Team:Evry/auxin production

From 2012.igem.org

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<h2>Model description</h2>
<h2>Model description</h2>
<p>
<p>
-
The plasmids containing the two genes involved in the auxin biosynthesis pathway, namely <i>iaaM</i> and <i>iaaH</i>, will be expressed in a constitutive and ubiquitous manner in a first step and in a second step in an inducible and tissue-specific manner. The <i>iaaM</i> gene encodes tryptophan-2-monooxygenase (IAAM) that catalyses the conversion of tryptophan (Trp) into indole-3-acetamide (IAM). The <i>iaaH</i> gene encodes indoleacetamide hydrolase (IAAH) that hydrolyse IAM to realease indole-3-acetic acid (IAA) <b>[2]</b>. At the same time, the synthesized IAM and IAA will competitively inhibit the enzyme activity of IAAM. Produced auxin will then diffuse through the plasma menbrane into the extracellular medium and finally into the blood. All the reactions involved in the auxin biosynthesis pathway are illustrated in Figure 1. </p>
+
The plasmids containing the two genes involved in the auxin biosynthesis pathway, namely <i>iaaM</i> and <i>iaaH</i>, will be expressed in a constitutive and ubiquitous manner in a first step and in a second step in an inducible and tissue-specific manner. The <i>iaaM</i> gene encodes tryptophan-2-monooxygenase (IAAM) that catalyses the conversion of tryptophan (Trp) into indole-3-acetamide (IAM). The <i>iaaH</i> gene encodes indoleacetamide hydrolase (IAAH) that hydrolyse IAM to release indole-3-acetic acid (IAA) <b>[2]</b>. At the same time, the synthesized IAM and IAA will competitively inhibit the enzyme activity of IAAM. Produced auxin will then diffuse through the plasma membrane into the extracellular medium and finally into the blood. All the reactions involved in the auxin biosynthesis pathway are illustrated in Figure 1. </p>
</br></br>
</br></br>
<center>
<center>
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     <li>Degradation rate constants are assumed to be the same for mRNA-IAAM and mRNA-IAAH; for the proteins IAAM and IAAH; and for the compounds Trp, IAM and IAA.</li>
     <li>Degradation rate constants are assumed to be the same for mRNA-IAAM and mRNA-IAAH; for the proteins IAAM and IAAH; and for the compounds Trp, IAM and IAA.</li>
     <li>We neglect the short time delay due to synthesis of IAAM-Trp (enzyme-substrate (ES) complex), IAAH-IAM (ES complex), IAAM-IAM (enzyme- inhibitor (EI) complex) and IAAM-IAA (enzyme- inhibitor (EI) complex) and assume that these species reach their equilibrium almost instantaneously.</li>
     <li>We neglect the short time delay due to synthesis of IAAM-Trp (enzyme-substrate (ES) complex), IAAH-IAM (ES complex), IAAM-IAM (enzyme- inhibitor (EI) complex) and IAAM-IAA (enzyme- inhibitor (EI) complex) and assume that these species reach their equilibrium almost instantaneously.</li>
-
     <li>The initial concentration of the number of plasmids, which determines the number of auxin-biosynthesis pathway genes, depends on the outcome of the <a href="https://2012.igem.org/Team:Evry/plasmid_splitting">plasmid repartition model</a> in the embryo cells. The average plasmid concentration per cell was set to 0.011 μM and assumed to be constant over time for constitutive promoter and variable for inducible promoter. </li>
+
     <li>The number of plasmids present in the cell, which determines the number of auxin-biosynthesis pathway. This value depends on the outcome of the <a href="https://2012.igem.org/Team:Evry/plasmid_splitting">plasmid repartition model</a>. The average number of plasmid per cell was set to 110 plasmids although plasmid distribution shows very high dispersion and some cells can contain much more plasmids. It is assumed to be constant over time. </li>
-
     <li>L-Tryptophan is an essential amino acid, which means that its concentration will depend on the uptake from the medium. The Tryptophan inicial concentration was set to 500 μM <b>[8][9][4]</b> and assumed to be constant over the time course. </li>
+
     <li>L-Tryptophan is an essential amino acid, which means that its concentration will depend on the uptake from the medium. The Tryptophan initial concentration was set to 500 μM <b>[8][9][4]</b> and assumed to be constant over the time course. </li>
     <li>All other initial concentrations were set to zero.</li>
     <li>All other initial concentrations were set to zero.</li>
</ol>
</ol>
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<h3>Equations</h3>
<h3>Equations</h3>
<center>
<center>
-
<img src="https://static.igem.org/mediawiki/2012/3/38/ODEs.png" style="width:800px"/>
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<img src="https://static.igem.org/mediawiki/2012/9/91/EquationsSynthesisCorrected.png" width=800px/>
</center>
</center>
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  <li> IAM: Indole-3-acetamide  </li>
  <li> IAM: Indole-3-acetamide  </li>
  <li> IAA: Indole-3-acetic acid or auxin  </li>
  <li> IAA: Indole-3-acetic acid or auxin  </li>
-
  <li> dIAA: diffused indole-3-acetic acid or diffused auxin  </li>
+
  <li> dIAA: diffused indole-3-acetic acid (auxin) </li>
</ul>
</ul>
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<h3>Parameters</h3>
<h3>Parameters</h3>
<center>
<center>
-
<img src="https://static.igem.org/mediawiki/2012/6/62/Parameters.png" style="width:700px"/>
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<table id="param">
 +
  <tr>
 +
    <th>Name</th>
 +
    <th>Value</th>
 +
    <th>Unit</th>
 +
    <th>Descrition</th>
 +
    <th>Reference</th>
 +
  </tr>
 +
 
