Team:Evry/auxin detection

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As for us, this model will also help our biologists to find the conditions upon which the reception can work and the help them guess the reasons of possible dysfunction in the auxin reception.
As for us, this model will also help our biologists to find the conditions upon which the reception can work and the help them guess the reasons of possible dysfunction in the auxin reception.
-
This is what's happening during auxin detection:
+
Very schematically, this is what's happening during auxin detection:
</p>
</p>
 +
</br></br>
 +
<center>
 +
<img src="https://static.igem.org/mediawiki/2012/0/04/Auxin_detection.png" style="width:800px"/>
 +
</br></br>
 +
Figure 1. Kinetic squeme depicting the auxin detection model in the cell.
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</center>
 +
</br></br>
<br>
<br>
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<center><img src="https://static.igem.org/mediawiki/2012/3/36/Scheme_degrad.png" width="800px"></center>
 
<br>
<br>
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<br>
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<p>Once TIR and GFP are produced and auxin has entered the cell, it binds with TIR and then this complex degrades GFP.
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<p>Thus, once TIR 1 ang GFP are produced and auxin has entered the cell, it binds with TIR1 and then this complex degrades GFP.
+
This is what we're going to model.
This is what we're going to model.
</p>
</p>
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<h2> Hypotheses </h2>
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<h2> Assumptions </h2>
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<p>The same promoter is used for the creation of GFP and TIR, so the efficiency  Gamma for the creation of GFP and TIR1 will be identical.
+
<p>
 +
In these reactions, we assimilate the complex Auxin-TIR to an enzyme that is able to degrade the GFP. Auxin would then be its activator.
 +
<br>
 +
The degradation rate of GFP is negligible; indeed a molecule of GFP takes 72 hours to degrade normally, whereas during auxin detection the complex auxin-TIR degrades it in less than an hour.
 +
<br>
 +
The Tir protein is continuously produced and degraded in the cell, 
 +
</p>
</p>
-
<h2> Descritpion of the model </h2>
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<h2> Model Description </h2>
-
Chemical equations corresponding to:
+
</br>
 +
<h3>Equations</h3>
 +
<center>
 +
<img src="https://static.igem.org/mediawiki/2012/2/2b/EquationsDegCorrected.png" width=800px/>
 +
</center>
 +
 
 +
 
 +
where:
 +
 
<ul>
<ul>
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<li> Creation of auxin-TIR1 complex : <center><img src="https://static.igem.org/mediawiki/2012/8/81/Reaction1_degradation.png" width="200px"></center>
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<li> <i>tir1</i>: open reading frame encoding the protein TIR1 coming from the plant<i>Oryza sativa </i> </li>
-
</li>
+
<li> <i>gfp-aid-nls</i>: open reading frame encoding the protein GFP fused to auxin-inducible degron (AID) system followed by an SV40 nuclear localization signal </li>
-
<li> Degradation of GFP by this complex: <center><img src="https://static.igem.org/mediawiki/2012/c/c1/Reaction2_degradation.png" width="250px"></center>
+
<li> mRNA-TIR1: mRNA coding the protein TIR1</li>
 +
<li> mRNA-GFP-AID-NLS: mRNA coding the fused protein GFP-AID-NLS </li>
 +
<li> TIR1: F-box transport inhibitor response 1 protein  </li>
 +
<li> GFP-AID: Green fluorescence protein fused to auxin-inducible degron system  </li>
 +
<li> degGFP-AID: degraded green fluorescence protein fused to auxin-inducible degron system </li>
 +
<li> dIAA: diffused indole-3-acetic acid (auxin)  </li>
 +
<li> IAA: Indole-3-acetic acid or auxin  </li>
</ul>
</ul>
-
<br>
+
 
-
After adding to these equations creation rates of TIR1 and GFP and desintegration rates of each actor whe obtain the system of equations:<center><img src="https://static.igem.org/mediawiki/2012/8/83/System_equations_degrad.png" width="500px" ></center>
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</br></br>
-
Where:
+
 
