Values for the sizes of the bioreactors and concentrations of IAA, Phosphate and Nitrate were obtained from our interviews conducted for integrated human practices, which you can read more about by clicking here!

The model was performed using equations from a paper written by W. Brock Neely et al. (1976) to model the spillage of Chloroform into the Mississipi river. However, we altered the parameters to explore the leakage of auxin, phosphate and nitrogen into the river Thames. The equation below is used to determine the concentration of compounds in compartment n at time t. EQ1 is equation used

M/V describes the concentration of the contaminant. The section following M/V describes the flow of the river from compartment to compartment. The exponential section describes the rate at which the contaminant leaves the system. In Brock Neeleys paper modeled chloroform which is highly volatile therfore the rate constant of the contaminant leaving the system in his paper was the evapouration constant and therefore we also chose to use the evapouration constant.

Figure 2 shows the values for the evapouration constants of each contaminant in meters per second.

In figure 3 we can see from graph A and C that due to the assumed high rate at which IAA and Nitrate leave the river their concentrations reach negligable amounts in 0.1s-0.15s. However, we can that from graph B that phosphate leaves the river much slower and from further modeling we found that it almost never leaves the river and at all points it is higher than the government regulation level of 0.1g/L as described before. Initially, Nitrate also is above the government regulation level of 0.5mg/L, however it quickly leaves they system and is therfore not problematic.

Based on our initial modeling we decided to investigate phosphate further to assess it's impact on the river. Therefore, we decided to investigate the concentration-time-distance profile of phoshpate. From figure 4, we can see that over distance the phosphate concentration drops quickly, but then plateaus, and stays at a consistent level. This suggests that phosphate would require cleanup.

From this we wanted to get a better idea of the concentration-distance profile of phoshpate. Therefore, we took the peak concentration of phoshpate in each compartment over a distance. Figure 5 represents the max concetration of phoshpate over a distance. What we can see is a similar quick drop in concentation (as in figure 3), followed by a steady decrease until 50m where the concentration drops much faster. At all distances, we can see that the concentration of phosphate is above the govenment regulation level. From this we suggest that during a leakage, the first 100 meters of a river needs to be cleaned of phosphate and evrything past it should be closely monitered.

Our model has been implemented in a MATLAB development environment and all of our code and parameters can be accessed via our supplementary materials link for any future iGEM teams to use.

Assumptions

Impact on Implementation

Leakage of phosphate is the primary concern as it is more persistent across longer distances. The Department for Environment, Food and Rural Affairs in the UK states that the concentration of phosphate in rivers should not exceed 0.1 mg/L. In our worst case scenario of a large bioreactor leaking, the starting concentration is 6000 g/L which is significantly above the limit and it remains above government regulation levels. Therefore, in the implementation of our project, we would recommend lower phoshpate concentrations in bioreactors.

Limitations of the Leakage model

Our model relies on estimations for some parameters, such as the evaporation rate of Nitrogen and IAA. Therefore, if we were to implement our project, we would run an experiment to determine these parameters rather than making educated guesses. We would also run an experiment similar to what W. Brock Neely (Neely, 1976) ran to determine the optimal mixing length to fit the data. Also, we did not model the leakage of BloomAid itself. This would require us to add an element to the equation used to model bacterial growth while moving.