The method of modelling we have chosen is an agent-based model that allows us to see how changes in the rate of naringenin production influences the behaviour of the whole nitrogen fixing bacteria community. The software we used is SimBiotics [1], the agent-based modelling tool developed at Newcastle University. SimBiotics presents a way to visualise our stochastic simulations via real-time animations. Supported by the data from our chemotaxis experiments and growth curves (link), the model can accurately predict the biofilm formation process.

Due to a lack of time and computational resources, we have excluded competition factor from the model assuming an infinite amount of resources. To make the model even simpler we have set the Pseudomonas layer to be steady. As no Pseudomonas growth is observed so we can focus solely on the nitrogen fixers behaviour.

The other bacteria growth is described by the first order kinetics (Reaction 1). To obtain understanding of bacterial growth, we monitored the change in absorbance (600nm) of our 3 nitrogen fixing bacteria grown at 30˚c for 72 hours. This data was then converted into cell density after experiments to identify cell count at specific optical densities. Through doing this, we obtained a conversion ratio. This allowed us to understand growth rate in a way that could be accurately incorporated into the model.

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 nonoverlapping 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). All data and sources are provided in Table 1.

Above certain concentrations, naringenin kills bacteria. The thresholds we set for the bacteria species (excluding Pseudomonas) is based on the experiments we conducted in the biological laboratory and its value is 150μM.

The model consists of three bacterial species (Pseudomonas fluorescens, Herbaspirillum seropedicae, and Azospirillum brasilense). Pseudomonas attaches to the top side of the modelled area which represents the rhizoplane. We described growth of nitrogen fixing bacteria using data from the laboratory and their morphology based on literature sources.