 +
  <tr>
 +
    <td>Pr</td>
 +
    <td>1</td>
 +
    <td>&micro;M.min<sup>-1</sup></td>
 +
    <td>Transcription rate for <i>iaaM</i> and <i>iaaH</i></td>
 +
    <td>[3]</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 IAAM and IAAH</td>
 +
    <td>[3]</td>
 +
  </tr>
 +
 
 +
 
 +
  <tr>
 +
    <td>Kz</td>
 +
    <td>1</td>
 +
    <td>min<sup>-1</sup></td>
 +
    <td>Translation rate constant for mRNA-IAAM and mRNA-IAAH</td>
 +
    <td>[3]</td>
 +
  </tr>
 +
 
 +
  <tr>
 +
    <td>d<sub>protein</sub></td>
 +
    <td>0.0017</td>
 +
    <td>min<sup>-1</sup></td>
 +
    <td>Degradation rate of IAAM and IAAH</td>
 +
    <td>[3]</td>
 +
  </tr>
 +
 
 +
 
 +
  <tr>
 +
    <td>d<sub>compound</sub></td>
 +
    <td>0.0013</td>
 +
    <td>min<sup>-1</sup></td>
 +
    <td>Degradation rate constant of compounds Trp, IAM and IAA</td>
 +
    <td>[4]</td>
 +
  </tr>
 +
 
 +
 
 +
  <tr>
 +
    <td>k<sub>IAAM</sub></td>
 +
    <td>0.2202</td>
 +
    <td>min<sup>-1</sup></td>
 +
    <td>Turnover number: the maximum number of Trp conveted to IAM</td>
 +
    <td>[5]</td>
 +
  </tr>
 +
 
 +
  <tr>
 +
    <td>Km<sub>IAAM</sub></td>
 +
    <td>50</td>
 +
    <td>&micro;M</td>
 +
    <td>Michaelis constant from Trp consumption to form IAM</td>
 +
    <td>[6]</td>
 +
  </tr>
 +
 
 +
 
 +
  <tr>
 +
    <td>Ki<sub>IAM</sub></td>
 +
    <td>7</td>
 +
    <td>&micro;M</td>
 +
    <td>Enzyme inhibition equilibrium constant for IAM</td>
 +
    <td>[6]</td>
 +
  </tr>
 +
 
