see a higher resolution.</p> |
| | <p align="center"><br> | | <p align="center"><br> |
| | <a href="https://static.igem.org/mediawiki/2008/8/8f/Equation_list.PNG" target="_blank"><img src="https://static.igem.org/mediawiki/2008/6/63/Equationa.PNG" alt="Set of ODEs" border="0"></a></p> | | <a href="https://static.igem.org/mediawiki/2008/8/8f/Equation_list.PNG" target="_blank"><img src="https://static.igem.org/mediawiki/2008/6/63/Equationa.PNG" alt="Set of ODEs" border="0"></a></p> |
| - | <p><strong><span class="style3"><br> | + | <p align="center"><a href="#top"><img src="https://static.igem.org/mediawiki/2008/c/cd/Boton_back.jpg" alt="Back to top" border="0"></a></p> |
| - | Assumptions of the model </span><br> | + | <p><strong><span class="style3"><img src="https://static.igem.org/mediawiki/2008/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /><br> |
| | + | <br> |
| | + | <a name="assumptions"></a>Assumptions of the model </span><br> |
| | <br> | | <br> |
| | </strong></p> | | </strong></p> |
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| | </li> | | </li> |
| | <li> | | <li> |
| - | <div align="justify"> <strong>The change in the transcription of cI* is only dependent on AHL concentration.</strong> There’s a basal production of cI*, however the change will always be due to the AHL concentration given that production of LuxR is constitutive. </div> | + | <div align="justify"> <strong>The change in the transcription of cI* is dependent only on AHL concentration.</strong> There’s a basal production of cI*, however the change will always be due to the AHL concentration given that production of LuxR is constitutive. </div> |
| | </li> | | </li> |
| | <li> | | <li> |
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| | </li> | | </li> |
| | </ol> | | </ol> |
| - | <strong class="style2">References</strong><br> | + | <p align="center"><a href="#top"><img src="https://static.igem.org/mediawiki/2008/c/cd/Boton_back.jpg" alt="Back to top" border="0"></a></p> |
| | + | <p><img src="https://static.igem.org/mediawiki/2008/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /></p> |
| | + | <p><strong class="style2">References</strong><br> |
| | + | </p> |
| | </div> | | </div> |
| | <div id="lev4"> | | <div id="lev4"> |
| - | <p> <strong>1. </strong> Iwig JS, Rowe JL and Chivers PT (2006) <strong>Nickel homeostasis in <em>Escherichia coli</em> – the rcnR-rcnA efflux pathway and its linkage to NikR function</strong> Mol Microbiol <strong> 62</strong>(1), 252–262.<br> | + | <p> <strong>1. </strong> Iwig JS, Rowe JL and Chivers PT (2006) <strong>Nickel homeostasis in <em>Escherichia coli</em> – the rcnR-rcnA efflux pathway and its linkage to NikR function</strong> Mol Microbiol <strong> 62</strong>(1), 252–262.<br> |
| - | <strong>2.</strong> Tian T and Burrage K (2006) <strong>Stochastic models for regulatory networks of the genetic toggle switch</strong> Proc Natl Acad Sci <strong>103</strong>(22):8372-8377.<br> | + | <strong>2.</strong> Tian T and Burrage K (2006) <strong>Stochastic models for regulatory networks of the genetic toggle switch</strong> Proc Natl Acad Sci <strong>103</strong>(22):8372-8377.<br> |
| - | <strong>3.</strong> Imperial College Team, iGEM 2006 WIKI. The I. CoLi Reporter (<a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/parts/BBa_I13207">http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/parts/BBa_I13207</a>)</p> | + | <strong>3.</strong> Imperial College Team, iGEM 2006 WIKI. The I. CoLi Reporter (<a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/parts/BBa_I13207">http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/parts/BBa_I13207</a>)</p> |
| - | <p><a name="parameters"></a><a href="#top"><img src="https://static.igem.org/mediawiki/2008/c/cd/Boton_back.jpg" alt="Back to top" border="0"></a><a href=" #parameters"><img src="https://static.igem.org/mediawiki/2008/ 4/ 43/ Model2.jpg" alt="Parameters&Kinetics" width="190" height="31" border="0"></a><a href=" #simulation"><img src="https://static.igem.org/mediawiki/2008/7/7f/Model3.jpg" alt="Simulation & Analysis" width="190" height="31" border="0"></a><br> | + | <p><a name="parameters"></a><a href="#top"><img src="https://static.igem.org/mediawiki/2008/c/cd/Boton_back.jpg" alt="Back to top" border="0"></a><a href=" https://2008.igem.org/Team:LCG-UNAM-Mexico/Parameters"><img src="https://static.igem.org/mediawiki/2008/ f/ fd/ Model2ae.jpg" alt="Parameters&Kinetics" width="190" height="31" border="0"></a><a href=" https://2008.igem.org/Team:LCG-UNAM-Mexico/Simulation"><img src="https://static.igem.org/mediawiki/2008/7/7f/Model3.jpg" alt="Simulation & Analysis" width="190" height="31" border="0"></a><br> |
| | <br> | | <br> |
| | <img src="https://static.igem.org/mediawiki/2008/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /></p> | | <img src="https://static.igem.org/mediawiki/2008/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /></p> |
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| | <p> </p> | | <p> </p> |
| | </div></td> | | </div></td> |
| - | </tr> | + | </tr><tr> |
