The method of choice is an agent-based model that allows us to see the behaviour of the whole nitrogen fixing bacterial community under the influence of a chemoattractant – naringenin. The software used is SimBiotics [1], the agent-based modelling tool developed at Newcastle University. SimBiotics provides a way to visualise stochastic simulations via real-time animations. Supported by data from our chemotaxis experiments and growth curves (link), the model was able to predict the microbial behaviour.

The model assumes infinite resources, i.e. no competition between the species. The bacterial species present are Azospirillum brasilense, Herbaspirillum seropedicae and engineered Pseudomonas sp. There are 30 Pseudomonas cells placed on the top side of the modelled area representing the rhizosphere and 100 cells of initial populations of each nitrogen fixing species capable of demonstrating a chemotactic response distributed randomly in the simulated space (Figure 1).

The growth of the nitrogen fixing bacteria is described by the first order kinetics (Reaction 1). To obtain understanding of bacterial growth, we monitored the change in absorbance (600 nm) of our nitrogen fixing bacteria grown at 30 ˚C for 72 hours. These data were then converted into cell density after experiments to identify cell count at specific optical densities. By doing this, we obtained a conversion ratio. This allowed us to understand growth rates in a way that could be accurately incorporated into the model. As soon as the bacteria reaches the size approaching double its starting size (Table 1) it divides into two cells of the same length.

The bacteria’s chemotactic movement is modelled with a modified version of micromotility and tumble run. Cells perform run and tumble, sample the chemoattractant concentration in periods of time Δ_{t memory} and compare it to the current concentration; C(t). If the value of C(t) - C(t – Δ_{t memory}) is lower than one, the cell is more likely to tumble. Otherwise, a probability to tumble decreases with increasing gradient and the bacterium is less likely to stop running [1].

Naringenin forms the gradient according to the finite volume method of Fick’s law. The simulation domain is divided into non-overlapping subdomains and the flux between them is calculated with the equation shown in Reaction 2. The chemical is degraded with rate kA [1](Reaction 3).

Our lab work identified that above certain concentrations, naringenin kills bacteria. The threshold we set for the bacterial species (excluding Pseudomonas sp.) is based on the experiments we conducted in the biological laboratory where a concentration of 150 μM was found to be toxic.