Team:NUS Singapore-A/shadow/Model

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OVERVIEW

Modelling was heavily utilised to obtain a better understanding of our system, as well as shaping our experimental designs to help us save time and resources. We constructed models that allowed us to achieve the following:

  1. Preliminary study of our intended biochemical pathway
  2. Optimal genetic circuit design
  3. Proof that optogenetics can work in our systems and improve upon existing inducible/repressible light systems
  4. 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).

Goal

In order to choose a suitable molecular product, the Wet Lab team must understand the feasibility of producing various compounds in E.Coli from a starting substrate. In this study, we looked at the production of two candidate flavone molecules (chrysanthemein and luteolin) using naringenin as a starting point. These molecules were chosen for their color as mentioned in the overview and because the necessary enzymes have been cloned before in E.Coli. By building a mathematical model of the pathway, we simulated the conversion of naringenin into the candidate products and chose the best candidate for the project. In addition, we explored how enzyme concentrations affect our system to provide insight into designing the genetic circuit.

Considerations

Given the limited time and resources, we consider the best candidate to be the one that has the highest yield. We also noted the existence of a secondary pathway leading to callistephin (an undesired product) in producing chrysanthemein. Our model thus had to take the callistephin pathway into account as well.

Fig. 1 Biochemical Pathway from starting substrate Naringenin

Methods

Modelling Product Yield

Among our criteria, understanding the yield was not something that could be done just by looking at the pathway or literature. Thus, it was necessary for us to simulate the conversion of naringenin by building a mathematical model of enzyme activity. The model consisted of a system of differential equations which was then solved with respect to time using MATLAB.

Assumptions

  1. Only the pathways shown in Figure 1 were present
  2. Conversion followed Michaelis-Menton kinetics
  3. Enzyme concentrations were in excess
  4. Degradation of intermediates was negligible

In accordance with Michaelis-Menton kinetics, the following parameters were taken into account when modelling the pathway.

  1. vm the maximum rate of substrate conversion.
  2. kcat the enzyme turnover and used to calculate vm. Equal to the product of kcat and enzyme concentration.
  3. km the concentration at which half of the maximum rate is reached.

The differential equations are as follows:

Substrate concentrations are denoted [substrate]. Parameters are given in the form parametersubstrate or parameterenzymesubstrate for substrates that react with more than one enzyme.

The table below contains the list of values we used for the parameters.

Parameter Value Source Parameter Value Source
kcatF3Hnar 756 hr-1 Click here kmF3Hnar 57800 nM Click here
kcatDFRdhk 0.2 hr-1 Click here kmDFRdhk 400 nM Click here
kcatlpg 1.26 hr-1 Estimated from ANS acting on substrate Leucocyanidin kmlpg 110 000 nM Click here
kcatpgd 2.53 hr-1 Estimated from 3GT acting on substrate Cyanidin kmpgd 4790 nM Estimated from 3GT acting on substrate Cyanidin
kcatF3'Hnar 4.53 hr-1 Click here kmF3'Hnar 19600 nM Click here
kcatFNSerd 97.2 hr-1 Click here km 8000 nM Click here
kcatF3Herd 756 hr-1 Click here kmF3Herd 57800 nM Click here
kcatF3'Hdhk 3.46 hr-1 Click here kmF3'Hdhk 19500 nM Click here
kcatdhq 0.287 hr-1 Click here kmdhq 400 nM Click here
kcatANSlcn 1.26 hr-1 Click here kmANSlcn 38800 nM Click here
kcatcnd 2.53 hr-1 Click here kmcnd 4790 nM Click here
kcatFNSnar 0.27 hr-1 Click here kmFNSnar 5000 nM Click here
kcatapi 4.0 hr-1 Click here kmapi 19000 nM Click here

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, 100% conversion of luteolin is achieved in 5.3 hours. Meanwhile, only ~11410nM of chrysanthemin is produced in 8 hours and ~2000nM of callistephin is present in the product. Thus, luteolin will have the better yield.

Conclusion

Without careful flux control, only luteolin can be produced in satisfactory yields. Hence luteolin was chosen as the product of choice. However, control of the enzyme concentrations is necessary to improve yield and give optogenetic control. Subsequent experiments hence focus on improving yield and control as well as the implications on genetic circuit design.

Goal

The genetic circuit should be an important design consideration; parts like the Ribosome Binding Site (RBS) affect the translation rates and thus, enzyme concentration, which ultimately affects yield and conversion rates. Two RBS parts are available: rbsD and rbs34. Unfortuantely, it is not possible to conjugate two of the same RBS parts on the same plasmid and a choice must be made on whcih RBS controls which enzyme. We thus investigated the difference in strength between the two parts as well as their effect on yield. The conclusion was to pair rbsD with F3'H and rbs34 with FNS.

