# IGEM:IMPERIAL/2006/project/Oscillator/project browser/Predator Construct/Modelling

Super Parts Molecular Prey-Predator Oscillator
Actual Part
Sub Parts Test Sensing Predator Construct Test Killing Predator Construct

## 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 degradation rate of luxR and aiiA is mainly due to the growth dilution.

## Model description of the growth of the predator

• mathematical description of the predator growth and death:
• $\frac{d[luxR]}{dt} = \frac{c * [AHL] * [luxR]}{(c0 + [AHL] * [luxR])} - gd * [luxR]$
• $\frac{d[aiiA]}{dt} = \frac{c * [AHL] * [luxR]}{(c0 + [AHL] * [luxR])} - gd * [aiiA]$
• insert a graphical representation if possible (e.g. CellDesigner display)
• link to SBML file or matlab.

## Model variables and parameters for the growth of the predator

(list all the variables and parameters of the model in a table, specifying if their values are known, unknown, to be measured.)

Name Description Initial Value Confidence Reference Variables AHL homoserine lactone acting as the prey-molecule 0 depends how good is the control of the prey positive feedback links luxR molecule acting as the sensing module for the predator 0 to be measured as we might have to deal with some leakage of the promoter links aiiA molecule acting as the killing module of the prey for the predator 0 to be measured as we might have to deal with some leakage of the promoter links
 Name Description Value Confidence Reference Parameters c maximum synthesis rate of the pLux promoter to be characterized to be measured links c0 dissociation constant according to Hill eq to be characterized to be measured links gd growth dilution to be characterized to be measured links

## Model description of the killing of the prey molecule by the predator

• mathematical description of the killing of the prey:
• $\frac{d[AHL]}{dt} = \frac{b * [aiiA] * [AHL]}{(b0 + [AHL])} - e * [AHL]$

## Model variables and parameters for the killing of the prey molecule by the predator

Name Description Initial Value Confidence Reference Variables AHL homoserine lactone acting as the prey-molecule 0 depends how good is the control of the prey positive feedback links aiiA molecule acting as the killing module of the prey for the predator 0 to be measured as we might have to deal with some leakage of the promoter links
 Name Description Value Confidence Reference Parameters b Maximum degradation rate catalyzed by aiiA ... to be measured links b0 Michaelis-Menten constant of enzyme reaction ... to be measured links e AHL wash-out variable to be measured/can be varied by chemostat links

## Dynamical and sensitivity analysis

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• analyze model in order to show how the part could fulfill its specifications
• insert graph and charts

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• We have decoupled the predator into sensing and killing parts
• For detail modelling, please refer to the modelling section in subparts.

## Characterization

• To characterize the part, we have to measure the production rate and aiiA enzyme activity seperately
• For details characterization, please refer to subparts