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
 * $$\displaystyle{x=[AHL]_{0}=[AHL]+[A]}$$
 * $$\displaystyle[A]=x-[AHL]$$
 * but $$\displaystyle[A]=K_{\alpha}[AHL]y$$

Commenting Text
 * $$\therefore\displaystyle{x-[AHL]=K_{\alpha}y}$$
 * $$\therefore[AHL]=\frac{x}{1+K_{\alpha}y}$$
 * $$[A]=K_{\alpha}\left(\frac{xy}{1+K_{\alpha}y}\right)$$

More comments
 * $$Ry(x)=\frac{K_{\alpha}K_{\beta}xy}{1+yK_{\alpha}+K_{\alpha}K_{\beta}xy}$$