Team:Grenoble/Modeling/Conclusion

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How does the entire system work?

Now, we need to answer two questions:

      Is the sensitivity of the amplification module satisfying regarding to the quantity of adenylate cyclase that the signaling module can create?
      What is the time of answer of our system?

Sensitivity



In the amplification module, we saw that we could get a signal if there was more than 10-6 mol/L of initial cAMP. In the signaling part, we saw that when the dipeptide is detected, it will lead to the production of adenylate cyclase. Then, when the adenylate cyclase is produced, it leads to the production of cAMP, and this will launch the amplification module. Thus, we will have:



thus we need:



Here I give the graph of the evolution of the adenylate cyclase in the signaling module in function of the dipeptide concentration:



We notice that for an initial concentration of dipeptide around 10-8,5 mol/L of dipeptide we can get a signal. If we make the conversion in number of molecule (we multiply by the Avogadro number (=6,02*1023 mol/L) and by the volume of the cell (given in the quorum sensing part = 10-15 L), we obtain that our detection threshold is around 20 molecules.

Conclusion: Our detection threshold is around 20 molecules.

Temporal evolution



Once activated, we need to know the time we will have to wait to start up the amplification module. We take the equations of the signaling module, when the production of adenylate cyclase is activated. We have:



We solve this equation, and we want to solve in function of the time:



we get



Conclusion

When we detect, we have to wait around 20 minutes to start the amplification module. Then we have to wait around 200 minutes to see the bacterium turns green. Then, we saw with the quorum sensing that we have to wait 100 minutes for the entire test tube becomes green. We can thus say that the time to see the detection is around 320 minutes=5,3h.

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