Team:Grenoble/Modeling/Amplification/ODE
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- | The QSSA enables us to have r<SUB>cAMP</SUB>=0. Then, we have: | + | The QSSA enables us to have r<SUB>cAMP</SUB> = 0. Then, we have: |
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- | To evaluate the time it will take to be able to detect a signal, we need to plot the evolution of the adenylate cyclase in the time for an initial concentration of cAMP<SUB>out</SUB> | + | To evaluate the time it will take to be able to detect a signal, we need to plot the evolution of the adenylate cyclase in the time for an initial concentration of cAMP<SUB>out</SUB> ≥ 10<SUP>-6</SUP> mol.L<span class="exposant">-1</span>. We first give the graph with cAMP<SUB>out</SUB> = 10<SUP>-3</SUP> mol.L<span class="exposant">-1</span> : |
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- | Then, we want to see the behavior of the system around the threshold. We give the evolution of the adenylate cyclase in the time in function with cAMP<SUB>out</SUB>=10<SUP>-6</SUP> mol.L<span class="exposant">-1</span> : | + | Then, we want to see the behavior of the system around the threshold. We give the evolution of the adenylate cyclase in the time in function with cAMP<SUB>out</SUB> = 10<SUP>-6</SUP> mol.L<span class="exposant">-1</span> : |
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- | Here, to be able to begin to detect a signal, we should wait around 1300 minutes. So even if our system can detect cAMP<SUB>out</SUB>=10<SUP>-6</SUP> mol.L<span class="exposant">-1</span>, we may not be able to say if it is a real detection or a false positive. We will be able to answer this question with the stochastic part. | + | Here, to be able to begin to detect a signal, we should wait around 1300 minutes. So even if our system can detect cAMP<SUB>out</SUB> = 10<SUP>-6</SUP> mol.L<span class="exposant">-1</span>, we may not be able to say if it is a real detection or a false positive. We will be able to answer this question with the stochastic part. |
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- | Then we give one temporal evolution of the adenylate cyclase for cAMP<SUB>out</SUB>=10<SUP>-8</SUP> mol.L<span class="exposant">-1</span>. It is bellow the threshold, but because of the basal values, we want to see exactly what happens. | + | Then we give one temporal evolution of the adenylate cyclase for cAMP<SUB>out</SUB> = 10<SUP>-8</SUP> mol.L<span class="exposant">-1</span>. It is bellow the threshold, but because of the basal values, we want to see exactly what happens. |
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- | <a href="https://static.igem.org/mediawiki/2012/9/9e/Steadys_state_study.zip">Here</a> you can find the scripts we worked with in this part. First, I give the isoclines with cAMP<SUB>init</SUB>=10<SUP>-5</SUP> mol.L<span class="exposant">-1</span>. | + | <a href="https://static.igem.org/mediawiki/2012/9/9e/Steadys_state_study.zip">Here</a> you can find the scripts we worked with in this part. First, I give the isoclines with cAMP<SUB>init</SUB> = 10<SUP>-5</SUP> mol.L<span class="exposant">-1</span>. |
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<center><img src="https://static.igem.org/mediawiki/2012/d/dc/Graphe7_ampli_grenoble.png" alt="" /></center> | <center><img src="https://static.igem.org/mediawiki/2012/d/dc/Graphe7_ampli_grenoble.png" alt="" /></center> | ||
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- | Isoclines of Ca and AraC with cAMP<SUB>init</SUB>=10<SUP>-5</SUP> mol.L<span class="exposant">-1</span>. | + | Isoclines of Ca and AraC with cAMP<SUB>init</SUB> = 10<SUP>-5</SUP> mol.L<span class="exposant">-1</span>. |
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- | Then I give the isoclines with cAMP<SUB>init</SUB>=10<SUP>-6</SUP> mol.L<span class="exposant">-1</span>. | + | Then I give the isoclines with cAMP<SUB>init</SUB> = 10<SUP>-6</SUP> mol.L<span class="exposant">-1</span>. |
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<center><img src="https://static.igem.org/mediawiki/2012/4/49/Graphe8_ampli_grenoble.png" alt="" /></center> | <center><img src="https://static.igem.org/mediawiki/2012/4/49/Graphe8_ampli_grenoble.png" alt="" /></center> | ||
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- | Ca and AraC isoclines with cAMP<SUB>init</SUB>=10<SUP>-6</SUP> mol.L<span class="exposant">-1</span>. | + | Ca and AraC isoclines with cAMP<SUB>init</SUB> = 10<SUP>-6</SUP> mol.L<span class="exposant">-1</span>. |
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<center><img src="https://static.igem.org/mediawiki/2012/0/08/Graphe9_ampli_grenoble.png" alt="" /></center> | <center><img src="https://static.igem.org/mediawiki/2012/0/08/Graphe9_ampli_grenoble.png" alt="" /></center> | ||
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- | Ca and Arac isoclines with cAMP<SUB>init</SUB>=10<SUP>-6</SUP> mol.L<span class="exposant">-1</span>, zoom around 0. | + | Ca and Arac isoclines with cAMP<SUB>init</SUB> = 10<SUP>-6</SUP> mol.L<span class="exposant">-1</span>, zoom around 0. |