 +
 
 +
  <tr>
 +
    <td>Ki<sub>IAA</sub></td>
 +
    <td>225</td>
 +
    <td>&micro;M</td>
 +
    <td>Enzyme inhibition equilibrium constant for IAM</td>
 +
    <td>[6]</td>
 +
  </tr>
 +
 
 +
  <tr>
 +
    <td>K<sub>IAAH</sub></td>
 +
    <td>0.2202</td>
 +
    <td>min<sup>-1</sup></td>
 +
    <td>Turnover number, the maximum number of IAM converted to IAA</td>
 +
    <td>[7]</td>
 +
  </tr>
 +
 
 +
 
 +
  <tr>
 +
    <td>Km<sub>IAAH</sub></td>
 +
    <td>80</td>
 +
    <td>&micro;M</td>
 +
    <td>Michaelis constant from IAM consumption to form IAA</td>
 +
    <td>[7]</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>[4]</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>[11]</td>
 +
  </tr>
 +
</table>
</center>
</center>
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<table>
<table>
<tr>
<tr>
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   <td><img src="https://static.igem.org/mediawiki/2012/1/15/Cp-IAM.jpg" style="width:300px"/></td>
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   <td><img src="https://static.igem.org/mediawiki/2012/d/db/Cp-IAM%2CIAA%2CdIAA_final.jpg" style="width:450px"/></td>
-
  <td><img src="https://static.igem.org/mediawiki/2012/5/5b/Cp-IAA%2CdIAA.jpg" style="width:300px"/></td>
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   <td><img src="https://static.igem.org/mediawiki/2012/3/38/Cp-dIAA_final.jpg" style="width:450px"/></td>
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   <td><img src="https://static.igem.org/mediawiki/2012/6/61/Cp-dIAA.jpg" style="width:300px"/></td>
+
</tr>
</tr>
</table>
</table>
-
<center><p>Figure 2. Cellular auxin production under a constitutive promoter. A. Time course for IAM production. B. Time course for IAA and dIAA production. C. Time course for dIAA production.</p></center></tr>
+
<center><p>Figure 2. Cellular auxin production under a constitutive promoter. A. Time course for IAM, IAA and dIAA production. B. Time course for dIAA production.</p></center></tr>
</br></br>
</br></br>
<table align="right">
<table align="right">
-
<tr><td><img src="https://static.igem.org/mediawiki/2012/c/cc/Cp-IAAM-IAAH.jpg" width="350px" ></td></tr>
+
<tr><td><img src="https://static.igem.org/mediawiki/2012/d/dd/Cp-IAAM-IAAH_final.jpg" width="350px" ></td></tr>
<tr><td class="caption"><center>Figure 3. Time course of proteins producing auxin.</center>
<tr><td class="caption"><center>Figure 3. Time course of proteins producing auxin.</center>
</td></tr>
</td></tr>
</table>
</table>
</br></br><p>
</br></br><p>
-
With the auxin-biosynthesis pathway genes, regulated by <b>constitutive promoters</b>, the auxin production reaches steady state around 7.5 hours (450 min) due to the equilibrium reached, around 4 hours (250 min), by the  transcription and translation rates and degradation rates involved in the production and consumption of proteins IAAM and IAAH (Figure 3). </br></br>
+
With the auxin-biosynthesis pathway genes, regulated by <b>constitutive promoters</b>, the auxin production reaches steady state around 4.7 hours (280 min) due to the equilibrium reached, around 4.5 hours (270 min), by the  transcription and translation rates and degradation rates involved in the production and consumption of proteins IAAM and IAAH (Figure 3). </br></br>
-
On the other hand, the concentration of diffused auxin is very low, 3.5 x 10<sup>-6</sup> μM at 16.7 hours (Figure 2.C), however it is increasing over time.</p>
+
On the other hand, the concentration of diffused auxin is very low, 10 μM at 16.7 hours (1000 min) (Figure 2.B), however it is increasing over time.</p>
-
</br></br></br></br></br></br></br>
+
</br></br></br></br></br></br></br></br></br></br></br>
<center><h4>Cellular auxin production under an inducible promoter</h4></center>
<center><h4>Cellular auxin production under an inducible promoter</h4></center>
</br></br>
</br></br>
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<table>
<table>
<tr>
<tr>
-
   <td><img src="https://static.igem.org/mediawiki/2012/c/cb/Ip-IAM.jpg" style="width:300px"/></td>
+
   <td><img src="https://static.igem.org/mediawiki/2012/b/ba/Ip-IAM%2CIAA%2CdIAA_final.jpg" style="width:450px"/></td>
