IGEM:IMPERIAL/2007/Projects/Biofilm Detector/Modelling/Construct2/Case 3

Construct 2: Case 3

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

Case 3 : Only y is controlled

[math]\displaystyle{ \displaystyle{x=[AHL]_{0}=[AHL]+[A]} }[/math]

[math]\displaystyle{ \displaystyle[A]=x-[AHL] }[/math]

but [math]\displaystyle{ \displaystyle[A]=K_{\alpha}[AHL]y }[/math]

Commenting Text

[math]\displaystyle{ \therefore\displaystyle{x-[AHL]=K_{\alpha}y} }[/math]

[math]\displaystyle{ \therefore[AHL]=\frac{x}{1+K_{\alpha}y} }[/math]

[math]\displaystyle{ [A]=K_{\alpha}\left(\frac{xy}{1+K_{\alpha}y}\right) }[/math]

More comments

[math]\displaystyle{ Ry(x)=\frac{K_{\alpha}K_{\beta}xy}{1+yK_{\alpha}+K_{\alpha}K_{\beta}xy} }[/math]