Method & Algorithm : ƒ2

= act_pBad

Specific Plasmid Characterisation for ƒ2

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 measures with well choosen [arab]i
conversion conversion ratio between
fluorescence and concentration
↓ gives ↓ (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 Disvision : 35 min.
ƒ2 activity of
pBad with RBS E0032

param signification
corresponding parameters in the equations
unit value comments
βbad total transcription rate of
pBad with RBS E0032
not in the Core System
(γ Kbad/const.expr(pBad)) activation constant of pBad
not in the Core System
nbad complexation order of pBad
not in the Core System
no dimension The literature [?] gives nbad =
Kara complexation constant Arabinose><AraC
not in the Core System
nM The literature [?] gives Kara =
nara complexation order Arabinose><AraC
not in the Core System
no dimension The literature [?] gives nara =
↓ Algorithms ↑


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)) );
% 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


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;
quant_ara = fsolve(F,1,options);

That will give us directly ƒ2([arab])

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