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Team:Grenoble/Modeling/Amplification/Stochastic/results
From 2012.igem.org
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<ul><ul><img src="https://static.igem.org/mediawiki/2012/4/49/1_mod.png" alt="" /> How much time do we need to wait to get a response ?</ul></ul> | <ul><ul><img src="https://static.igem.org/mediawiki/2012/4/49/1_mod.png" alt="" /> How much time do we need to wait to get a response ?</ul></ul> | ||
| - | <ul><ul><img src="https://static.igem.org/mediawiki/2012/1/1e/2_mod.png" alt="" /> Is the | + | <ul><ul><img src="https://static.igem.org/mediawiki/2012/1/1e/2_mod.png" alt="" /> Is the sensitivity given by stochastic modeling the same as in ODE modeling ? |
</ul></ul> | </ul></ul> | ||
<ul><ul><img src="https://static.igem.org/mediawiki/2012/5/57/3_mod.png" alt="" /> What is the part of false positives ? | <ul><ul><img src="https://static.igem.org/mediawiki/2012/5/57/3_mod.png" alt="" /> What is the part of false positives ? | ||
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<h1><img src="https://static.igem.org/mediawiki/2012/1/1e/2_mod.png" alt="" /> Sensibility </h1> | <h1><img src="https://static.igem.org/mediawiki/2012/1/1e/2_mod.png" alt="" /> Sensibility </h1> | ||
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| - | The ODE modeling gave 10<SUP>-6</SUP> mol/L of CAMP<SUB>i</SUB> as the | + | The ODE modeling gave 10<SUP>-6</SUP> mol/L of CAMP<SUB>i</SUB> as the sensitivity. This means, if we have 10<SUP>-6</SUP> mol/L of CAMP at the initial point, the system will turn on. |
| - | But this result is given by a deterministic analysis. What happens if we take into account the random phenomena of the bacterium ? Is the | + | But this result is given by a deterministic analysis. What happens if we take into account the random phenomena of the bacterium ? Is the sensitivity still so good ? |
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<center><img src="https://static.igem.org/mediawiki/2012/4/47/Ca_Deterministic.png" alt="" /></center> | <center><img src="https://static.igem.org/mediawiki/2012/4/47/Ca_Deterministic.png" alt="" /></center> | ||
<center><img src="https://static.igem.org/mediawiki/2012/c/cf/CA_Stoch.png" alt="" /></center> | <center><img src="https://static.igem.org/mediawiki/2012/c/cf/CA_Stoch.png" alt="" /></center> | ||
| - | We can notice that, when we add stochastic variations to the model, the | + | We can notice that, when we add stochastic variations to the model, the sensitivity decreases from 10<SUP>-5,5</SUP> mol/L to 3,3.10<SUP>-5</SUP> mol/L. In other words, we loose a sensitivity of 2,98.10<SUP>-5</SUP> mol/L, that is 18 000 molecules of CAMP<SUB>i</SUB>. However this loss of sensitivity is low and doesn't penalize our device at all. |
</section> | </section> | ||
<section> | <section> | ||
Revision as of 12:12, 19 September 2012
Goal
In this part we would like to answer 3 questions thanks to the stochastic modeling.
How much time do we need to wait to get a response ?
Is the sensitivity given by stochastic modeling the same as in ODE modeling ?
What is the part of false positives ?
Time
The purpose of our device is to act more quickly than current techniques to detect the Golden Staph. Therefore we would like to evaluate the time needed to get an answer. We need to establish a time not to small to avoid false negatives and not to long to avoid false positives and to be performing.
In this first part we try to determine that time and in the third part we will analyse if it still be a good scale of time with respect to false positives.
Sensibility
The ODE modeling gave 10-6 mol/L of CAMPi as the sensitivity. This means, if we have 10-6 mol/L of CAMP at the initial point, the system will turn on.
But this result is given by a deterministic analysis. What happens if we take into account the random phenomena of the bacterium ? Is the sensitivity still so good ?
To perform that study, we use a Gillespie Algorithm to add randomness in our system. We want to obtain the evolution of the output signal (CA or GFP) depending on the concentration of the input signal (CAMPi) after 6h40 (400 min).
To get that graph we simulate the algorithm hundreed times for each concentration of CAMPi (1, 5, 10, …, 100 000 molecules).
We can compare the graph obtained with the one from the ODE modeling.
