<h1>Introduction</h1>

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.

As we designed a biosensor, when the molecule to detect is detected by our bacterium, our bacterium will send us a signal. This signal is a green light. Our bacterium activates the production of a protein, called GFP, which makes it become green. In our system the production of GFP begins when the production of an other protein, the adenylate cyclase (Ca) begins. Indeed, they are under the control of the same promotor, paraBAD (pBad), and thus they have exatly the same behavior:

The protein GFP is only the protein that enables us to control the behavior of the adenylate cyclase. Thus, in the development, I won’t speak about the gfp, but always about the adenylate cyclase, and we will consider that the adenylate cyclase gives us the signal.

When one bacterium detects the dipeptide, it will become green. However, if only one bacterium becomes green, we won’t be able to get the signal. That is why we decided to use the communication between the bacteria, called the quorum sensing: if one bacterium becomes green, the surrounding bacteria will become green too, and thus we will be able to get the signal.

The question became: How to do this?

First, we had to choose a molecule, which would enable the communication between the bacteria. We chose the cyclic AMP, which production is catalyzed by the adenylate cyclase. Thus, we designed:

As soon as some cAMP is produced, it will start a new production of adenylate cyclase, which will catalyse the production of cAMP and so forth. We had enough cAMP! However, if some adenylate cyclase was produced though it shouldn’t (because of the promotor let off for example), the system would have started start. Thus, we needed to increase the robustness of our system to false positives. We added a classic feed forward loop. The production of the aenylate cyclase would begin if and only if there is enough cAMP AND enough of an intermediary protein, here AraC. We finally got: