IGEM:IMPERIAL/2007/Projects/Biofilm Detector/Modelling/Construct1/Case 1

=Construct 1: Case 1=

 Introduction Case 1 References  

Case 1 : Constituitive Expression of LuxR

From Previous work
 * $$[A]=K_{\alpha}[AHL][LuxR]\cdots\cdots(1)$$
 * $$\frac{d[LuxR]}{dt}=k_{1}-\delta_{LuxR}[LuxR]\cdots\cdots(2)$$

Assume : that concentration of AHL is constant Reasons :
 * Degradation term is negligible
 * Biofilm [AHL] is constant
 * $$\therefore\frac{d[AHL]}{dt}=0\cdots\cdots(3)$$

Also Because [A] is constant and [AHL] is constant $$\Rightarrow$$ [luxR] must also be constant.
 * $$\therefore\frac{d[LuxR]}{dt}=0\cdots\cdots(4)$$
 * $$\Rightarrow[luxR]=\frac{k_{1}}{\delta_{LuxR}}\cdots\cdots(5)$$

Plot of Ry(x) vs. X with y being held constant at above value and limit of Ry(x) being 1