Team:LCG-UNAM-Mexico/Parameters
From 2008.igem.org
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Parameters & kinetics </div></td> | Parameters & kinetics </div></td> | ||
<tr> | <tr> | ||
- | <td valign="top" class="bodyText"><p align="justify"><br> | + | <td valign="top" class="bodyText"><p align="center"><a href="#reactions">Biochemical Reactions</a> | <a href="#initial">Defining the Initial State of the Model </a></p> |
- | The complete model uses 18 kinetic parameters and 11 biochemical reactions. We got 13 of these parameters researching the literature and we estimated the range of values for 2 of them. 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> | + | <p align="justify"><br> |
- | <br> | + | The complete model uses 18 kinetic parameters and 11 biochemical reactions. We got 13 of these parameters researching the literature and we estimated the range of values for 2 of them. 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> |
- | 1. <span class="style4">Degradation of AHL by AiiA</span></p> | + | <br> |
+ | <a name="reactions"></a>1. <span class="style4">Degradation of AHL by AiiA</span></p> | ||
<table width="418" border="0"> | <table width="418" border="0"> | ||
<tr> | <tr> | ||
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<td valign="top"><strong>Parameters:</strong></td> | <td valign="top"><strong>Parameters:</strong></td> | ||
- | <td><em>k</em><sub>1cat</sub> = 27.97 s<sup>-1</sup> | + | <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> | <em>K</em><sub>1m</sub> = 3.723 mM = 224.20427E5 molecules</td> | ||
</tr> | </tr> | ||
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<tr> | <tr> | ||
<td valign="top"><strong>Parameters:</strong></td> | <td valign="top"><strong>Parameters:</strong></td> | ||
- | <td><p><em>k</em><sub>2</sub> = 10 <sup>-5</sup> | + | <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> | + | <em>k</em><sub>-2</sub> = 3.33 x 10 <sup>-3</sup> s<sup>-1</sup> |
<br> | <br> | ||
</p> </td> | </p> </td> | ||
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</table> | </table> | ||
<p align="justify"><br> | <p align="justify"><br> | ||
- | 2.1. <span class="style4"><strong>Dimer formation and dissociation between AHL:LuxR complexes</strong></span></p> | + | 2.1. <span class="style4"><strong><a name="Reaction2_1"></a>Dimer formation and dissociation between AHL:LuxR complexes</strong></span></p> |
<table width="577" border="0"> | <table width="577" border="0"> | ||
<tr> | <tr> | ||
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<tr> | <tr> | ||
<td valign="top"><strong>Parameters:</strong></td> | <td valign="top"><strong>Parameters:</strong></td> | ||
- | <td><p><em>k</em><sub>2.1</sub> = 10 <sup>-5</sup> | + | <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> | + | <em>k</em><sub>-2.1</sub> = 10 <sup>-2</sup> s<sup>-1</sup> <br> |
</p></td> | </p></td> | ||
</tr> | </tr> | ||
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<tr> | <tr> | ||
<td valign="top"><strong>Parameters:</strong></td> | <td valign="top"><strong>Parameters:</strong></td> | ||
- | <td><p><em>k</em><sub>3on</sub> = 10 <sup>-2</sup> | + | <td><p><em>k</em><sub>3on</sub> = 10 <sup>-2</sup> molecules<sup>-1</sup> s<sup>-1</sup> |
<br> | <br> | ||
</p></td> | </p></td> | ||
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<tr> | <tr> | ||
<td valign="top"><strong>Parameters:</strong></td> | <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> | + | <td><p><em>k</em><sub>3off</sub> = 4 x 10 <sup>-2</sup> s<sup>-1</sup> <br> |
</p></td> | </p></td> | ||
</tr> | </tr> | ||
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<td valign="top"><strong>Notes:</strong></td> | <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 <a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Notebook/2008- | + | <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 <a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Notebook/2008-August_2#21ago">lower than the constitutive rate constant</a>, regardless the implication of a greater threshold to achieve the <em>on </em>state<sup>3</sup>.</div></td> |
</tr> | </tr> | ||
</table></td> | </table></td> | ||
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<tr> | <tr> | ||
<td valign="top"><strong>Parameters:</strong></td> | <td valign="top"><strong>Parameters:</strong></td> | ||
- | <td><p><em>k</em><sub>4</sub> = 0.002888 <sup></sup> s<sup>-1</sup> | + | <td><p><em>k</em><sub>4</sub> = 0.002888 <sup></sup> s<sup>-1</sup> <br> |
</p></td> | </p></td> | ||
</tr> | </tr> | ||
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<tr> | <tr> | ||
