IGEM:IMPERIAL/2006/project/Oscillator/project browser/Full System/Modelling: Difference between revisions

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!height="25pt" width="80pt"|Actual Part
!height="25pt" width="80pt"|Actual Part
!colspan="2"| [[Image:J37036 logo.png]]
!colspan="2"| Full System logo
|-
|-
!height="25pt" width="80pt"|Sub Parts
!height="25pt" width="80pt"|Sub Parts
! [[IGEM:IMPERIAL/2006/project/Oscillator/project browser/Prey_Construct| Prey Construct]]  
! [[IGEM:IMPERIAL/2006/project/Oscillator/project browser/Prey_Construct| Prey Molecule Generator]]  
! [[IGEM:IMPERIAL/2006/project/Oscillator/project browser/Predator_Construct| Predator Construct]]   
! [[IGEM:IMPERIAL/2006/project/Oscillator/project browser/Predator_Construct| Predator Molecule Generator]]   
|}
|}
<div class="tabs-blue">
<div class="tabs-blue">
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<br style="clear:both">
<br style="clear:both">


==Model assumptions and relevance==
==Model description of the Molecular Predation Oscillator==
*General assumptions on gene expression modelling:
**Quasi-steady state hypothesis on mRNA expression.
**Gene activation can be approximated by [http://en.wikipedia.org/wiki/Hill_equation Hill equations].


*Assumptions linked to the quorum sensing:
{| border="1" width="100%"
**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 complex is in equilibrium with the concentration of AHL
|rowspan="2"|
**LuxR is constitutively produced and reaches steady state before AHL production begins. [LuxR] in the prey can be considered constant.
**The concentration of AHL-lactonase is 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:


'''This system of ODEs describes the full system in a chemostat.'''<br><br><br>
*<math>\frac{d[AHL]}{dt}= \frac{a * [AHL]}{(a0 + [AHL])} - \frac{b * [AiiA] * [AHL]}{(b0 + [AHL])} - gd * [AHL]</math>
*<math>\frac{d[AHL]}{dt}= \frac{a * [AHL]}{(a0 + [AHL])} - \frac{b * [AiiA] * [AHL]}{(b0 + [AHL])} - gd * [AHL]</math>
<showhide>
__HIDER__
<hide>
[[Image:Slide5b.PNG]]
[[Image:Slide6a.PNG]]
</hide></showhide>
*<math>\frac{d[luxR]}{dt} = \frac{c * [AHL] * [luxR]}{(c0 + [AHL] * [luxR])} - gd * [luxR]</math>
*<math>\frac{d[luxR]}{dt} = \frac{c * [AHL] * [luxR]}{(c0 + [AHL] * [luxR])} - gd * [luxR]</math>
*<math>\frac{d[aiiA]}{dt} = \frac{c * [AHL] * [luxR]}{(c0 + [AHL] * [luxR])} - gd * [aiiA]</math>
*<math>\frac{d[aiiA]}{dt} = \frac{c * [AHL] * [luxR]}{(c0 + [AHL] * [luxR])} - gd * [aiiA]</math>
<showhide>
||
__HIDER__
[[Image:2d model 5a3.PNG |thumb|center|Phase diagram (Prey Vs Predator) showing the existence of a limit cycle]]
<hide>
|-
 
|[[Image:2d model 5a4.PNG|thumb|center|Time series of the prey molecules. Depending on the parameters, very different profiles can be achieved]]
[[Image:Slide7b.PNG]]
|-
[[Image:Slide8c.PNG]]
|rowspan="1"|A detailed '''[[IGEM:IMPERIAL/2006/project/Oscillator/Theoretical Analyses/Results | theoretical study and simulations]]''' have shown that the properties of this system are '''able to fulfill our specifications''':
[[Image:Slide9b.PNG]]
*existence of a limit cycle for '''stable and robust oscillations'''.
[[Image:Slide10.PNG]]
*ability to tune the '''frequency''' and '''amplitude''' of the AHL output signal.
 
