Inverter Model

Introduction

Now that we have a sensing model with results regarding the iron sensing delay, we can continue towards our main goal, by modeling the inverter system. So, this second part of the Enterobactin production model focuses on the synthetic inverter system our team implemented in the bacteria.

Observations

As shown in the Figure 1, the enterobactin production regulation is based on two consecutives inhibitions, which, in the end, is an activator with a certain delay. The model will follow this principle.

Figure 1:

Second construction

Goals

Our goal in this part of the model is to create a generic LacI-LacO inverter model so that:

• We can determine the delay of our bacteria's inverter
• The model can can be reused by other projects

Materials and methods

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To simulate the inhibition phenomenon, we chose to use our logistic function under its differential form. Since it is the Fe-FUR that represses it, the LacI can be expressed as a logistic fuction of the Fe-FUR:

Ki1 is a non-dimensional parameter that repesents the inhibition power, and Kf is the fixation rate of the Fe-FUR on the FBS. Finally, Nbrpla1 is the number of pasmids containing the LacI.
In the same way, LacO is modeled with a logistic funtion. LacO is repressed by LacI:

Ki2 is the inhibition power and Nbrpla2 is the number of plasmimds containing LacO.
LacI and LacO are both ruled by a normal logistic function. If we were to track the number of expressed LacI/LacO, we would be using two inverted logistic fuctions to model a double inverter. The thing is, since LacI represents the number of repressed genes and LacO the number of expressed genes, the double inverter is still there, but the calculations are easier.

Results

Conclusion

Models and scripts