Team:Grenoble/Modeling/Amplification/Stochastic/results
From 2012.igem.org
![Project](https://static.igem.org/mediawiki/2012/3/3c/Modeling.png)
Goal
In this part we would like to answer 3 questions thanks to the stochastic modeling.![](https://static.igem.org/mediawiki/2012/4/49/1_mod.png)
![](https://static.igem.org/mediawiki/2012/1/1e/2_mod.png)
![](https://static.igem.org/mediawiki/2012/5/57/3_mod.png)
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 too small to avoid false negatives and not too long to avoid false positives and to be performing. Indeed, if we take a short time we can miss some visible output signals which are longer to appear. Then we will conclude that nothing has been detected whereas there was something to detect. If we wait too long, some visible output signals can appear whereas there was nothing to detect. This phenomenon is due to the randomness inside the bacterium and espacially because of basal values.
In this first part we try to determine that time and in the third part we will analyse if it would still be a good scale of time with respect to false positives.
Thanks to the deterministic modeling we can have an estimation of the time needed to get an answer in differentt proportions. In the graph below you can observe the evolution of the output signal through time for an initial concentration of CAMP of 10-3 mol/L.
![](https://static.igem.org/mediawiki/2012/8/81/Time_det.png)
![](https://static.igem.org/mediawiki/2012/1/11/Tab_per.png)
Sensitivity
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 ?
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 (10, 101,5, 102, …, 106 molecules).
We can compare the graph obtained with the one from the ODE modeling.
![](https://static.igem.org/mediawiki/2012/4/47/Ca_Deterministic.png)
![](https://static.igem.org/mediawiki/2012/c/cf/CA_Stoch.png)
False positives
We know the time we need to wait to get a response and the sensitivity of our device. But we don't know yet if that device is reliable.
To answer this question we generate 10 000 simulations of the Gillespie Algorithm when there is no CAMP at the initial point. After 400 minutes we evaluate the number of output signals to establish the percentage of false positives. We consider as "output signal" the production of 35 molecules of CA which represents the lower bound of molecules of CA produced for an initial concentration of CAMP equal to the sensitivity of our device after 400 minutes according to our last modeling (part 2).
We get the results below.
![](https://static.igem.org/mediawiki/2012/f/fc/False_positives.png)