# Team:Evry/Modelmeta2

### From 2013.igem.org

# 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.

## Goals

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

- We can determine the delay of our bacteria's inverter
- The model can can be reused by other projects using a LacI-pLac inverter
- We can answer the question
*"Which plasmid's copy should we prioritize in our bacteria?"*

## Materials and methods

**From Iron to FBS:**

The first equations remain the same (from the sensing model):

**RFP expression:**

RFP expression is repressed by *FBS* (Logistic function under its differential form):

K_{i2} is the inhibition power and N_{pla2} is the number of plasmimds containing the RFP.

Note that *FBS* and *RFP _{expressed}* 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

*FBS*represents the number of

**repressed**genes and

*RFP*the number of

_{expressed}**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

*"Which plasmid's copy should we prioritize in our bacteria?"*

In order to answer that question, we ran simulations with different numbers of plasmids containing LacI and plasmids containing pLac. Since we don't know the efficiency of the pLac promoter, we set its value equal to K_{i1} (the efficiency of the LacI promoter).

The Figure 1 shows that, even with the same promoter strenght, the plasmid containing pLac is more efficient than the one containing LacI.

This result underlines the importance of the second plasmid, thus making it preferable for high copy. Consequently, the bacteria was indeed equiped with 15 LacI-plasmids and 300 pLac-plasmids.

## Conclusion

To conclude, we modeled the second construction of our team : we made a **generic inverter system model** with an upstream iron sensor.

The results of this model allowed us to:

- Determine which plasmid's copy we should prioritize
- Continue the determination of the entrobactin production speed of our bacteria. The next step being the Final enterobactin production model.

## Models and scripts

This model was made using the Python language. You can download the python script here.