Team:LCG-UNAM-Mexico/Modeling

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Latest revision as of 06:33, 30 October 2008

LCG-UNAM-Mexico:Modeling

LCG-UNAM-Mexico

iGEM 2008 TEAM

Modeling the system

Metabolites & Enzymes | Reactions | Ordinary Differential Equations | Assumptions of the Model

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.
Our system is composed of 13 species and 11 coupled biochemical reactions that completely describe it. This can be represented through a set of ordinary differential equations (ODEs). The simulations were done using Simbiology, a package from Matlab.

Iwig 2006

FIG 1: Our system is conformed by two regulation mechanisms. The first mechanism is the one controlled by us through AHL. LuxR and AiiA 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 CI*, which represses RcnA. The second of these mechanisms is the natural regulation of RcnA in response to the intracellular nickel 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.

Metabolites and enzymes relevant to the model

AiiA
AHL
LuxR
AHL:LuxR
(AHL:LuxR):(AHL:LUXR)
ρcI
CI
CI:CI
ρ
RcnA
Ni_int
Ni_ext
Unk

Acyl-Homoserine Lactone Lactonase
Acyl-Homoserine Lactone
Transcriptional Activator
Complex formed by AHL and LuxR
Dimer of AHL:LuxR complexes
cI* promoter, inducible by the dimer of AHL:LuxR complexes
λ phage repressor (CI) modified with a LVA tail for quick degradation
Repressor, dimer of CI molecules
rcnA promoter, modified to be repressible by CI:CI
Escherichia coli nickel efflux pump
Intracellular nickel
Extracellular nickel
Unknown nickel import channel

Reactions

You can click on the next image to see a table of our reactions with their kinetics.

* 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.

Ordinary Differential Equations

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.

Assumptions of the model

Once there is nickel in the medium, RcnR no longer participates in the pump’s regulation. If there’s nickel in the medium, we can assume that RcnR is always coupled with a Ni molecule, so it will not be capable of repressing RcnA (The few RcnR molecules in the cell will cause noise, but this will be indistinguishable from the pump’s normal behavior).¹
Cell membrane permeability to AHL is not considered inside the model. The model assumes all AHL enters the cell, however the concentration needed in the model to obtain the desired results is changed by us accordingly. ²
All decrease in AHL concentration is due to AiiA. We consider the natural degradation of AHL to be unimportant given the time taken to make the analysis (AHL half-life is long, from 3 to 24 hours). ³
The change in the transcription of cI* is dependent only on AHL concentration. 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.
It is a homogeneous system. This means that the coefficients of the equations are constant (so we don’t have compartmentalization).
The quantity of nickel used by the cell is negligible compared to the concentrations in and out of the cell. This means we don’t need to include an equation describing the change in the Ni concentration due to cell consumption in the time used by the experiment.¹
The production of RcnR, LuxR and AiiA is constitutive and their concentrations have reached the steady state at the beginning of the experiment.
NikABCDE will not play a role in our model. NikABCDE serves to import nickel to the cell, however it only works in anaerobic conditions and our experiment will be made in aerobic conditions. This therefore implies that the nickel import will only take place by the unknown mechanism, which nonetheless is constant and constitutive.¹

References

1. Iwig JS, Rowe JL and Chivers PT (2006) Nickel homeostasis in Escherichia coli – the rcnR-rcnA efflux pathway and its linkage to NikR function Mol Microbiol 62(1), 252–262.
2. Tian T and Burrage K (2006) Stochastic models for regulatory networks of the genetic toggle switch Proc Natl Acad Sci 103(22):8372-8377.
3. Imperial College Team, iGEM 2006 WIKI. The I. CoLi Reporter (http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/parts/BBa_I13207)

