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

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!height="25pt" width="80pt"|Sub Parts
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! [[Image:R0062 logo.png|40px]]
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! [[Image:B0034 logo.png|40px]]
! <bbpart>B0034</bbpart>
! [[Image:C0062 logo.png|40px]]
! <bbpart>C0062</bbpart>
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! <bbpart>I13504</bbpart>
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__NOTOC__
==Model assumptions and relevance==


[[image:Model_predetor_sensor.JPG]]
*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].


*Input = AHL
*Assumptions linked to the quorum sensing:
*Output = GFP
**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 degradation rate of luxR and aiiA is mainly due to the growth dilution.


The model produces GFP and LuxR as a function of LuxR + AHL
==Model description of the oscillator==


An interesting dynamic has been observed in this system.  
'''[http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/Oscillator/Modelling Full derivation of the above equations.]'''
*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


==Model description of the growth of the predator==
*mathematical description of the predator growth and death:
**<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>


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.
*insert a graphical representation if possible (e.g. CellDesigner display)
*link to SBML file or matlab.


[[image:Model_predetor_sensor_output_low_AHL.JPG]]
==Model variables and parameters for the growth of the predator==
Amount of AHL below critical value
[[image:Model_predetor_sensor_output_high_AHL.JPG]]
Amount of AHL above critical value


(list all the variables and parameters of the model in a table, specifying if their values are known, unknown, to be measured.)


 
{| border="1" width="100%"
'''Values (unrealistic)'''
| style="background:lightblue" colspan="5"| '''Variables'''
 
|- style="background:lightgrey"
<blockquote style="background: white; border: 1px solid rgb(153, 153, 153); padding: 1em;">
!Name !! Description !! Initial Value !! Confidence !! Reference
{| border="1"
|+ Unrealistic Values
! Name !! Value  
|-
! LuxR
| 0.8
|-
|-
! AHL (Low)
|width="100"| AHL || homoserine lactone acting as the prey-molecule || 0|| depends how good is the control of the prey positive feedback || links
| 0.07
|-
|-
! AHL (High)
|width="100"| 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
| 0.11
|-
|-
! GFP
|width="100"| aiiA || molecule acting as the killing module of the prey for the predator  || 0 || to be measured as we might have to deal with some leakage of the promoter || links
| 0  
 
|}
|}
</blockquote>


 
{| border="1" width="100%"
'''Parameters (Un-realistic)'''
| style="background:lightblue" colspan="5"| '''Parameters'''
 
|- style="background:lightgrey"
<blockquote style="background: white; border: 1px solid rgb(153, 153, 153); padding: 1em;">
! Name !! Description !! Value !! Confidence !! Reference
{| border="1"
|+ Unrealistic Perameters
! Name !! Value  
|-
|-
! Vm LuxR
|width="100"| c || maximum synthesis rate of the pLux promoter || to be characterized || to be measured || links
| 2
|-
|-
! Km LuxR
|width="100"| c0 || dissociation constant according to Hill eq || to be characterized|| to be measured || links
| 1.87
|-
|-
! K_Deg_LuxR
|width="100"| gd || growth dilution  || to be characterized || to be measured || links
| 0.1
|-
! K_Deg_GFP
| 0.1
 
|}
|}
</blockquote>
* 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.
<big>
<br>
'''To work out Km and Vm'''
<br>
</big>
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'''


[[image:Transfer_Function_Predator_Sensor.JPG]]
==Characterization==


''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).''
*Parameters c & c0 for characterization have to be extracted.
*gd[luxR] and gd[aiiA] can be controlled by the chemostat.

Latest revision as of 08:13, 29 October 2006

Super Parts Predator Construct
Actual Part
Sub Parts <bbpart>R0062</bbpart> <bbpart>B0034</bbpart> <bbpart>C0062</bbpart> <bbpart>I13504</bbpart>


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 degradation rate of luxR and aiiA is mainly due to the growth dilution.

Model description of the oscillator

Full derivation of the above equations.

Model description of the growth of the predator

  • mathematical description of the predator growth and death:
    • [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 0 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 to be characterized to be measured links

Characterization

  • Parameters c & c0 for characterization have to be extracted.
  • gd[luxR] and gd[aiiA] can be controlled by the chemostat.
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