-
<ul>
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<h3>Parameters</h3>
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   <li> A stands for auxin</li>
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<center>
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  <li> T stands for TIR1</li>  
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<table id="param">
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   <li> AT stands for the complex auxin-TIR1</li>
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  <tr>
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   <li> G stands for GFP</li>
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    <th>Name</th>
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   <li>P<sub>X</sub> is the quantity of X in the cell</li>
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    <th>Value</th>
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   <li>&#404;<sub>X</sub> is the "efficiency" of the promoter used to create X</li>
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    <th>Unit</th>
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   <li>f<sub>e<sub>aux</sub></sub>(t) is the quantity of auxin that enters in the cell at time t</li>
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    <th>Descrition</th>
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   <li>K<sub>1</sub> is the reaction constant of the creation of the auxin-TIR1 complex</li>
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    <th>Reference</th>
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   <li>K<sub>2</sub> is the reaction constant of the degradation o f GFP</li>
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  </tr>
-
   <li>d<sub>X</sub> is the degradation rate of X</li>
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 +
  <tr>
 +
    <td>Pr</td>
 +
    <td>1</td>
 +
    <td>&micro;M.min<sup>-1</sup></td>
 +
    <td>Transcription rate for <i>tir1</i> and <i>gfp-aid-nls</i></td>
 +
    <td>[1]</td>
 +
   </tr>
 +
 
 +
 
 +
  <tr>
 +
    <td>d<sub>mRNA</sub></td>
 +
    <td>0.017</td>
 +
    <td>min<sup>-1</sup></td>
 +
    <td>Degradation rate of mRNA for TIR1 and GFP-AID</td>
 +
    <td>[1]</td>
 +
   </tr>
 +
 
 +
 
 +
  <tr>
 +
    <td>Kz</td>
 +
    <td>1</td>
 +
    <td>min<sup>-1</sup></td>
 +
    <td>Translation rate constant for mRNA-TIR1 and mRNA-GFP-AID</td>
 +
    <td>[1]</td>
 +
   </tr>
 +
 
 +
  <tr>
 +
    <td>d<sub>protein</sub></td>
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    <td>0.0017</td>
 +
    <td>min<sup>-1</sup></td>
 +
    <td>Degradation rate for TIR1 </td>
 +
    <td>[1]</td>
 +
   </tr>
 +
 
 +
 
 +
  <tr>
 +
    <td>d<sub>GFP</sub></td>
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    <td>0.001</td>
 +
    <td>min<sup>-1</sup></td>
 +
    <td>Degradation rate for GFP-AID</td>
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    <td>[2]</td>
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   </tr>
 +
 
 +
 
 +
  <tr>
 +
    <td>d<sub>compound</sub></td>
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    <td>0.0013</td>
 +
    <td>min<sup>-1</sup></td>
 +
    <td>Degradation rate constant of compound IAA</td>
 +
    <td>[3]</td>
 +
   </tr>
 +
 
 +
 
 +
  <tr>
 +
    <td>k<sub>A</sub></td>
 +
    <td>100</td>
 +
    <td>&micro;M.min<sup>-1</sup></td>
 +
    <td>Association rate for auxin (IAA) and TIR1 </td>
 +
    <td>[4]</td>
 +
  </tr>
 +
 
 +
  <tr>
 +
    <td>k<sub>-A</sub></td>
 +
    <td>1</td>
 +
    <td>min<sup>-1</sup></td>
 +
    <td>Dissociation rate for auxin (IAA) and TIR1</td>
 +
    <td>[4]</td>
 +
   </tr>
 +
 
 +
 
 +
  <tr>
 +
    <td>k<sub>G</sub></td>
 +
    <td>0.5</td>
 +
    <td>&micro;M.min<sup>-1</sup></td>
 +
    <td>Association rate for IAA:TIR1 complex and GFP-AID</td>
 +
    <td>[4]</td>
 +
   </tr>
 +
 
