# Team:Paris/Modeling/f5

Method & Algorithm : ƒ5

= act_pFliL

Specific Plasmid Characterisation for ƒ5

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 = {coefflhDC} ƒ1([aTc]i) and [FliA]real = {coeffliA} ƒ2([arab]i)

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

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 γGFP dilution-degradation rate of GFP(mut3b) ↓ gives ↓ min-1 0.0198 Time Cell Division : 35 min. ƒ5 activity of pFliL with RBS E0032 nM.min-1

 param signification corresponding parameters in the equations unit value comments β24 total transcription rate of FlhDC>
↓ 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