Team:Grenoble/Modeling/Amplification/ODE
From 2012.igem.org
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- | The sensitivity of our system is 10<SUP>-6</SUP> mol | + | The sensitivity of our system is 10<SUP>-6</SUP> mol.L<span class="exposant">-1</span> of initial cyclic AMP. When we introduced this quantity in the system, the bacteria will turn on. |
Then, the next question is to know when we are under this value in how much time we will be able to observe that one bacteria turned on. | Then, the next question is to know when we are under this value in how much time we will be able to observe that one bacteria turned on. | ||
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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>≥10<SUP>-6</SUP> mol | + | 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 | + | 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 | + | 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’s 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 | + | 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 | + | <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 | + | 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 | + | 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 | + | 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 | + | 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 | + | 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 | + | 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 | + | 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 | + | - 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> *0.167058129527727 mol | + | Arac steady state =10<SUP>-4</SUP> *0.167058129527727 mol.L<span class="exposant">-1</span> |
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- | Ca seady states = 10<SUP>-6</SUP>*0.1837444563636 mol | + | Ca seady states = 10<SUP>-6</SUP>*0.1837444563636 mol.L<span class="exposant">-1</span> |
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- | - cAMP<SUB>init</SUB>=10<SUP>-6</SUP> mol | + | - 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> *0.166879570344986 mol | + | Arac steady state =10<SUP>-4</SUP> *0.166879570344986 mol.L<span class="exposant">-1</span> |
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- | Ca seady states = 10<SUP>-6</SUP>*0.1832826298080 mol | + | Ca seady states = 10<SUP>-6</SUP>*0.1832826298080 mol.L<span class="exposant">-1</span> |
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- | - cAMP<SUB>init</SUB>=10<SUP>-7</SUP> mol | + | - 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> *0.182361098919416 mol | + | Arac steady state = 10<SUP>-6</SUP> *0.182361098919416 mol.L<span class="exposant">-1</span> |
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- | Ca seady states = 10<SUP>-9</SUP>*0.249177541683 mol | + | Ca seady states = 10<SUP>-9</SUP>*0.249177541683 mol.L<span class="exposant">-1</span> |
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<h1>Conclusion</h1> | <h1>Conclusion</h1> | ||
- | The sensitivity of our system is around 10<SUP>-7</SUP> mol | + | 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’s 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. That’s what we are going to do in the next part. | In addition, to know if our system is fast we need to link this part with the signaling too. That’s what we are going to do in the next part. | ||
</section> | </section> |
Revision as of 20:51, 25 September 2012
Preliminary
We will use the quasi steady state approximation (QSSA) then. The idea is that there are quick reactions, such as enzymatic ones, complexations, etc… And there are slow reactions such as protein production. We assume that the evolution speed of an element that is created only by quick reaction is null.Goal
In this part, we want to answer to three questions:- What is the sensitivity of our system?
- What is the time response?
- What steady states will our system always reach?