IGEM:IMPERIAL/2007/Projects/Biofilm Detector/Modelling/Construct2/Case 1

Construct 2: Case 1

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

Case 1 : Both initial concentrations of LuxR and AHL are controllled

[math]\displaystyle{ \displaystyle[A]=K_{\alpha}[AHL]_{0}[LuxR]_{0} }[/math]

[math]\displaystyle{ [AP]=\frac{K_{\alpha}K_{\beta}[AHL]_{0}[LuxR]_{0}[P]_{0}}{1+K_{\alpha}K_{\beta}[AHL]_{0}[LuxR]_{0}} }[/math]

[math]\displaystyle{ R_{y}(x)=\frac{[AP]}{[P]_{0}}=\frac{K_{\alpha}K_{\beta}xy}{1+K_{\alpha}K_{\beta}xy} }[/math]

[math]\displaystyle{ R_{y}(x)=1-\frac{1}{1+K_{\alpha}K_{\beta}xy} }[/math]

[math]\displaystyle{ R_{y}'(x)=\frac{K_{\alpha}K_{\beta}y}{\left(1+K_{\alpha}K_{\beta}xy\right)^2} }[/math]