In this part we will model the amplification module. Our work in this module is subdivided in three main parts: A deterministic model of the reactions at the local scale, another version of the former taking into account some random noise/perturbations, and a model of the signal's diffusion in space.
In the deterministic model, we check the sensitivity of our system and we give the link with the signaling module. Then, in the diffusion part we check if our system has a fast answer. Eventually, in the random perturbations model, we check that it is robust to perturbations.
Overview
We wanted to create a detector, thus we could have designed it like following:
Where X is the molecule to detect, and Z the fluorescent signal. However, with this design, the communication between the bacteria (quorum sensing) wouldn’t have worked really well, we would have needed an important quantity of X at the initial time to be able to obtain an important diffusion that we could actually see. Indeed, the evolution of X would have been like following:
Thus, the next idea was to amplify X:
Like this, as soon as it would be detected, by a bacterium, the bacterium would re-create some X, and the quorum sensing would work, as we would have this evolution of X:
Thanks to the quorum sensing if we detect X, we can easily measure it.
Now, we had a last problem: the false positives. Indeed, we have a detector, so we don’t want to have a signal if there is nothing to detect. Thus, we decided to add a classic feed forward loop, because it is known to reduce the false positives. Finally, we got our system:
X is a molecule that has the ability to be transmitted from bacterium to an other. It is a quorum-sensing molecule.
Y, and Z are 2 genes. X is the transcription factor of Y. Thus when it is introduced, the gene Y is expressed. Then, the molecule X and the protein Y together will be the transcription factor of Z. When Z is expressed it creates more X.
Conclusion:
Now that we designed our system, we wanted to really study the behavior of this topology before going further in this project.
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