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 growth of the predator
- mathematical description of the predator growth and death:
- [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]
- insert a graphical representation if possible (e.g. CellDesigner display)
- link to SBML file or matlab.
Model the production 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 |
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
(list all the variables and parameters of the model in a table, specifying if their values are known, unknown, to be measured.)
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 |
XXX |
known/unknown/to be measured |
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]
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
|
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 measured |
links
|
b0 |
Michaelis-Menten constant of enzyme reaction |
... |
to be measured |
links
|
e |
AHL wash-out |
variable |
to be measured/can be varied by chemostat |
links
|
Dynamical and sensitivity analysis
- analyze model in order to show how the part could fulfill its specifications
- insert graph and charts
Characterization
- Describe how you plan to use the modelling to characterize the part