Team:NUS Singapore-A/shadow/Modelling
OVERVIEW
Modelling was heavily utilised to obtain a better understanding of our systems, as well as, shaping our experimental designs which helped us save unnecessary wastage of resources and time. We constructed models that allowed us to achieve the following:
- Preliminary study of our intended biochemical pathway
- Optimal genetic circuit design
- Proof that optogenetics can work in our systems and improve upon existing inducible/repressible light systems
- Simulation and optimisation of our entire experimental process
Our MATLAB scripts can be found here.
Our team started with the intention to produce dyes consisting of the primary colours, red, yellow and blue, that can be easily mixed to create a plethora of colours for the textile industry. However, we have decided to produce namely, Chrysanthemin (red) and Luteolin (yellow) instead. This decision was due in part to our interview with Mr Holger Schlaefke (link to our interview here), Global Marketing Manager of DyStar Pte Ltd, that advised us to produce vibrant colours, and how numerous past iGEM teams have attempted to produce Indigo (a colour similar to blue).
PART 1: THE BIOCHEMICAL PATHWAY
Goal of model
Thus, Wet Lab needs to verify the feasibility of producing these two flavone compounds in E.Coli from the starting substrate, Naringenin, by considering only the biochemical reactions using mathematical modelling in-silico (refer to the biochemical pathway in Fig 1.). In addition to this, we explore how enzyme concentrations affect our system in hopes that it may aid us in our experimental design.
Fig. 1 Biochemical Pathway from starting substrate Naringenin
Considerations
Since there was a competing biochemical pathway which produces Callistephin – an undesired product – for the production pathway of Chrysanthemin, it had to be considered in our model as well.
Methods
Using the ODE15s solver on MATLAB, we solved for the following ordinary differential equations (ODEs) with respect to time. The following parameters were obtained from literature1 and the ODEs were derived from the mass balancing of the Michaelis-Menten equation2. Initial enzyme concentrations were set to high (in excess) amounts to create a simplified model for our initial study of our biochemical system.
The chemical and differential equations for the model are shown below:
Therefore, in order to obtain the maximal velocity, V_m, of the enzyme acting on a particular substrate, the concentration of the enzyme is multiplied by its turnover rate, kcat.
Table 1. Parameters for preliminary study model
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| Parameter | Meaning | Value | Reference |
|---|---|---|---|
| [enzyme] | Concentration of enzyme reacting with the substrate | Predetermined parameter, but set to 10000nM for our initial | NA |
| Eve | Jackson | 94 | |
| John | Doe | 80 |
As can be observed from Table 1 above, the concentration of all enzymes was manually altered to observe the following effects:
- How each individual enzyme concentration affect the conversion rate of Naringenin into its desired products
- Whether production of desired flavonoids (Chrysanthemin and Luteolin) were plausible
Luteolin production was studied independently from Callistephin’s and Chrysanthemin’s production pathway since there is no competition between them. Production of Callistephin and Chrysanthemin were studied simultaneously.
Assumptions of model
- Negligible substrate degradation (these substrates refer to the starting compound Naringenin, as well as reaction intermediates such as Apigenin, Eriodictyol, Cyanidin etc.).
- Negligible basal expression of enzymes.
- No scarcity of bioproduction resources (nutrients, amino acids) and no other factors affecting production of enzymes (OD, cell stress, inhibition).
Findings
Fig. 2 Concentration (nM) of intermediates and final product (Luteolin) converted from Naringenin over time (hour)
Fig. 3 Concentration (nM) of intermediates and final products (Callistephin and Chrysanthemin) converted from Naringenin over time (hour)
The results prove that production of flavonoids was theoretically feasible in E.Coli, allowing for decent yield of Chrysanthemin and Luteolin. Assuming the starting amount of Naringenin substrate to be 20000nM, Fig. 2 illustrates the 100% conversion of Luteolin (yellow dye) in 5.3 hours, while Fig. 3 shows the production of ~11410nM of Chrysanthemin and ~2000nM of Callistephin in 8 hours. This indicates 57.05% Naringenin conversion at 8 hours, with 17.53% contamination in the final Chrysanthemin product. There is contamination because Callistephin is orange in colour and will alter the colouration of our desired red dye. This proves that there will be an unsatisfactory yield and purity of Chrysanthemin due to an existing competing pathway, pushing the flux towards Callistephin to be formed.
Alterations of the [enzyme] parameter in our script also show us that there could be an optimal enzyme-to-enzyme ratio for our system, as varying our enzyme concentrations allowed us to obtain vastly different yields of our final products.
Conclusions
Focusing on the production of Luteolin was the best way forward as flux control to obtain a pure Chrysanthemin product was too difficult and unfeasible due to time frame limitations. In future experiments, the Wet Lab team was also given recommendations to consider tightly controlling enzyme concentrations in order to achieve higher yield, which would influence future plasmid designs. Hence, optimisation of our genetic circuit would improve our Naringenin conversion rates.
