IGEM:IMPERIAL/2006/project/Oscillator/project browser/Prey Construct/Modelling

 Specifications Design Modelling Implementation Testing/Validation  

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. This gives a good approximation if LuxR is in excess of AHL (ie not saturated by AHL) but this is unlikely to occur all the time as LuxI levels increase to very high amounts).
 * 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.)


 * LuxI can be ignored:
 * LuxI levels vary throughout, and it is these levels that are directly responsible for AHL production (this may account for a flaw in the model)
 * 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

Model description for growth of prey

 * A full derivation for the growth of the prey yields the following equation:


 * $$\frac{d[AHL]}{dt}= \frac{a * [AHL]}{(a0 + [AHL])} - gd * [AHL]$$



Characterization

 * We need to characterize the rate of synthesis of AHL.
 * To do this we use the predator sensing test construct which shares the same tetR promoter as the prey.

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