Modelling

N-acyl Homoserine lactone diffusion in agar medium

To build a binary full adder our system must be able to communicate a carry if necessary. We chose to use one of the N-acyl Homoserine Lactone (AHL), 3-oxohexanoyl-homoserine lactone. The AHL is the biological messenger in our system.

Different systems can be devised to implement the expression and diffusion of the AHL.

The system of Figure 1 operates as follows:
A petri dish containing colonies equidistant from each other. The lights provide the information for the addition to perform, and the expression & 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 rapid diffusion of the messenger, we can well imagine a system in which liquid precultures may be deposited. So we get a higher cell density and a greater production of AHL.

Inoculation of cultures

The gradual inoculation of wells during the addition allows, first, to the AHL to diffuse into the medium, and second, not to fall in cell death.

The ideal distance between well

In order to find the ideal distance between two colonies we have searched a model which allow us to know: how does AHL diffuse into the medium and how many time the diffusion need to pass one colony to another.

One dimension model:
To overcome the problem of the amount of AHL required for rapid diffusion of the messenger, we can well imagine a system in which liquid precultures may be deposited. So we get a higher cell density and a greater production of AHL.

Figure 3 shows that the largest amount of AHL is between 2.5 and 20 mm. This information is important but we need to develop a model based on time.

Two dimension model:
We realized many experiences in order to measure how AHL diffuse into agar medium. We used a particular bacteria, Chromobacterium violaceum, which is capable to detect presence of AHl by producing a purple pigment, the violacein.

Figure 4 shows petri dishes containing eight colonies of bacteria placed at 5, 10, 15, 20, 25, 30, 35 and 40 mm from the center of the box. With this experience we can track the diffusion of the AHL. Figure 5 represent the evolution of AHL diffusion versus time.

Figure 5 : Evolution of AHL diffusion into petri dish.

We can see that the ideal distance between two wells is probably between 15 and 25 mm depending on the amount of AHL produced by the bacteria. Indeed, the AHL diffuses rapidly into the medium during the first 5 hours, then the concentration gradient decreases and the diffusion is slower. However, if the bacteria produce too AHL, the diffusion to colony n+1 will be in the first 5 hours but affect the colony n+2 after 24h. In the ideal case would have bacteria produce about 1 nmol per well of AHL.

Figure 6: Radar graph of AHL diffusion into petri dish.