# IGEM:IMPERIAL/2006/project/Oscillator/project browser/Full System/Modelling

Super Parts Not applicable
Actual Part Full System logo
Sub Parts Prey Molecule Generator Predator Molecule Generator

## Model description of the Molecular Predation Oscillator

 This system of ODEs describes the full system in a chemostat. $\frac{d[AHL]}{dt}= \frac{a * [AHL]}{(a0 + [AHL])} - \frac{b * [AiiA] * [AHL]}{(b0 + [AHL])} - gd * [AHL]$ $\frac{d[luxR]}{dt} = \frac{c * [AHL] * [luxR]}{(c0 + [AHL] * [luxR])} - gd * [luxR]$ $\frac{d[aiiA]}{dt} = \frac{c * [AHL] * [luxR]}{(c0 + [AHL] * [luxR])} - gd * [aiiA]$ Phase diagram (Prey Vs Predator) showing the existence of a limit cycle Time series of the prey molecules. Depending on the parameters, very different profiles can be achieved A detailed theoretical study and simulations have shown that the properties of this system are able to fulfill our specifications: existence of a limit cycle for stable and robust oscillations. ability to tune the frequency and amplitude of the AHL output signal. Control of Amplitude & Frequency

## Model variables and parameters

Variables
Name Description Initial Value Confidence Reference
AHL homoserine lactone acting as the prey-molecule 0 depends how good is the control of the prey positive feedback. Should be measured. links
luxR molecule acting as the sensing module for the predator generator 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 molecule for the predator generator to be measured to be measured as we might have to deal with some leakage of the promoter links

Parameters
Name Description Value Confidence Reference
a maximum synthesis rate of the pLux promoter to be characterized to be measured links
a0 dissociation constant to be characterized to be measured links
b catalysis rate of the AHL-lactonase(aiiA) variable to be measured/can be varied by chemostat links
b0 Michaelis constant for the AHL-lactonase(aiiA) to be characterized to be measured links
c maximum synthesis rate of the pLux promoter to be characterized to be measured links
c0 dissociation constant variable to be measured/can be varied by chemostat links
dg growth dilution due to chemostat wash-out to be characterized to be measured links

## 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.
• Assumption on the Chemostat:
• It assumes that the prey molecule generator and the predator molecule generator populations are stable (the cell populations have reached steady-state).
• the degradation of the molecules is mainly due to the wash-out of the chemostat.
• 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 concentration of the heterodimer is in equilibrium with the concentration of AHL
• LuxR is constitutively produced and reaches steady state before AHL production begins. [LuxR] in the prey can be considered constant
• The degradation rate of luxR and AHL-lactonase is due to the growth dilution which, in this case, is controlled by the chemostat
• AHL is diffusing freely throughout the system