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Part 2: Parts Improvement

Goal of the model

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 model an inducible and a repressible system to understand the kinetics behind the mechanism. Next, we analyze the information to understand trends observed and possible weaknesses of the study. Finally, we discuss 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. 1. 8hr off
  2. 2. 3hr off/3hr on
  3. 3. 8hr on
  4. 4. 2hr off/4hr on
  5. 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. synmRFP 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. degRFP 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.

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 usefolness of our model for an blue light inducible system.

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. synmRFP 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. degRFP 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.

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.

Weakness 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.



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