Construct 1: Introduction
With the chemical pathway below for construct 1 we can make form some initial equations about the system.
Our aim in modelling Infector Detector is to determine the concentration of biofilm we can detect such that we report a visible signal. Therefore we want to relate the GFP concentration to the concentration of AHL. Starting that the rate of change in GFP concentration:
Aussume : [AP] reaches a constant level
Reason : Treat 1st formation of AP complex as a black box - it just reaches steady state.
Assume : Conservation of Plux Promoters
Reason : no damage to Promoters will occour eg. no DNA damage due to old age or cell defence mechanisms attacking the DNA
Substitute this into (3)
Solving for [AP]
From 9 [AP] is a constant [A] is a constant
From Reaction pathways at top of page we can see that because 3 is in equilibrium 2 is in equilibrium
From these two statements we can say that at equilibrium:
Substituting all of this into expression for GFP