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: Our second construction, our Inverter system

See our sensor page for more details

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

From Iron to FBS:
The first equations remain the same (from the sensing model):

RFP expression:
To simulate the RFP expression, we used the same method as in our sensing model (with the use of our Logistic function under its differential form).

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.
RFP expression is repressed by LacI:

Ki2 is the inhibition power and Nbrpla2 is the number of plasmimds containing the RFP.
Note that LacI and RFP are both ruled by a normal logistic function. If we were to track the number of expressed LacI or RFP, 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 RFP the number of expressed genes, the double inverter is still there, but the calculations are easier.

RFP Production:
The [mRNA] and [GFP] equations are alike. The prodction rates are K_r for the mRNA and K_p for the GFP. Since FBS represents the number of inhibited Fur Binding Sites, we have to substract it from N_pla1.
Both variables also have a negative degadation term:

Results

Figure 1: "High copy or Low copy that is question !"

Conclusion

Models and scripts