-
  <td><img src="https://static.igem.org/mediawiki/2012/d/df/Ip-IAA%2CdIAA.jpg" style="width:300px"/></td>
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   <td><img src="https://static.igem.org/mediawiki/2012/4/4e/Ip-dIAA_final.jpg" style="width:450px"/></td>
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   <td><img src="https://static.igem.org/mediawiki/2012/7/72/Ip-dIAA.jpg" style="width:300px"/></td>
+
</tr>
</tr>
</table>
</table>
-
<center><p>Figure 4.Cellular auxin production under an inducible promoter. A. Time course for IAM production. B. Time course for IAA and dIAA production. C. Time course for dIAA production.</p></center></tr>
+
<center><p>Figure 4.Cellular auxin production under an inducible promoter. A. Time course for IAM, IAA and dIAA production. B. Time course for dIAA production.</p></center></tr>
</br></br>
</br></br>
<table align="right">
<table align="right">
-
<tr><td><img src="https://static.igem.org/mediawiki/2012/a/a4/Ip-IAAM-IAAH.jpg" width="350px" ></td></tr>
+
<tr><td><img src="https://static.igem.org/mediawiki/2012/e/e5/Ip-IAAM-IAAH_final.jpg" width="350px" ></td></tr>
<tr><td class="caption"><center>Figure 5. Time course of proteins producing auxin.</center>
<tr><td class="caption"><center>Figure 5. Time course of proteins producing auxin.</center>
</td></tr>
</td></tr>
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</br></br>
</br></br>
<p>
<p>
-
With the auxin-biosynthesis pathway genes, regulated by <b>inducible promoters</b>, the auxin production shows a transient response around 1.5 hours (100 min) due to the transient responses reached, around 50 min, by the degradation rates and transcription and translation rates of the involved proteins, i.e. IAAM and IAAH (Figure 5).
+
With the auxin-biosynthesis pathway genes, regulated by <b>inducible promoters</b>, the auxin production shows a transient response around 1.5 hours (90 min) due to the transient responses reached, around 50 min, by the degradation rates and transcription and translation rates of the involved proteins, i.e. IAAM and IAAH (Figure 5).
</br></br>
</br></br>
-
Similarly, the concentration of diffused auxin is much lower with inducible promoter, 5.4 x 10<sup>-8</sup> μM from around 7 hours (430 min)  (Figure 4.C). In contrast with the constitutive promoter, the diffused auxin concentration does not increase over time but instead stabilizes after 7 hours.
+
Similarly, the concentration of diffused auxin is much lower with inducible promoter, 0.87 μM from around 7.7 hours (460 min)  (Figure 4.B). In contrast with the constitutive promoter, the diffused auxin concentration does not increase over time but, instead, stabilizes after 7.7 hours.
</p>
</p>
-
</br></br></br>
+
</br></br></br></br></br></br></br>
<h2>Sensitivity analysis </h2>
<h2>Sensitivity analysis </h2>
</br><p>
</br><p>
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<center>
<center>
-
<img src="https://static.igem.org/mediawiki/2012/f/f5/Sens_1000min_Constitutive-p_ultimo.jpg" style="width:800px"/>
+
<img src="https://static.igem.org/mediawiki/2012/9/93/Sens_1000min_Constitutive-p_final.jpg" style="width:800px"/>
<p>Figure 6. Sensitivity analysis of initial concentrations: 1. Trp, 2. <i>iaaH</i>, 3. <i>iaaM</i>; and parameters: 4. Km<sub>IAAH</sub>, 5. d<sub>compound</sub>, 6. d<sub>mRNA</sub>, 7. d<sub>protein</sub>, 8. k<sub>IAAM</sub>, 9. k<sub>IAAH</sub>, 10. Ki<sub>IAA</sub>, 11. Ki<sub>IAM</sub>, 12. Km<sub>IAAM</sub>, 13. Kz, 14. p, 15. Pr.</p></center></tr>
<p>Figure 6. Sensitivity analysis of initial concentrations: 1. Trp, 2. <i>iaaH</i>, 3. <i>iaaM</i>; and parameters: 4. Km<sub>IAAH</sub>, 5. d<sub>compound</sub>, 6. d<sub>mRNA</sub>, 7. d<sub>protein</sub>, 8. k<sub>IAAM</sub>, 9. k<sub>IAAH</sub>, 10. Ki<sub>IAA</sub>, 11. Ki<sub>IAM</sub>, 12. Km<sub>IAAM</sub>, 13. Kz, 14. p, 15. Pr.</p></center></tr>
</br></br>
</br></br>
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<center>
<center>
-
<img src="https://static.igem.org/mediawiki/2012/d/de/Sens_1000min_Inducible-p_ultimo.jpg" style="width:800px"/>
+
