IGEM:IMPERIAL/2007/Projects/Biofilm Detector/Modelling/Construct2/Case 5

Construct 2: Case 5

• Introduction
• Case 1
• Case 2
• Case 3
• Case 4
• Case 5
• References

Case 5 : Including Degradation Terms

[math]\displaystyle{ \frac{d[LuxR]}{dt}=-\delta_{LuxR}-k_{3}[A]-k_{2}[LuxR][AHL]\cdots\cdots(1) }[/math]

[math]\displaystyle{ \frac{d[AHL]}{dt}=-\delta_{AHL}[AHL]+k_{3}[A]-k_{2}[LuxR][AHL]\cdots\cdots(2) }[/math]

[math]\displaystyle{ \frac{d[A]}{dt}\cdots\cdots(3) }[/math]

[math]\displaystyle{ \frac{d[A]}{dt}=-k_{3}[A]+k_{2}[LuxR][AHL]\cdots\cdots(4) }[/math]

Lumping degradation of LuxR and AHL into Activator Degradation term

[math]\displaystyle{ [A]=[A]_{0}e^{-\left(\delta_{LuxR}+\delta_{AHL}\right)t}\cdots\cdots(5) }[/math]

We are not sure whether the natural degradation of the Activator complex is more dominate than the combined effects of the degradation rates of AHL and LuxR.