Team:Macquarie Australia/Model
Overview
We set out to model the production of chlorophyll from aminolevulinic acid based on the kinetic parameters of the enzymes in the system and the realistic ranges of concentrations of those enzymes that would be achievable in an E. coli cell. We looked at what the concentrations of enzymes could be based on the volume of an E. coli cell and what the actual amounts of protein could exist in an E. coli cell based on published literature values.
Assumptions
Given that the average length of an E. coli cell is 2um and average diameter is 1um, we can calculate the volume of the cell by assuming that an E.coli cell is shaped like a cylinder
V=π r2h
V = π (1µm/2)2*2µm
V = 1.57µm3 = 1.57*10-18m3
Vcell = 1.57*10-15L/cell
Using this volume of a cell (1.57*10-15L/cell), and assuming that the concentration of expressed protein is 1nM (1*10-9M), the number of molecules per cell can be calculated.
1*10-9 moles/Litre * 6.022*1023 = 6.022*1014 molecules/L
6.022*1014 molecules/L * 1.57*10-15 Litres/cell = 0.94 molecules/cell
Therefore, 1nM is equivalent to ≈ 1 molecule/cell
Enzymes parameters were taken from published literature, and input into our Matlab model (Table 1)
| Enzyme | Function | Km(µM) | Kcat(1/s) | k1 | k-1 |
|---|---|---|---|---|---|
| Porphobilogen synthase | ALA → PPB | 1800 | 0.37 | 0.000197 | 0.0037 |
| Hydroxymethylbilane synthase | PPB → HMB | 7 | 0.105 | 0.0145 | 0.00105 |
| Uroporphyrinogin III synthase | HMB → URO | 5 | 500 | 101 | 5 |
| Uroporphyrinogin III decarboxylase | URO → CPO | 6 | 0.0039 | 0.000621 | 0.0000369 |
| Corproporphyrinogen oxidase | CPO → POIX | 2.6 | 0.00283 | 0.00110 | 0.0000283 |
| Protoporphyrinogen oxidase | POIX → PPIX | 7 | 0.292 | 0.0421 | 0.00292 |
| Magnesium chelatase subunit H | PPIX → MgPPIX | 3.2 | 0.00162 | 0.00005 | 0.0000162 |
| Magnesium protoporphyrin O-methyltransferase | MgPPIX → MgPPIXmono | 2.37 | 0.057 | 0.024 | 0.00057 |
| Magnesium-protoporphyrin IX monomethyl ester (oxidative) cyclase | MgPPIXmono → Divi | 3 | 0.1 | 0.034 | 0.001 |
| Divinyl chlorophyllide a 8-vinyl-reductase | Divi → Proto | 3 | 0.1 | 0.00033 | 0.001 |
| Protochlorophyllide reductase and light-independent protochlorophyllide reductase subunit L | Proto → Clide | 1.84 | 0.1 | 0.055 | 0.001 |
| Chlorophyll a synthase | Clide → Chloro | 69 | 0.1 | 0.0015 | 0.001 |
Protein concentration
The upper and lower limits of protein expression were defined to establish a range of expression. The upper limit was obtained from the cellular concentration of EF-Tu, which makes up 5.5% total protein in E. coli strain NC3, and is expressed at a concentration of 58140 molecules/cell ≈ 58140nM (Pedersen et. al. 1978). The lower limit was defined to be 1 molecule per cell ≈ 1nM.
Model Refinement
We set out the expand the capabilities of the chlorophyll biosynthesis model used in previous years by giving the user greater control over input parameters, allowing for them to more efficiently test an array of inputs to better match realistic cellular conditions. We accomplished this by adding the ability to alter the enzyme concentration of each component in the pathway separately, as part of the input prompt that appears when the program starts. This allows for easier manipulation of the program, which in turn results in faster modeling refinement and without any of the required programming prerequisites needed to manipulate the code.
We aimed to refine our model to match the experimental data collected from data collected from Macquarie University’s 2015 iGEM team (Graph 1) using realistic cellular enzyme concentrations from published literature. This model will allow us to check for the presence of any limiting factors and maximize chlorophyll expression by increasing expression of select enzymes.
Figure 1. Experimental data quantifying the concentration of PPIX over time, using different Concentrations of input ALA. Data taken from Macquarie University’s 2015 iGEM team.