<img src="https://static.igem.org/mediawiki/2012/9/99/Sens_1000min_Inducible-p_final.jpg" style="width:800px"/>
-
<p>Figure 7. Sensitivity analysis of initial concentrations: 1. Trp, 2. <i>iaaH</i>, 3. <i>iaaM</i>; and parameters: 4. Km<sub>IAAH</sub>, 5. d<sub>compound</sub>, 6. d<sub>mRNA</sub>, 7. d<sub>protein</sub>, 8. k<sub>IAAM</sub>, 9. k<sub>IAAH</sub>, 10. Ki<sub>IAA</sub>, 11. Ki<sub>IAM</sub>, 12. Km<sub>IAAM</sub>, 13. Kz, 14. p, 15. Pr..</p></center></tr>
+
<p>Figure 7. Sensitivity analysis of initial concentrations: 1. Trp, 2. <i>iaaH</i>, 3. <i>iaaM</i>; and parameters: 4. Km<sub>IAAH</sub>, 5. d<sub>compound</sub>, 6. d<sub>mRNA</sub>, 7. d<sub>protein</sub>, 8. k<sub>IAAM</sub>, 9. k<sub>IAAH</sub>, 10. Ki<sub>IAA</sub>, 11. Ki<sub>IAM</sub>, 12. Km<sub>IAAM</sub>, 13. Kz, 14. p, 15. Pr.</p></center></tr>
</br></br>
</br></br>
-
<p>By doing the sensitivity analysis, we can highlight the parameters that influence the most in the outcome of the auxin production model, for instance, the transcription rate constant of <i>iaaM</i> and <i>iaaH</i> (Pr) and the translation rate constant of mRNA-IAAM and mRNA-IAAH (Kz) are the most sensitive parameters in the production of auxin (IAA) and difussed auxin (dIAA).</p>
+
<p>By doing the sensitivity analysis, we can highlight the parameters that influence the most in the outcome of the auxin production model, for instance, the transcription rate constant of <i>iaaM</i> and <i>iaaH</i> (Pr) and the translation rate constant of mRNA-IAAM and mRNA-IAAH (Kz) (Figure 6 and 7) are the most sensitive parameters in the production of auxin (IAA) and difussed auxin (dIAA).</p>
 +
</br>
<h2>Conclusion</h2>
<h2>Conclusion</h2>
<p></br>
<p></br>
Our auxin production model predicts the formation of auxin over time catalyzed by enzymes whose transcription is regulated by constitutive and inducible promoters. In the first case, the auxin concentration increases over time and in the second case, the auxin concentration stabilizes after 7 hours.
Our auxin production model predicts the formation of auxin over time catalyzed by enzymes whose transcription is regulated by constitutive and inducible promoters. In the first case, the auxin concentration increases over time and in the second case, the auxin concentration stabilizes after 7 hours.
</br></br>
</br></br>
-
Comparing the two sensitivity analyses for auxin-biosynthesis pathway genes under constitutive and inducible promoters, we only detected that the translation rate constant of mRNA-IAAM and mRNA-IAAH (Kz) is more sensitive in the production of IAM in the genes under inducible promoters than in the genes under constitutive promoters.</p>
+
By doing the sensitivity analyses for auxin-biosynthesis pathway genes under constitutive and inducible promoters, we can detect which parameters are more sensitive in the production of IAM, IAA and dIAA in the genes under inducible promoters compared to the genes under constitutive promoters.</p>
 +
</br>
 +
<h2>Download code for auxin production model</h2><a href="https://static.igem.org/mediawiki/2012/7/7a/Production_model.zip">HERE</a>
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  <li>Kim, D. K., Kanai, Y., Chairoungdua, A., Matsuo, H., Cha, S. H. & Endou, H. 2001. Expression Cloning of a Na+ -independent Aromatic Amino Acid Transporter with Structural Similarity to H+/Monocarboxylate Transporters. J Biol Chem 276, 17221-17228.</li>
  <li>Kim, D. K., Kanai, Y., Chairoungdua, A., Matsuo, H., Cha, S. H. & Endou, H. 2001. Expression Cloning of a Na+ -independent Aromatic Amino Acid Transporter with Structural Similarity to H+/Monocarboxylate Transporters. J Biol Chem 276, 17221-17228.</li>
  <li><a href="http://www.mathworks.fr/fr/help/simbio/ug/example--calculating-sensitivities.html">http://www.mathworks.fr/fr/help/simbio/ug/example--calculating-sensitivities.html</a></li>
  <li><a href="http://www.mathworks.fr/fr/help/simbio/ug/example--calculating-sensitivities.html">http://www.mathworks.fr/fr/help/simbio/ug/example--calculating-sensitivities.html</a></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>
</ol>
</ol>
</div>
</div>

