Team:Bristol/Model
Our team produced two main models to inform on the design of our project and to simulate areas that we could not test practically. The ambitious nature of our project meant that there were a number of areas that can be supported by modelling, as we did
not set out to have a fully working prototype pod over the short summer, and these models will be of use to any future work on our project. The modelling aspect of our project was also one of the most interdisciplinary, with the engineers working
with the biologists on a directly overlapping subject. This required a lot of learning on both sides, as well as compromises (with the engineers encountering just how limited biologists are by the vast unknown at the biochemical level, and the
biologists learning just how much engineers love numbers)!
Our code is on Github
Single Cell Model
The single cell model incorporated a gene regulatory network (GRN) and the kinetics of our enzymes Nap and Nrf. Thus, we were able to obtain rates for the conversion of nitrite and nitrate (i.e. dissolved NOx) to ammonia specifically within our system containing bacteria that are overexpressing the enzymes. An overview of this model is given below:
The GRN enabled us to model the production rates and extent of Nrf and Nap. The concentrations of both enzymes are able to be predicted when the rates of transcription, translation and degradation (of both mRNA and protein) are known. Because our construct included an IPTG-inducible promoter, the concentration of IPTG was relevant and therefore also had to be considered.
Having obtained enzyme concentrations from our GRN or estimating them, the next step was to model the kinetics of these enzymes within a cell. Modelling the enzyme kinetics involved understanding of differential equations, and the derivations are listed in the modelling supplement PDF. This model takes initial concentrations of all substances present and rate constants as inputs; a sample result is given below (note the values are arbitrary).
Given this model, we then searched the literature extensively for all the constants we required. With valuable correspondence with Professor Julea Butt (of the University of East Anglia) we were able to obtain some values for the required
constants (Kcat, Kd and Km) for both enzymes, however we found that these values came from conflicting sources using very different measurement techniques, rendering them of little use for our modelling. Equally, we were unable find any values
for the Kcat and Kd of Nap. Listed below, however, are the values we were able to find:
*Value obtained is in Paracoccus pantotrophus, E. coli values being absent in the literature
There are a number of factors that could influence the system that we have not incorporated in the model. These include the rate of uptake of nitrate/nitrite into the periplasm by the cells, but E. coli are equipped to do this and we assume
that this will not be rate limiting. We are also assuming that ammonia produced will diffuse out of the cell and not be toxic; E. coli are tolerant of fairly high ammonia concentrations. If the ammonia did begin to be toxic to the cells, a
future amendment to pod design could be to actively remove ammonia from the bacterial component to be fed into the fuel cell.
The combination of the GRN (giving us enzyme concentrations) and the enzyme kinetics (giving us the rates at which our substrates (nitrite and nitrate) are converted to product (ammonia) provides the information required to establish the capacity of an E. coli cell to metabolise NOx, i.e. the single cell model.
Future work
In future the single-cell model could be scaled up to a population model, such as Bristol iGEM 2008’s software BSim. Within such an agent-based model, each "agent" would represent a bacterium overexpressing our enzymes, which degrade NOx as per the enzyme kinetics equations. Rules can be added to each cell to define its viability in the presence of the overexpressed enzymes or of ammonia, as well as longevity and random efficiency.
This population model can be fed with data from the atmospheric model – i.e. accurate NOx concentrations in the city of Bristol - to enable us to simulate the entire system that would be contained within a pod, assessing efficiency, nutrient requirements and other factors that would influence pod design, such as the necessary size of the pod, as well as the prediction of problems that may arise. This enabled a more realistic simulation of how efficient our pods would be in a real-world setting.
References
1. Lockwood, C. W. J. et al. Resolution of key roles for the distal pocket histidine in cytochrome c nitrite reductases. J. Am. Chem. Soc. 137, 3059–3068 (2015).
2. Gates, A. J., Butler, C. S., Richardson, D. J. & Butt, J. N. Electrocatalytic reduction of nitrate and selenate by NapAB. Biochem. Soc. Trans. 39, 236–42 (2011).
Atmospheric Modelling
Motivation
The BREATHE project aims to reduce NOx pollution levels around Bristol and other urban areas by placing pods with genetically engineered E. coli bacteria that convert NOx into Ammonia. In order to make the biggest impact whilst minimising costs it is crucial to have pods placed in strategic areas of high pollution. To achieve this we have developed a simple atmospheric model to predict the pollution levels in Bristol city.
Aim
The aims of this model are:
• Predict levels of NOx pollution to a reasonable accuracy.
• Find areas of high NOx concentration in Bristol City depending on the wind conditions.
• Use real traffic flow and car engine data to generate inputs.
• Predict the effectiveness of placing Pods in strategic points.