| - | <td class="pageName"><div align="center">Parameters & kinetics </div></td>
| + | |
| - | <tr>
| + | |
| | <td valign="top" class="bodyText"><p align="justify"><br> | | <td valign="top" class="bodyText"><p align="justify"><br> |
| - | The complete model uses 18 kinetic parameters and 11 biochemical reactions. We got 13 of these parameters researching the literature, and of the other 5 we estimated 2. The remaining 3 we adjusted to the observed results. Reaction kinetics were gotten from the literature, and if no evidence was found then we assumed it to be Law of Mass Action.<br>
| |
| - | <br>
| |
| - | 1. <span class="style4">Degradation of AHL by AiiA</span></p>
| |
| - | <table width="418" border="0">
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| - | <tr>
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| - | <td width="61"> </td>
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| - | <td width="347"><table width="326" border="0">
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| - | <tr>
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| - | <td colspan="2"><div align="left" class="style5">AiiA + AHL → AiiA</div></td>
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| - | </tr>
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| - | <tr>
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| - | <td width="88" valign="top"><strong>Kinetics:</strong></td>
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| - | <td width="228">Michaelis-Menten<sup>1,2</sup></td>
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| - | </tr>
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| - | <tr>
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| - | <td valign="top"><strong>Parameters:</strong></td>
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| - | <td><em>k</em><sub>1cat</sub> = 27.97 s<sup>-1</sup> <br>
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| - | <em>K</em><sub>1m</sub> = 3.723 mM = 224.20427E5 molecules</td>
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| - | </tr>
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| - | <tr>
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| - | <td valign="top"><strong>Flux:</strong></td>
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| - | <td><img src="https://static.igem.org/mediawiki/2008/9/9c/Eq1a.PNG" alt="Equation 1" width="151" height="40"></td>
| |
| - | </tr>
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| - | </table></td>
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| - | </tr>
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| - | </table>
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| - | <br>
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| - | <br>
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| - | <p align="justify">2. <span class="style4">Complex formation and dissociation between AHL and LuxR </span></p>
| |
| - | <table width="575" border="0">
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| - | <tr>
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| - | <td width="61"> </td>
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| - | <td width="504"><table width="459" border="0">
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| - | <tr>
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| - | <td colspan="2"><div align="left" class="style5">AHL + LuxR ↔ AHL:LuxR</div></td>
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| - | </tr>
| |
| - | <tr>
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| - | <td width="88" valign="top"><strong>Kinetics:</strong></td>
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| - | <td width="361">Mass Action<sup>3</sup></td>
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| - | </tr>
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| - | <tr>
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| - | <td valign="top"><strong>Parameters:</strong></td>
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| - | <td><p><em>k</em><sub>2</sub> = 10 <sup>-5</sup> molecules<sup>-1</sup> s<sup>-1</sup> <br>
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| - | <em>k</em><sub>-2</sub> = 3.33 x 10 <sup>-3</sup> s<sup>-1</sup>
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| - | <br>
| |
| - | </p> </td>
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| - | </tr>
| |
| - | <tr>
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| - | <td valign="top"><strong>Flux:</strong></td>
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| - | <td><img src="https://static.igem.org/mediawiki/2008/6/6b/Eq2a.PNG" alt="Equation 2" width="256" height="20"></td>
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| - | </tr>
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| - | <tr>
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| - | <td valign="top"><strong>Notes:</strong></td>
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| - | <td><p align="justify">The complex formation is slow and its dissociation is fast, so with few AHL and LuxR the complex concentration is negligible. </p> </td>
