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

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Construct 2: Case 1


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}

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