Team:Paris/Modeling/f6

From 2008.igem.org

Method & Algorithm : ƒ6

= act_pTet

Specific Plasmid Characterisation for ƒ6

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

we have [FlhDC]_real = {coef_flhDC} ƒ1([aTc]_i) and [FliA]_real = {coef_fliA} ƒ2([arab]_i)

but we use [aTc]_i = Inv_ƒ1( [FlhDC] ) and [arab]_i = Inv_ƒ2( [FliA] )

So, at steady-states,

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 mesures with well choosen values of [aTc]_i and for 20 mesures with well choosen values of [arab]_i and 5x5 measures for the relation below?
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	Time Cell Division : 35 min.
ƒ6	activity of pFlgA with RBS E0032	nM.min^-1

param	signification corresponding parameters in the equations	unit	value	comments
β₂₆	total transcription rate of FlhDC><pFlgA with RBS E0032 β₂₆	nM.min^-1
(K₃/{coef_fliA})	activation constant of FlhDC><pFliL K₃	nM
n₃	complexation order of FlhDC><pFliL n₃	no dimension
β₂₇	total transcription rate of FliA><pFliL with RBS E0032 β₂₇	nM.min^-1
(K₉/{coef_flhDC})	activation constant of FliA><pFliL K₉	nM
n₉	complexation order of FliA><pFliL n₉	no dimension

↓ Algorithm ↑

find_ƒP

function optimal_parameters = find_FP(X_data, Y_data, initial_parameters)
% gives the 'best parameters' involved in f4, f5, f6, f7 or f8  
% with FlhDC = 0 or FliA = 0 by least-square optimisation
 
% X_data = vector of given values of [FliA]i or [FlhDC]i (experimentally
% controled)
% Y_data = vector of experimentally measured values f4, f5, f6, f7 or f8
% corresponding of the X_data
% initial_parameters = values of the parameters proposed by the literature
%                       or simply guessed
%                    = [beta, K -> (K)/(coef), n]
 
     function output = act_pProm(parameters, X_data)
         for k = 1:length(X_data)
                 output(k) = parameters(1)*hill(X_data(k), 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) act_pProm(parameters, X_data),...
     initial_parameters, X_data, Y_data, options );
% search for the fittest parameters, between 1/10 and 10 times the initial
% parameters
 
end

Then, if we have time, we want to verify the expected relation

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