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


 * $$\frac{d[LuxR]}{dt}=-\delta_{LuxR}-k_{3}[A]-k_{2}[LuxR][AHL]\cdots\cdots(1)$$
 * $$\frac{d[AHL]}{dt}=-\delta_{AHL}[AHL]+k_{3}[A]-k_{2}[LuxR][AHL]\cdots\cdots(2)$$
 * $$\frac{d[A]}{dt}\cdots\cdots(3)$$
 * $$\frac{d[A]}{dt}=-k_{3}[A]+k_{2}[LuxR][AHL]\cdots\cdots(4)$$

Lumping degradation of LuxR and AHL into Activator Degradation term
 * $$[A]=[A]_{0}e^{-\left(\delta_{LuxR}+\delta_{AHL}\right)t}\cdots\cdots(5)$$

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.