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 is the pathway of the enterobactin:

This chain of reaction is the main topic of this model. Starting with the delays from the sensor and the inverter models, we build an enzymatic kinetic model to determine the reaction's delay.

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)