IGEM:IMPERIAL/2006/project/Oscillator/project browser/Full System/Modelling: Difference between revisions
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==Dynamical and sensitivity analysis== | ==Dynamical and sensitivity analysis== | ||
[http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/Oscillator/Theoretical_Analyses Full system modelling and analysis] | |||
==Characterization== | ==Characterization== |
Revision as of 07:03, 28 October 2006
Super Parts | Not applicable | |
---|---|---|
Actual Part | ||
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 complex 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 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:
- [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]
Click here to find the full derivation of the above equations.
Graphical representation of oscillator and simulation of oscillations
- link to SBML file or matlab.
Model variables and parameters for the growth of the prey
- [math]\displaystyle{ \frac{d[AHL]}{dt}= \frac{a * [AHL]}{(a0 + [AHL])} - gd * [AHL] }[/math]
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
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:
- [math]\displaystyle{ \frac{d[AHL]}{dt} = \frac{b * [aiiA] * [AHL]}{(b0 + [AHL])} - e * [AHL] }[/math]
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
- Characterization of the parameters a, ao shall be done using the prey test contstruct
- Characterization of the parameters c, c0 shall be done using the predator sensing test construct
- Characterization of the parameters b, b0 shall be done using the predator killing test construct
- gd[luxR], gd[AHL] and gd[AiiA] can be controlled by the chemostat washout