Methodology
The results from 2015 experimental data indicate that the concentration of PPIX formed by Protoporphyrinogen oxidase) should peak about 6 days when 1000uM of ALA is used in the media (Figure 1). Experimental data from both 2015 and 2018 indicated a presence of CPO via fluorescence spectroscopy. We should therefore expect our model to match these results if we are to reasonably expect our model to be accurate to reality.
The median protein concentration for E. coli, 1485nM (Pedersen et. al. 1978), was used as a starting point for refinement (Figure 2), alongside 40uM as the ALA concentration in media, which is the realistic concentration of ALA in E. coli cytosol (Willows 2004). This model has chlorophyll production peak at about 1 day, PPIX peak at about 0.5 days, and had a low abundance of CPO.
Figure 2. Predicted concentrations of chlorophyll biosynthesis intermediates over time, where every enzyme has a concentration of 1485nM
After refining the data from Pedersen et. al. (1978) to only include the concentration of enzymes (all of which are tRNA ligases), we found that the median concentration of enzymes characterized was 44.8% lower than the median concentration for all enzymes characterized by Pedersen et. al. (1978). Our model was then adjusted by lowering the mean concentration by 10 times, and setting this value (148.5nM) to be the concentration of all enzymes except for Uroporphyrinogin III decarboxylase and Corproporphyrinogen oxidase, which has a concentration set to be tenfold higher than other enzymes (1485nM) in order to compensate for URO accumulation (Figure 3), which does not occur in natural cells (Willows 2004). A marked improvement was seen in this iteration, as PPIX peak was doubled from 0.5 to 1 day. Higher concentrations of CPO can also be observed.
Figure 3. Predicted concentrations of chlorophyll biosynthesis intermediates over time, where every enzyme has a concentration of 148.5nM except for Uroporphyrinogin III decarboxylase and Corproporphyrinogen oxidase, which have concentrations of 1485nM
Additional data was also collected for E. coli ’s native Heme synthesis pathway (Schmidt et. al. 2016), and the cellular concentration for PBG-synthase to Protogen oxidase (enzymes #1-6) was obtained and directly input into our model. Additionally, the median enzyme concentrations of E. coli 's native Heme biosynthesis pathway was calculated to be 111nM based off Schmidt et. al.’s (2016) data, which was rounded to 100nM and applied to the remainder of the enzymes, which are not native in E. coli. An exception was made of Uro-III decarboxylase, which also had its enzyme concentration set to the new default of 100nM, as the confidence score for this enzyme was extremely low (49.13), indicating that Schmidt et. al.’s data for this enzyme is likely incorrect (Schmidt et. al. 2016). Lastly, ALA concentration was increased to 1000uM to match the concentration used by 2016’s team (Figure 4). This refinement brought the modeling prediction to be closer to the experimental results of PPIX peaking at 6 days. However, insufficient CPO is being produced to be detectible, likely due to low concentrations Uro-III decarboxylase that also leads to a massive buildup of URO almost immediately after addition of exogenous ALA to 1mM.
Figure 4. Predicted concentrations of chlorophyll biosynthesis intermediates over time, where every enzymes up to (and including) Protoporphyrinogen oxidase have a concentration based on empirical data (Schmidt et. al. 2016), and all other enzymes have a concentration of 100nM
Based on what the model was predicting and comparison to the experimental results we targeted the concentration of three enzymes: Uro-III synthase, Uro-III decarboxylase, Copro-gen oxidase, as these enzymes are likely limiting factors, preventing our model data from matching the experimental data. Our final model was developed by converting the concentration of Uro-III synthase back to Schmidt et. al.’s (2016) experimental values and increasing the concentration of Uro-III decarboxylase and Copro-gen oxidase by 10x and 100x respectively (Table 2)(Figure 5). A prominent peak of PPIX can be seen at 4.5 days alongside a moderate accumulation of CPO, finally matched our experimental data.
Figure 5. Optimided model, using modified concnetrations from Schmidt et. al. (2016).
