Modelling

The full adder was tailored taking into account the diffusion of the carry from the bit n to the bit n+1. Evidently, the molecule should reach the n+1 colony prior the calculation step! Therefore, we have modeled the diffusion of AHL through the agar plate. The model would then help us determine the spacing between the different E. calculus colonies and the time necessary between two bits counting.
For the modelling, we used a strain of Chromobacterium violaceum deleted in the gene producing AHL. This strai can then only react to the externalm presence of AHL, coloring nicely with violacein, a violet(!!) pigment.

N-acetyl Homoserine lactone diffusion in agar medium

N-acyl Homoserine Lactone (AHL), 3-oxohexanoyl-homoserine lactone was chosen as the biological messenger in our system. Let's imagine a simple system. A petri dish containing colonies equidistant from each other. The lights provide the information for the addition to perform, and the expression and diffusion of AHL from one colony to another allows the carry propagation.

This system seems quite simple but nevertheless raises a certain number of problems:

Production of AHL

To overcome the problem of the amount of AHL required for a rapid diffusion of the messenger, we also imagined a system in which liquid precultures may be deposited. A higher cell density would be obtained as well as a greater production of AHL.

Inoculation of cultures

A gradual inoculation of wells during the addition process allows, first to avoid the direct interference between the wells. Furthermore, progressive innoculation would lower the problem cells dying on the plate that could not respond anymore to the AHL messenger.

The ideal distance between well

In order to find the ideal distance between two colonies we searched a model that would calculate how does AHL diffuse into the medium and how long does the diffusion process takes place to pass from one colony to another.

Diffusion reminder

The graph above represents cylinder containing bacterias. Bacterias can produce AHL to send a message to another well. Here we can imagine that AHL diffuse into the medium. In order to introduce the theory of diffusion we can realize a simple model, with stationary state condition. In fact, we can establish a mass balance on AHL over a thickness of Δr :

In fact, we can establish a mass balance on AHL over a thickness of Δr :

Here we can introduce the Fick’s law of diffusion.

With this equation we can establish the concentration profile (figure 3) of diffusion of AHL. This equation is only valid in our case of well geometry. But this model is not depending on time, that’s why we must try to develop a more complex model in order to modelling the diffusion of AHL into LBagar medium with time.