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

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

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

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

$$R_{y}(x)=1-\frac{1}{1+K_{\alpha}K_{\beta}xy}$$

$$R_{y}'(x)=\frac{K_{\alpha}K_{\beta}y}{\left(1+K_{\alpha}K_{\beta}xy\right)^2}$$