# Team:Evry/Modelmeta3

### From 2013.igem.org

# 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:

## 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 K_{r} for the mRNA and K_{p} 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.

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.

## Models and scripts

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