Methods

Comparing of RBS strength

In the first part of this study, we used characterisation data from a Synthetic Biology lab at E6 Engineering (NUS) 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. We then determined that rbsD was twice as strong as rbs 34. This is shown below:

Figure 1 pBAD/rbsD RFP expression curve

Figure 2 pBAD/rbs34 RFP expression curve

Table 1. 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

Simulation

The next step was to let the enzyme concentrations vary in accordance with various RBS-enzyme combinations.

Assumptions

  1. Samples were subjected to identical conditions during the characterisation experiments of rbsD and rbs34
  2. Degradation of product and intermediates was negligible
  3. Basal expression independent of RBS and/or human input was negligible
  4. All cellular and nutrional resources were in excess
  5. Translation rates RFP were representative of that of FNS and F3’H
The results are shown below.

Figure 3 Conversion of Naringenin to Luteolin (rbsD assigned to FNS and rbs34 assigned to F3’H)

Figure 4 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 Figure 4 that 100% conversion occurs faster in the rbsD/F3’H construct.

Weaknesses and Future Improvement

We have identified the following sources of error and weaknesses in our model:

Conditions were assumed to be similar to that in the characterization experiments.

Enzyme expression and activity depend on the conditions such as temperature. It is possible that the conditions in a bioreactor will be such that the difference between the RBS will be smaller or larger depending on the bioreactor environment.

All intermediates and the product are consumed without degradation.

The stability of the intermediates are unclear but they are certainly oxidizable. Similarly, luteolin can also be degraded by oxidative reactions1. Thus, future models can look into how yield changes with stability of the compounds.

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.

References

  1. Ramešová, Š., Sokolová, R., Degano, I., Bulíčková, J., Žabka, J., & Gál, M. (2012). On the stability of the bioactive flavonoids quercetin and luteolin under oxygen-free conditions. Analytical and bioanalytical chemistry, 402(2), 975-982.

Goal

EL222 is a protein that dimerizes in blue light and induces or represses a genetic circuit depending on the type of promoter used. In this study, we modelled an inducible and a repressible system to understand the kinetics behind the mechanism. Next, we analyzed the information to understand trends observed and possible weaknesses of the study. Finally, we discussed how the information from this study impacts future work for our project.

Methods

Repressible System Modelling

The first part of this study was the modeling of the repressible system by performing curve fitting on experimental data on RFP expression over time.

Experiments were performed for the following scenarios:

  1. 8hr off
  2. 3hr off/3hr on
  3. 8hr on
  4. 2hr off/4hr on
  5. 45min off/6hr on

Curve fitting was done on scenarios 1 to 3. The resultant model was tested by simulating the system response for scenario 4 and 5 and comparing it with experimental data.

Assumptions

  1. The initial concentration of activated EL222 was 0
  2. The initial concentration of mRNA was 0
  3. The initial concentration of nascent RFP was 0
  4. All nascent RFP would mature before being degraded

The following 10 factors were taken into account when modelling the repressible system.

  1. ka the rate of EL222 dimerization in blue light.
  2. kd the rate of degrdation of dimerized EL222.
  3. synmRNA the max rate of transcription.
  4. h the Hill coefficient for EL222 dimers binding to the promoter.
  5. krep the maximum amount of repression possible.
  6. km the concentration of EL222 dimers at which half of maximum transcription rate is reached
  7. degmRNA the rate of mRNA degradation.
  8. synRFP the rate of translation.
  9. Kmat the rate of protein maturation.
  10. degRFPm the rate of degrdation of mature RFP.

The differential equations are as follows:

Unfortunately, the concentration of intermediates were not measured in light of equipment constraints. Thus, values of ka, kd, km are arbitrary and do not correspond to actual physical values. The rest of the parameters were allowed to vary within an order of magnitude in accordance literature values of similar systems.

Figure 1: Curve fitting for repressible system, light 8hr off

Figure 2: Curve fitting for repressible system, light 3hr off/3hr on

Figure 3: Curve fitting for repressible system, light 8hr on

Figure 4: Model testing for repressible system, light 2hr off/4hr on

Figure 5: Model testing for repressible system, light 45min off/6hr on

Running the optimizer in MATLAB gave us the following values for the parameters.

Parameter Value Parameter Value
ka 9.57 M hr-1 km 0.247 M
kd 3.765 hr-1 degmRNA 4.49 hr-1
synmRNA 8.45e-5 M hr-1 synRFP 0.121 hr-1
h 1.00 Kmat 0.21
krep 0.601 degRFPm Ctrl 0.35 hr-1
DAS 0.47 hr-1

We found that our model was able to capture the trends in RFP concentration over time for scenario 5 quite well but less so for scenario 4. We hypothesize that more factors were present that were not accounted for and that they probably play a much smaller role when the light is on or off all the way but become important for "intermediate" scenarios. In any case, it appears that the performance of the system can be predicted with reasonable accuracy for lighting regimes close to the scenario 1 and 3. Meanwhile, more complex regimes will require a better model.

