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	<h3>Equations</h3>		<h3>Equations</h3>
	<center>		<center>
-	<img src="" style="width:800px"/>	+	<img src="https://static.igem.org/mediawiki/2012/2/2b/EquationsDegCorrected.png" width=800px/>
	</center>		</center>
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	<td>&micro;M.min<sup>-1</sup></td>		<td>&micro;M.min<sup>-1</sup></td>
	<td>Transcription rate for <i>tir1</i> and <i>gfp-aid-nls</i></td>		<td>Transcription rate for <i>tir1</i> and <i>gfp-aid-nls</i></td>
-	<td>[3]</td>	+	<td>[1]</td>
	</tr>		</tr>
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	<td>min<sup>-1</sup></td>		<td>min<sup>-1</sup></td>
	<td>Degradation rate of mRNA for TIR1 and GFP-AID</td>		<td>Degradation rate of mRNA for TIR1 and GFP-AID</td>
-	<td>[3]</td>	+	<td>[1]</td>
	</tr>		</tr>
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	<td>min<sup>-1</sup></td>		<td>min<sup>-1</sup></td>
	<td>Translation rate constant for mRNA-TIR1 and mRNA-GFP-AID</td>		<td>Translation rate constant for mRNA-TIR1 and mRNA-GFP-AID</td>
-	<td>[3]</td>	+	<td>[1]</td>
	</tr>		</tr>
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	<td>min<sup>-1</sup></td>		<td>min<sup>-1</sup></td>
	<td>Degradation rate for TIR1 </td>		<td>Degradation rate for TIR1 </td>
-	<td>[3]</td>	+	<td>[1]</td>
	</tr>		</tr>
Line 108:		Line 108:
	<td>min<sup>-1</sup></td>		<td>min<sup>-1</sup></td>
	<td>Degradation rate for GFP-AID</td>		<td>Degradation rate for GFP-AID</td>
-	<td>[3]</td>	+	<td>[2]</td>
	</tr>		</tr>
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	<td>min<sup>-1</sup></td>		<td>min<sup>-1</sup></td>
	<td>Degradation rate constant of compound IAA</td>		<td>Degradation rate constant of compound IAA</td>
-	<td>[4]</td>	+	<td>[3]</td>
	</tr>		</tr>
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	<td>k<sub>A</sub></td>		<td>k<sub>A</sub></td>
	<td>100</td>		<td>100</td>
-	<td>min<sup>-1</sup></td>	+	<td>&micro;M.min<sup>-1</sup></td>
	<td>Association rate for auxin (IAA) and TIR1 </td>		<td>Association rate for auxin (IAA) and TIR1 </td>
-	<td>[5]</td>	+	<td>[4]</td>
	</tr>		</tr>
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	<td>k<sub>-A</sub></td>		<td>k<sub>-A</sub></td>
	<td>1</td>		<td>1</td>
-	<td>&micro;M</td>	+	<td>min<sup>-1</sup></td>
	<td>Dissociation rate for auxin (IAA) and TIR1</td>		<td>Dissociation rate for auxin (IAA) and TIR1</td>
-	<td>[6]</td>	+	<td>[4]</td>
	</tr>		</tr>
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	<td>k<sub>G</sub></td>		<td>k<sub>G</sub></td>
	<td>0.5</td>		<td>0.5</td>
-	<td>&micro;M</td>	+	<td>&micro;M.min<sup>-1</sup></td>
	<td>Association rate for IAA:TIR1 complex and GFP-AID</td>		<td>Association rate for IAA:TIR1 complex and GFP-AID</td>
-	<td>[6]</td>	+	<td>[4]</td>
	</tr>		</tr>
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	<td>k<sub>-G</sub></td>		<td>k<sub>-G</sub></td>
	<td>0.1</td>		<td>0.1</td>
-	<td>&micro;M</td>	+	<td>min<sup>-1</sup></td>
	<td>Dissociation rate for IAA:TIR1 complex and GFP-AID</td>		<td>Dissociation rate for IAA:TIR1 complex and GFP-AID</td>
-	<td>[6]</td>	+	<td>[4]</td>
	</tr>		</tr>
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	<td>min<sup>-1</sup></td>		<td>min<sup>-1</sup></td>
	<td>Ubiquitination rate of IAA:TIR1 complex to GFP-AID</td>		<td>Ubiquitination rate of IAA:TIR1 complex to GFP-AID</td>
-	<td>[7]</td>	+	<td>[4]</td>
	</tr>		</tr>
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	<td>cm.min<sup>-1</sup></td>		<td>cm.min<sup>-1</sup></td>
	<td>Permeability of plasma membrane for IAA </td>		<td>Permeability of plasma membrane for IAA </td>
-	<td>[4]</td>	+	<td>[3]</td>
	</tr>		</tr>
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	<td>cm</td>		<td>cm</td>
	<td>Thickness of plasma membrane in <i>Xenopus</i> cells </td>		<td>Thickness of plasma membrane in <i>Xenopus</i> cells </td>
-	<td>[11]</td>	+	<td>[5]</td>
	</tr>		</tr>
	</table>		</table>
	</center>		</center>
		+	</ul>
		+	</br>
		+	<h2>Download code for auxin detection model</h2><a href="https://static.igem.org/mediawiki/2012/0/07/Detection_model.zip">here</a>
-	Chemical equations:	+	<div id="citation_box">
-	<center><img src="https://static.igem.org/mediawiki/2012/a/a8/Eqschim.png" width="400px"></center>	+	<p id="references">References:</p>
		+	<ol>
		+	<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>
-	<br>
-	After adding to these equations the creation rate of GFP and desintegration rate of auxin whe obtain the system of equations:<center><img src="https://static.igem.org/mediawiki/2012/2/25/Eqs.png" width="600px"></center>
-	Where:
-	<ul>
-	<li> [A] stands for auxin concentration</li>
-
-	<li> [AT] stands for the complex auxin-TIR concentration</li>
-	<li> [ATG] stands for the complex auxin-TIR-GFP concentration</li>
-	<li> [G] stands for GFP concentration</li>
-	<li> [T<sub>0</sub>] stands for TIR concentration, that we assume to be constant</li>
-	<li>k<sub>cat</sub> is the turnover number. Thus k<sub>cat</sub>[T<sub>0</sub>] corresponds to V<sub>max</sub> of the Michaelis-Menten equation.
-	<li>&#404; is the strength of the promoter used to create GFP</li>
-	<li>f<sub>e<sub>aux</sub></sub>(t) is the quantity of auxin that enters in the cell at time t</li>
-	<li> V is the volume of the cell.</li>
-	<li>K<sub>A</sub> is the reaction constant of the creation of the auxin-TIR1 complex</li>
-	<li>K<sub>G</sub> is the reaction constant of the degradation of GFP</li>
-	<li>&delta; is the degradation rate of auxin</li>
-	<li>P<sub>G</sub> are the proteins left after degradation of GFP.</li>
-
-	</ul>
		+	</ol>
		+	</div>
	<script type="text/javascript">writeFooter()</script>		<script type="text/javascript">writeFooter()</script>
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	</html>		</html>

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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