Team:Paris/Modeling/f1

From 2008.igem.org

Method & Algorithm : ƒ1

= act_pTet

Specific Plasmid Characterisation for ƒ1

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 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
γ_GFP	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
β_tet	basal activity of pTet with RBS E0032 β₁₆	nM.min^-1
(K_tet/{coef_tetR})	activation constant of TetR><pTet K₁₃	nM		The optimisation program will give us (γ K_tet / {coef_tet} ƒ0) The literature [?] gives K_tet =
n_tet	complexation order of TetR><pTet n₁₃	no dimension		The literature [?] gives n_tet =
K_aTc	complexation constant aTc><TetR K₁₂	nM		The literature [?] gives K_aTc =
n_aTc	complexation order aTc><TetR n₁₂	no dimension		The literature [?] gives n_aTc =

↓ Algorithms ↑

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 enable us to know the expression of ƒ1 :

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