IGEM:IMPERIAL/2007/Projects/Biofilm Detector/Modelling/Construct1/Case 1
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Construct 1: Case 1
Case 1 : Constituitive Expression of LuxR
From Previous work
- [math]\displaystyle{ [A]=K_{\alpha}[AHL][LuxR]\cdots\cdots(1) }[/math]
- [math]\displaystyle{ \frac{d[LuxR]}{dt}=k_{1}-\delta_{LuxR}[LuxR]\cdots\cdots(2) }[/math]
Assume : that concentration of AHL is constant
Reasons :
- Degradation term is negligible
- Biofilm [AHL] is constant
- [math]\displaystyle{ \therefore\frac{d[AHL]}{dt}=0\cdots\cdots(3) }[/math]
Also Because [A] is constant and [AHL] is constant [math]\displaystyle{ \Rightarrow }[/math] [luxR] must also be constant.
- [math]\displaystyle{ \therefore\frac{d[LuxR]}{dt}=0\cdots\cdots(4) }[/math]
- [math]\displaystyle{ \Rightarrow[luxR]=\frac{k_{1}}{\delta_{LuxR}}\cdots\cdots(5) }[/math]
Plot of Ry(x) vs. X with y being held constant at above value and limit of Ry(x) being 1