PHOCUS

# 2D biofilm simulation

The aim of PHOCUS is to develop a fast acting biopesticide. Using our first model, we showed that PHOCUS can produce high toxin concentrations within seven days. However, in that model we made the simplifying assumption that our system is always well-mixed, making it in effect ‘0-dimensional’. In the desert locust gut, bacteria most likely reside in microcolonies [Dr. O. Lavy, personal interview, 1, 2]. The spatial organization of cells in these microcolonies can influence phage propagation and toxin production in the locust gut. We hypothesized that spatial effects, such as phage mobility and substrate diffusivity, may have an important influence on the performance of our biopesticide. We therefore modelled the temporal evolution of the number of bacteria, phages and produced toxin with a more detailed 2D biofilm simulation framework, to investigate the influence of these spatial effects on toxin production (Q1). Furthermore, as our biopesticide does not target all bacteria of the locust gut, we investigated the influence of biofilm heterogeneity on the resulting toxin production (Q2).

## Model Explanation

We were inspired by a model simulation created by Simmons et al. [3]. We adapted this model to help us to answer our research questions (Figure 1).

In this model we simulate discrete bacteria and phages on a defined 2D grid. The growth of bacteria is governed by growth-limiting substrate that diffuses from the top of the 2D space into the biofilm, where substrate is depleted due to consumption by bacteria. Based on the substrate availability, bacteria grow and divide - filling up the grid. Once the number of bacteria on a given grid point reaches its maximum volume, the bacteria are redistributed to nearby grid points. Convection is modelled implicitly: the biofilm surface erodes in a height-dependent manner, reflecting the increase in shear force with distance from the surface (biomass erosion) and any free floating bacteria are removed from the system (biomass detachment). Phages move in the system according to a random walk, where the probability of moving depends on the interaction with the biofilm. Phages either associate with bacteria in the biofilm and initiate infection or diffuse into the bulk liquid, where they are removed from the system due to convection. Infected cells lyse after a defined time, releasing new phages and our locust specific toxins as they do so.

This biofilm framework simulates all these aforementioned events in discrete time steps ($$dt$$) along the following order:

1. Diffusion of the nutrient substrate
2. Biomass growth and division
3. Lysis of infected bacteria and phage burst
4. Erosion of biomass
5. Phage movement
6. Detachment of biomass
7. Biofilm relaxation
8. Phage infection

The toxins $$T$$ were added to the system by counting the lysed cells ($$X_I$$) multiplied by the number of toxins produced per cell ($$\alpha$$) and are removed from the system with degradation rate $$\eta$$ (Eq. 1).

$$\frac{dT}{dt} = \alpha X_{lysed}(t) - \eta T \tag{1}$$

As our toxins are small compared to bacterial cells and a single time step $$dt$$ is relatively large (60 minutes), we assumed that the toxin diffusion is instantaneous compared to the other processes in the simulation. We therefore implemented the toxin production in a space-independent manner. This implementation should be sufficient to study the influence of spatial effects such as phage mobility (Q1) and biomass heterogeneity on the toxin production (Q2).

A more detailed explanation of the model can be found below:

## Q1. Which spatial effects are key for the performance of our biopesticide?

The ultimate goal of our biopesticide PHOCUS is to kill the locust within 7 days. To investigate the effect of spatial effects on our biopesticide, we analysed the influence of phage mobility on the maximum produced number of toxins toxin. For increasing values of the impedance $$I$$, the ability of the phage to diffuse through the biofilm decreases. We performed a parameter sweep varying the impedance $$I$$ and burst size $$\beta$$ (Figure 10). The main result of this parameter sweep is that the burst size ($$\beta$$) could be used to compensate for impaired phage mobility.

Therefore, selecting a high burst size phage is an effective strategy to compensate for impaired phage mobility and thus results in a higher toxin production.

To further investigate which strategies could be used to compensate for impaired phage mobility, we performed a second parameter sweep to study if increasing the initial phage concentration would increase the maximum number of produced toxins (Figure 11).

This sweep again demonstrates the importance of phage mobility to toxin production and indicates that phage propagation and toxin production do not depend much on the initial phage concentration. This result indicates that biofilm structures actually promote phage propagation, as all bacteria are packed relatively close together. For our biopesticide, this implies that only a small number of phages would have to be delivered to a microcolony in the gut to induce toxin production. This makes PHOCUS feasibly suited for application using the Ultra-Low-Volume standard of the FAO.

## Q2. What is the influence of biofilm heterogeneity on the resulting toxin production?

Our bacteriophage-based biopesticide will most likely not target all bacteria of the locust gut. Our second goal of this model was to investigate the effect that this biomass heterogeneity could have on the toxin production. Therefore, we performed additional simulations where a second bacterial species was introduced in the system. This species had exactly the same bacterial properties as the first species, but that was non-susceptible to the phage. During these simulations, we varied the fraction at which susceptible/non-susceptible cells were introduced in the system. For each fraction, the simulation was repeated 3 times. Figure 12 shows the result of such a simulation that started with 5% susceptible and 95% non-susceptible cells.

From this result, we could qualitatively observe that in the simulation, the susceptible cells (red) were not getting reached while there were still phages in the system. In this simulation, this led to almost no toxin production (Figure 13, yellow line), while the other two replicate simulations led to an expected toxin production profile (Figure 13, green and blue lines).

From this we can qualitatively observe that low fractions of susceptible bacteria in the biofilm leads to a decrease in the probability of phages to actually propagate before being removed from the system by convection. We only observed this qualitative behaviour for susceptible bacteria fractions smaller than 10%. For higher fractions we did not observe any difficulty for the phage to propagate and produce toxins, which again demonstrates the strength of our biopesticide in toxin production in such biofilm structure. For our biopesticide this would imply that, if the fraction of bacteria we target is too low, then the effectiveness of our biopesticide can be reduced. PHOCUS should therefore target a minimum fraction of the bacteria in the gut to prevent loss of effectiveness.

Due to the probabilistic nature of some processes in this framework, we were only able to draw qualitative conclusions from our simulations. To strengthen the observed qualitative behaviour we suggest to increase the amount of simulation repeats to eliminate any probabilistic variance. Furthermore, to be able to more quantitatively conclude on the effect of the fraction of susceptible/non-susceptible bacteria, we suggest performing an extensive parameter sweep varying this fraction. From this data, it can be determined if the relation between fraction of susceptible cells and the resulting produced toxin is linear or if spatial constraints prevent the phages from infecting the susceptible bacteria at lower fractions.

## What did we learn?

With this model, we demonstrated the importance of phage mobility in the ability of our biopesticide to produce high toxin quantities. Interestingly, we showed that selecting a phage with a higher burst size could help overcome limitations in phage mobility and would therefore be a good strategy to increase toxin production. This observation differs from the results of our first model, where we showed that increasing the burst size has a negligible effect on the maximum produced number of toxins (see model 1). From this, we conclude that phage infection and toxin production in spatially structured biofilm contexts fundamentally differs from ideally-mixed systems, as assumed in our first model. Furthermore, we showed that the initial amount of phages introduced into the system has a negligible effect on toxin production. From this, we conclude that biofilm structures promote phage propagation as cells are closely packed together. For PHOCUS, this is an advantage as only a small number of phages has to be delivered to a microcolony in the gut to induce toxin production.

Additionally, we showed that biomass heterogeneity, i.e. a biofilm consisting of both susceptible and non-susceptible bacteria, can lead to a decrease in the probability of phages to actually propagate before being removed from the system by convection. Our biopesticide should therefore target a minimum fraction of the bacteria in the gut to prevent loss of effectiveness.