|| [[Image:2d model 5a5.PNG|thumb|center|Control of Amplitude & Frequency]]
</hide></showhide>
|}
 
*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 prey==
 
**<math>\frac{d[AHL]}{dt}= \frac{a * [AHL]}{(a0 + [AHL])} - gd * [AHL]</math>


==Model variables and parameters==


{| border="1" width="100%"
{| border="1" width="100%"
| style="background:lightblue" colspan="5"| '''Variables'''
! style="background:green" colspan="5"| '''Variables'''
|- style="background:lightgrey"
|- style="background:lightgreen"
!Name !! Description !! Initial Value !! Confidence !! Reference
!Name !! Description !! Initial Value !! Confidence !! Reference
|-
|-
|width="100"| AHL || homoserine lactone acting as the prey-molecule || 0|| depends how good is the control of the prey positive feedback || links
|width="100" align="center"| AHL || homoserine lactone acting as the prey-molecule || 0|| depends how good is the control of the prey positive feedback. Should be measured. || links
|-
|width="100" align="center"| 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
|-
|-
|width="100"| 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
|width="100" align="center"| 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
|}
|}
<br><br>


{| border="1" width="100%"  
{| border="1" width="100%"  
| style="background:lightblue" colspan="5"| '''Parameters'''
! style="background:blue" colspan="5"| '''Parameters'''
|- style="background:lightgrey"
|- style="background:lightblue"
! Name !! Description !! Value !! Confidence !! Reference
! Name !! Description !! Value !! Confidence !! Reference
|-
|-
|width="100"| a || Maximum rate of production of AHL || to be characterized || to be measured || links
|width="100" align="center"| a || maximum synthesis rate of the pLux promoter || to be characterized || to be measured || links
|-
|width="100"| a0 || ... || to be characterized || to be measured || links
|-
|width="100"| gd || AHL wash-out  || variable || to be measured/can be varied by chemostat || links
|}
 
 
==Model variables and parameters for the growth of the predator==
 
 
{| border="1" width="100%"
| style="background:lightblue" colspan="5"| '''Variables'''
|- style="background:lightgrey"
!Name !! Description !! Initial Value !! Confidence !! Reference
|-
|-
|width="100"| AHL || homoserine lactone acting as the prey-molecule || 0|| depends how good is the control of the prey positive feedback || links
|width="100" align="center"| a0 || dissociation constant  || to be characterized|| to be measured || links
|-
|-
|width="100"| 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
|width="100" align="center"| b || catalysis rate of the AHL-lactonase(aiiA)  || variable || to be measured/can be varied by chemostat  || links
|-
|-
|width="100"| 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
|width="100" align="center"| b0 || Michaelis constant for the AHL-lactonase(aiiA) || to be characterized || to be measured || links
|}
 
{| border="1" width="100%"
| style="background:lightblue" colspan="5"| '''Parameters'''
|- style="background:lightgrey"
! Name !! Description !! Value !! Confidence !! Reference
|-
|-
|width="100"| c || maximum synthesis rate of the pLux promoter || to be characterized || to be measured || links
|width="100" align="center"| c || maximum synthesis rate of the pLux promoter || to be characterized|| to be measured || links
|-
|-
|width="100"| c0 || dissociation constant according to Hill eq || to be characterized|| to be measured || links
|width="100" align="center"| c0 || dissociation constant || variable || to be measured/can be varied by chemostat  || links
|-
|-
|width="100"| gd || growth dilution || variable || to be measured/can be varied by chemostat  || links
|width="100" align="center"| dg || growth dilution due to chemostat wash-out || to be characterized || to be measured || links
|}
|}


'''[http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/Oscillator/Modelling Full derivation of the above equations.]'''