Latest revision as of 19:18, 2 January 2013

Auxin production

Overview

The 2011 Imperial College iGEM [1] project showed that the plant hormone auxin or indole-3-acetic acid (IAA) can be synthetized in Escherichia coli through a two-step pathway from tryptophan. In their work, the genes encoding the auxin biosynthesis pathway, originally coming from Pseudomonas savastanoi, were expressed in E. coli. In our project, we aim to express this auxin biosynthesis pathway in Xenopus tropicalis . First, we plan to reengineer the auxin biosynthesis pathway in the tadpole with a constitutive and ubiquitous promoter. Once the system is functional, we intend to put the system under the control of inducible and tissue-specific promoters.

By modelling the auxin biosynthesis pathway, we will be able to determine the number of produced auxin molecules per plasmids injected in the cell, as well as, the number of diffused auxin molecules through the plasma membrane into the extracellular medium.

Model description

The plasmids containing the two genes involved in the auxin biosynthesis pathway, namely iaaM and iaaH, will be expressed in a constitutive and ubiquitous manner in a first step and in a second step in an inducible and tissue-specific manner. The iaaM gene encodes tryptophan-2-monooxygenase (IAAM) that catalyses the conversion of tryptophan (Trp) into indole-3-acetamide (IAM). The iaaH gene encodes indoleacetamide hydrolase (IAAH) that hydrolyse IAM to release indole-3-acetic acid (IAA) [2]. At the same time, the synthesized IAM and IAA will competitively inhibit the enzyme activity of IAAM. Produced auxin will then diffuse through the plasma membrane into the extracellular medium and finally into the blood. All the reactions involved in the auxin biosynthesis pathway are illustrated in Figure 1.





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


Most reactions were modelled using mass-action kinetics. Reactions involving enzymes (i.e. IAAM, IAAH) were modelled using competitive inhibition kinetics and irreversible Michaelis-Menten.