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      <td colspan="3" rowspan="2"><img src="https://static.igem.org/mediawiki/igem.org/b/b3/LCG_copy.png" alt="Header image" width="524" height="143" border="0" /></td>
-     <td height="50" colspan="3" id="logo" valign="bottom" align="center" nowrap="nowrap">LCG-UNAM-Mexico</td>
+     <td height="50" colspan="3" id="logo" valign="bottom" align="center" nowrap="nowrap"><a name="top"></a>LCG-UNAM-Mexico</td>
      <td width="132" rowspan="2"><img src="https://static.igem.org/mediawiki/2008/1/1d/TeamLogo_00.png" width="120" height="142" /></td>
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-           <td width="165" bgcolor="#5C743D"><a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Team" class="navText">About Us</a></td>
+           <td width="165" bgcolor="#5C743D"><a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Project" class="navText">Our project</a></td>
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-           <td width="165" bgcolor="#5C743D"><a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Project" class="navText">Our Project</a></td>
+           <td width="165" bgcolor="#5C743D"><a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Modeling" class="navText">Modeling</a></td>
          </tr>
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-           <td width="165" bgcolor="#5C743D"><a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Experiments" class="navText">Experiments</a></td>
+           <td width="165" bgcolor="#5C743D"><a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Experiments" class="navText">Wet Lab</a></td>
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-           <td width="165" bgcolor="#5C743D"><a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Modeling" class="navText">Modeling</a></td>
+           <td width="165" bgcolor="#5C743D"><a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Notebook" class="navText">Notebook</a></td>
          </tr>
          <tr>
-           <td width="165" bgcolor="#5C743D"><a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Notebook" class="navText">Notebook</a></td>
+           <td width="165" bgcolor="#5C743D"><a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Story" class="navText">Our story</a></td>
+        </tr>
+ <tr>
+          <td width="165" bgcolor="#5C743D"><a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Team" class="navText">About us</a></td>
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-      </table>
- 	 <br />
+    </table> <br />
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-       &nbsp;<img src="https://static.igem.org/mediawiki/2008/5/5b/Model1a.jpg" /> <img src="https://static.igem.org/mediawiki/2008/4/43/Model2.jpg" /> <img src="https://static.igem.org/mediawiki/2008/7/7f/Model3.jpg" /><br>
+       &nbsp;<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>
-       <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>
        <table border="0" cellspacing="0" cellpadding="2" width="590">
              <tr>
            <td class="pageName"><div align="center">
-             <p>Modeling the system </p>
+             <p><br>
+              Modeling the system </p>
            </div></td>
          </tr>
          <tr>
-           <td class="bodyText"><p align="justify">The objective of our modelling 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&nbsp; 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 &amp; 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 species and 11 coupled biochemical reactions that completely describe it. This can be represented through a set of ordinary differential equations (ODEs). The simulations 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&nbsp; 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="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 AHL. LuxR and AiiA 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 cI*, which represses RcnA. The second of these mechanisms is the natural regulation of RcnA in response to the intracellular nickel 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>
-            </p>
+              <img src="https://static.igem.org/mediawiki/2008/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /></p>
-             <p class="style3"><strong>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>
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-             <br>
+             <p align="center">&nbsp;</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">Reactions</span><br>
+             <p><strong><span class="style3"><a name="reactions"></a>Reactions</span><br>
                </strong><br>
                You can click on the next image to see a table of our reactions with their kinetics.</p>
-             <p><img src="https://static.igem.org/mediawiki/2008/1/12/Bichem_react_table.PNG" alt="Table of biochemical reactions" width="581" height="279"><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>
-             <p class="style2">Ordinary Differential Equations</p>