==Model description of the killing of the prey molecule by the predator==
==SBML Model==


*mathematical description of the killing of the prey:
[[Image:Slide14b.PNG]]
[[Media:IGEM_IMPERIAL_FullSystem_Model.sbml]]


**<math>\frac{d[AHL]}{dt} = \frac{b * [aiiA] * [AHL]}{(b0 + [AHL])} - e * [AHL]</math>


==Model assumptions and relevance==
*General assumptions on gene expression modelling:
**Quasi-steady state hypothesis on mRNA expression.
**Gene activation can be approximated by [http://en.wikipedia.org/wiki/Hill_equation Hill equations].


{| border="1" width="100%"
*Assumption on the Chemostat:
| style="background:lightblue" colspan="5"| '''Variables'''
**It assumes that the prey molecule generator and the predator molecule generator populations are stable (the cell populations have reached steady-state).
|- style="background:lightgrey"
**the degradation of the molecules is mainly due to the wash-out of the chemostat.
!Name !! Description !! Initial Value !! Confidence !! Reference
|-
|width="100"| AHL || homoserine lactone acting as the prey-molecule || 0|| depends how good is the control of the prey positive feedback || links
|-
|width="100"| 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
|}
 
{| border="1" width="100%"
| style="background:lightblue" colspan="5"| '''Parameters'''
|- style="background:lightgrey"
! Name !! Description !! Value !! Confidence !! Reference
|-
|width="100"| b || Maximum degradation rate catalyzed by aiiA || to be characterized || to be measured || links
|-
|width="100"| b0 || Michaelis-Menten constant of enzyme reaction || to be characterized || to be measured || links
|-
|width="100"| e || AHL wash-out || variable || to be measured/can be varied by chemostat || links
|}


*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


==Dynamical and sensitivity analysis==


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


*Characterization of the parameters a, ao shall be done using the '''[[IGEM:IMPERIAL/2006/project/Oscillator/project_browser/Test_Sensing_Prey_Construct/Modelling | Prey Generator Test Contstruct]]'''
*Characterization of the parameters c, c0 shall be done using the '''[[IGEM:IMPERIAL/2006/project/Oscillator/project_browser/Test_Sensing_Predator_Construct/Modelling | Predator Generator Sensing Test Construct]]'''
*Characterization of the parameters b, b0 shall be done using the '''[[IGEM:IMPERIAL/2006/project/Oscillator/project_browser/Test_Killing_Predator_Construct/Modelling | Predator Generator Killing Test Construct]]'''
*The growth dilution can be controlled by the chemostat washout.


==Characterization==
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*Characterization of the parameters a, ao shall be done using the [http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/Oscillator/project_browser/Test_Sensing_Prey_Construct/Modelling prey test contstruct]
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*Characterization of the parameters c, c0 shall be done using the [http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/Oscillator/project_browser/Test_Sensing_Predator_Construct/Modelling predator sensing test construct]
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*Characterization of the parameters b, b0 shall be done using the [http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/Oscillator/project_browser/Test_Killing_Predator_Construct/Modelling predator killing test construct]
</html>

Latest revision as of 09:39, 30 October 2006

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.


  • [math]\displaystyle{ \frac{d[AHL]}{dt}= \frac{a * [AHL]}{(a0 + [AHL])} - \frac{b * [AiiA] * [AHL]}{(b0 + [AHL])} - gd * [AHL] }[/math]
  • [math]\displaystyle{ \frac{d[luxR]}{dt} = \frac{c * [AHL] * [luxR]}{(c0 + [AHL] * [luxR])} - gd * [luxR] }[/math]
  • [math]\displaystyle{ \frac{d[aiiA]}{dt} = \frac{c * [AHL] * [luxR]}{(c0 + [AHL] * [luxR])} - gd * [aiiA] }[/math]
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

Full derivation of the above equations.

SBML Model

Media:IGEM_IMPERIAL_FullSystem_Model.sbml


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


Characterization

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