# Team:Evry/Modelmeta3

Iron coli project

# Final Enterobactin production model

## Introduction

This is the final step of the Enterobactin production model. We just have to combine all the previous models and add the delay of enzymes production as well as the enterobactin production time.This model includes the synthetic sensing system, the inverter system and the chemical reactions leading to the enterobactin.

## Observations

Here are the final constructions:

Figure 1: Final construction
This includes the sensing system, with the inverter system, which leads to a double inverter followed by the production of the enzymes.

## Goals

Our goal is to answer this question: "how much time is needed for our bacteria to start producing enterobactins from the moment they sense the iron?"

## Materials and methods

Enzymes production
The first equations are taken from the sensing model and the inverter model.

The [mRNA] and [Enz] equations are alike. The prodction rates are Kr for the mRNA and Kp for the enzymmes, and both variables have a negative degadation term:

Enterobactin production
Now that we have all the equations needed from the Iron to the Enzymes concentrations, we can include the chemical delay of the enterobactin production.

The input of the chemical sytem is the chorismic acid, and the output is the enterobactin.

Those chemical equations naturally lead to this system:

Where :
(from the Chemical reasoning page)

The final system:
To reduce the number of equations, simpified the model by assuming that all the enzymes concentrations are equal. They are all computed under the [Enz] variable.

## Results

"How much time is needed for our bacteria to start producing enterobactins from the moment they sense the iron?"
To determine the delay of the enterobactin production, we set a short pulse of iron as the model's input and compute the normalized concentrations of enzymes and enterobacin.

Figure 1: "Normalized concentrations of Iron, Enzyme and Enterobactin"

The Figure 1 shows that the enterobactin production is a much slower process than the production of enzymes.
According to the model, our bacteria takes approximately 2 hours to start producing enterobactins at a constant rate.

## Conclusion

The delay of siderophore production is predicted to be way to long if you choose for the flush strategy. As a consequence, these result directly impacted our chelating strategy. Thus, our final decision is to try to implant the bacteria in the intestins (here in the jejunum) to statically enhance its growth and let it enough time to recover for a dessicated environment.