IGEM:IMPERIAL/2006/project/Oscillator/project browser/Full System/Modelling

Super Parts	Not applicable
Actual Part
Sub Parts	Prey Construct	Predator Construct

• Specifications
• Design
• Modelling
• Implementation
• Testing/Validation

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 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