IGEM:IMPERIAL/2007/Projects/Biofilm Detector/Modelling/Construct1/Case 1

Construct 1: Case 1

• Introduction
• Case 1
• References

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