IGEM:IMPERIAL/2007/Projects/Biofilm Detector/Modelling
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<br>We want to have n% of the promoters bound, thus [AP] = n[P<sub>0</sub>]  <br>We want to have n% of the promoters bound, thus [AP] = n[P<sub>0</sub>]  
  <math> ([A_0]n[P_0])([  +  <math> ([A_0]n[P_0])([P_0]n[P_0]) = nK_D[P_0] </math><br> 
<math> [A_0]n[P_0] = \frac{n}{1n}K_D </math><br>  <math> [A_0]n[P_0] = \frac{n}{1n}K_D </math><br>  
<math> [A_0] = \frac{n}{1n}K_D+n[P_0] </math><br>  <math> [A_0] = \frac{n}{1n}K_D+n[P_0] </math><br>  
Substituting 0.1nM for K<sub>D</sub> and 0.1nM for [P<sub>0</sub>], and let ''n'' be 95%...<br>  Substituting 0.1nM for K<sub>D</sub> and 0.1nM for [P<sub>0</sub>], and let ''n'' be 95%...<br>  
The concentration of A<sub>0</sub> required is 2nM.<br>  The concentration of A<sub>0</sub> required is 2nM.<br>  
  +  Knowing that at eqm:<br>  
  The concentration of LuxR<sub>0</sub> required is ~  +  <math> [AHL][LuxR] = K_D[A_0] </math><br> 
+  <math> ([AHL_0][A_0])([LuxR_0][A_0]) = K_D[A_0] </math><br>  
+  <math> [LuxR_0] = \frac{K_D[A_0]}{[AHL_0][A_0]} + [A_0] </math><br>  
+  The concentration of AHL<sub>0</sub> would be 50nM, K<sub>D</sub> would be 1nM.<br>  
+  The concentration of LuxR<sub>0</sub> required is ~3nM.<br>  
Note that the K<sub>D</sub> of AHLLuxR is only an estimate and may be incorrect.  Note that the K<sub>D</sub> of AHLLuxR is only an estimate and may be incorrect. 
Revision as of 11:37, 26 September 2007
Infector Detector: Modelling
Overview of Modelling
Welcome to our Portal Page for the modelling of Infector Detector.
Infector Dectector (ID) is based on the Quorum Sensing Pathway and our aim in modelling of ID is to determine the concentration of AHL in biofilm we can detect such that we report a visible signal .We are looking at two constructs to emulate the quorum sensing pathway:
The main feature of this construct is that it constitutively expresses LuxR Here is what our construct looks like composed of biobricks 
The main feature of this construct is that it does not constitutively expresses LuxR and therefore enables us to determine the initial concentration of LuxR 
Here is a Block Diagram Picture of how construct 1 will work 
Here is a Block Diagram Picture of how construct 2 will work 
Transient response of construct 1 [LuxR]o=0 ; [AHL]o=variable ; [A]o=0 ; [P]o=1 ; [AP]o=0 ; [FP]o=0 
Transient response of construct 2 [LuxR]o=10 ; [AHL]o=variable ; [A]o=0 ; [P]o=1 ; [AP]o=0 ; [FP]o=0 
 As can be seen from the above plots, construct 1 takes longer to reach steady state [FP], meaning that over the same time period it reaches a lower maximum value
Transfer function of system:

Transfer function of system:

Transfer function of system:

Transfer function of system:

Advanced plot of transfer function:

Advanced plot of transfer function:




As can be seen from the plots above the the threshold moves according to the level of LuxR. Looking at our plots we can see that at time, s=0.5 the threshold is different for construct 1 to construct 2
17.08.07 Modelling General Concerns
For protocols to figure out :
 Degradation terms:GFP,LuxR,AHL  want expt to find delta as a function of chassis
 If we put protease inhibitors in the mixture and can we assume negligible degradation for GFP and luxR, not sure about AHL have to look in literature for that.
 What is the visual threshold of [GFP]  want expt to find this
 Do you need to do it for GFP or just for the final reporter used, which is dsRED
 What is the concentration of promoters  is this chassis dependant ?
 You know  the weight of DNA added, and the mass of each plasmid. Knowing that there is only one promoter on each plasmid, you can calculate the concentration of promoters.
 Activation/Response Time of Plux (F2620)?
 You might want to check the part F2620, not sure if the information is useful, or valid for in vitro.
(Protocols) Construct 1 specific:
 What is the lifespan of the whole system?
 Can we get steadystateof LuxR?  When will this happen ?  Before cell dies ?
 Having reached steady state is there enough E left to express [GFP]
(Protocols) Construct 2 specific:
 Can we obtain purified LuxR to be injected into System  protocol for prep of LuxR
 Protease inhibitors available?
 Yes, in homemade extract. For commercial extract, still waiting for reply from promega.
 How long will it take to get construct 2 ready ?
 Week 8, earliest (unfortunately)
For modelling to figure out :
 Kvalues for rxn pathway
 k5/k4 = 5*10^{10}M [source: pmid=17400743]
 Response of Biofilm : Is [AHL] constant ?
 Simulation of [LuxR] vs. Time
Concentration of LuxR for construct 2
At equilibrium:
[A][P] = K_{D}[AP]
Let us assign initial concentrations as [A_{0}] and [P_{0}]
We want to have n% of the promoters bound, thus [AP] = n[P_{0}]
([A_{0}] − n[P_{0}])([P_{0}] − n[P_{0}]) = nK_{D}[P_{0}]
Substituting 0.1nM for K_{D} and 0.1nM for [P_{0}], and let n be 95%...
The concentration of A_{0} required is 2nM.
Knowing that at eqm:
[AHL][LuxR] = K_{D}[A_{0}]
([AHL_{0}] − [A_{0}])([LuxR_{0}] − [A_{0}]) = K_{D}[A_{0}]
The concentration of AHL_{0} would be 50nM, K_{D} would be 1nM.
The concentration of LuxR_{0} required is ~3nM.
Note that the K_{D} of AHLLuxR is only an estimate and may be incorrect.