# IGEM:IMPERIAL/2006/project/Oscillator/project browser/Test Sensing Prey Construct/Modelling

Super Parts Prey Construct
Actual Part
T9002: Test Sensing Prey Construct
Sub Parts F2620 intermediate_part intermediate_part

## Model assumptions and relevance

• General assumptions on gene expression modelling:
• Quasi-steady state hypothesis on mRNA expression.
• Gene activation can be approximated by Hill equations.
• Assumptions linked to the quorum sensing:
• As a first approximation, we assume that luxR and AHL molecules form a heterodimer (even if it has been found that the complex formed is more complicated)
• The relationship between the heterodimer formed from LuxR and AHL in activating genes is linear
• LuxR is at steady state since it is under the control of the constitutive promoter tetR
• LuxR is in excess of AHL (ie not saturated by AHL)

## Model description

• Mathematical Description of GFP levels (prey sensitivity):
$\frac{d[GFP]}{dt} = \frac{a \times [AHL]}{a_{0} + [AHL]} - d_{GFP} \times [GFP]$
For a full derivation, see Modelling Prey Sensing Test Construct

 Graphical Representation of Model in Cell Designer Output from model in Cell Designer based on modelling equation above

## Model variables and parameters

Name Description Initial Value Confidence Reference Variables AHL Acyl Homoserince Lactone representing the prey molecule Concentration Range varying between 0nM and 10uM known links GFP Green Fluorescent Protein to act as PoPs 0 to be measured links
 Name Description Value Confidence Reference Parameters a population-dependent ? to be extracted using experimental data links a0 constant ? to be extracted using experimental data links dGFP degradation constant due to GFP degradation (Half-life 45min.) ? to be extracted using experimental data links

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## Characterization

• Describe how you plan to use the modelling to characterize the part