 +
 
 +
  <tr>
 +
    <td>k<sub>-G</sub></td>
 +
    <td>0.1</td>
 +
    <td>min<sup>-1</sup></td>
 +
    <td>Dissociation rate for IAA:TIR1 complex and GFP-AID</td>
 +
    <td>[4]</td>
 +
   </tr>
 +
 
 +
  <tr>
 +
    <td>k<sub>cat</sub></td>
 +
    <td>5.10<sup>-4</sup></td>
 +
    <td>min<sup>-1</sup></td>
 +
    <td>Ubiquitination rate of IAA:TIR1 complex to GFP-AID</td>
 +
    <td>[4]</td>
 +
  </tr>
 +
 
 +
 
 +
  <tr>
 +
    <td>p</td>
 +
    <td>6.10<sup>-5</sup></td>
 +
    <td>cm.min<sup>-1</sup></td>
 +
    <td>Permeability of plasma membrane for IAA </td>
 +
    <td>[3]</td>
 +
  </tr>
 +
 
 +
 
 +
  <tr>
 +
    <td>th</td>
 +
    <td>5.10<sup>-7</sup></td>
 +
    <td>cm</td>
 +
    <td>Thickness of plasma membrane in <i>Xenopus</i> cells </td>
 +
    <td>[5]</td>
 +
  </tr>
 +
</table>
 +
</center>
 +
 
</ul>
</ul>
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<h2> Model's calibration </h2>
 
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<h2> Results </h2>
 
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<h2>Criticisms <h2>
 
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<h2> Confrontation with experiences</h2>
 
-
<h2>Conclusion </h2>
 
-
<h2> References </h2>
 
 +
</br>
 +
<h2>Download code for auxin detection model</h2><a href="https://static.igem.org/mediawiki/2012/0/07/Detection_model.zip">here</a>
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<script type="text/javascript">writeFooter()</script>
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<div id="citation_box">
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<p id="references">References:</p>
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<ol>
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<li>Paulsen, M., Legewie, S., Eils, R., Karaulanov, E. & Niehrs, C. 2011. Negative feedback in the bone morphogenetic protein 4 (BMP4) synexpression group governs its dynamic signaling range and canalizes development. PNAS 108, 10202-10207 (Supporting Information Appendixm ,SI Table 1. Kinetic parameters of the model).</li>
 +
<li>Nicolas Pollet's data </li>
 +
<li>Urakami, M., Ano, R., Kimura, Y., Shima, M., Matsuno, R., Ueno, T. & Akamatsu, M. (2003). Relationship between structure and permeability of tryptophan derivatives across human intestinal epithelial (Caco-2) cells. Zeitschrift für Naturforschung C, Journal of biosciences 58c, 135-42.</li>
 +
<li>Muraro, D., Byrne, H., King, J., Voss, U., Kieber, J. & Bennett, M. (2011). The influence of cytokinin-auxin cross-regulation on cell-fate determination in <i>Arabidopsis thaliana</i> root development. Journal of Theoretical Biology 283, 152-167 </li>
 +
<li>Schillers, H., Danker, T., Schnittler, H.-J., Lang, F. & Oberleithner, H. (2000). Plasma Membrane Plasticity of Xenopus laevis Oocyte Imaged with Atomic Force Microscopy. Cellular Physiol Biochem 10, 1-9.</li>
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 +
</ol>
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</div>
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<script type="text/javascript">writeFooter()</script>
</html>
</html>

Latest revision as of 17:15, 2 January 2013

Auxin detection

Overview

Now that we’ve managed to model auxin creation and transport, you may be asking yourself ; great, those guys have done all those models, but how can we link it to what we see ? That’s the aim of this model that will link the quantity of auxin transported into the cell to GFP degradation that we can observe in our tadpole’s cells. As for us, this model will also help our biologists to find the conditions upon which the reception can work and the help them guess the reasons of possible dysfunction in the auxin reception. Very schematically, this is what's happening during auxin detection:





Figure 1. Kinetic squeme depicting the auxin detection model in the cell.




