IGEM:IMPERIAL/2006/project/Oscillator/project browser/Test Sensing Predator Construct/Modelling

Super Parts	Predator Construct
Actual Part
Sub Parts

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

• Input = AHL
• Output = GFP

The model produces GFP and LuxR as a function of LuxR + AHL

An interesting dynamic has been observed in this system.

• The rate of synthesis of luxR depends on the AHL concentration and the luxR concentration and a constant
• The rate of degredation of LuxR depends on only the LuxR constant and the rate of degredation

This means that the rate of degredation can be higher than the rate of syntheses so the steady state will be no LuxR for very low values of AHL but after a critical value of AHL the steady state will be positive.

Amount of AHL below critical value Amount of AHL above critical value

Values (unrealistic)

Unrealistic Values

Name	Value
LuxR	0.8
AHL (Low)	0.07
AHL (High)	0.11
GFP	0

Parameters (Un-realistic)

Unrealistic Perameters

Name	Value
Vm LuxR	2
Km LuxR	1.87
K_Deg_LuxR	0.1
K_Deg_GFP	0.1

• We assume HSL is constant
• (the gene expression was moddeled using mechiles menten kenitics so luxR has a Km and Vm of binding to the gene)

Key paremeter - Km of LuxR

This must be high. We can increace the apparant Km in real cells using recombinant plasmids. A high Km will reduce the rate of reaction and increace the range at which AHL can alter the reaction.

To work out Km and Vm

Transcription at lux pR is proportional to the amount of LuxR+HSL present. This is dependent on the amount of HSL added so the rate of GFP production will be proportional to the amount of HSL added.

If we know the Rate of GFP degradation and the equilibrium conc of GFP then we can work out the rate of GFP synthesis for that amount of HSL as degradation = synthesis at equilibrium.

If we know the rates and the substrate conc for those rates we can make a lineweaver burke plot. Plot 1/v against 1/[s].

1 / V = (Km / Vm)(1 / [S]) + (1 / Vm)

Y = M X + C

[:http://openwetware.org/images/3/3b/Lineweaver_Buke_Plot.JPG]

This will allow us to work out the real values of Km and Vm for LuxR+AHL when it binds LuxPr, :-D

Transfer Function

The transfer function of this part shows an unusual property in that the system will not produce any GFP at low HSL values (rather than tending to 1/infinity). This is caused by the critical value of the system described above. This should make this device function as a low pass filter, this property is of no use to the oscilator, but should be noted. The predator cells will not become de-sensitised to HSL because the luxpR operon shows leaky expression, this keeps a low conc of LuxR in the cells at all times (this property was not modeled).