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| - | </tr>
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| - | </table></td>
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| - | </tr>
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| - | </table>
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| - | <p align="justify"><br>
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| - | 2.1. <span class="style4"><strong>Dimer formation and dissociation between AHL:LuxR complexes</strong></span></p>
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| - | <table width="577" border="0">
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| - | <tr>
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| - | <td width="61"> </td>
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| - | <td width="506"><table width="496" border="0">
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| - | <tr>
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| - | <td colspan="2"><div align="left" class="style5">2 AHL:LuxR ↔ (AHL:LuxR):(AHL:LuxR)</div></td>
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| - | </tr>
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| - | <tr>
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| - | <td width="88" valign="top"><strong>Kinetics:</strong></td>
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| - | <td width="398">Mass Action<sup>3</sup></td>
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| - | </tr>
| |
| - | <tr>
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| - | <td valign="top"><strong>Parameters:</strong></td>
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| - | <td><p><em>k</em><sub>2.1</sub> = 10 <sup>-5</sup> molecules<sup>-1</sup> s<sup>-1</sup> <br>
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| - | <em>k</em><sub>-2.1</sub> = 10 <sup>-2</sup> s<sup>-1</sup> <br>
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| - | </p></td>
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| - | </tr>
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| - | <tr>
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| - | <td valign="top"><strong>Flux:</strong></td>
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| - | <td><img src="https://static.igem.org/mediawiki/2008/e/e7/Eq3a.PNG" alt="Equation 2.1" width="382" height="22"></td>
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| - | </tr>
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| - |
| |
| - | </table></td>
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| - | </tr>
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| - | </table>
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| - | <p align="justify"><br>
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| - | 3.1. <span class="style4">CI synthesis induced by AHL and LuxR complexes dimer</span></p>
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| - | <table width="577" border="0">
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| - | <tr>
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| - | <td width="61"> </td>
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| - | <td width="506"><table width="457" border="0">
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| - | <tr>
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| - | <td colspan="2"><div align="left" class="style5">ρcI + (AHL:LuxR):(AHL:LuxR) → ρcI + (AHL:LuxR):(AHL:LuxR) + CI</div></td>
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| - | </tr>
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| - | <tr>
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| - | <td valign="top"><strong>Kinetics:</strong></td>
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| - | <td>Mass Action<sup>3</sup></td>
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| - | </tr>
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| - | <tr>
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| - | <td valign="top"><strong>Parameters:</strong></td>
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| - | <td><p><em>k</em><sub>3on</sub> = 10 <sup>-2</sup> molecules<sup>-1</sup> s<sup>-1</sup>
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| - | <br>
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| - | </p></td>
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| - | </tr>
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| - | <tr>
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| - | <td valign="top"><strong>Flux:</strong></td>
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| - | <td><img src="https://static.igem.org/mediawiki/2008/3/3d/Eq4a.PNG" alt="Equation 3.1" width="278" height="22"></td>
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| - | </tr>
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| - | </table></td>
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| - | </tr>
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| - | </table>