Assumptions

  1. As most of the parameters in the system are unknown because the auxin biosynthesis pathway has never been put into Xenopus, we took the average transcription, translation and degradation rate constants from other genes in Xenopus [3].
  2. Transcription and translation rate constants are assumed to be the same for iaaM and iaaH genes.
  3. Degradation rate constants are assumed to be the same for mRNA-IAAM and mRNA-IAAH; for the proteins IAAM and IAAH; and for the compounds Trp, IAM and IAA.
  4. We neglect the short time delay due to synthesis of IAAM-Trp (enzyme-substrate (ES) complex), IAAH-IAM (ES complex), IAAM-IAM (enzyme- inhibitor (EI) complex) and IAAM-IAA (enzyme- inhibitor (EI) complex) and assume that these species reach their equilibrium almost instantaneously.
  5. The number of plasmids present in the cell, which determines the number of auxin-biosynthesis pathway. This value depends on the outcome of the plasmid repartition model. The average number of plasmid per cell was set to 110 plasmids although plasmid distribution shows very high dispersion and some cells can contain much more plasmids. It is assumed to be constant over time.
  6. L-Tryptophan is an essential amino acid, which means that its concentration will depend on the uptake from the medium. The Tryptophan initial concentration was set to 500 μM [8][9][4] and assumed to be constant over the time course.
  7. All other initial concentrations were set to zero.

Equations

where:
  • iaaM: open reading frame encoding the enzyme IAAM coming from P. savastanoi
  • iaaH: open reading frame encoding the enzyme IAAH coming from P. savastanoi
  • mRNA-IAAM: mRNA coding the enzyme IAAM
  • mRNA-IAAH: mRNA coding the enzyme IAAH
  • IAAM: Tryptophan 2-monooxygenase
  • IAAH: Indoleacetamide hydrolase
  • Trp: L-Tryptophan
  • IAM: Indole-3-acetamide
  • IAA: Indole-3-acetic acid or auxin
  • dIAA: diffused indole-3-acetic acid (auxin)


Parameters

Name Value Unit Descrition Reference
Pr 1 µM.min-1 Transcription rate for iaaM and iaaH [3]
dmRNA 0.017 min-1 Degradation rate of mRNA for IAAM and IAAH [3]
Kz 1 min-1 Translation rate constant for mRNA-IAAM and mRNA-IAAH [3]
dprotein 0.0017 min-1 Degradation rate of IAAM and IAAH [3]
dcompound 0.0013 min-1 Degradation rate constant of compounds Trp, IAM and IAA [4]
kIAAM 0.2202 min-1 Turnover number: the maximum number of Trp conveted to IAM [5]
KmIAAM 50 µM Michaelis constant from Trp consumption to form IAM [6]
KiIAM 7 µM Enzyme inhibition equilibrium constant for IAM [6]
KiIAA 225 µM Enzyme inhibition equilibrium constant for IAM [6]
KIAAH 0.2202 min-1 Turnover number, the maximum number of IAM converted to IAA [7]
KmIAAH 80 µM Michaelis constant from IAM consumption to form IAA [7]
p 6.10-5 cm.min-1 Permeability of plasma membrane for IAA [4]
th 5.10-7 cm Thickness of plasma membrane in Xenopus cells [11]

Results


Cellular auxin production under a constitutive promoter



Figure 2. Cellular auxin production under a constitutive promoter. A. Time course for IAM, IAA and dIAA production. B. Time course for dIAA production.



Figure 3. Time course of proteins producing auxin.


With the auxin-biosynthesis pathway genes, regulated by constitutive promoters, the auxin production reaches steady state around 4.7 hours (280 min) due to the equilibrium reached, around 4.5 hours (270 min), by the transcription and translation rates and degradation rates involved in the production and consumption of proteins IAAM and IAAH (Figure 3).

On the other hand, the concentration of diffused auxin is very low, 10 μM at 16.7 hours (1000 min) (Figure 2.B), however it is increasing over time.












Cellular auxin production under an inducible promoter



Figure 4.Cellular auxin production under an inducible promoter. A. Time course for IAM, IAA and dIAA production. B. Time course for dIAA production.



Figure 5. Time course of proteins producing auxin.


With the auxin-biosynthesis pathway genes, regulated by inducible promoters, the auxin production shows a transient response around 1.5 hours (90 min) due to the transient responses reached, around 50 min, by the degradation rates and transcription and translation rates of the involved proteins, i.e. IAAM and IAAH (Figure 5).

