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"| | !colspan="2"| Full System logo | ||
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!height="25pt" width="80pt"|Sub Parts | !height="25pt" width="80pt"|Sub Parts | ||
! [[IGEM:IMPERIAL/2006/project/Oscillator/project browser/Prey_Construct| Prey | ! [[IGEM:IMPERIAL/2006/project/Oscillator/project browser/Prey_Construct| Prey Molecule Generator]] | ||
! [[IGEM:IMPERIAL/2006/project/Oscillator/project browser/Predator_Construct| Predator | ! [[IGEM:IMPERIAL/2006/project/Oscillator/project browser/Predator_Construct| Predator Molecule Generator]] | ||
|} | |} | ||
<div class="tabs-blue"> | <div class="tabs-blue"> | ||
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==Model | ==Model description of the Molecular Predation Oscillator== | ||
{| border="1" width="100%" | |||
|- | |||
|rowspan="2"| | |||
'''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> | ||
*<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> | ||
|| | |||
[[Image:2d model 5a3.PNG |thumb|center|Phase diagram (Prey Vs Predator) showing the existence of a limit cycle]] | |||
|- | |||
|[[Image:2d model 5a4.PNG|thumb|center|Time series of the prey molecules. Depending on the parameters, very different profiles can be achieved]] | |||
|- | |||
|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''': | |||
*existence of a limit cycle for '''stable and robust oscillations'''. | |||
*ability to tune the '''frequency''' and '''amplitude''' of the AHL output signal. | |||
|| [[Image:2d model 5a5.PNG|thumb|center|Control of Amplitude & Frequency]] | |||
|} | |||
==Model variables and parameters== | |||
==Model variables and parameters | |||
{| border="1" width="100%" | {| border="1" width="100%" | ||
! style="background:green" colspan="5"| '''Variables''' | |||
|- style="background: | |- 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"| | |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" 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:blue" colspan="5"| '''Parameters''' | |||
|- style="background: | |- style="background:lightblue" | ||
! Name !! Description !! Value !! Confidence !! Reference | ! Name !! Description !! Value !! Confidence !! Reference | ||
|- | |- | ||
|width="100"| a || | |width="100" align="center"| a || maximum synthesis rate of the pLux promoter || to be characterized || to be measured || links | ||
|- | |- | ||
|width="100"| | |width="100" align="center"| a0 || dissociation constant || to be characterized|| to be measured || links | ||
|- | |- | ||
|width="100"| | |width="100" align="center"| b || catalysis rate of the AHL-lactonase(aiiA) || variable || to be measured/can be varied by chemostat || links | ||
|- | |- | ||
|width="100"| | |width="100" align="center"| b0 || Michaelis constant for the AHL-lactonase(aiiA) || to be characterized || to be measured || links | ||
|- | |- | ||
|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 | |width="100" align="center"| c0 || dissociation constant || variable || to be measured/can be varied by chemostat || links | ||
|- | |- | ||
|width="100"| | |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 | ==SBML Model== | ||
[[Image:Slide14b.PNG]] | |||
[[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 [http://en.wikipedia.org/wiki/Hill_equation 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== | ||
[ | *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. | |||
== | <html> | ||
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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.
|
|
A detailed theoretical study and simulations have shown that the properties of this system are able to fulfill our specifications:
|
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
- Characterization of the parameters a, ao shall be done using the Prey Generator Test Contstruct
- Characterization of the parameters c, c0 shall be done using the Predator Generator Sensing Test Construct
- Characterization of the parameters b, b0 shall be done using the Predator Generator Killing Test Construct
- The growth dilution can be controlled by the chemostat washout.
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