Team:Paris/Modeling/f2

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Method & Algorithm : ƒ2


Specific Plasmid Characterisation for ƒ2

The experience would give us

F2expr.jpg

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

Exprpbad.jpg


↓ Table ↑


param signification unit value comments
(fluorescence) value of the observed fluorescence au need for 20 measures with well choosen [arab]i
conversion conversion ratio 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 Disvision : 35 min.
ƒ2 activity of
pBad with RBS E0032 		nM.min-1



param signification
corresponding parameters in the equations 		unit value comments
βbad total transcription rate of
pBad with RBS E0032
not in the Core System 		nM.min-1
(γ Kbad/const.expr(pBad)) activation constant of pBad
not in the Core System 		nM
nbad complexation order of pBad
not in the Core System 		no dimension The literature [?] gives nbad =
Kara complexation constant Arabinose><AraC
not in the Core System 		nM The literature [?] gives Kara =
nara complexation order Arabinose><AraC
not in the Core System 		no dimension The literature [?] gives nara =


↓ Algorithm ↑


find_ƒ2 

function optimal_parameters = find_f2(X_data, Y_data, initial_parameters)
% gives the 'best parameters' involved in f2 by least-square optimisation
 
% X_data = vector of given values of a [arab]i (experimentally
% controled)
% Y_data = vector of experimentally measured values f2 corresponding of
% the X_data
% initial_parameters = values of the parameters proposed by the literature
%                       or simply guessed
%                    = [betabad, (Kbad -> (gamma.Kbad)/(const.expr(pBad))), nbad, Kara, nara]
 
     function output = expr_pBad(parameters, X_data)
         for k = 1:length(X_data)
                 output(k) = parameters(1) * ( hill( ...
                     (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_pBad(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_ƒ2 

function quant_ara = Inv_f2(inducer_quantity)
% gives the quantity of [ara]i needed to get inducer_quantity of a protein
% throught a gene behind pBad
 
     function equa = F(x)
         equa = f2( x ) - inducer_quantity;
     end
 
options=optimset('LevenbergMarquardt','on','TolX',1e-10,'MaxFunEvals',1e10,'TolFun',1e-10,'MaxIter',1e4);
 
quant_ara = fsolve(F,1,options);
 
end

That will give us directly ƒ2([arab])


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