+              <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 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>
-               <img src="https://static.igem.org/mediawiki/2008/6/63/Equationa.PNG" alt="Set of ODEs"></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>
              </strong></p>
@@ Line 180: / Line 195: @@
                  </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>
@@ Line 195: / Line 210: @@
                  </li>
                </ol>
-               <strong>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 id="lev4">
-               <p> 1- Nickel homeostasis in Escherichia coli – the rcnR-rcnA efflux pathway and its linkage to NikR function Jeffrey S. Iwig, Jessica L. Rowe and Peter T. Chivers* Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, St Louis, MO, 63110, USA. Molecular Microbiology (2006) 62(1), 252–262 doi:10.1111/j.1365-2958.2006.05369.x </p>
+               <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>2- Biological Sciences - Biophysics: Tianhai Tian and Kevin Burrage Stochastic models for regulatory networks of the genetic toggle switch PNAS 2006 103:8372-8377; published ahead of print May 19, 2006, doi:10.1073/pnas.0507818103 </p>
+               <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>
-               <p>3- http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/parts/BBa_I13207 </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><img src="https://static.igem.org/mediawiki/2008/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /></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="https://2008.igem.org/Team:LCG-UNAM-Mexico/Parameters"><img src="https://static.igem.org/mediawiki/2008/f/fd/Model2ae.jpg" alt="Parameters&amp;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 &amp; Analysis" 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>
                <p> </p>
              </div></td>
-         </tr>
+         </tr><tr>
-    <td class="pageName"><div align="center">Parameters &amp; kinetics </div></td>
-        <tr>
            <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>
-. <span class="style4">Degradation of AHL by AiiA</span></p>
-            <table width="418" border="0">
-              <tr>
-                <td width="61">&nbsp;</td>
-                <td width="347"><table width="326" border="0">
-                  <tr>
-                    <td colspan="2"><div align="left" class="style5">AiiA + AHL → AiiA</div></td>
-                  </tr>
-                  <tr>
-                    <td width="88" valign="top"><strong>Kinetics:</strong></td>
-                    <td width="228">Michaelis-Menten<sup>1,2</sup></td>
-                  </tr>
-                  <tr>
-                    <td valign="top"><strong>Parameters:</strong></td>
-                    <td><em>k</em><sub>1cat</sub> = 27.97 s<sup>-1</sup>      <br>
-                        <em>K</em><sub>1m</sub> = 3.723 mM = 224.20427E5 molecules</td>
-                  </tr>
-                  <tr>
-                    <td valign="top"><strong>Flux:</strong></td>
-                    <td><img src="https://static.igem.org/mediawiki/2008/9/9c/Eq1a.PNG" alt="Equation 1" width="151" height="40"></td>
-                  </tr>
-                </table></td>
-              </tr>
-            </table>
-            <br>
-            <br>
-            <p align="justify">2. <span class="style4">Complex formation and dissociation between AHL and LuxR </span></p>
-            <table width="575" border="0">
-              <tr>
-                <td width="61">&nbsp;</td>
-                <td width="504"><table width="459" border="0">
-                    <tr>
-                      <td colspan="2"><div align="left" class="style5">AHL + LuxR ↔ AHL:LuxR</div></td>
-                    </tr>
-                    <tr>
-                      <td width="88" valign="top"><strong>Kinetics:</strong></td>
-                      <td width="361">Mass Action<sup>3</sup></td>
-                    </tr>
-                    <tr>
-                      <td valign="top"><strong>Parameters:</strong></td>
-                      <td><p><em>k</em><sub>2</sub> = 10 <sup>-5</sup> molecules<sup>-1</sup> s<sup>-1</sup>    <br>
-                        <em>k</em><sub>-2</sub> = 3.33 x 10 <sup>-3</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/2008/6/6b/Eq2a.PNG" alt="Equation 2" width="256" height="20"></td>
-                    </tr>
-                    <tr>
-                      <td valign="top"><strong>Notes:</strong></td>
-                      <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>
-                    </tr>
-                </table></td>
-              </tr>
-            </table>
-            <p align="justify"><br>
-.1. <span class="style4"><strong>Dimer formation and dissociation between AHL:LuxR complexes</strong></span></p>
-            <table width="577" border="0">
-              <tr>
-                <td width="61">&nbsp;</td>
-                <td width="506"><table width="496" border="0">
