# IGEM:IMPERIAL/2007/Projects/Biofilm Detector/Modelling/Construct1

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# 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