Once TIR and GFP are produced and auxin has entered the cell, it binds with TIR and then this complex degrades GFP. This is what we're going to model.

Assumptions

In these reactions, we assimilate the complex Auxin-TIR to an enzyme that is able to degrade the GFP. Auxin would then be its activator.
The degradation rate of GFP is negligible; indeed a molecule of GFP takes 72 hours to degrade normally, whereas during auxin detection the complex auxin-TIR degrades it in less than an hour.
The Tir protein is continuously produced and degraded in the cell,

Model Description


Equations

where:
  • tir1: open reading frame encoding the protein TIR1 coming from the plantOryza sativa
  • gfp-aid-nls: open reading frame encoding the protein GFP fused to auxin-inducible degron (AID) system followed by an SV40 nuclear localization signal
  • mRNA-TIR1: mRNA coding the protein TIR1
  • mRNA-GFP-AID-NLS: mRNA coding the fused protein GFP-AID-NLS
  • TIR1: F-box transport inhibitor response 1 protein
  • GFP-AID: Green fluorescence protein fused to auxin-inducible degron system
  • degGFP-AID: degraded green fluorescence protein fused to auxin-inducible degron system
  • dIAA: diffused indole-3-acetic acid (auxin)
  • IAA: Indole-3-acetic acid or auxin


Parameters

Name Value Unit Descrition Reference
Pr 1 µM.min-1 Transcription rate for tir1 and gfp-aid-nls [1]
dmRNA 0.017 min-1 Degradation rate of mRNA for TIR1 and GFP-AID [1]
Kz 1 min-1 Translation rate constant for mRNA-TIR1 and mRNA-GFP-AID [1]
dprotein 0.0017 min-1 Degradation rate for TIR1 [1]
dGFP 0.001 min-1 Degradation rate for GFP-AID [2]
dcompound 0.0013 min-1 Degradation rate constant of compound IAA [3]
kA 100 µM.min-1 Association rate for auxin (IAA) and TIR1 [4]
k-A 1 min-1 Dissociation rate for auxin (IAA) and TIR1 [4]
kG 0.5 µM.min-1 Association rate for IAA:TIR1 complex and GFP-AID [4]
k-G 0.1 min-1 Dissociation rate for IAA:TIR1 complex and GFP-AID [4]
kcat 5.10-4 min-1 Ubiquitination rate of IAA:TIR1 complex to GFP-AID [4]
p 6.10-5 cm.min-1 Permeability of plasma membrane for IAA [3]
th 5.10-7 cm Thickness of plasma membrane in Xenopus cells [5]

Download code for auxin detection model

here

References:

  1. Paulsen, M., Legewie, S., Eils, R., Karaulanov, E. & Niehrs, C. 2011. Negative feedback in the bone morphogenetic protein 4 (BMP4) synexpression group governs its dynamic signaling range and canalizes development. PNAS 108, 10202-10207 (Supporting Information Appendixm ,SI Table 1. Kinetic parameters of the model).
  2. Nicolas Pollet's data
  3. Urakami, M., Ano, R., Kimura, Y., Shima, M., Matsuno, R., Ueno, T. & Akamatsu, M. (2003). Relationship between structure and permeability of tryptophan derivatives across human intestinal epithelial (Caco-2) cells. Zeitschrift für Naturforschung C, Journal of biosciences 58c, 135-42.
  4. Muraro, D., Byrne, H., King, J., Voss, U., Kieber, J. & Bennett, M. (2011). The influence of cytokinin-auxin cross-regulation on cell-fate determination in Arabidopsis thaliana root development. Journal of Theoretical Biology 283, 152-167
  5. Schillers, H., Danker, T., Schnittler, H.-J., Lang, F. & Oberleithner, H. (2000). Plasma Membrane Plasticity of Xenopus laevis Oocyte Imaged with Atomic Force Microscopy. Cellular Physiol Biochem 10, 1-9.

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