Team:Paris/Modeling/f2

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Revision as of 01:53, 30 October 2008

Method & Algorithm : ƒ2

Specific Plasmid Characterisation for ƒ2

According to the characterization plasmid (see right) and to our modeling, in the exponential phase of growth, at the steady state, the experiment would give us

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

we use this analytical expression to determine the parameters :

↓ Table of Values ↑

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
γ_GFP	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
β_bad	total transcription rate of pBad with RBS E0032 not in the Core System	nM.min^-1
(γ K_bad/const.expr(pBad))	activation constant of pBad not in the Core System	nM
n_bad	complexation order of pBad not in the Core System	no dimension		The literature [?] gives n_bad =
K_ara	complexation constant Arabinose><AraC not in the Core System	nM		The literature [?] gives K_ara =
n_ara	complexation order Arabinose><AraC not in the Core System	no dimension		The literature [?] gives n_ara =

↓ Algorithms ↑

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])

<Back - to "Implementation" |
<Back - to "Protocol Of Characterization" |

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+we use this analytical expression to determine the parameters :
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