PART 2: GETTING THE OPTIMAL GENETIC CIRCUIT
Goal
The genetic circuit should be an important design consideration as parts like the Ribosome Binding Site (RBS) affect the translation rates and thus, the concentrations of the enzymes, which would ultimately affect yield and conversion rates. Therefore, simulations to aid Wet Lab select RBS parts can help improve our system greatly.
The lab has two RBS parts available to them, namely rbsD and rbs34. However, two of the same RBS parts cannot be conjugated into our plasmids and thus, we have to decide which RBS we want to assign to FNS and F3’H.
The promoter site will be discussed in Part 3 as we plan to use light inducible and repressible promoters to reduce our need for chemical inducers.
Methods
Utilising characterisation data from a Synthetic Biology lab at E6 Engineering (NUS), we were able to compare relative strengths of rbs34 and rbsD by their ability to produce RFP. The final expression concentrations of varying inducer concentrations (of 0.002g/100ml, 0.008g/100ml, 0.031g/100ml and 0.125g/100ml) were compared between the two RBS systems and the average was taken for all inducer concentrations to obtain the relative strengths of the RBS systems. This is shown below:
Fig. 4 pBAD/rbsD RFP expression curve
Fig. 5 pBAD/rbs34 RFP expression curve
Table 2. Relative strengths of rbsD over rbs34
| Inducer Concentrations | Relative strength of rbsD:rbs34 |
|---|---|
| 0.002g/100ml | 2.75 |
| 0.008g/100ml | 2.3077 |
| 0.031g/100ml | 1.9667 |
| 0.125g/100ml | 1.3208 |
| Average | 2.086 |
Using the MATLAB script written above in Part 1 and the parameter values from Table 1, more constraints were added to our model by altering the [enzyme] parameter to simulate the different strengths of the RBS that we have determined in Table 2. This will allow us to determine which RBS system is the most suitable for FNS and F3’H respectively.
Assumptions of the model
- Samples were subjected to identical conditions during the characterisation experiments of rbsD and rbs34.
- Negligible substrate degradation (these substrates refer to the starting compound Naringenin, as well as reaction intermediates such as Apigenin, Eriodictyol, Cyanidin etc.)
- Negligible basal expression of enzymes (=enzymes are not being produced by the cell without any induction or human input).
- No scarcity of bioproduction resources (nutrients, amino acids) and no other factors affecting production of enzymes (OD, cell stress, inhibition).
- Production rates (= translation rates) of Red Fluorescence Protein (RFP) is representative of the production rates of the enzymes, FNS and F3’H.
Findings
Fig. 6 Conversion of Naringenin to Luteolin (rbsD assigned to FNS and rbs34 assigned to F3’H)
Fig. 7 Conversion of Naringenin to Luteolin (rbsD assigned to F3’H and rbs34 assigned to FNS)
By comparison, it is observed that 100% naringenin conversion occurs at the 2.4 hour mark for the rbs34/FNS and rbsD/F3’H system while 100% conversion for the rbsD/FNS and rbs34/F3’H system occurs at 4.7 hours. It can also be observed from Fig. 7 that 100% conversion occurs faster in the rbsD/F3’H construct.
Conclusion
A recommendation was given to Wet Lab to construct a gene circuit for rbsD/F3’H and rbs34/FNS.
After this, a proper study of light inducible and repressible promoter systems needs to be conducted to test for the viability of the promoter parts.
PART 4: THE COMPLETE MODEL
Goal
The model aims to facilitate the experimental design constructed by the Wet Lab team using in-silico simulations. This model would also serve as a guide to troubleshoot experimental design flaws as it’s a representative model of our entire system.
Methods
By constructing a mathematical model to simulate the Luteolin production process experimentally step-by-step, we are able to create a more comprehensive, accurate model that is representative of such conditions. We do so by improving upon the models built for the biochemical pathway in Part 1 and utilising parameters from model fittings in Part 3, while including the process of Naringenin addition and cell growth (OD).
We’ve obtained the parameter values for cell growth from experimental data fittings (Repressible 8 hour OFF data – link here). The Verhulst isothermal cell growth model was used for model fittings since cells are grown in an incubator under isothermal (no temperature change) conditions. The other parameter values were either obtained from literature or our own model fittings with experimental data. These are depicted below:
Since rbsD and rbs34 have different relative strengths, synthesis rates are different due to different rates of translation. From Part 2, a discovery that rbsD would be more suitable for F3'H, while rbs34 would be for FNS, this indicates that the synthesis rates of both enzymes will be different. However, we cannot directly apply the average relative expression value gotten from Table 2 because we cannot assume protein expression is linearly proportional to synthesis or translation rate of an enzyme. Fig.
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Table 3. Comparison of fittings
| Parameter | Meaning | Value | Reference |
|---|---|---|---|
| [enzyme] | Concentration of enzyme reacting with the substrate | Predetermined parameter, but set to 10000nM for our initial | NA |
| Eve | Jackson | 94 | |
| John | Doe | 80 |
Table 4. Parameters for the complete model
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Assumptions of the model
- Isothermal conditions during cell growth (no change in temperature). This assumption is valid as cells are grown in a temperature-controlled condition.