-                    <tr>
-                      <td colspan="2"><div align="left" class="style5">2 AHL:LuxR ↔ (AHL:LuxR):(AHL:LuxR)</div></td>
-                    </tr>
-                    <tr>
-                      <td width="88" valign="top"><strong>Kinetics:</strong></td>
-                      <td width="398">Mass Action<sup>3</sup></td>
-                    </tr>
-                    <tr>
-                      <td valign="top"><strong>Parameters:</strong></td>
-                      <td><p><em>k</em><sub>2.1</sub> = 10 <sup>-5</sup> molecules<sup>-1</sup> s<sup>-1</sup>    <br>
-                              <em>k</em><sub>-2.1</sub> = 10 <sup>-2</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/e7/Eq3a.PNG" alt="Equation 2.1" width="382" height="22"></td>
-                    </tr>
-                </table></td>
-              </tr>
-            </table>
-            <p align="justify"><br>
-.1. <span class="style4">CI synthesis induced by AHL and LuxR complexes dimer</span></p>
-            <table width="577" border="0">
-              <tr>
-                <td width="61">&nbsp;</td>
-                <td width="506"><table width="457" border="0">
-                    <tr>
-                      <td colspan="2"><div align="left" class="style5">ρcI + (AHL:LuxR):(AHL:LuxR) → ρcI + (AHL:LuxR):(AHL:LuxR) + CI</div></td>
-                    </tr>
-                    <tr>
-                      <td valign="top"><strong>Kinetics:</strong></td>
-                      <td>Mass Action<sup>3</sup></td>
-                    </tr>
-                    <tr>
-                      <td valign="top"><strong>Parameters:</strong></td>
-                      <td><p><em>k</em><sub>3on</sub> = 10 <sup>-2</sup> molecules<sup>-1</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/2008/3/3d/Eq4a.PNG" alt="Equation 3.1" width="278" height="22"></td>
-                    </tr>
-                </table></td>
-              </tr>
-            </table>
-            <p align="justify"><br>
-.2. <span class="style4">Constitutive CI synthesis</span></p>
-            <table width="577" border="0">
-              <tr>
-                <td width="61">&nbsp;</td>
-                <td width="506"><table width="457" border="0">
-                    <tr>
-                      <td colspan="2"><div align="left" class="style5">ρcI → ρcI + 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>3off</sub> = 4 x 10 <sup>-2</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/2008/4/49/Eq5a.PNG" alt="Equation 3.2" width="108" height="24"></td>
-                    </tr>
-                    <tr>
-                      <td valign="top"><strong>Notes:</strong></td>
-                      <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  lower than the constitutive rate constant, regardless the implication  of a greater threshold to achieve the <em>on </em>state<sup>3</sup>.</div></td>
-                    </tr>
-                </table></td>
-              </tr>
-            </table>
-            <p align="justify"><br>
-. <span class="style4">Natural degradation of  CI</span></p>
-            <table width="577" border="0">
-              <tr>
-                <td width="61">&nbsp;</td>
-                <td width="506"><table width="457" border="0">
-                    <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, the rate constant was calculated..</div></td>
-                    </tr>
-                </table></td>
-              </tr>
-            </table>
-            <p align="justify"><br>
-.1. <span class="style4">Dimer formation and dissociation between   CI molecules </span></p>
-            <table width="577" border="0">
-              <tr>
-                <td width="61">&nbsp;</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>
-. <span class="style4">RcnA production </span></p>
-            <table width="577" border="0">
-              <tr>
-                <td width="61">&nbsp;</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>
-. <span class="style4">Nickel efflux by RcnA </span></p>
-            <table width="577" border="0">
-              <tr>
-                <td width="61">&nbsp;</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>
-.<span class="style4"> Natural degradation of RcnA </span></p>
-            <table width="577" border="0">
-              <tr>
-                <td width="61">&nbsp;</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 personal communication with Peter T. Chivers  (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>
-.<span class="style4"> Nickel import by unknown channel </span></p>
-            <table width="577" border="0">
-              <tr>
-                <td width="61">&nbsp;</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></p>
-            <p align="justify"><br>
              </p></td>
 		</tr>
-         <td class="pageName">Modeling details </td>
+      </table>
-    </table>
+         <div align="justify">&nbsp;<br>
-        <br />
+          <br />
-	&nbsp;<br />
+      </div>
      <td width="132">&nbsp;</td>
    </tr>