Alternative Roots

Microbial Community Modelling


In the lab, we demonstrated that Pseudomonas sp. was a genetically tractable chassis organism, and that it can colonise Arabidopsis roots. One proposed application of for our root-colonising Pseudomonas sp. endophyte chassis is to produce the chemoattractant naringenin. The substance, as demonstrated in our experimental work, attracts free-living nitrogen-fixing bacteria. Under the right conditions, this could benefit the plant by increasing nitrogen availability, and reduce use of synthetic nitrogen fertilisers.

We therefore propose that plant roots, colonised with our Pseudomonas sp. and carrying an operon containing the four genes encoding naringenin biosynthesis enzymes, would create a naringenin concentration gradient in the surrounding soil environment. To provide insight into the effect that naringenin production would have on the surrounding microbial community, and to provide visualisations for ourselves and those we have engaged with, we developed a microbial community model to simulate what is happening in the soil around a Pseudomonas sp. colonised root.

Model Design

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 sp. 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 100x50x50 μm (Figure 1).

Figure 1. Visualisation of the model in time step (from the left to the right respectively): 0, 100, 250, 500.

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 Δt memory and compare it to the current concentration; C(t). If the value of C(t) - C(t – Δt 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.

μ = Gr ± Gv
Reaction 1. first order kinetics.

Ji→j = DcSij/dij(uj-ui)
Reaction 2. flux between neighbouring subdomains (finite volume method of Fick's Law).
Dc - diffusion coefficient, Sij - cross-section, dij distance between the centres of the two subdomains, uj and ui concentrations in the subdomains.

A → ⌀ kA
Reaction 3: degradation of naringenin.

Parameter Value Source
Growth Rate Herbaspirillum seropedicae 4*10-4 fg per second growth curves (link)
Growth Rate Azospirillum brasilense 1.314*10-4 fg per second growth curves (link)
Naringenin concentration threshold 150 μM experiment (link)
Diameter, initial length of Herbaspirillum seropedicae 0.7μm, 1.5μm [2]
Diameter, initial length of Azospirillum brasilense 0.5μm, 2.9 μm [3]
Diameter, initial length of Pseudomonas sp. 0.5μm, 1.5μm [4]
Table 1: Table of the parameters used to create the soil community model and the references.


We ran three simulations 500 time steps long (1 time step is an equivalent of 100 seconds) with three different naringenin biosynthesis rates: 0.1, 0.01 and 10-6 μmol per second per cell. We observed that the simulations lead to a formation of the biofilm on the top side of the modelled area (root) in each case. As the bacterial growth is independent from the other parameters, the number of cells changes were identical in all three simulations (Figure 2). We have also measured the naringenin concentration in the point very close to the root (where Pseudomonas sp. cells were placed) (Figure 3) and average thickness of the biofilm formed (Figure 4).

Figure 2. Number of cells versus time (given in time steps)

Figure 3. Concentration of naringenin close to the root against time given in time steps.
A: 0.1 μmol of naringenin production per second per cell, B: 0.01 μmol per second per cell, C: 10-6 μmol per second per cell.

Figure 4. Average biofilm thickness against time given in time steps.
D: 0.1 μmol of naringenin production per second per cell, E: 0.01 μmol per second per cell, F: 10-6 μmol per second per cell.

Conclusions and Future Development

The presented model indicates that the nitrogen-fixing bacteria attracted to the root forms biofilms over time. A. brasilense cells grow faster than H. seropedicae and may dominate the system. If deployed in contained environment, as proposed by Alternative Roots, it would be reasonable to attempt to optimise the initial species populations ratios to obtain a more diverse nitrogen-fixing community. The results show that the naringenin point concentration variations are more stable when the biosynthesis rate is very low and peak and drop when it is higher. They are however, not likely to reach a concentration in which bacteria are killed in the first 5000 seconds, or while the biofilm is forming. Biofilm formation looks the same in all three cases is a result of the underpinning mathematics behind the chemotaxis modelling in the Simbiotics software as explained in the Model Design section.

The current model represents a very small fraction of the total soil community. With more chemotaxis experiments performed in the laboratory we could perform a more ambitious model that would provide more data about dynamics of the biofilm formation. Likewise, the identification and chemotactic characterisation of more nitrogen-fixing bacteria that are attracted to naringenin could be fed into the model allowing us to optimise beneficial starting concentrations of each bacteria when deployed in controlled and contained growth scenarios. Moreover, knowing more about Pseudomonas sp. behaviour in the root, we could also include its kinetics in the model and learn how it interferes with the other species. Supported with data from experiments on plants on the effectiveness of the nitrogen-fixing by the microbes, the model could help designing an ultimate biofertiliser by indicating the right ratio of the bacteria species and the most effective chemoattractant’s biosynthesis rate.

link to download the model file

References & Attributions

Attributions: Patrycja Ubysz, Connor Trotter

1. Naylor J, Fellermann H, Ding Y, Mohammed W, Jakubovics N, Mukherjee J, Biggs C, Wright P, Krasnogor N (2016) Simbiotics: A Multiscale Integrative Platform for 3D Modeling of Bacterial Populations. ACS Synthetic Biology 2016 DOI: 10.1021/acssynbio.6b00315 (link)

2. Baldani JI, Baldani VLD, Seldin L, Doebereiner J (1986) Characterization of Herbaspirillum seropedicae gen. nov., sp. nov., a Root-Associated Nitrogen-Fixing Bacterium International Journal of Systematic and Evolutionary Microbiology 36: 86-93, doi: 10.1099/00207713-36-1-86

3. Tarrand JJ, Kried NR, Doebereiner J (1978) A Taxonomic Study of the Spirillum lipoferum Group, with Descriptions of a New Genus, Azospirillum gen. nov. and two species, Azospirillum lipoferum (Beijerinck) comb. nov. and Azospirillum brasilense sp. nov. Canadian Journal of Microbiology 24: 967-980

4. Rhodes ME (1959) The Characterization of Pseudomonas fluorescens. Journal of General Microbiology 21: 221-263