Model
We need to be able to model the behaviour of NOx molecules in the atmosphere and predict how they propagate over time. The main considerations for the model are to capture the effects caused by wind, diffusion and the sources of NOx pollution. An appropriate equation for this is the advection-diffusion equation shown here.
where:
- • f is the concentration of NOx. ug/m²
- • u is the velocity field. m/s
- • c is the diffusion constant. m²/s
- • S is the source value of the production of NOx. ug/m²s
This is the underlying equation used in the model and is solved numerically by taking a Forward Time Central Space (FTCS) finite difference scheme, derived using a Taylor series expansion. Further details regarding the model and describing how this equation is derived can be found in the modelling supplement document.
Parameters
In order to run the simulation and achieve realistic results we required real input data and parameters. The diffusion coefficient of NO2 was used and found to be approximately 1.36×10⁻⁵m²s⁻¹ [1]. Realistic
wind conditions in Bristol could be found from the Met Office [2] however, as the weather varies throughout the year in the UK a range of wind conditions could be used.
Data for the NO2 sources is not something that is available for the entire Bristol city area or for any city as a matter of fact. Therefore, a plan was devised in order to estimate what the rate of pollution production would
be for a given type of road. This was done by aggregating data from different databases together to come up with an approximation. The steps involved are shown in the diagram below.
Traffic Flow Data
Data from the UK Department for Transport on the Annual Average Daily Flow (ADDF) on A roads and Motorways in Bristol City [3] was used to estimate traffic flow statistics. The database consists of actual and estimated data for a large amount of A Roads/Motorways in Bristol. The data was aggregated into the different road types and their respective means calculated. A histogram showing the distribution of the data and the mean values are shown below.
Figure 1: Two plots showing the distribution of traffic flow for A Roads (Left) and Motorways(Right) in Bristol City with the mean value shown for both..
The means were normalised against a 24 hour period and the road distances to get the following values representing the traffic flow for every metre second.
Table 1: Average traffic flow values based on AADF traffic data for different road types.
| Road Type | Average Traffic Flow (1/ms) 1×10⁻³ |
|---|---|
| Motorway | 1.0436 |
| A Road | 0.4891 |
| *B Road | 0.2445 |
*No data was available for B Roads in Bristol and so it was grossly assumed that it would be half of an A road traffic flow.
Petrol to Diesel Ratio
NOx pollution varies dramatically between petrol and diesel with the latter being the bigger source of pollution. In order to account for this it was important to get data regarding the distribution of different car fuel types currently being used in the UK. This data came from UK Department for Transport Vehicle Licensing Statistics [4] on the car fuel type distribution for the UK.
The database included data for Gas, Hybrid, Electric and Other vehicle fuel types. Because these were in such small percentages, some of which don't produce NOx pollution, so they were ignored in the simulation.
Table 2: Percentage of UK cars based on engine fuel type.
| Fuel Type | Percentage of UK cars |
|---|---|
| Petrol | 59.7 |
| Diesel | 39.1 |
| Gas | 1.0 |
| Electric | 0.1 |
| Other | 0.1 |
Engine Pollution Statistics
Data was required in order to quantify how much NOx pollution one car emits. This data was available from the UK Department for Environment, Food & Rural Affairs [5].
Engines have improved over the years and produce less and less pollutants with each new generation. As it was not possible to get data regarding the distribution of emission standards for all the cars in the UK, it was assumed all cars emit at the level of the Euro IV standard.
Table 3: Car NO2 emission levels based on fuel type and engine emissions standard for different environmental areas.
| gNOx/km | Emissions Standard | Urban | Rural | Motorway |
|---|---|---|---|---|
| Petrol | Euro I | 0.257 | 0.368 | 0.663 |
| Petrol | Euro II | 0.229 | 0.245 | 0.370 |
| Petrol | Euro III | 0.137 | 0.147 | 0.222 |
| Petrol | Euro IV | 0.073 | 0.078 | 0.118 |
| Diesel | Euro I | 0.537 | 0.465 | 0.693 |
| Diesel | Euro II | 0.547 | 0.505 | 0.815 |
| Diesel | Euro III | 0.547 | 0.505 | 0.815 |
| Diesel | Euro IV | 0.273 | 0.253 | 0.407 |
Ordnance Survey Maps of Bristol
An important part of the simulation is knowing where to place the source values. This was calculated by obtaining shapefile data from the Ordnance Survey (OS) [6] for all the roads in Bristol and converting it to a set of grid points using the Bresenham’s line algorithm.
This presented itself with the issue that the traffic flow data and engine pollution statistics don’t match directly to all the road types given in the OS road data. The data was matched depending on which data was the most relevant and are shown in the table below along with the calculated source values.