<td valign="top"><strong>Notes:</strong></td> | <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,<a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Notebook/2008- | + | <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,<a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Notebook/2008-August_2#21ago"> the rate constant was calculated</a>.</div></td> |
</tr> | </tr> | ||
</table></td> | </table></td> | ||
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</table> | </table> | ||
<p align="justify"><br> | <p align="justify"><br> | ||
- | <a name="cidimer"></a>4.1. <span class="style4">Dimer formation and dissociation between CI molecules </span></p> | + | <a name="cidimer"></a>4.1. <span class="style4"><a name="DimerizationCI"></a>Dimer formation and dissociation between CI molecules </span></p> |
<table width="577" border="0"> | <table width="577" border="0"> | ||
<tr> | <tr> | ||
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<tr> | <tr> | ||
<td valign="top"><strong>Parameters:</strong></td> | <td valign="top"><strong>Parameters:</strong></td> | ||
- | <td><p><em>k</em><sub>7</sub> = | + | <td><p><em>k</em><sub>7</sub> = 500 molecules<sup>-1</sup> s<sup>-1</sup> <br> |
<br> | <br> | ||
</p></td> | </p></td> | ||
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<tr> | <tr> | ||
<td valign="top"><strong>Notes:</strong></td> | <td valign="top"><strong>Notes:</strong></td> | ||
- | <td><div align="justify">Biologically possible range of values estimated through the model.</div></td> | + | <td><div align="justify"><a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Simulation#nickel">Biologically possible range of values estimated through the model.</a></div></td> |
</tr> | </tr> | ||
</table></td> | </table></td> | ||
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<tr> | <tr> | ||
<td valign="top"><strong>Notes:</strong></td> | <td valign="top"><strong>Notes:</strong></td> | ||
- | <td><div align="justify">This kinetic parameter wasn’t found in our bibliographic search and <a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Notebook/2008- | + | <td><div align="justify">This kinetic parameter wasn’t found in our bibliographic search and <a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Notebook/2008-August_2#letter">personal communication with Peter T. Chivers</a> (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> | </tr> | ||
</table></td> | </table></td> | ||
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<tr> | <tr> | ||
<td valign="top"><strong>Parameters:</strong></td> | <td valign="top"><strong>Parameters:</strong></td> | ||
- | <td><p><em>k</em><sub>9</sub> = | + | <td><p><em>k</em><sub>9</sub> = 500 molecules<sup>-1</sup> s<sup>-1</sup> <br> |
<br> | <br> | ||
</p></td> | </p></td> | ||
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<tr> | <tr> | ||
<td valign="top"><strong>Notes:</strong></td> | <td valign="top"><strong>Notes:</strong></td> | ||
- | <td><div align="justify">Biologically possible range of values estimated through the model | + | <td><div align="justify"><a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Simulation#nickel">Biologically possible range of values estimated through the model</a>.</div></td> |
</tr> | </tr> | ||
</table></td> | </table></td> | ||
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</table> | </table> | ||
<p><strong>NOTE:</strong> The average volume of an <em>E. coli </em>cell is 10<sup>-15</sup> liters.</p> | <p><strong>NOTE:</strong> The average volume of an <em>E. coli </em>cell is 10<sup>-15</sup> liters.</p> | ||
- | <p> | + | <p align="center"><a href="#top"><img src="https://static.igem.org/mediawiki/2008/c/cd/Boton_back.jpg" alt="Back to top" width="190" height="31" border="0"></a></p> |
- | <p class="style2">Defining the initial state of the system</p> | + | <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="initial"></a>Defining the initial state of the system</p> | ||
<p align="justify"> The initial concentrations of the constitutive proteins (AiiA, LuxR, CI -constitutive synthesis- and CI:CI -due to constitutive synthesis-) were estimated based on the efficiency rate of their promoters, number of promoters per cell, degradation rate of their mRNAs, translation efficiency and degradation rate of the proteins. Initial concentrations of AHL:LuxR complex, the dimer of complexes, CI and CI:CI due to complex activation were set to 0, given these are all due to the action of AHL. Number of copies of both <em>cI</em> and <em>rcnA</em> promoters are 10 based on plasmid copy number. RcnA and Unk were estimated experimentally and set consistent to the observed rate. Concentration of AHL and nickel is determined by us to obtain the desired results. </p> | <p align="justify"> The initial concentrations of the constitutive proteins (AiiA, LuxR, CI -constitutive synthesis- and CI:CI -due to constitutive synthesis-) were estimated based on the efficiency rate of their promoters, number of promoters per cell, degradation rate of their mRNAs, translation efficiency and degradation rate of the proteins. Initial concentrations of AHL:LuxR complex, the dimer of complexes, CI and CI:CI due to complex activation were set to 0, given these are all due to the action of AHL. Number of copies of both <em>cI</em> and <em>rcnA</em> promoters are 10 based on plasmid copy number. RcnA and Unk were estimated experimentally and set consistent to the observed rate. Concentration of AHL and nickel is determined by us to obtain the desired results. </p> | ||
