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

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(Model description of the oscillator)
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'''[http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/Oscillator/Modelling Click here to find the full derivation of the above equations.]'''
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'''[http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/Oscillator/Modelling Full derivation of the above equations.]'''
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==Graphical representation of oscillator and simulation of oscillations==
==Graphical representation of oscillator and simulation of oscillations==

Revision as of 11:10, 29 October 2006

Super Parts Not applicable
Actual Part Image:J37036 part.png
Sub Parts Prey Construct 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 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

Model description of the oscillator

  • mathematical description of the oscillator:
  • \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]


Full derivation of the above equations.

Graphical representation of oscillator and simulation of oscillations

<showhide> __HIDER__ <hide> Image:Slide14b.PNG </hide></showhide>

  • link to SBML file or matlab.

Model variables and parameters for the growth of the prey

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


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 links
LuxR LuxR is constitutively produced. It forms a complex with AHL to promote production of LuxI which produces AHL constitutively produced, AHL assumed to be 'added' when LuxR production reaches steady state ... links
Parameters
Name Description Value Confidence Reference
a Maximum rate of production of AHL to be characterized to be measured links
a0 ... to be characterized to be measured links
gd AHL wash-out variable to be measured/can be varied by chemostat links


Model variables and parameters for the growth of the predator

  • \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]


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 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 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
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 variable to be measured/can be varied by chemostat 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]


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 links
aiiA molecule acting as the killing module of the prey for the predator 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
b Maximum degradation rate catalyzed by aiiA to be characterized to be measured links
b0 Michaelis-Menten constant of enzyme reaction to be characterized to be measured links
e AHL wash-out variable to be measured/can be varied by chemostat links


Dynamical and sensitivity analysis

Full system modelling and analysis

Characterization

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