Similarly, the concentration of diffused auxin is much lower with inducible promoter, 0.87 μM from around 7.7 hours (460 min) (Figure 4.B). In contrast with the constitutive promoter, the diffused auxin concentration does not increase over time but, instead, stabilizes after 7.7 hours.








Sensitivity analysis


Parametric sensitivity analysis was applied to study the effect of infinitesimal changes in system parameters on system variables (the output of the system). Examples of system parameters include the individual reaction rate constants and the initial conditions of the system. System variables include individual species concentrations. Sensitivity can be used to study the change of the dynamics of a system due to variations in the parameter values and initial state variables [10]. Hence, we will use the sensitivity analysis to explore the influence of constitutive and inducible promoter on auxin production. We will determine which initial state variables and parameters from the system are the most sensitive to the auxin production dynamics.


Cellular auxin production under a constitutive promoter


Figure 6. Sensitivity analysis of initial concentrations: 1. Trp, 2. iaaH, 3. iaaM; and parameters: 4. KmIAAH, 5. dcompound, 6. dmRNA, 7. dprotein, 8. kIAAM, 9. kIAAH, 10. KiIAA, 11. KiIAM, 12. KmIAAM, 13. Kz, 14. p, 15. Pr.



Cellular auxin production under an inducible promoter


Figure 7. Sensitivity analysis of initial concentrations: 1. Trp, 2. iaaH, 3. iaaM; and parameters: 4. KmIAAH, 5. dcompound, 6. dmRNA, 7. dprotein, 8. kIAAM, 9. kIAAH, 10. KiIAA, 11. KiIAM, 12. KmIAAM, 13. Kz, 14. p, 15. Pr.



By doing the sensitivity analysis, we can highlight the parameters that influence the most in the outcome of the auxin production model, for instance, the transcription rate constant of iaaM and iaaH (Pr) and the translation rate constant of mRNA-IAAM and mRNA-IAAH (Kz) (Figure 6 and 7) are the most sensitive parameters in the production of auxin (IAA) and difussed auxin (dIAA).


Conclusion


Our auxin production model predicts the formation of auxin over time catalyzed by enzymes whose transcription is regulated by constitutive and inducible promoters. In the first case, the auxin concentration increases over time and in the second case, the auxin concentration stabilizes after 7 hours.

By doing the sensitivity analyses for auxin-biosynthesis pathway genes under constitutive and inducible promoters, we can detect which parameters are more sensitive in the production of IAM, IAA and dIAA in the genes under inducible promoters compared to the genes under constitutive promoters.


Download code for auxin production model

HERE

References:

  1. https://2011.igem.org/Team:Imperial_College_London
  2. Cheng, Y. Dai, C. Zhao, Y. 2006. Auxin biosynthesis by the YUCCA flavin monooxygenases controls the formation of floral organs and vascular tissues in Arabidopsis. Genes & Dev 20: 1790-1799. Doi: 10.1101/gad.1415106
  3. 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).
  4. 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.
  5. Brenda: The Comprehensive Enzyme Information System http://www.brenda-enzymes.info/php/result_flat.php4?ecno=1.13.12.3
  6. http://biocyc.org/META/NEW-IMAGE?type=ENZYME&object=MONOMER-7661
  7. https://2011.igem.org/Team:Imperial_College_London/Project_Auxin_Modelling
  8. Boado, R. J., Li, J. Y., Nagaya, M., Zhang, C. & Pardridge, W. M. 1999. Selective expression of the large neutral amino acid transporter at the blood–brain barrier. PNAS 96, 12079-12084.
  9. Kim, D. K., Kanai, Y., Chairoungdua, A., Matsuo, H., Cha, S. H. & Endou, H. 2001. Expression Cloning of a Na+ -independent Aromatic Amino Acid Transporter with Structural Similarity to H+/Monocarboxylate Transporters. J Biol Chem 276, 17221-17228.
  10. http://www.mathworks.fr/fr/help/simbio/ug/example--calculating-sensitivities.html
  11. 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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