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| - | <p align="justify"><br>
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| - | <a name="cisynthesis" id="cisynthesis"></a>3.2. <span class="style4">Constitutive CI synthesis</span></p>
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| - | <table width="577" border="0">
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| - | <tr>
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| - | <td width="61"> </td>
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| - | <td width="506"><table width="457" border="0">
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| - | <tr>
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| - | <td colspan="2"><div align="left" class="style5">ρcI → ρcI + CI</div></td>
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| - | </tr>
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| - | <tr>
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| - | <td width="88" valign="top"><strong>Kinetics:</strong></td>
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| - | <td width="359">Mass Action<sup>3</sup></td>
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| - | </tr>
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| - | <tr>
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| - | <td valign="top"><strong>Parameters:</strong></td>
| |
| - | <td><p><em>k</em><sub>3off</sub> = 4 x 10 <sup>-2</sup> s<sup>-1</sup> <br>
| |
| - | </p></td>
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| - | </tr>
| |
| - | <tr>
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| - | <td valign="top"><strong>Flux:</strong></td>
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| - | <td><img src="https://static.igem.org/mediawiki/2008/4/49/Eq5a.PNG" alt="Equation 3.2" width="108" height="24"></td>
| |
| - | </tr>
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| - | <tr>
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| - | <td valign="top"><strong>Notes:</strong></td>
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| - | <td><div align="justify">To give more stability to the <em>off</em> state in the model, the rate constant in the presence of the inducer is <a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Notebook/2008-August#20ago">lower than the constitutive rate constant</a>, regardless the implication of a greater threshold to achieve the <em>on </em>state<sup>3</sup>.</div></td>
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| - | </tr>
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| - | </table></td>
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| - | </tr>
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| - | </table>
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| - | <p align="justify"><br>
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| - | <a name="cidegradation"></a>4. <span class="style4">Natural degradation of CI</span></p>
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| - | <table width="577" border="0">
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| - | <tr>
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| - | <td width="61"> </td>
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| - | <td width="506"><table width="457" border="0">
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| - | <tr>
| |
| - | <td colspan="2"><div align="left" class="style5">CI → Ø</div></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td width="88" valign="top"><strong>Kinetics:</strong></td>
| |
| - | <td width="359">Mass Action<sup>3</sup></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td valign="top"><strong>Parameters:</strong></td>
| |
| - | <td><p><em>k</em><sub>4</sub> = 0.002888 <sup></sup> s<sup>-1</sup> <br>
| |
| - | </p></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td valign="top"><strong>Flux:</strong></td>
| |
| - | <td><img src="https://static.igem.org/mediawiki/2008/e/e5/Eq6a.PNG" alt="Equation 4" ></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td valign="top"><strong>Notes:</strong></td>
| |
| - | <td><div align="justify">The half life of CI with LAA tail is 4 minutes<sup>8</sup>. Andersen JB <em>et al.</em><sup>9</sup> conclude that LAA tail and LVA tail modified the half life of GFP in a similar extent. Given this value,<a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Notebook/2008-August#21ago"> the rate constant was calculated</a>.</div></td>
| |
| - | </tr>
| |
| - | </table></td>
| |
| - | </tr>
| |
| - | </table>
| |
| - | <p align="justify"><br>
| |
| - | <a name="cidimer"></a>4.1. <span class="style4">Dimer formation and dissociation between CI molecules </span></p>
| |
| - | <table width="577" border="0">
| |
| - | <tr>
| |
| - | <td width="61"> </td>
| |
| - | <td width="506"><table width="457" border="0">
| |
| - | <tr>
| |
| - | <td colspan="2"><div align="left" class="style5">2 CI ↔ CI:CI</div></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td width="88" valign="top"><strong>Kinetics:</strong></td>
| |
