Team:Paris/Modeling/f2

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Revision as of 18:07, 29 October 2008

Method & Algorithm : ƒ2

Specific Plasmid Characterisation for ƒ2

The experience would give us

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

↓ 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
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 =

↓ 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])

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

@@ Line 9: / Line 9: @@
 [[Image:f2expr.jpg|center]]
-Thus, at steady-state and in the exponential phase of growth :
+and at steady-state and in the exponential phase of growth, we expect :
 [[Image:Exprpbad.jpg|center]]