IGEM:IMPERIAL/2007/Projects/Biofilm Detector/Modelling/Construct2/Case 4: Difference between revisions
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More will follow shortly, concerning the nature of roots and stability | More will follow shortly, concerning the nature of roots and stability | ||
<math>\Delta = \left((x+y) + \frac{1}{K_{\alpha}}\right)^2 - 4xy </math> | |||
Latest revision as of 07:12, 17 August 2007
Construct 2: Case 4
[math]\displaystyle{ \ y = [LuxR] + [A] \Rightarrow [LuxR] = y - [A]\cdots\cdots(1) }[/math]
Likewise
[math]\displaystyle{ \ x = [AHL] + [A] \Rightarrow [AHL] = x - [A]\cdots\cdots(2) }[/math]
Substitute (1) and (2) into [math]\displaystyle{ \ [A] = K_{\alpha}[AHL][LuxR] }[/math]
[math]\displaystyle{ \therefore [A] = K_{\alpha}(x - [A])(y - [A])\cdots\cdots(3) }[/math]
Expand (3)
[math]\displaystyle{ [A]^2 - \left((x+y) + \frac{1}{K_{\alpha}}\right) [A] + xy = 0 }[/math]
More will follow shortly, concerning the nature of roots and stability
[math]\displaystyle{ \Delta = \left((x+y) + \frac{1}{K_{\alpha}}\right)^2 - 4xy }[/math]
