Team:Paris/Modeling/f1

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{{Paris/Toggle|Algorithm|Team:Paris/Modeling/More_f1_Algo}}  
{{Paris/Toggle|Algorithm|Team:Paris/Modeling/More_f1_Algo}}  
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</div>
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{|border="1" style="text-align: center"
 
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|param
 
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|signification
 
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|unit
 
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|value
 
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|comments
 
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|-
 
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|[expr(pTet)]
 
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|expression rate of <br> pTet '''with RBS E0032'''
 
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|nM.min<sup>-1</sup>
 
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|
 
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|need for 20 values with well choosen [aTc]<sub>i</sub> <br>
 
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with 5 measures for each
 
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|-
 
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|γ<sub>GFP</sub>
 
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|dilution-degradation rate <br> of GFP(mut3b)
 
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|min<sup>-1</sup>
 
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|0.0198
 
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|Time for Cell Division : 35 min. ; No degradation
 
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|-
 
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|[GFP]
 
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|GFP concentration at steady-state
 
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|nM
 
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|
 
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|need for 100 measures
 
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|-
 
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|(''fluorescence'')
 
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|value of the observed fluorescence
 
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|au
 
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|
 
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|need for 100 measures
 
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|-
 
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|''conversion''
 
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|conversion ration between <br> fluorescence and concentration
 
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|nM.au<sup>-1</sup>
 
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|(1/79.429)
 
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|
 
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|}
 
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<br><br>
 
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{|border="1" style="text-align: center"
 
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|param
 
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|signification <br> corresponding parameters in the [[Team:Paris/Modeling/Oscillations#Resulting_Equations|equations]]
 
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|unit
 
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|value
 
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|comments
 
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|-
 
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|β<sub>tet</sub>
 
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|production rate of pTet '''with RBS E0032''' <br> β<sub>1</sub>
 
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|nM.min<sup>-1</sup>
 
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|
 
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|
 
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|-
 
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|(K<sub>tet</sub>/{coef<sub>tet</sub>})
 
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|activation constant of pTet <br> K<sub>20</sub>
 
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|nM
 
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|
 
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|The [[Team:Paris/Modeling/Codes|optimisation program]] will give us (&gamma; K<sub>tet</sub> / {coef<sub>tet</sub>} &#131;0) <br> The literature [[Team:Paris/Modeling/Bibliography|[?] ]] gives K<sub>tet</sub> =
 
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|-
 
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|n<sub>tet</sub>
 
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|complexation order of pTet<br> n<sub>20</sub>
 
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|no dimension
 
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|
 
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|The literature [[Team:Paris/Modeling/Bibliography|[?] ]] gives n<sub>tet</sub> =
 
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|-
 
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|K<sub>aTc</sub>
 
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|complexation constant aTc-TetR <br> K<sub>19</sub>
 
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|nM
 
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|
 
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|The literature [[Team:Paris/Modeling/Bibliography|[?] ]] gives K<sub>aTc</sub> =
 
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|-
 
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|n<sub>aTc</sub>
 
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|complexation order aTc-TetR <br> n<sub>19</sub>
 
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|no dimension
 
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|
 
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|The literature [[Team:Paris/Modeling/Bibliography|[?] ]] gives n<sub>aTc</sub> =
 
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|}
 
Also, this experiment will allow us to know the expression of &#131;1 :
Also, this experiment will allow us to know the expression of &#131;1 :
[[Image:ExprF1.jpg|center]]
[[Image:ExprF1.jpg|center]]

Revision as of 08:58, 29 October 2008

Method & Algorithm : ƒ1


Specific Plasmid Characterisation for ƒ1

The experience would give us

F1expr.jpg

Thus, at steady-state and in the exponential phase of growth :

ExprptetF0.jpg


↓ Table ↑


param signification unit value comments
(fluorescence) value of the observed fluorescence au need for 20 values with well choosen [aTc]i
conversion conversion ration between
fluorescence and concentration
↓ gives ↓ 		nM.au-1 (1/79.429)
[GFP] GFP concentration at steady-state nM
γGFP dilution-degradation rate
of GFP(mut3b)
↓ gives ↓ 		min-1 0.0198 Only dilution :
Time Cell Division : 35 min.
ƒ1 activity of
pTet with RBS E0032 		nM.min-1



param signification
corresponding parameters in the equations 		unit value comments
βtet basal activity of
pTet with RBS E0032
β16 		nM.min-1
(Ktet/{coeftetR}) activation constant of TetR><pTet
K13 		nM The optimisation program will give us (γ Ktet / {coeftet} ƒ0)
The literature [?] gives Ktet =
ntet complexation order of TetR><pTet
n13 		no dimension The literature [?] gives ntet =
KaTc complexation constant aTc><TetR
K12 		nM The literature [?] gives KaTc =
naTc complexation order aTc><TetR
n12 		no dimension The literature [?] gives naTc =


↓ Algorithm ↑


find_ƒ1 

function optimal_parameters = find_f1(X_data, Y_data, initial_parameters)
% gives the 'best parameters' involved in f1 by least-square optimisation
 
% X_data = vector of given values of a [aTc]i (experimentally
% controled)
% Y_data = vector of experimentally measured values f1 corresponding of
% the X_data
% initial_parameters = values of the parameters proposed by the literature
%                       or simply guessed
%                    = [beta16, (K13 -> (gamma.K13)/(coefTet.f0)), n13, K12, n12]
 
% Warning : in the global parameters, K20 -> K20/coefTet
 
     function output = expr_pTet(parameters, X_data)
         for k = 1:length(X_data)
                 output(k) = parameters(1) * (1 - ...
                     hill((1 - hill(X_data(k),parameters(4),parameters(5))),parameters(2),parameters(3)));
         end
     end
 
options=optimset('LevenbergMarquardt','on','TolX',1e-10,'MaxFunEvals',1e10,'TolFun',1e-10,'MaxIter',1e4);
% options for the function lsqcurvefit
 
optimal_parameters = lsqcurvefit( @(parameters, X_data) expr_pTet(parameters, X_data), ...
     initial_parameters, X_data, Y_data, 1/10*initial_parameters, 10*initial_parameters, options );
% search for the fittest parameters, between 1/10 and 10 times the initial
% parameters
 
end

Inv_ƒ1 

function quant_aTc = Inv_f1(inducer_quantity)
% gives the quantity of [aTc]i needed to get inducer_quantity of a protein
% throught a gene behind pTet
 
global gamma, f0;
% parameters
 
     function equa = F(x)
         equa = f1( (f0/gamma) , x ) - inducer_quantity;
     end
 
options=optimset('LevenbergMarquardt','on','TolX',1e-10,'MaxFunEvals',1e10,'TolFun',1e-10,'MaxIter',1e4);
 
quant_aTc = fsolve(F,1,options);
 
end

Also, this experiment will allow us to know the expression of ƒ1 :

ExprF1.jpg
Retrieved from "http://2008.igem.org/Team:Paris/Modeling/f1"