Table 4: Calculated source values for different OS road types based on other aggregated pollution and traffic data.
| OS Road Type | Average No. Cars [1/ms 1×10⁻³] | Engine Emissions Environment (Petrol/Diesel) [µg/m] | Source Value [µg/m²s] |
|---|---|---|---|
| A Road | 0.4891 | 0.078 / 0.253 | 0.2360 |
| B Road | 0.2445 | 0.073 / 0.273 | 0.0791 |
| Local Street | 0.2445 | 0.073 / 0.273 | 0.0791 |
| Minor Road | 0.2445 | 0.073 / 0.273 | 0.0791 |
| Motorway | 1.0436 | 0.078 / 0.253 | 0.5036 |
| Pedestrianised | 0 | 0 | 0 |
| Primary Road | 1.0436 | 0.078 / 0.253 | 0.5036 |
| Private Road | 0 | 0 | 0 |
Calculating Source Values
To calculate the rate of change of NOx concentration for a given road type an empirical formula was created based on the data gathered that satisfies dimensional homogeneity:
Assumptions
As with any modelling there are some assumptions made:
• Although NO and NO2 are unstable, this instability mostly arises from them switching between each other through atmospheric processes therefore, together they can be considered mostly stable.
• Highly diffusive effects of turbulence are ignored.
• There are no viscous effects experienced by NOx gases when travelling through the atmosphere.
• Modelling the canopy above the streets as complex flows at street level are hard and expensive to model.
• All engine emissions are similar to that of the Euro IV standard.
• B Roads in Bristol see on average half as much traffic as A roads.
Results
The simulation was computationally expensive to run due to the small resolution used to capture road details whilst looking at an entire city area. In the end the simulation was only run for a zoomed in section of the city center. Five runs were completed in total with varying wind speeds and directions and the results of the simulations are shown below. Surrounding building, roads, and rovers were included in the background of the plot to give those unfamiliar with Bristol an idea of how the pollution looks over the city area.
Figures 4, 5, 6, 7, 8: Five plots showing the NOx concentration levels around the city of Bristol for winds varying from 5-15mph in varying directions.
Conclusion
The simple advection diffusion equation captures the plume behaviour of the pollution adequately, as it is progated across the city. Currently there are no citywide NOx measurements to compare this data with but, there are a couple air quality measurement stations in Bristol. Overall the results from the atmospheric modelling were surprising, with the level of NOx concentrations being similar to levels recorded at the Bristol, St. Pauls measuring station [7]. The concentrations are still on the low side with only some areas reaching the levels that have been recorded previously in Bristol. It can be seen that the pollution builds up when there are many neighbouring roads. This means that NOx concentrations from outside the computation area is being neglected and the calculated levels are going to be lower that they should be.
The diffusion coefficient caused a lot of issues regarding the stability of the numerical solution therefore, the timestep and change in distances had to be altered to provide stability at the loss of smoothness in the solution.
The model was able to satisfy most of the original aims set out in the beginning. The NOx levels were predicted to within a reasonable accuracy compared to measured data. Real traffic data along with engine emissions data were used to create succesful estimates of the source values used in the simulation inputs. Results also show areas of high NOx concentrations depending on the wind conditions which can be used to strategically place pods with the aim of reducing pollution. We were not able to assess the impact our pods would have in removing pollution. This was due to not having sufficient modelling and lab data to accurately predict how much the pods would clean up.
In going forward with these results there are a couple of things we would like to address in the future. The most important is getting data for our pods and inputting it into the simulation so we can build a picture of how effective these pods will be once placed in strategic areas. In order to create a more accurate model it would be good to refine the data used to create the source values. Instead of generalising the traffic data it would be better to apply it to each individual road seperately. As well as having a distribution of different engines with different emissions standards instead of solely choosing the Euro IV standard. This would require a lot more time and data processing which is why it was not covered during this project. Lastly the computational area needs to be increased to capture the entire Bristol area. This will require more computing power or the grid resolution will have to be lowered in order to run the simulation in a reasonable amount of time.
References
1. Cape, J. N., Review of the use of passive diffusion tubes for measuring concentrations of nitrogen dioxide in air. Retrieved from [accessed 01/11/2017].
2. Met Office., UK Weather Forecasts Retrieved from [accessed 01/11/2017]
3. Department for Transport., Traffic Data, Annual Average Daily Flows Retrieved from [accessed 01/11/2017]
4. Department for Transport., Licensed cars by propulsion or fuel type: Great Britain and United Kingdom Retrieved from [accessed 01/11/2017]
5. UK Department for Environment, Food & Rural Affairs., Nitrogen Dioxide in the UK, Chapter 2, p[40-41] Retrieved from [accessed 01/11/2017]
6. Ordnance Survey., CDRC 2015 OS Geodata Pack - Bristol, City of (E06000023).
7. OpenAQ., The Open Source Air Quality database., Retrieved from [accessed 01/11/2017]
