Team:LCG-UNAM-Mexico/Modeling

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          <td class="pageName"><div align="center">
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            <p><br>
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              Modeling the system </p>
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          </div></td>
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        </tr>
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        <tr>
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          <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>
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            <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>
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            <p align="center"> <img alt="Iwig 2006" src="https://static.igem.org/mediawiki/2008/4/47/Diagrama3.jpg"> </p>
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            <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>
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            <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>
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              <br>
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              <img src="https://static.igem.org/mediawiki/2008/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /></p>
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            <p class="style3"><strong><a name="metabolites"></a>Metabolites and enzymes relevant to the model </strong></p>
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            <table width="585" border="0" bordercolor="#75923C">
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              <tr>
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                <td width="170"><ol>
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                    <li> AiiA </li>
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                              <li> AHL </li>
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                              <li> LuxR </li>
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                              <li> AHL:LuxR </li>
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                              <li> (AHL:LuxR):(AHL:LUXR)<br>
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                              </li>
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                              <li> ρcI </li>
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                              <li> CI </li>
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                              <li> CI:CI </li>
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                              <li> ρ </li>
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                              <li> RcnA </li>
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                              <li> Ni<sub>int</sub></li>
 +
                              <li> Ni<sub>ext</sub> </li>
 +
                              <li> Unk</li>
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                </ol>                </td>
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                <td width="405" valign="top" bordercolor="1"><p>Acyl-Homoserine Lactone Lactonase<br>
 +
Acyl-Homoserine Lactone<br>
 +
Transcriptional Activator<br>
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Complex formed by AHL and LuxR<br>
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Dimer of AHL:LuxR complexes<br>
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cI* promoter, inducible by the dimer of AHL:LuxR complexes<br>
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λ phage repressor (CI) modified with a LVA tail for quick degradation<br>
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Repressor, dimer of CI molecules<br>
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<em>rcnA</em> promoter, modified to be repressible by CI:CI<br>
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<em>Escherichia coli</em> nickel efflux pump<br>
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Intracellular nickel<br>
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Extracellular nickel<br>
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Unknown nickel import channel<br>
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                </p>                </td>
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              </tr>
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            </table>
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            <p align="center">&nbsp;</p>
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            <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><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>
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            <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> 
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            <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>
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            <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>
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              </span><br>
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              <img src="https://static.igem.org/mediawiki/2008/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /></p>
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            <p class="style2"><a name="odes"></a>Ordinary Differential Equations</p>
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            <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>
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            <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>
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            <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>
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            <p><strong><span class="style3"><img src="https://static.igem.org/mediawiki/2008/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /><br>
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                  <br>
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              <a name="assumptions"></a>Assumptions of the model </span><br>
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              <br>
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            </strong></p>
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            <div id="lev4">
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              <ol>
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                <li>
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                  <div align="justify"> <strong>Once there is nickel in the medium, RcnR no longer participates in the pump’s regulation.</strong> 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).<sup>1</sup><strong></strong> </div>
 +
                </li>
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                <li> <strong>Cell membrane permeability to AHL is not considered inside the model.</strong> 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. <sup>2</sup><br>
 +
                </li>
 +
                <li>
 +
                  <div align="justify"> <strong>All decrease in AHL concentration is due to AiiA.</strong> 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). <sup>3</sup> </div>
 +
                </li>
 +
                <li>
 +
                  <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>
 +
                  <div align="justify"> <strong>It is a homogeneous system.</strong> This means that the coefficients of the equations are constant (so we don’t have compartmentalization). </div>
 +
                </li>
 +
                <li>
 +
                  <div align="justify"> <strong>The quantity of nickel used by the cell is negligible compared to the concentrations in and out of the cell.</strong> 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.<sup>1</sup> </div>
 +
                </li>
 +
                <li>
 +
                  <div align="justify"> <strong>The  production of RcnR, LuxR and AiiA is constitutive and their  concentrations have reached the steady state at the beginning of the  experiment.</strong> </div>
 +
                </li>
 +
                <li>
 +
                  <div align="justify"> <strong>NikABCDE will not play a role in our model.</strong> 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.<sup>1</sup> </div>
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                </li>
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              </ol>
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              <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>
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              <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><strong class="style2">References</strong><br>
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              </p>
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            </div>
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            <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>
 +
              <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>
 +
              <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>
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                <br>
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              <p><br>
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              </p>
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              <p> </p>
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          <td valign="top" class="bodyText"><p align="justify"><br>
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        <div align="justify">&nbsp;<br>
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Latest revision as of 06:33, 30 October 2008

LCG-UNAM-Mexico:Modeling

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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.

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Metabolites and enzymes relevant to the model

  1. AiiA
  2. AHL
  3. LuxR
  4. AHL:LuxR
  5. (AHL:LuxR):(AHL:LUXR)
  6. ρcI
  7. CI
  8. CI:CI
  9. ρ
  10. RcnA
  11. Niint
  12. Niext
  13. 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

 

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Reactions

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

Table of biochemical reactions
* 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.

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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.


Set of ODEs

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Assumptions of the model

  1. 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
  2. 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
  3. 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
  4. 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.
  5. It is a homogeneous system. This means that the coefficients of the equations are constant (so we don’t have compartmentalization).
  6. 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
  7. The production of RcnR, LuxR and AiiA is constitutive and their concentrations have reached the steady state at the beginning of the experiment.
  8. 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

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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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