<p align="justify"> <span class="style3">AHL:</span> It’s an arbitrary and adjustable value. Different outcomes can be observed <a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Simulation">manipulating this initial value</a>.<br> | <p align="justify"> <span class="style3">AHL:</span> It’s an arbitrary and adjustable value. Different outcomes can be observed <a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Simulation">manipulating this initial value</a>.<br> | ||
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Nickel (total):</span> It’s an arbitrary and adjustable value. Different outcomes can be observed <a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Simulation">manipulating this initial value</a>.<br> | Nickel (total):</span> It’s an arbitrary and adjustable value. Different outcomes can be observed <a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Simulation">manipulating this initial value</a>.<br> | ||
<span class="style3"><br> | <span class="style3"><br> | ||
- | Unk:</span> Both the Unk concentration and its rate constant are unknown. They are arbitrarily defined in such a way that | + | Unk:</span> Both the Unk concentration and its rate constant are unknown. They are arbitrarily defined in such a way that it is consistent with the <a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Simulation#nickel">desired flux.</a><br> |
| | ||
- | <strong>[Unk]</strong>= | + | <strong>[Unk]</strong>= 3,315 molecules<br> |
- | + | ||
- | + | ||
- | + | ||
- | + | ||
<span class="style3"><br> | <span class="style3"><br> | ||
ρ and ρCI:</span> Their concentration is defined by the copy number of the plasmids that contain them.<br> | ρ and ρCI:</span> Their concentration is defined by the copy number of the plasmids that contain them.<br> | ||
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<span class="style3"><br> | <span class="style3"><br> | ||
AiiA:</span> The constant concentration of AiiA is calculated taking into account the following parameters retrieved from literature:<br> | AiiA:</span> The constant concentration of AiiA is calculated taking into account the following parameters retrieved from literature:<br> | ||
- | - pLac average transcription rate<sup> | + | - pLac average transcription rate<sup>12</sup>: 0.003 s<sup>-1</sup><br> |
- | - mRNA average degradation rate<sup> | + | - mRNA average degradation rate<sup>13</sup>: 0.00766 s<sup>-1</sup><br> |
- | - Average translation rate<sup> | + | - Average translation rate<sup>13</sup>: 0.31333 s<sup>-1</sup><br> |
- AiiA degration rate: 0.00012 s<sup>-1</sup> <br> | - AiiA degration rate: 0.00012 s<sup>-1</sup> <br> | ||
The half life of RcnA with LVA tail is approximately 2 minutes<sup>14</sup>; Andersen JB et al. found that this tail reduces the half life of GFP forty-eight times.9 Therefore the half life of wildtype AiiA can be estimated to 96 minutes.<br> | The half life of RcnA with LVA tail is approximately 2 minutes<sup>14</sup>; Andersen JB et al. found that this tail reduces the half life of GFP forty-eight times.9 Therefore the half life of wildtype AiiA can be estimated to 96 minutes.<br> | ||
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<strong> [LuxR]</strong>= 22000 molecules<br> | <strong> [LuxR]</strong>= 22000 molecules<br> | ||
</p> | </p> | ||
+ | <p align="center"><a href="#top"><img src="https://static.igem.org/mediawiki/2008/c/cd/Boton_back.jpg" alt="Back to top" width="190" height="31" border="0"></a></p> | ||
+ | <p align="justify"><img src="https://static.igem.org/mediawiki/2008/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /></p> | ||
<p align="justify"> <span class="style2"><strong>References</strong></span><strong><br> | <p align="justify"> <span class="style2"><strong>References</strong></span><strong><br> | ||
- | </strong><strong>1. | + | </strong><strong>1. </strong>Wang LH <em>et al</em>. (2004) <strong>Specificity and Enzyme Kinetics of the Quorum-quenching <em>N-</em>Acyl Homoserine Lactone Lactonase (AHL-Lactonase). </strong>J Biol Chem <strong>279:</strong>4, 13645-13651. <br> |
