IGEM:IMPERIAL/2007/Projects/Biofilm Detector/Modelling/Construct2/Case 4

=Construct 2: Case 4=

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

$$\ y = [LuxR] + [A] \Rightarrow [LuxR] = y - [A]\cdots\cdots(1)$$ Likewise $$\ x = [AHL] + [A] \Rightarrow [AHL] = x - [A]\cdots\cdots(2)$$

Substitute (1) and (2) into $$\ [A] = K_{\alpha}[AHL][LuxR]$$

$$\therefore [A] = K_{\alpha}(x - [A])(y - [A])\cdots\cdots(3)$$

Expand (3)

$$ [A]^2 - \left((x+y) + \frac{1}{K_{\alpha}}\right) [A] + xy = 0 $$

More will follow shortly, concerning the nature of roots and stability

$$\Delta = \left((x+y) + \frac{1}{K_{\alpha}}\right)^2 - 4xy $$