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

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Construct 2: Case 4


\ 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

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