Team:Paris/Modeling/f1

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Revision as of 18:06, 29 October 2008

Method & Algorithm : ƒ1

Specific Plasmid Characterisation for ƒ1

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 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 =

↓ Algorithm ↑

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 :

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

@@ Line 9: / Line 9: @@
 [[Image:f1expr.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:ExprptetF0.jpg|center]]