Team:Grenoble/Modeling/Amplification/Stochastic/results

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iGEM Grenoble 2012

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Project

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 ?
Thanks to those 3 questions we will be able to establish if our device is still performing when we take into account random variations.

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 wheras there was nothing to detect. This phenomenon is due to the randomness the bacterium and espacially beacouse of basal values.

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.

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.

After 200 minutes we get half of the maximum output signal. If we wait 200 minutes more we reach 80% of the output signal. Therefore we can assess the time needed to get a correct answer as 400 minutes for the time being. We then have to check if that time is still appropriate when we take into accout the randomness.

We would like to observe what happens after 400 minutes of waiting for several initial concentrations of CAMP. To perform that study, we use a Gillespie Algorithm to add randomness in our system. Moreover, we simulate the algorithm 100 times for each initial concentration of CAMP which interest us.



We can notice that when we wait 400 minutes we get a visible output signal as soon as we have an initial concentration of CAMP of 5,25.10-5 mol/L (104,5 molecules of CAMPi). We will see in the next part that this concentration corresponds to the sensitivity of our system. Thus, our stochastic model doesn't contradict our deterministic model and we can make our further studies at a time of 400 minutes.

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 ?

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.
We can notice that, when we add stochastic variations to the model, the sensitivity decreases from 10-5,5 mol/L to 3,3.10-5 mol/L. In other words, we loose a sensitivity of 2,98.10-5 mol/L, that is 18 000 molecules of CAMPi. However this loss of sensitivity is low and doesn't penalize our device at all.

False positives

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