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

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==Model assumptions and relevance==
==Model assumptions and relevance==
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*LuxR is at steady state
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*General assumptions on gene expression modelling:
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**A good approximation if LuxR gene is left in an active state while cells are growing in medium
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::*Quasi-steady state hypothesis on mRNA expression.
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*LuxR and AHL bind in a linear second order fashion
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::*Gene activation can be approximated by Hill equations.
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**This is not strictly true as LuxR and AHL bind using pseudo-Michaelis-Menten kinetics
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*Assumptions linked to the quorum sensing:
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**Gives a good approximation if LuxR is in excess of AHL (ie not saturated by AHL)
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::*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).
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***Unlikely to occur all the time as LuxI levels increase to very high amounts
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::*The concentration of the heterodimer is in equilibrium with the concentration of AHL
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*LuxI can be ignored
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::*LuxR is constitutively produced and reaches steady state before AHL production begins. ([LuxR] in the prey can be considered constant.)
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**LuxI levels vary throughout, and it is these levels that are directly responsible for AHL production
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*LuxI can be ignored:
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**This could be a major flaw in the model
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::*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
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==Model description==
 
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[[image:J37015_Model.JPG]]
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==Model description for growth of prey==
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*A [http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/Oscillator/Modelling/J37015 full derivation for the growth of the prey] yields the following equation:
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[http://openwetware.org/images/1/1c/J37015.xml J37015 SBML File]
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*<math>\frac{d[AHL]}{dt}= \frac{a * [AHL]}{(a0 + [AHL])} - \frac{b * [AiiA] * [AHL]}{(b0 + [AHL])} - gd * [AHL]</math>
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==Model variables and parameters==
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[[Image:Slide6a.PNG]]
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==Model variables and parameters for growth of prey==
{| border="1" width="100%"
{| border="1" width="100%"
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!Name !! Description !! Initial Value !! Confidence !! Reference
!Name !! Description !! Initial Value !! Confidence !! Reference
|-
|-
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|width="100"|AHL||Starting [AHL], must be >0|| 1 ||Unknown|| links
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|width="100"|AHL|| homoserine lactone acting as the prey-molecule || 0 || depends how good is the control of the prey positive feedback. Should be measured. || links
|}
|}
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! Name !! Description !! Value !! Confidence !! Reference
! Name !! Description !! Value !! Confidence !! Reference
|-
|-
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|width="100"| AHL Degredation || Rate of AHL Degredation || Half-Life = 24 Hours || Known || links
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|width="100"| a || maximum synthesis rate of the pLux promoter || to be characterized || to be measured || links
|-
|-
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|width="100"| AHL Vmax|| Maximum rate of production of AHL ||10|| Unknown || links
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|width="100"| a0 || dissociation constant || to be characterized || to be measured || links
|-
|-
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|width="100"| AHL Kd || Value at which [Substrate] gives 50% Vmax || 1000 || Unknown|| links
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|width="100"| dg || growth dilution due to chemostat wash-out || to be characterized || to be measured || links
|}
|}
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==Characterization==
 +
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*We need to characterize the rate of synthesis of AHL.
 +
*To do this we use the [http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/Oscillator/project_browser/Test_Sensing_Prey_Construct/Modelling predator sensing test construct] which shares the same tetR promoter as the prey.

Revision as of 22:13, 29 October 2006

Super Parts Molecular Prey-Predator Oscillator
Actual Part Image:J37015page.JPG
Sub Parts Test Sensing Prey Construct <bbpart>C0261</bbpart> <bbpart>I13401</bbpart>


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

  • \frac{d[AHL]}{dt}= \frac{a * [AHL]}{(a0 + [AHL])} - \frac{b * [AiiA] * [AHL]}{(b0 + [AHL])} - gd * [AHL]

Image:Slide6a.PNG

Model variables and parameters for growth of prey

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
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
dg growth dilution due to chemostat wash-out to be characterized to be measured links

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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