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- | Eventually, I give the isoclines with cAMP<SUB>init</SUB>=10<SUP>-7</SUP> mol.L<span class="exposant">-1</span>: | + | Eventually, I give the isoclines with cAMP<SUB>init</SUB> = 10<SUP>-7</SUP> mol.L<span class="exposant">-1</span>: |
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<center><img src="https://static.igem.org/mediawiki/2012/8/85/Graphe10_ampli_grenoble.png" alt="" /></center> | <center><img src="https://static.igem.org/mediawiki/2012/8/85/Graphe10_ampli_grenoble.png" alt="" /></center> | ||
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- | Ca and AraC isoclines with cAMP<SUB>init</SUB>=10<SUP>-7</SUP> mol.L<span class="exposant">-1</span>. | + | Ca and AraC isoclines with cAMP<SUB>init</SUB> = 10<SUP>-7</SUP> mol.L<span class="exposant">-1</span>. |
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<center><img src="https://static.igem.org/mediawiki/2012/6/60/Graphe11_ampli_grenoble.png" alt="" /></center> | <center><img src="https://static.igem.org/mediawiki/2012/6/60/Graphe11_ampli_grenoble.png" alt="" /></center> | ||
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- | Ca and AraC isoclines with cAMP<SUB>init</SUB>=10<SUP>-7</SUP> mol.L<span class="exposant">-1</span>, zoom around 0. | + | Ca and AraC isoclines with cAMP<SUB>init</SUB> = 10<SUP>-7</SUP> mol.L<span class="exposant">-1</span>, zoom around 0. |
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- | - cAMP<SUB>init</SUB>=10<SUP>-5</SUP> mol.L<span class="exposant">-1</span> : | + | - cAMP<SUB>init</SUB> = 10<SUP>-5</SUP> mol.L<span class="exposant">-1</span> : |
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- | AraC steady state =10<SUP>-4</SUP> | + | AraC steady state = 0.167058129527727 10<SUP>-4</SUP> mol.L<span class="exposant">-1</span> |
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- | Ca seady states = 10<SUP>-6</SUP> | + | Ca seady states = 0.1837444563636 10<SUP>-6</SUP> mol.L<span class="exposant">-1</span> |
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- | λ<SUB>1</SUB>= -0.006000000912526 λ<SUB>2 </SUB>= -0.005763188664176 | + | λ<SUB>1</SUB> = -0.006000000912526 λ<SUB>2</SUB> = -0.005763188664176 |
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- | - cAMP<SUB>init</SUB>=10<SUP>-6</SUP> mol.L<span class="exposant">-1</span> : | + | - cAMP<SUB>init</SUB> = 10<SUP>-6</SUP> mol.L<span class="exposant">-1</span> : |
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- | AraC steady state =10<SUP>-4</SUP> | + | AraC steady state = 0.166879570344986 10<SUP>-4</SUP> mol.L<span class="exposant">-1</span> |
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- | Ca seady states = 10<SUP>-6</SUP> | + | Ca seady states = 0.1832826298080 10<SUP>-6</SUP> mol.L<span class="exposant">-1</span> |
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- | λ<SUB>1</SUB>= -0.006000000910603 λ<SUB>2</SUB>= -0.005745344108236 | + | λ<SUB>1</SUB>= -0.006000000910603   λ<SUB>2</SUB>= -0.005745344108236 |
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- | - cAMP<SUB>init</SUB>=10<SUP>-7</SUP> mol.L<span class="exposant">-1</span> : | + | - cAMP<SUB>init</SUB> = 10<SUP>-7</SUP> mol.L<span class="exposant">-1</span> : |
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- | AraC steady state = 10<SUP>-6</SUP> | + | AraC steady state = 0.182361098919416 10<SUP>-6</SUP> mol.L<span class="exposant">-1</span> |
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- | Ca seady states = 10<SUP>-9</SUP> | + | Ca seady states = 0.249177541683 10<SUP>-9</SUP> mol.L<span class="exposant">-1</span> |
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- | λ<SUB>1</SUB>= -0.006000006994365 λ<SUB>2 </SUB>= -0.002117175391388 | + | λ<SUB>1</SUB>= -0.006000006994365   λ<SUB>2 </SUB>= -0.002117175391388 |
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<b>Conclusion:</b> | <b>Conclusion:</b> | ||
- | Now, we can be sure that our system | + | Now, we can be sure that our system will not always be turned on. In function of the quantity of initial cAMP, our system will stay at a low or a high steady state. |
</section> | </section> | ||
<section> | <section> | ||
<h1>Conclusion</h1> | <h1>Conclusion</h1> | ||
- | The sensitivity of our system is around 10<SUP>-7</SUP> mol.L<span class="exposant">-1</span>. To be able to know if | + | The sensitivity of our system is around 10<SUP>-7</SUP> mol.L<span class="exposant">-1</span>. To be able to know if it is satisfying, we need to link it with the signaling part. |
- | In addition, to know if our system is fast we need to link this part with the signaling too. | + | In addition, to know if our system is fast we need to link this part with the signaling too. That is what we are going to do in the next part. |
</section> | </section> | ||
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Latest revision as of 03:47, 27 September 2012