Model
Modelling
Introduction
This year, our modelling focus has been primary on enzyme kinetics involved in the production of pterostilbene in our genetically engineered E. coli. From this modelling we aimed to validate the optimal plasmid number copy and promoter strength used by the wet lab team to engineer E. coli to achieve the highest possible yields of pterostilbene, viable for therapeutic use, whilst also considering limitations with E. coli metabolism.
Additionally, we aimed to determine the oral bioavailability of pterostilbene in humans, alongside its blood brain barrier (BBB) permeability. Through discussions with experts, namely Professor Ian McFazdean, and limitations with numerical data needed for these models, we did not end up completing this, however we made some calculations based on details we did know and curated protocols for future modelling we would expect to execute beyond the scope of iGEM.
This page details our journey within modelling, including the limitations met at particular stages and how we overcame them.
Pterostilbene synthesis in E. coli modelling: (enzyme kinetics modelling)
- Intro to what this modelling achieves
- The steps involved in reaching our model
- The inspirations (Uppsala_Sweden 2013 model) and improvements from this
- The Parameters used
- How the information used in the model was chosen
- The results from our model
- Analysis and conclusions of these results
Other models we considered/plan to execute in later stages:
- Blood-brain barrier (BBB) permeability
- Bioavailability
- Issues we had with both and why we did not consider either
- When we plan to execute these and the protocols and parameters needed
- Molecular docking
Kinetic Model
Model Characterisation
Assumptions
- We can model the metabolic strain of the synthesis on the E. coli by tracking the amount of intracellular L-Tyrosine available for the cell for carry out normal cell function .
- That toxic intermediates such as P-coumeric acid have a negligible effect on the cell function.
- S-adenosyl methionine is readily available within the cell.
- The reaction takes place within 3 hours or less.
- The degradation rate of mRNA is more than 10 hours.
- The constants can be reasonably be reduced
Table 1: Reagents being considered within the model and the proportionality constants for their ROC
Table 2: Relationships between reagents and the resulting ODEs
Table 3: Constants and their derivations.
Model Outputs
The model can be run two different ways. One version of the code, produces two dimensional outputs and relies on user input. It produces three figures, as shown below and can only account for one combination of promoter strengths and copy number.optimal plasmid number copy and promoter strengths.
Final Model and Conclusions
The first final model (Fig 6a) only accounts for one combination of promoter strengths and produces the pterostilbene production over time for this combination, dependent on the plasmind copy number
The second final model shown (Fig 6b) simulates the result of the synthesis for every possible combination of promoter strength and plasmid copy number. This means the model accounts for 65536 unique iterations. Many of these iterations are excluded from consideration when deducing the ideal Pterostilbene yield as they are not viable for the E. coli , without forcing the cell to undergo impractical amounts of metabolic strain. Note how the model favours moderate copy numbers, and how the output pterostilbene concentration decreases at too high of a copy number.
Before attempting this model, we had no indication of the ideal plasmid copy number and promoter strengths to use that were not completely based on existing literature. Using the model described above we were able to suggest two plasmid copy numbers that would give the highest yield according to the model (5 and 13). In terms of justifying the choice of promoter strengths, the model also confirmed the use of the selected Anderson promoters provided the largest yield of pterostilbene (0.043, 0.043,0.043,0.043). The software is very malleable and with adjustments could be used for similar pathways. In terms of minimising computational time, the code only takes around 5-10 minutes to produce a model for all 65536 combinations.
Overall following the use of the model we were able to generate a prediction of the maximum output pterostilbene concentration and the ideal promoter strengths/copy number combination, whilst making simplified assumptions to represent metabolic strain. In the future, we would aim to use more complex equations to model metabolic strain, by applying principles regarding cellular trade-off the model would be able to provide data that could be extremely useful by allowing the user to identify the best relative combination of promoter strengths and plasmid copy number. We would look to include more variables such as gene length, ribosomal binding site and half-life of the protein. We would then look to use optimization algorithms to maximise pterostilbene yield, whilst minimising metabolic strain. The outputs would then be tested via wet lab.