Team:Grenoble/Modeling/Amplification/ODE
From 2012.igem.org
(Difference between revisions)
(6 intermediate revisions not shown) | |||
Line 190: | Line 190: | ||
</br> | </br> | ||
</br> | </br> | ||
- | 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: |
</br> | </br> | ||
</br> | </br> | ||
Line 239: | Line 239: | ||
</br> | </br> | ||
</br> | </br> | ||
- | 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> : |
</br> | </br> | ||
</br> | </br> | ||
Line 248: | Line 248: | ||
</br> | </br> | ||
</br> | </br> | ||
- | 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> : |
</br> | </br> | ||
</br> | </br> | ||
Line 254: | Line 254: | ||
</br> | </br> | ||
</br> | </br> | ||
- | 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. |
</br> | </br> | ||
</br> | </br> | ||
- | 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. |
</br> | </br> | ||
</br> | </br> | ||
Line 268: | Line 268: | ||
<b>Conclusion:</b> | <b>Conclusion:</b> | ||
The more cAMP<SUB>out</SUB> is introduced in the system, the fastest the answer is. The quickest answer would be 200 minutes to reach half of the maximal expression of ca enabling us to get a signal. | The more cAMP<SUB>out</SUB> is introduced in the system, the fastest the answer is. The quickest answer would be 200 minutes to reach half of the maximal expression of ca enabling us to get a signal. | ||
- | Because of the basal values, the adenylate cyclase is always expressed. Thus, we will make a steady state study of the system. This is useful seeing that with the sensitivity graph we | + | Because of the basal values, the adenylate cyclase is always expressed. Thus, we will make a steady state study of the system. This is useful seeing that with the sensitivity graph we could not see the low expression of adenylate cyclase and it is only in the temporal part that we could notice it, so we need a real study. |
- | Then, the stochastic part will be really important to be sure that there | + | Then, the stochastic part will be really important to be sure that there will not be too many false positives because of these basal values. |
</section> | </section> | ||
<section> | <section> | ||
Line 287: | Line 287: | ||
</br> | </br> | ||
</br> | </br> | ||
- | <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>. |
</br> | </br> | ||
</br> | </br> | ||
<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> | ||
</br> | </br> | ||
- | 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>. |
</br> | </br> | ||
</br> | </br> | ||
Line 299: | Line 299: | ||
</br> | </br> | ||
</br> | </br> | ||
- | 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>. |
</br> | </br> | ||
</br> | </br> | ||
<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> | ||
</br> | </br> | ||
- | 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>. |
</br> | </br> | ||
</br> | </br> | ||
Line 312: | Line 312: | ||
<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> | ||
</br> | </br> | ||
- | 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. |
</br> | </br> | ||
</br> | </br> | ||
Line 318: | Line 318: | ||
</br> | </br> | ||
</br> | </br> | ||
- | 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>: |
</br> | </br> | ||
</br> | </br> | ||
<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> | ||
</br> | </br> | ||
- | 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>. |
</br> | </br> | ||
</br> | </br> | ||
Line 331: | Line 331: | ||
<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> | ||
</br> | </br> | ||
- | 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. |
</br> | </br> | ||
</br> | </br> | ||
Line 372: | Line 372: | ||
</br> | </br> | ||
</br> | </br> | ||
- | - 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> : |
</br> | </br> | ||
</br> | </br> | ||
- | AraC steady state =10<SUP>-4</SUP> | + | AraC steady state = 0.167058129527727 10<SUP>-4</SUP> mol.L<span class="exposant">-1</span> |
</br> | </br> | ||
</br> | </br> | ||
- | Ca seady states = 10<SUP>-6</SUP> | + | Ca seady states = 0.1837444563636 10<SUP>-6</SUP> mol.L<span class="exposant">-1</span> |
</br> | </br> | ||
</br> | </br> | ||
- | λ<SUB>1</SUB>= -0.006000000912526 λ<SUB>2 </SUB>= -0.005763188664176 | + | λ<SUB>1</SUB> = -0.006000000912526 λ<SUB>2</SUB> = -0.005763188664176 |
</br> | </br> | ||
</br> | </br> | ||
</br> | </br> | ||
- | - 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> : |
</br> | </br> | ||
</br> | </br> | ||
- | AraC steady state =10<SUP>-4</SUP> | + | AraC steady state = 0.166879570344986 10<SUP>-4</SUP> mol.L<span class="exposant">-1</span> |
</br> | </br> | ||
</br> | </br> | ||
- | Ca seady states = 10<SUP>-6</SUP> | + | Ca seady states = 0.1832826298080 10<SUP>-6</SUP> mol.L<span class="exposant">-1</span> |
</br> | </br> | ||
</br> | </br> | ||
- | λ<SUB>1</SUB>= -0.006000000910603 λ<SUB>2</SUB>= -0.005745344108236 | + | λ<SUB>1</SUB>= -0.006000000910603   λ<SUB>2</SUB>= -0.005745344108236 |
</br> | </br> | ||
</br> | </br> | ||
</br> | </br> | ||
- | - 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> : |
</br> | </br> | ||
</br> | </br> | ||
- | AraC steady state = 10<SUP>-6</SUP> | + | AraC steady state = 0.182361098919416 10<SUP>-6</SUP> mol.L<span class="exposant">-1</span> |
</br> | </br> | ||
</br> | </br> | ||
- | Ca seady states = 10<SUP>-9</SUP> | + | Ca seady states = 0.249177541683 10<SUP>-9</SUP> mol.L<span class="exposant">-1</span> |
</br> | </br> | ||
</br> | </br> | ||
- | λ<SUB>1</SUB>= -0.006000006994365 λ<SUB>2 </SUB>= -0.002117175391388 | + | λ<SUB>1</SUB>= -0.006000006994365   λ<SUB>2 </SUB>= -0.002117175391388 |
</br> | </br> | ||
</br> | </br> | ||
Line 418: | Line 418: | ||
</br> | </br> | ||
<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> | ||
</div> | </div> |
Latest revision as of 03:47, 27 September 2012