Inducible System Modelling

Our team proceeded to investigate the usefulness of our model for an blue light inducible system.

Experiments were performed for the following scenarios:

  1. 8hr on
  2. 3hr on/3hr off
  3. 8hr off
  4. 2hr on/4hr off
  5. 45min on/6hr off

Assumptions

  1. The initial concentration of activated EL222 was 0
  2. The initial concentration of mRNA was 0
  3. The initial concentration of nascent RFP was 0
  4. All nascent RFP would mature before being degraded

The following 10 factors were taken into account when modelling the inducible system.

  1. ka the rate of EL222 dimerization in blue light.
  2. kd the rate of degrdation of dimerized EL222.
  3. synmRNA the max rate of transcription.
  4. h the Hill coefficient for EL222 dimers binding to the promoter.
  5. basal the transcription rate in the absence of inducer.
  6. km the concentration of EL222 dimers at which half of maximum transcription rate is reached
  7. degmRNA the rate of mRNA degradation.
  8. synRFP the rate of translation.
  9. Kmat the rate of protein maturation.
  10. degRFPm the rate of degrdation of mature RFP.

The differential equations are as follows:

Reusing the same values for degmRFP, synRFP, degRFP (Control and DAS), we were able to get the following fit.

Figure 1: Curve fitting for inducible system, light 8hr on

Figure 2: Curve fitting for inducible system, light 3hr on/4hr off

Figure 3: Curve fitting for inducible system, light 8hr off

Figure 4: Model testing for inducible system, light 2hr on/4hr off

Figure 5: Model testing for inducible system, light 45min on/6hr off

Running the optimizer in MATLAB gave us the following values for the parameters.

Parameter Value Parameter Value
ka 2.214 M hr-1 km 1.17 M
kd 2.487 hr-1 degmRNA 4.49 hr-1
synmRNA 5.71e-5 M hr-1 synRFP 0.121 hr-1
h 1.66 Kmat 0.21
basal 1.48e-5 M hr-1 degRFPm Ctrl 0.35 hr-1
DAS 0.47 hr-1
AAV 0.70 hr-1

Compared to the repressible system, the fit was not as good. In particolar, the model could not capture the drop in RFP concentration that appeared at the start of the experiment in many cases. In other cases, the model was unable to capture the increase in RFP concentration correctly. Unfortuantely, even when degmRFP, synRFP, degRFP were allowed to vary, we were still unable to improve the fit significantly.

Weaknesses and Future Improvement

We have identified the following sources of error and weaknesses in our model:

All RFP matures before degradation

Given the long maturation time for RFP, it is likely that degradation of nascent RFP could have played a significant role.

Initial mRNA concentration was assumed to be 0

This is unlikely to be true given the presence of RFP even at the start of the experiment. Future work measuring mRNA concentration will greatly reduce unvertainty during modelling.

Initial concentration of nascent RFP was assumed to be 0

This assumption is valid only if RFP matures quickly enough for the nascent form to undectable. However, our model indicated a long maturation time which implies that nascent RFP could have been present in siginificant amounts at the start.

All nascent RFP was assumed to be converted into mature RFP without degradation.

It is likely that whatever mechanisms causing degradation of mature of RFP can act on nascent RFP too even if not as efficiently. Furthermore, the long maturation time of RFP means it is possible that degradation of nascent RFP may be significant.

Assumed no reversal in the effect of EL222 concentration on the inducible promoter.

High EL222 concentration can have an inhibitory effect on the inducible promoter. The wet lab team can use a weaker promoter in the future to avoid EL222 reaching inhibitory concentrations.

Changing conditions of media during the experiment

Over the course of the experiment, nutrients are depleted from the media while metabolic waste is produced and accumulates in it. Such inconsistencies in growing conditions can affect the performance of the system. The wet-lab team attempted to minimize such effects by keeping the experiment under 8 hours. Future work starting with a lower OD, using a continuous setup or a cell-free environment can help us study the system in isolation.

Achieving on-off Cycles

We found that the slow maturation of the nascent RFP protein acted as a buffer against changes in mature RFP concentration. Using a faster maturing RFP would however significantly improve the results. This implies that the system works better on proteins that do not require additional time for steps after translation. This includes additional folding, post-translational modification and transport.

