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 questions:

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 avoids the direct interference between the wells. Furthermore, progressive innoculation would lower the problem of cells dying on the plate that could not respond anymore to the AHL messenger.

The ideal distance between wells

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 conditions.

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

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

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