| - | <td width="359">Mass Action<sup>3</sup></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td valign="top"><strong>Parameters:</strong></td>
| |
| - | <td><p><em>k</em><sub>4.1</sub> = 0.00001 molecules<sup>-1</sup> <sup></sup> s<sup>-1</sup><br>
| |
| - | <em>k</em><sub>-4.1</sub> = 0.01 <sup></sup> s<sup>-1</sup><br>
| |
| - | </p></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td valign="top"><strong>Flux:</strong></td>
| |
| - | <td><img src="https://static.igem.org/mediawiki/2008/7/72/Eq7.PNG" alt="Equation 4.1" width="193" height="24"></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td valign="top"><strong>Notes:</strong></td>
| |
| - | <td><div align="justify">Kenneth <em>et al.</em> estimated the change in free Gibbs energy in this reaction (with wildtype CI) as -11.1 kcal/mol,<sup>10</sup> which leads to an equilibrium constant of 8.32186E16 molecules<sup>-1</sup>. This implies that the forward rate constant should be at least sixteen orders of magnitude greater than the reverse rate constant, which means a constant repression of RcnA even with the constitutive CI synthesis. A parameter scan was run to determine the range of values that gives the desired behavior and the rate constants were chosen arbitrarily within this range. These values are comparable to others typical biochemical parameters. It has been shown that kinetic parameters can be modified by changing amino acid sequences (for example, CI half life is reduced by adding a LVA tail in the C-terminal), it’s proposed that it’s possible to engineer the protein to reach an acceptable dissociation constant. </div></td>
| |
| - | </tr>
| |
| - | </table></td>
| |
| - | </tr>
| |
| - | </table>
| |
| - | <p align="justify"><br>
| |
| - | <a name="rcnaproduction" id="rcnaproduction"></a>6. <span class="style4">RcnA production </span></p>
| |
| - | <table width="577" border="0">
| |
| - | <tr>
| |
| - | <td width="61"> </td>
| |
| - | <td width="506"><table width="457" border="0">
| |
| - | <tr>
| |
| - | <td colspan="2"><div align="left" class="style5">ρ → ρ + RcnA</div></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td width="88" valign="top"><strong>Kinetics:</strong></td>
| |
| - | <td width="359">Cooperative inhibition (Hill kinetics)<sup>4,5,6,7</sup></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td valign="top"><strong>Parameters:</strong></td>
| |
| - | <td><p><em>n</em><sub>5</sub> =1.9<br>
| |
| - | <br>
| |
| - | <sup></sup><img src="https://static.igem.org/mediawiki/2008/4/4b/Eq9.1.PNG"><br>
| |
| - | <img src="https://static.igem.org/mediawiki/2008/5/5f/Eq9.2.PNG" width="300" height="41"><br>
| |
| - | <img src="https://static.igem.org/mediawiki/2008/c/c2/Eq9.3.PNG" width="300" height="39"> <sup><br>
| |
| - | </sup><br>
| |
| - | </p>
| |
| - | </td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td valign="top"><strong>Flux:</strong></td>
| |
| - | <td><img src="https://static.igem.org/mediawiki/2008/c/c6/Eq8.PNG" alt="Equation 6" width="199" height="49"></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td valign="top"><strong>Notes:</strong></td>
| |
| - | <td><div align="justify">ΔG<sub>CI:CI-OR1</sub>=-11.6 kcal/mol<br>
| |
| - | ΔG<sub>CI:CI-OR2</sub>=-10.1 kcal/mol<br>
| |
| - | ΔG<sub>CI:CI-OR1-OR2</sub>=-23.8 kcal/mol<br>
| |
| - | <em>ν</em><sub>6</sub>(<em>Pl</em>)=20mM/h=3346.111 molecules/s with 20 promoter copies (ρ<sub>0</sub>)<sup>7</sup>.<br>
| |
| - | The promoter in our construction is Pr, which is similar to Pl, the one used to estimated the parameter<sup>7</sup>.</div></td>
| |
| - | </tr>
| |
| - | </table></td>
| |
| - | </tr>
| |
| - | </table>
| |
| - | <p align="justify"><br>
| |
| - | 7. <span class="style4">Nickel efflux by RcnA </span></p>
| |
| - | <table width="577" border="0">
| |
| - | <tr>
| |
| - | <td width="61"> </td>
| |
| - | <td width="506"><table width="457" border="0">
| |
| - | <tr>
| |
| - | <td colspan="2"><div align="left" class="style5">RcnA + Ni<sub>int</sub> → RcnA + Ni<sub>ext</sub></div></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td width="88" valign="top"><strong>Kinetics:</strong></td>
| |
| - | <td width="359">Mass Action<sup>3</sup></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td valign="top"><strong>Parameters:</strong></td>
| |
| - | <td><p><em>k</em><sub>7</sub> = ? <br>
| |
| - | <br>
| |
| - | </p></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td valign="top"><strong>Flux:</strong></td>
| |
| - | <td><img src="https://static.igem.org/mediawiki/2008/a/a6/Eq10.PNG" width="139" height="21"></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td valign="top"><strong>Notes:</strong></td>
| |
| - | <td><div align="justify">Experimentally measured.</div></td>
| |
| - | </tr>
| |
| - | </table></td>
| |
| - | </tr>
| |
| - | </table>
| |
| - | <p align="justify"><br>
| |
| - | <a name="rcnadegradation"></a>8.<span class="style4"> Natural degradation of RcnA </span></p>
| |
| - | <table width="577" border="0">
| |
| - | <tr>
| |
| - | <td width="61"> </td>
| |
| - | <td width="506"><table width="457" border="0">
| |
| - | <tr>
| |
