Team:Paris/Modeling/f1

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Method & Algorithm : ƒ1


Specific Plasmid Characterisation for ƒ1

The experience would give us

F1expr.jpg

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

ExprptetF0.jpg


↓ 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
γGFP 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
βtet basal activity of
pTet with RBS E0032
β16 		nM.min-1
(Ktet/{coeftetR}) activation constant of TetR><pTet
K13 		nM The optimisation program will give us (γ Ktet / {coeftet} ƒ0)
The literature [?] gives Ktet =
ntet complexation order of TetR><pTet
n13 		no dimension The literature [?] gives ntet =
KaTc complexation constant aTc><TetR
K12 		nM The literature [?] gives KaTc =
naTc complexation order aTc><TetR
n12 		no dimension The literature [?] gives naTc =


↓ 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

param signification unit value comments
[expr(pTet)] expression rate of
pTet with RBS E0032 		nM.min-1 need for 20 values with well choosen [aTc]i

with 5 measures for each

γGFP dilution-degradation rate
of GFP(mut3b) 		min-1 0.0198 Time for Cell Division : 35 min. ; No degradation
[GFP] GFP concentration at steady-state nM need for 100 measures
(fluorescence) value of the observed fluorescence au need for 100 measures
conversion conversion ration between
fluorescence and concentration 		nM.au-1 (1/79.429)



param signification
corresponding parameters in the equations 		unit value comments
βtet production rate of pTet with RBS E0032
β1 		nM.min-1
(Ktet/{coeftet}) activation constant of pTet
K20 		nM The optimisation program will give us (γ Ktet / {coeftet} ƒ0)
The literature [?] gives Ktet =
ntet complexation order of pTet
n20 		no dimension The literature [?] gives ntet =
KaTc complexation constant aTc-TetR
K19 		nM The literature [?] gives KaTc =
naTc complexation order aTc-TetR
n19 		no dimension The literature [?] gives naTc =

Also, this experiment will allow us to know the expression of ƒ1 :

ExprF1.jpg
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