- | <strong>2. | + | <strong>2. </strong>Hee Kim <em>et al. </em>(2005) <strong>The molecular structure and catalytic mechanism of a quorum-quenching N-acyl-L-homoserine lactone hydrolase.</strong> Proc Natl Acad Sci USA 102:49, 17606-17611. <br> |
- | <strong>3. | + | <strong>3. </strong>Goryachev AB, Toh DJ, Lee T (2006). <strong>Systems analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants.</strong> Biosystems 83, 178-187. <strong>4. </strong>Babic AC, Little JW (2007) <strong>Cooperative binding by CI repressor is dispensable in a phage </strong><strong>λ </strong><strong>variant. </strong>Proc Natl Acad Sci USA 104: 17741-17746. <br> |
- | <strong>5. | + | <strong>5. </strong>Ackers GK, Johnson AD, Shea MA (1982). <strong>Quantitative model for gene regulation by </strong><strong>λ</strong> <strong>phage repressor.</strong>Proc Natl Acad Sci USA 79: 1129-1133. <br> |
- | <strong>6. | + | <strong>6. </strong>Reinitz J, Vaisnys JR (1990) <strong>Theoretical and Experimental Analysis of the Phage Lambda Genetic Switch Implies Missing Levels of Co-operativity</strong>. J Theor Biol 145: 295-318. <br> |
- | <strong>7. | + | <strong>7. </strong>Iadevaia S, Mantzaris NV (2006) <strong>Genetic Network Driven Control of PHBV Copolymer Composition. </strong>J Biotechnol 122: 99-121. <br> |
- | <strong>8. | + | <strong>8. </strong>Elowitz MB & Leibler S (2000). <strong>A synthetic oscillatory network of transcriptional regulators. </strong>Nature 403 335-338. <br> |
- | <strong>9. | + | <strong>9. </strong>Andersen JB <em>et al </em> (1998). <strong>New Unstable of Green Fluorescent Protein for Studies of Transient Gene Expression in Bacteria. </strong> Appl Environ Microbiol 64,6: 2240-2246. <br> |
- | <strong>10. | + | <strong>10. </strong>Kenneth S.<strong> </strong>Koblan and Gary K. Ackers (1991) <strong>Energetics of Subunit Dimerization in Bacteriophage </strong><strong>λ </strong><strong>cI </strong><strong>Repressor: Linkage to</strong><strong> </strong><strong>Protons, Temperature, and KCl.</strong> Biochemistry 1991, 30, 7817-7821. <br> |
- | <strong>11. | + | |
- | <strong>12. | + | <strong>11. </strong>M. Santillán and M. C. Mackey (2004). <strong>Influence of catabolite repression and inducer exclusion on the bistable behavior of the lac operon.</strong> Biophys J. 86: 1282-1292 <br> |
- | <strong>13. | + | <strong>12. </strong>Malan, T. P., A. Kolb, H. Buc, and W. R. McClure (1984). <strong>Mechanism of CRP-cAMP activation of lac operon transcription initiation activation of the P1 promoter.</strong> J. Mol. Biol. 180:881–909. <br> |
- | <strong>14. | + | <strong>13. </strong>Kennell, D., and H. Riezman (1977). <strong>Transcription and translation initiation frequencies of the <em>Escherichia coli</em> lac operon.</strong> J. Mol. Biol. 114:1–21. <br> |
- | <strong>15. | + | <strong>14. </strong>Christopher Batten. <strong>Modeling the Lux/AiiA Relaxation Oscillator</strong><strong>.</strong> Unpublished (<a href="http://www.mit.edu/%7Ecbatten/work/ssbc04/modeling-ssbc04.pdf">http://www.mit.edu/~cbatten/work/ssbc04/modeling-ssbc04.pdf</a>). <br> |
- | <strong>16. | + | <strong>15. </strong>Bologna Cesena Campus, iGEM 2007 WIKI. (<u><a href="https://2007.igem.org/Bologna">https://2007.igem.org/Bologna</a></u>) <br> |
+ | <strong>16. </strong>KULeuven team, iGEM 2008 WIKI. Dr. Coli, the bacterial drug delivery system. (<a href="https://2008.igem.org/Team:KULeuven/Model/CellDeath" target="_blank">https://2008.igem.org/Team:KULeuven/Model/CellDeath</a>) </p> | ||
<p align="justify"><a name="simulation"></a><a href="#top"><img src="https://static.igem.org/mediawiki/2008/c/cd/Boton_back.jpg" alt="Back to top" width="190" height="31" border="0"></a><a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Modeling"><img src="https://static.igem.org/mediawiki/2008/5/5b/Model1a.jpg" alt="Modeling the system" 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&Analysis" width="190" height="31" border="0"></a><br> | <p align="justify"><a name="simulation"></a><a href="#top"><img src="https://static.igem.org/mediawiki/2008/c/cd/Boton_back.jpg" alt="Back to top" width="190" height="31" border="0"></a><a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Modeling"><img src="https://static.igem.org/mediawiki/2008/5/5b/Model1a.jpg" alt="Modeling the system" 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&Analysis" width="190" height="31" border="0"></a><br> | ||
<img src="https://static.igem.org/mediawiki/2008/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /></p> | <img src="https://static.igem.org/mediawiki/2008/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /></p> |
Latest revision as of 06:37, 30 October 2008
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