| - | <td colspan="2"><div align="left" class="style5">RcnA → Ø<sub></sub></div></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td width="88" valign="top"><strong>Kinetics:</strong></td>
| |
| - | <td width="359">Mass Action<sup>3</sup></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td valign="top"><strong>Parameters:</strong></td>
| |
| - | <td><p><em>k</em><sub>8</sub> = 1.666E-4 s<sup>-1</sup> <br>
| |
| - | <br>
| |
| - | </p></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td valign="top"><strong>Flux:</strong></td>
| |
| - | <td><img src="https://static.igem.org/mediawiki/2008/0/0f/Eq11.PNG" width="96" height="22"></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td valign="top"><strong>Notes:</strong></td>
| |
| - | <td><div align="justify">This kinetic parameter wasn’t found in our bibliographic search and <a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Notebook/2008-August#letter">personal communication with Peter T. Chivers</a> (Washington University School of Medicine) confirmed that this parameter is unknown. The value used is the degradation rate of LacY, the lactose permease of <em>E. coli</em>, which is also a transmembran protein.<sup>11</sup></div></td>
| |
| - | </tr>
| |
| - | </table></td>
| |
| - | </tr>
| |
| - | </table>
| |
| - | <p align="justify"><br>
| |
| - | 9.<span class="style4"> Nickel import by unknown channel </span></p>
| |
| - | <table width="577" border="0">
| |
| - | <tr>
| |
| - | <td width="61"> </td>
| |
| - | <td width="506"><table width="457" border="0">
| |
| - | <tr>
| |
| - | <td colspan="2"><div align="left" class="style5">Unk + Ni<sub>ext</sub> → Unk + Ni<sub>int</sub></div></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td width="88" valign="top"><strong>Kinetics:</strong></td>
| |
| - | <td width="359">Mass Action<sup>3</sup></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td valign="top"><strong>Parameters:</strong></td>
| |
| - | <td><p><em>k</em><sub>9</sub> = ? <sup></sup> <br>
| |
| - | <br>
| |
| - | </p></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td valign="top"><strong>Flux:</strong></td>
| |
| - | <td><img src="https://static.igem.org/mediawiki/2008/9/9b/Eq12.PNG" width="131" height="22"></td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td valign="top"><strong>Notes:</strong></td>
| |
| - | <td><div align="justify">Experimentally measured <sup></sup></div></td>
| |
| - | </tr>
| |
| - | </table></td>
| |
| - | </tr>
| |
| - | </table>
| |
| - | <p><strong>NOTE:</strong> The average volume of an <em>E. coli </em>cell is 10<sup>-15</sup> liters.</p>
| |
| - | <p> </p>
| |
| - | <p class="style2">Defining the initial state of the system</p>
| |
| - | <p align="justify"> The initial concentrations of the constitutive proteins (AiiA, LuxR, CI -constitutive synthesis- and CI:CI -due to constitutive synthesis-) were estimated based on the efficiency rate of their promoters, number of promoters per cell, degradation rate of their mRNAs, translation efficiency and degradation rate of the proteins. Initial concentrations of AHL:LuxR complex, the dimer of complexes, CI and CI:CI due to complex activation were set to 0, given these are all due to the action of AHL. Number of copies of both <em>cI</em> and <em>rcnA</em> promoters are 10 based on plasmid copy number. RcnA and Unk were estimated experimentally and set consistent to the observed rate. Concentration of AHL and nickel is determined by us to obtain the desired results. </p>
| |
| - | <p align="justify"> <span class="style3">AHL:</span> It’s an arbitrary and adjustable value. Different outcomes can be observed <a href="#simulation">manipulating this initial value</a>.<br>
| |
| - | <span class="style3"><br>
| |
| - | Nickel (total):</span> It’s an arbitrary and adjustable value. Different outcomes can be observed <a href="#simulation">manipulating this initial value</a>.<br>
| |
| - | <span class="style3"><br>
| |
| - | Unk:</span> Both the Unk concentration and its rate constant are unknown. They are arbitrarily defined in such a way that the flux of the reaction 9 is consistent with experimental measurements.<br>
| |
| - |
| |
| - | <strong>[Unk]</strong>= (SLOPE) molecules<br>
| |
| - | <span class="style3"><br>
| |
| - | Ni<sub>int</sub>:</span> The initial concentration of Nickel inside the cell is estimated based on experimental measurements in absence of AHL.<br>
| |
| - |
| |
| - | <strong>[Ni<sub>int</sub>]</strong>= (SLOPE) molecules<br>
| |
| - | <span class="style3"><br>
| |
| - | ρ and ρCI:</span> Their concentration is defined by the copy number of the plasmids that contain them.<br>
| |
| - | <strong>[ρ]</strong>= 10 molecules<br>
| |
| - | <strong>[ρcI]</strong>= 10 molecules<br>
| |
| - | <span class="style3"><br>
| |
| - | <a name="ciciconstitutive"></a>CI and CI:CI:</span> Given the <a href="#cisynthesis">constitutive synthesis</a> and <a href="#cidegradation">degradation</a> rate of CI, as well as its <a href="#cidimer">dimerization constant</a>, CI and CI:CI concentrations are estimated in absence of AHL.<br>
| |