Table 2. Enzyme concentrations obtained from Schmidt et. al. (2016), modifications, to these values, and final concentration input
| Enzyme Name | Enzyme concentration in E. coli (nM) | Modification | Final Concentration (nM) |
|---|---|---|---|
| Porphobilinogen synthase | 440 | n/a | 440 |
| Hydrymethylbilane synthase | 224 | n/a | 224 |
| Uroporphyrinogen III synthase | 12 | n/a | 12 |
| Uroporphyrinogen decarboxylase | 30 | 100x | 3000 |
| Coproporphyrinogen oxidase | 106 | 10x | 106 |
| Protoporphyrinogen oxidase | 106 | n/a | 106 |
| Magnesium chelatase subunit H | 100 | n/a | 100 |
| Magnesium protoporphyrin O-methyltransferase | 100 | n/a | 100 |
| Magnesium-protoporphyrin IX monomethyl ester (oxidative) cyclase | 100 | n/a | 100 |
| Divinyl chlorophyllide a 8-vinyl-reductase | 100 | n/a | 100 |
| Protochlorophyllide reductase and light-independent protochlorophyllide reductase subunit L | 100 | n/a | 100 |
| Chlorophyll a synthase | 100 | n/a | 100 |
Implications:
The requirement that two enzymes need to have their concentration changed from what is found in vivo to match experimental data has implications on the current literature surrounding the chlorophyll/heme biosynthesis pathway. Firstly, Uroporphyrinogen decarboxylase (encoded by HemE in E.coli ’s native Heme pathway) needed to have its concentration increased 100x above Schmidt et. al.’s (2016) values. And secondly, Copro-gen oxidase (equivalent to HemF) needed to have its concentration increased 10x.
The required increase in Copro-gen oxidase (HemF) concentration is likely due to the fact that Copro-gen oxidase has two types of enzyme, other other being the anaerobic form encoded by HemN, which both perform the same function (Willows 2004). However, only the kinetic parameters of HemF are known, leaving open the possibility that HemN is also functioning and accounting for the addition activity required.
Uroporphyrinogen decarboxylase needed a very large increase in concentration from what is measured by Schmidt in order to match experimental data. One possible explanation for this is that the published enzyme kinetics parameters measured in vitro for this enzyme may not reflect the in vivo parameters. This could occur for a variety of reasons, such as additional factors required for optimal activity, activating factors or possibly substrate channelling with the other enzymes.
Implementation:
In our model, an accumulation of PPIX can be observed, indicating that Protoporphyrinogen oxidase is a limiting factor that is stalling the entire pathway, leading to only 10% of input ALA being converted to chlorophyll after 10 days (Figure 5). To improve the efficiency of the entire pathway, we considered designing the chlorophyll biosynthesis plasmid in such a way that the expression of select enzymes was increased, preventing accumulation of any one reagent. Using the ability to alter enzyme concentrations independently in our model, we increased the concentration of enzymes involved in the later half of the pathway in order to evaluate which enzymes are likely to be limiting factors.
Of all enzymes tested, the enzyme that produced the greatest increase in chlorophyll production when increased was Magnesium chelatase (Figure 6), which was increased tenfold to 1000nM. By changing only one enzyme, the sustained accumulation of PPIX and all proceeding intermediated was eliminated, producing an extremely efficient biosynthesis pathway that converts almost 100% of the input ALA into chlorophyll within 10 days.
Based of this result, the Magnesium chelatase operon, containing ChlI1, ChlI2 and ChlD, had their promoter swapped from lac to a promoter with higher expression rates (trc) (Tegel et. al. 2011).
Figure 6. Model with 1000nM concentration of Magnesium chelitase.
Conclusion:
The model generated was successfully able to model the production of 12 different constituents based of the enzyme kinetics parameters, indicating that our program is robust and capable of predicting complex pathways with many enzymes of varying kinetic parameters. As our program condenses our enzyme parameters, such as Kcat and Km values, into a series of single-line arrays, our script can be easily re-programmed to model other metabolic pathways, making it versatile and flexible. In addition, individual enzyme concentrations can be altered through prompts before running the model, allowing for fast re-programming to quickly generate a set of models, and allow for efficient testing.
References
- Pedersen, S., Bloch, P.L., Reeh, S. and Neidhardt, F.C., 1978. Patterns of protein synthesis in E. coli: a catalog of the amount of 140 individual proteins at different growth rates. Cell, 14(1), pp.179-190.
- Schmidt, A., Kochanowski, K., Vedelaar, S., Ahrné, E., Volkmer, B., Callipo, L., Knoops, K., Bauer, M., Aebersold, R. and Heinemann, M., 2016. The quantitative and condition-dependent Escherichia coli proteome. Nature biotechnology, 34(1), p.104.
- Tegel, H., Ottosson, J. and Hober, S., 2011. Enhancing the protein production levels in Escherichia coli with a strong promoter. The FEBS journal, 278(5), pp.729-739.
- Willows, R. (2004). Chlorophylls.
