The digital bacterial-based minesweeper

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

Reaction-Diffusion Model

In our first spatio-temporal model, we wanted to find out if (1) a suitable AHL gradient forms at all and (2) validate the model with experimental data. Essentially we model the receiver cells (E. coli DH5α strain) being transformed with a plasmid containing GFP. Subsequently, we simulate a 2D spatio-temporal reaction-diffussion system with COMSOL Multiphysics.

AHL: Reaction-Diffusion Equation

The change of AHL concentration over time is influenced by two processes: (1)local chemical reactions and (2)diffusion; which causes the molecule to spread 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 diffusion, we have 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 assume 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 over time is given by an 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. DF is the dimensionless dilution factor, where N₀ is the initial concentration and N_m is the carrying capacity.

Finally, we need to specify the initial conditions (at time t = 0) and boundary conditions. At the starting point there is no AHL in the agar plate, thus the initial concentration is zero ([AHL(r,t=0)] = 0 M). For the boundary condition, we take into account that there is not flux out of the agar plate.

Figure 4: Neummann Boundary Condition.