| - | <strong>[CI]</strong>= 138 molecules<br>
| |
| - | <strong>[CI:CI]</strong>= 19 molecules<br>
| |
| - | <span class="style3"><br>
| |
| - | RcnA:</span> Given the <a href="#rcnaproduction">synthesis</a> and <a href="#rcnadegradation">degradation</a> rate of RcnA, as well as the <a href="#ciciconstitutive">constitutive concentration of CI:CI</a>, RcnA concentration is estimated in absence of AHL.<br>
| |
| - | <strong>[RcnA]</strong>= 33150 molecules<br>
| |
| - | <span class="style3"><br>
| |
| - | AiiA:</span> The constant concentration of AiiA is calculated taking into account the following parameters retrieved from literature:<br>
| |
| - | - pLac average transcription rate<sup>1,2</sup>: 0.003 s<sup>-1</sup><br>
| |
| - | - mRNA average degradation rate<sup>1,3</sup>: 0.00766 s<sup>-1</sup><br>
| |
| - | - Average translation rate<sup>1,3</sup>: 0.31333 s<sup>-1</sup><br>
| |
| - | - AiiA degration rate: 0.00012 s<sup>-1</sup> <br>
| |
| - | The half life of RcnA with LVA tail is approximately 2 minutes<sup>14</sup>; Andersen JB et al. found that this tail reduces the half life of GFP forty-eight times.9 Therefore the half life of wildtype AiiA can be estimated to 96 minutes.<br>
| |
| - | <strong> [AiiA]</strong>= 10000 molecules<br>
| |
| - | <span class="style3"><br>
| |
| - | LuxR:</span> The constant concentration of LuxR is calculated taking into account the following parameters retrieved from literature:<br>
| |
| - | - pTet average transcription rate<sup>12,15</sup>: 0.003 s<sup>-1</sup><br>
| |
| - | - mRNA average degradation rate<sup>13</sup>: 0.00766 s<sup>-1</sup><br>
| |
| - | - LuxR translation rate<sup>16</sup>: 0.556 s<sup>-1</sup><br>
| |
| - | - LuxR degration rate<sup>16</sup>: 9.627E-5 s<sup>-1</sup><br>
| |
| - | <strong> [LuxR]</strong>= 22000 molecules<br>
| |
| - | </p>
| |
| - | <p align="justify"> <span class="style2"><strong>References</strong></span><strong><br>
| |
| - | </strong><strong>1. </strong>Wang LH <em>et al</em>. (2004) <strong>Specificity and Enzyme Kinetics of the Quorum-quenching <em>N-</em>Acyl Homoserine Lactone Lactonase (AHL-Lactonase). </strong>J Biol Chem <strong>279:</strong>4, 13645-13651. <br>
| |
| - | <strong>2. </strong>Hee Kim <em>et al. </em>(2005) <strong>The molecular structure and catalytic mechanism of a quorum-quenching N-acyl-L-homoserine lactone hydrolase.</strong> Proc Natl Acad Sci USA 102:49, 17606-17611. <br>
| |
| - | <strong>3. </strong>Goryachev AB, Toh DJ, Lee T (2006). <strong>Systems analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants.</strong> Biosystems 83, 178-187. <strong>4. </strong>Babic AC, Little JW (2007) <strong>Cooperative binding by CI repressor is dispensable in a phage </strong><strong>λ </strong><strong>variant. </strong>Proc Natl Acad Sci USA 104: 17741-17746. <br>
| |
| - | <strong>5. </strong>Ackers GK, Johnson AD, Shea MA (1982). <strong>Quantitative model for gene regulation by </strong><strong>λ</strong> <strong>phage repressor.</strong>Proc Natl Acad Sci USA 79: 1129-1133. <br>
| |
| - | <strong>6. </strong>Reinitz J, Vaisnys JR (1990) <strong>Theoretical and Experimental Analysis of the Phage Lambda Genetic Switch Implies Missing Levels of Co-operativity</strong>. J Theor Biol 145: 295-318. <br>
| |
| - | <strong>7. </strong>Iadevaia S, Mantzaris NV (2006) <strong>Genetic Network Driven Control of PHBV Copolymer Composition. </strong>J Biotechnol 122: 99-121. <br>
| |
| - | <strong>8. </strong>Elowitz MB & Leibler S (2000). <strong>A synthetic oscillatory network of transcriptional regulators. </strong>Nature 403 335-338. <br>
| |
| - | <strong>9. </strong>Andersen JB <em>et al </em> (1998). <strong>New Unstable of Green Fluorescent Protein for Studies of Transient Gene Expression in Bacteria. </strong> Appl Environ Microbiol 64,6: 2240-2246. <br>
| |
| - | <strong>10. </strong>Kenneth S.<strong> </strong>Koblan and Gary K. Ackers (1991) <strong>Energetics of Subunit Dimerization in Bacteriophage </strong><strong>λ </strong><strong>cI </strong><strong>Repressor: Linkage to</strong><strong> </strong><strong>Protons, Temperature, and KCl.</strong> Biochemistry 1991, 30, 7817-7821. <br>
| |
| - | <strong>11. </strong>M. Santillán and M. C. Mackey (2004). <strong>Influence of catabolite repression and inducer exclusion on the bistable behavior of the lac operon.</strong> Biophys J. 86: 1282-1292 <br>
| |
| - | <strong>12. </strong>Malan, T. P., A. Kolb, H. Buc, and W. R. McClure (1984). <strong>Mechanism of CRP-cAMP activation of lac operon transcription initiation activation of the P1 promoter.</strong> J. Mol. Biol. 180:881–909. <br>
| |
| - | <strong>13. </strong>Kennell, D., and H. Riezman (1977). <strong>Transcription and translation initiation frequencies of the <em>Escherichia coli</em> lac operon.</strong> J. Mol. Biol. 114:1–21. <br>
| |
| - | <strong>14. </strong>Christopher Batten. <strong>Modeling the Lux/AiiA Relaxation Oscillator</strong><strong>.</strong> Unpublished (<a href="http://www.mit.edu/%7Ecbatten/work/ssbc04/modeling-ssbc04.pdf">http://www.mit.edu/~cbatten/work/ssbc04/modeling-ssbc04.pdf</a>). <br>
