The digital bacterial-based minesweeper

We created a 2D spatio-temporal model of the Colisweeper bacterial game in order to evaluate our network and design. For the simulation, we used the software COMSOL Multiphysics. Most of the parameters we used in the model are derived from literature, and some are fitted. Note: For parameter values and references click on a parameter or see the parameters section.

Reaction-Diffusion Model

In our first spatiotemporal model, we wanted to find out if a suitable AHL gradient would be formed at all and validate the model with experimental data. In this case, the receiver cells (E. coli DH5α strain) have been transformed with a plasmid containing GFP. We simulated a spatio-temporal reaction-diffussion system in 2D with COMSOL Multiphysics.

AHL: Reaction-Diffusion Equation

To explain how the concentration of AHL changes over time, we have to consider the influence of two processes: local chemical reactions and diffusion which causes the molecule to spread out over the agar plate (Fig. 1).

Figure 1: General partial differential equation for AHL reaction-diffusion. D(AHL(r,t),r) is the diffusive term, R(AHL(r,t)) is the reaction term

For the Diffusion, the equation is a partial differential equation (Fig. 2) which describes density fluctuations over time and space. D_AHL(AHL(r,t),r) denotes the collective diffusion coefficient for AHL at location r. However, we are assuming that the diffusion coefficient does not depend on the density, i.e., D_AHL is a constant. The value reported in the literature for the diffusion constant corresponds to measurements performed in water at 25^oC. Since diffusion in our system happens in agar, we scaled the diffusion constant by a factor C_agar (Fatin-Rouge et al., 2004).

Figure 2: Diffusive term for AHL

For the reaction component, the change of AHL concentrations in time is given by a ordinary differential equation (ODE), that comprises production and linear degradation. The synthesis of the signalling molecule depends on the product of luxI gene. Now for the degradation, we consider that AHL degrades at different rates depending on the localization, i.e. cytoplasmic or extracellular. Given that the intracellular degradation is driven by enzymatic degradation, whereas the extracellular decay is a non active process. Our model also includes a dilution factor due to the cell growth (Fig 3).

Figure 3: Reaction term for AHL