IGEM:IMPERIAL/2007/Dry Lab/Modelling/ID

Analysis of the Model of the Infector Detector

Generalities of the Model

• Introduction

The Infector Detector system can be modelled by the following Dynamical System:

[math]\displaystyle{ \frac{d[LuxR]}{dt} = k_1\bigg(\frac{[E]^n}{K_E^n + [E]^n}\bigg) + k_3[A] - k_2[LuxR][AHL]- \delta_{LuxR}[LuxR] }[/math]
[math]\displaystyle{ \frac{d[AHL]}{dt} = k_3[A] - k2[LuxR][AHL]- \delta_{AHL}[AHL] }[/math]

[math]\displaystyle{ \frac{d[A]}{dt} = -k_3[A] + k2[LuxR][AHL]- k_4[A][P] + k_5[AP] }[/math]

[math]\displaystyle{ \frac{d[P]}{dt} = -k_4[A][P] + k_5[P] }[/math]

[math]\displaystyle{ \frac{d[AP]}{dt} = k_4[A][P] - k_5[AP] }[/math]

[math]\displaystyle{ \frac{d[GFP]}{dt} = k_6[AP]\bigg(\frac{[E]^n}{K_E^n + [E]^n}\bigg) - \delta_{GFP}[GFP] }[/math]

[math]\displaystyle{ \frac{d[E]}{dt} = -\alpha_{1}k_1\bigg(\frac{[E]^n}{K_E^n + [E]^n}\bigg) - \alpha_{2}k_6[AP]\bigg(\frac{[E]^n}{K_E^n + [E]^n}\bigg) }[/math]

[math]\displaystyle{ \alpha_i \ }[/math] represents the energy consumption due to gene transcription. It is a function of gene length.