Conclusion

The repressible and inducible systems can be modelled using the ten parameters as long the lighting regime does not deviate far from completely on or completely off states. The model is more accurate for the repressible. However, the errors observe indicate that the model still needs more work to provide comprehensice coverage for the various situations the system may be subjected to. In particular, the validity assumptions need be reassessed while concentrations of the intermediates should be measured during future work.

Future Work

We found that the slow maturation of the nascent RFP protein acted as a buffer against changes in mature RFP concentration. Using a faster maturing RFP would however significantly improve the results. This implies that the system works better on proteins that do not require additional time for steps after translation. This includes additional folding, post-translational modification and transport.

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 is a representative model of our entire system.

Methods

Modelling Cell Growth

Whereas concentrations in Part 3 were given in nM/OD, we now want to know the actual concentration of protein produced. Thus, we had consider how the cell density changes with time. The Verhulst isothermal cell growth model was chosen since the cells are grown under isothermal conditions.

Putting the Equations Together

Combining the Verhulst model with the equations from previous parts, we get the final system of differential equations shown below.

The following 10 factors were taken into account when modelling the repressible system.

  1. ka the rate of EL222 dimerization in blue light.
  2. kd the rate of degrdation of dimerized EL222.
  3. synmRNA the max rate of transcription.
  4. h the Hill coefficient for EL222 dimers binding to the promoter.
  5. krep the maximum amount of repression possible.
  6. km the concentration of EL222 dimers at which half of maximum transcription rate is reached
  7. degmRNA the rate of mRNA degradation.
  8. synRFP the rate of translation.
  9. Kmat the rate of protein maturation.
  10. degRFPm the rate of degrdation of mature RFP.

Parameter Value Parameter Value
ka 9.57 M hr-1 km 0.247 M
kd 3.765 hr-1 degmRNA 4.49 hr-1
synmRNA 8.45e-5 M hr-1 synRFP 0.121 hr-1
h 1.00 Kmat 0.21
krep 0.601 degRFPm 0.35 hr-1

In accordance with Michaelis-Menton kinetics, the following parameters were taken into account when modelling the pathway.

  1. vm the maximum rate of substrate conversion.
  2. kcat the enzyme turnover and used to calculate vm. Equal to the product of kcat and enzyme concentration.
  3. km the concentration at which half of the maximum rate is reached.

Parameter Value Source Parameter Value Source
kcatF3Hnar 756 hr-1 Click here kmF3Hnar 57800 nM Click here
kcatDFRdhk 0.2 hr-1 Click here kmDFRdhk 400 nM Click here
kcatlpg 1.26 hr-1 Estimated from ANS acting on substrate Leucocyanidin kmlpg 110 000 nM Click here
kcatpgd 2.53 hr-1 Estimated from 3GT acting on substrate Cyanidin kmpgd 4790 nM Estimated from 3GT acting on substrate Cyanidin
kcatF3'Hnar 4.53 hr-1 Click here kmF3'Hnar 19600 nM Click here
kcatFNSerd 97.2 hr-1 Click here km 8000 nM Click here
kcatF3Herd 756 hr-1 Click here kmF3Herd 57800 nM Click here
kcatF3'Hdhk 3.46 hr-1 Click here kmF3'Hdhk 19500 nM Click here
kcatdhq 0.287 hr-1 Click here kmdhq 400 nM Click here
kcatANSlcn 1.26 hr-1 Click here kmANSlcn 38800 nM Click here
kcatcnd 2.53 hr-1 Click here kmcnd 4790 nM Click here
kcatFNSnar 0.27 hr-1 Click here kmFNSnar 5000 nM Click here
kcatapi 4.0 hr-1 Click here kmapi 19000 nM Click here

Assumptions

  1. The cells grow at 37C at isothermal conditions
  2. Degradation of intermediates and products was negligible
  3. All cellular and nutrional resources were in excess
  4. Cell growth of BL21* strain E.Coli was similar to TOP10 strain from Part 3
  5. Light scatters across the LB medium evenly. This assumption is valid because LB does not excessively absorb light allowing it to reach all cells

Figure 1 Cell Density Curve over Time

Figure 15 shows the cell growth over time in the system using the Verhulst isothermal cell growth model. The 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.

Figure 2 Time Response of Repressor in light repressible system

Figure 2 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.

Figure 3 Enzyme F3’H concentration

Figure 4 Enzyme FNS concentration

Figure 3 and 4 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 Figure 2 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.

Figure 5 Naringenin (substrate) concentration

Figure 5 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.

Figure 6 Eriodyctiol flavonoid concentration

Figure 7 Apigenin flavonoid concentration

Figure 6 and 7 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. This shows the high efficiency of our system in converting the intermediates down the pathway to our final desired product.

Figure 8 The concentration profiles for the substrate, intermediates and the product upon setting mRNA half-life to be 24 min following the case of BL21*

Figure 8 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.



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