- No degradation of flavones (Apigenin, Eriodictyol and Luteolin).
- No scarcity of bioproduction resources (nutrients, amino acids) and no other factors affecting production of enzymes (cell stress, inhibition).
- Cell growth of BL21* strain E.Coli is similar to TOP10 strain.
- Light scatters across the LB medium evenly. This assumption is valid because LB does not excessively absorb light and can be spread across evenly and reach all cells.
Findings
Fig. 15 Cell Density Curve over Time
Fig. 15 shows the cell growth over time in the system using the Verhulst isothermal cell growth model. Wet lab plans to allow the cell to grow up until OD = 0.6 before triggering the cell to produce colour producing enzymes (doing so allows the cell to conserve resources for cell growth). This graph shows that OD reaches 0.6 at t = 4 h and approaches steady-state at about 2 after t =10 hr.
At t = 4 h, we intend to switch OFF the light using the light REPRESSIBLE system to allow the cell to produce the enzymes that catalyse colour bioproduction.
Fig. 16 Time Response of Repressor in light repressible system
Fig. 16 represents the aforementioned step with the rapid production of repressor proteins due to the presence of light until t = 4 h. Once the light is switched off after t = 4 h, a steep drop is observed. There is a 2 to 3 hour delay in the system before all production of repressors are stopped.
Fig. 17 Enzyme F3’H concentration
Fig. 18 Enzyme FNS concentration
Fig. 17 and Fig. 18 show a low production in concentration of F3’H and FNS respectively (colour-producing enzyme) for the first four hours even when blue light is ON. This is due to the leakiness (krep) from the blue light repressible promoter, a parameter obtained from model fittings in Part 3.
After light is turned OFF at t = 4 h, repression is lifted and the production of the F3’H and FNS enzyme is increased by nearly twofold. The protein expression levels are different due to the difference in their synthesis rates (=protein translation rates) due to their different RBS systems.
The aforementioned 2 to 3 hour delay observed in Fig. 16 has shaped our experimental design, acknowledging us that the substrate Naringenin should be added 3 hours after OD reaches 0.6 (t = 4 h) because the light system has become unrepressed and more stable (healthier for cells - less stress). This also allows the accumulation of the two catalysed enzymes before kickstarting the bioconversion process.
Fig. 19 Naringenin (substrate) concentration
Fig 19 shows a spike in the concentration of Naringenin (our substrate) at t = 7 h due to the administration of the substrate to our system for the cell factories E.coli to convert into Luteolin, which is the yellow dye.
Fig. 20 Eriodyctiol flavonoid concentration
Fig. 21 Apigenin flavonoid concentration
Fig. 20 and 21 demonstrate the intermediates of the biochemical reaction over time. It was observed that the concentrations are in extremely small amounts (〖10e〗^(-7) and 10e^(-6)) compared to the substrate and product, which shows the high efficiency of our system due to the fast conversion of the intermediates down the pathway to our final desired product.
Fig. 22 The concentration profiles for the substrate, intermediates and the product upon setting mRNA half-life to be 24 min following the case of BL21*
Fig. 22 Illustrates the 100% conversion of Naringenin to Luteolin (yellow dye product) in 16 hours using BL21* strain.
Conclusion
The model proves that Luteolin should be able to be produced under the right conditions and shows the feasibility and efficiency in our design.
Increasing our yield of Luteolin
Goal
To use in-silico modelling (on MATLAB) to determine why no Luteolin was produced experimentally.
Methods
Using the complete model created above, various parameters were varied to see which ones had the largest impact on our Luteolin yield. Parameters that were varied include, turnover rate (k_cat), synthesis rate of the particular enzyme (syn_(F3^' H)/syn_FNS), transcription rate of the mRNA for the enzymes in the pathway (syn_mRNA) and degradation rate of the enzyme’s mRNA (deg_mRNA).
Technical Findings
Fig. 23 (a)Enzyme FNS time profile curves (b) Enzyme F3'H time profile curves
Fig. 24 Concentration profiles for the substrate, intermediates and the product upon setting mRNA half-life to be 24 min and 5 min following the case of BL21* and TOP10 respectively
It was discovered that by increasing mRNA stability (increasing mRNA half-life/decreasing mRNA degradation rate) shown in the figure above, Luteolin would exhibit the highest increase in yield (300% increase). Therefore, an E.Coli strain like BL21* that has a higher mRNA stability (24 min half-life vs the usual 3-5 min half-life of TOP10 strains) would be preferred.
Conclusion
Therefore, a recommendation was given to Wet Lab to switch the TOP10 strain to the BL21* strain.
References
Kim, J et al. (2007). Flavanone 3-hydroxylases from rice: Key enzymes for favonol and anthocyanin biosynthesis. Molecules and Cells 25(2), pp. 312-316. Saito, K et al. (1999). Direct evidence for anthocyanidin synthase as a 2-oxoglutarate-dependent oxygenase. The Plant Journal 17(2), pp. 181-189.PART 3: OPTOGENETICS AND PARTS IMPROVEMENT
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