| |
| - | <strong>15. </strong>Bologna Cesena Campus, iGEM 2007 WIKI. (<u><a href="http://parts.mit.edu/igem07/index.php/Bologna">http://parts.mit.edu/igem07/index.php/Bologna</a></u>) <br>
| |
| - | <strong>16. </strong>KULeuven team, iGEM 2008 WIKI. Dr. Coli, the bacterial drug delivery system. (<a href="https://2008.igem.org/Team:KULeuven/Model/CellDeath" target="_blank">https://2008.igem.org/Team:KULeuven/Model/CellDeath</a>) </p>
| |
| - | <p align="justify"><a name="simulation"></a><a href="#top"><img src="https://static.igem.org/mediawiki/2008/c/cd/Boton_back.jpg" alt="Back to top" width="190" height="31" border="0"></a><a href="#modeling"><img src="https://static.igem.org/mediawiki/2008/5/5b/Model1a.jpg" alt="Modeling the system" width="190" height="31" border="0"></a><a href="#simulation"><img src="https://static.igem.org/mediawiki/2008/7/7f/Model3.jpg" alt="Simulation&Analysis" width="190" height="31" border="0"></a><br>
| |
| - | <img src="https://static.igem.org/mediawiki/2008/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /></p>
| |
| - | <p align="justify"><br>
| |
| | </p></td> | | </p></td> |
| | </tr> | | </tr> |
| - | <td class="pageName"><div align="center">Simulation & Analysis </div></td>
| + | </table> |
| - | </table>
| + | <div align="justify"> <br> |
| - | <div align="justify"> | + | <br /> |
| - | <p><br>
| + | </div> |
| - | <span class="bodyText">With the aim of predicting the behavior of the system, the biochemical reactions were implemented in the SimBiology package of MATLAB, using the previously defined parameters (link a parameters and kinetics). Simulations were run for different values of the initial concentration of AHL and Ni<sub>total</sub> (Ni<sub>int</sub> + Ni<sub>ext</sub>) which are the metabolites that we can directly manipulate in our experiments. A parameter scan was also run for some parameters to understand their influence on the system.</span><br>
| + | |
| - | <span class="bodyText">In order to gain insights into the system dynamics to elucidate the conditions needed to get the desired behavior, we performed a series of analysis on it: sensitivity analysis allowed us to identify critical parameters that needed to be defined on the most stringent way. Basis for the (right) null and left null space were calculated to obtain information about the general network behavior. Steady-states were calculated by numerical integration of the non-linear ODEs system. Finally the Jacobian of the system was calculated around the steady-states. All simulations and analysis were implemented and performed on MATLAB.</span></p> | + | |
| - | <p> <span class="style2">Simulation and parameter scan</span><br>
| + | |
| - | <br>
| + | |
| - | <span class="bodyText">Describir el comportamiento que queremos ver y por qué.<br>
| + | |
| - | Incluir las gráficas de parameter scan, la gráfica de la vida, y el escaneo con el que definimos algunas constantes </span></p>
| + | |
| - | <p class="style2"> Sensitivity analysis </p>
| + | |
| - | <p> Definir brevemente de que se trata, mostrar análisis a diferentes tiempos. Señalar los resultados que esperábamos y los que no</p>
| + | |
| - | <p class="style2"> Stoichiometric matrix </p>
| + | |
| - | <p class="bodyText"> Definir la información que contiene la matriz estequimétrica. <br>
| + | |
| - | Definir los espacios nulos (link a wikipedia o matworld?) <br>
| + | |
| - | Presentar las bases calculadas y una interpretación concisa </p>
| + | |
| - | <p class="style2"> Steady-states </p>
| + | |
| - | <p> <span class="bodyText">Definir estado estacionario, decir algo de la complejidad del problema y justificar la estrategia elegida (aproximación numérica)</span></p>
| + | |
| - | <p> Presentar la solución ontenida. </p>
| + | |
| - | <p class="style2"> Jacobian </p>
| + | |
| - | <p class="bodyText"> Definición general del jacobiano (link a wikipedia o mathworld?). Definición en redes bioquímicas. <br>
| + | |
| - | Presentar el método para calcularlo y las matrices modales, junto con su interpretación y las escalas de tiempo. <br>
| + | |
| - | Si da tiempo poner algo de análiss de estabilidad del estado estacionario (lo más probable s que no sea estable).<br>
| + | |
| - | </p>
| + | |
| - | <p><a href="#top"><img src="https://static.igem.org/mediawiki/2008/c/cd/Boton_back.jpg" alt="Back to top" width="190" height="31" border="0"></a> <a href="#modeling"><img src="https://static.igem.org/mediawiki/2008/5/5b/Model1a.jpg" alt="Modeling the system" width="190" height="31" border="0"></a><a href="#parameters"><img src="https://static.igem.org/mediawiki/2008/4/43/Model2.jpg" alt="Parameters & kinetics" width="190" height="31" border="0"></a><br>
| + | |
| - | <br>
| + | |
| - | <img src="https://static.igem.org/mediawiki/2008/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /></p>
| + | |
| - | <p><br />
| + | |
| - | </p>
| + | |
| - | </div>
| + | |
| | <td width="132"> </td> | | <td width="132"> </td> |
| | </tr> | | </tr> |
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