We have produced this informative model, that provides knowledge into the scalability of our filtration system and incorporated it within a user-friendly interface on our wiki to inform the future implementation of our research. The model can guide future-users on the most efficient flowrate and volume of metal binding reactor (MBR) to use for their purpose.

It can be used to resolve the issue of knowing when the metal binding reactor is saturated as it informs when the E. coli in the metal binding reactor are too saturated to still be efficient, therefore, the filter needs changing. This can be used in conjunction with the 'backwash' method suggested by representatives at South West Water. For the 'backwash' method we would require two or more filters in series such that one can be turned offline without leading to a complete shutdown. Then we would pass water through the offline filter to be tested. The model can then help inform how often the water should be tested and can be rescaled for more accuracy based on these results.

How the Model Works

User Interface

We have a designed and developed a user interface for the model to make it easily accessible to future users. Once the users values are inputted and the "run model" button is clicked, the outputs for their specific inputs will be produced along with a graph of output concentration against time to provide a visual representation

Example Graphs and their Physical Explanations

Example 1

Using a small metal binding reactor, like the one in our prototype (which has a volume of 1.5L and a pump which allows for a flow rate of 0.07L/s) we will find that if we pump through a zinc solution of 10g/L with the intention of reducing the concentration to below 9g/L, then an inverse exponential decay curve is produced for concentration over time. This is because initially there are lots of unbound pili able to bind to the zinc ions and so a higher proportion of zinc ions is taken out of solution. As more pili become bound to the zinc ions, fewer collisions occur between the zinc ions and the unbound pili resulting in the zinc becoming bound less frequently. As such, the filter becomes less efficient and a lower proportion of zinc ions is taken out of solution until eventually the filter is not taking enough zinc out of the water to meet the desired concentration. A similar shape graph was obtained experimentally using a solution of mannose and unmodified MG-1655 E.coli.

Example 2

If, however, we had access to a metal binding reactor just ten times larger with a volume of 15 litres, then the model predicts that this graph would be obtained.The larger reactor needs replacing significantly less often. Initially the graph is almost horizontal with an output concentration of approximately 0. This is because there is such an abundance of pili in the reactor that the zinc ions are very likely to have a successful collision with an unbound pilus in the time it takes to get through the reactor. Thus, the vast majority of zinc ions entering the reactor become bound to pili. The exponential curve is also more pronounced. This is because the greater size of the filter and so the greater abundance of pili, means that smaller proportion of the pili need to be free in order to continue taking a sufficient number of zinc ions out of solution. As the proportion of free pili reduces, the number of successful collisions between pili and zinc ions decreases and so the number of free pili reduces far more slowly. This allows for an extended period of time when the filter is operating at a lower, but sufficient efficiency.

Example 3

On the contrary, if the volume of the metal binding reactor were reduced to just 1 litre, then the graph looks almost linear. This is because of the relative abundance of the zinc ions in comparison to the number of pili, means that each pilus is experiencing much more collisions per unit time and so the pili are all bound very quickly and there is no extended period of time where the reactor can operate at a lower efficiency, as in the other scenarios.

Stakeholder Engagement

Veolia Water

We contacted Veolia Water Treatment Plant, a current treatment plant that removes metal ions from contaminated mine water, to obtain feedback on the model, particularly to find out whether there were other outputs that it would be useful for the model to produce. Their response was that we had covered similar bases to those required at their treatment plant.

In order to inform the future implementation of our research we ran the model with values provided by a representative from Veolia water treatment plant to see how our metal binding reactor system would work at an industrial scale. We were provided with data for the minewater intial concentrations, final effluent permit limit (desired concentration) and the flowrates of the system. The volume of the metal binding reactor was estimated on the scale of their reactor chamber seen during our visit to the site. The model was ran for the values provided for Zinc and Iron. The values for the other 4 metals were not used for the following reasons: the inital concentration of Nickel and Copper were already below the final effluent permit limit, Magnesium did not have a final permit effluent limit and no data was provided for Cobalt.

The input values for Zinc were: Initial Concentration 19.95 mg/L, Desired Concentration 0.02 mg/L. The input values for Iron were: Initial Concentration 82.20 mg/L, Desired Concentration 3 mg/L. The Flowrate and MBR Volume were the same for both metals, with the Flowrate input 600 L/s and MBR Volume input 960000 L. Below is the graphs of output concentration against time for Zinc and Iron.

The graph indicates that our metal binding reactor system would be effective in extracting the metals down to their required concentrations from the minewater metal concentrations at an industrial scale.

Centre for Biomedical Modelling and Analysis

They suggested the idea of creating a user interface for the model to display on our presentation at the iGEM Jamboree. We built on this idea and integrated the model within a graphical user interface on our group website, as seen above.

Assumptions

We made an assumption for the "number of pili per E. coli". The decision made was based on information from literature (Group, 2017) (Christof K. Biebricher, 1984). We used sensitivity analysis to check the effect that an inaccuracy in this value would have on the output of the model and we concluded that it would not have a large effect on the output. Additionally, there may be a range of number of pili per E. coli but due to the large number of E. coli considered in this model we can assume an average for this. Another assumption made was that the metal ions will have the same binding rate to our modified pili as mannose have to the pili on the MG-1655 E. coli. With further time, however, it would be possible to alter the model to take this into account by comparing it to relevant experimental data. Additionally, this model implicitly assumes that the metal binding reactor is a long, narrow pipe. As such, if this reactor was in the shape of a wide vat then the results of our model may be less accurate.

Parameter Finding

Senstivity Analysis

We performed sensitivity analysis, on all of the parameters in the above table and the timestep that the model depends on, in order to identify the parameters requiring further investigation. Using MATLAB, we ran the model varying one parameter at a time over a range of values, keeping the other parameters constants. The output values were stored then plotted against the parameter to see the effect that a change in that parameter had on the output. See the graphs below which show the effect that a change the parameter ' E. coli per Unit Area' have on efficiency and output concentration.

Areas of high perturbation indicated the range at which parameters are sensitive because any change in parameters value has a larger effect on the output when in this range. In this graph we can see it occurs around 3X10¹¹ and below. Originally the value calculated for 'Number of E. coli per Unit Area' was 5X10¹¹ which is close to this region. This indicated that a small error in calculating this could have a large effect on the output. To deal with we sent off samples for imaging again and recalculated the parameter value to check for any errors, the recalculated value for this parameter is 9.22x10¹⁰.

Below are the graphs for the parameters ‘Surface Area of Torus’, ‘Volume of Torus’ and ‘Average Number of Pili per E. coli’ and ‘Timestep’.

We can see from the above graphs that the parameter values calculated for ‘Surface Area of Torus’, ‘Volume of Torus’ and ‘Average Number of Pili per E. coli’ are not in particularly sensitive regions. However, ‘timestep’ appears to affect the output value with greater perturbation as it increases in value. Therefore, it is important to keep the timestep value as low as possible to gain the most accurate value from the model, this is as expected.

The Model's Evolution

References