Team:Paris/Modeling/f3

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{{Paris/Header|Method & Algorithm : ƒ3}}
{{Paris/Header|Method & Algorithm : ƒ3}}
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<center> = act_''pFlhDC'' </center>
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<br>
[[Image:f3omp.jpg|thumb|Specific Plasmid Characterisation for &#131;3]]
[[Image:f3omp.jpg|thumb|Specific Plasmid Characterisation for &#131;3]]
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According to the characterization plasmid (see right) and to our modeling, in the '''exponential phase of growth''', at the steady state,
According to the characterization plasmid (see right) and to our modeling, in the '''exponential phase of growth''', at the steady state,
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we have <span style="color:#0000FF;">[OmpR<sup>*</sup>]<sub>''real''</sub> = {coef<sub>''ompR''</sub>} &#131;1([aTc]<sub>i</sub>)</span>
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we have ''' [''OmpR<sup>*</sup>'']<sub>''real''</sub> = {coef<sub>''ompR''</sub>} &#131;1([aTc]<sub>i</sub>) '''
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and <span style="color:#0000FF;">[FliA]<sub>''real''</sub> = {coef<sub>FliA</sub>} &#131;2([arab]<sub>i</sub>)</span>
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and ''' [FliA]<sub>''real''</sub> = {coef<sub>FliA</sub>} &#131;2([arab]<sub>i</sub>) '''
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but we use <span style="color:#0000FF;">[aTc]<sub>i</sub> = Inv_&#131;1( [OmpR<sup>*</sup>] ) </span>
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but we use ''' [aTc]<sub>i</sub> = Inv_&#131;1( [OmpR<sup>*</sup>] ) '''
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and        <span style="color:#0000FF;">[arab]<sub>i</sub> = Inv_&#131;2( [FliA] ) </span>
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and        ''' [arab]<sub>i</sub> = Inv_&#131;2( [FliA] ) '''
So, at steady-states,
So, at steady-states,
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[[Image:F3ompfinal.jpg|center]]
[[Image:F3ompfinal.jpg|center]]
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<br><br>
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we use this analytical expression to determine the parameters :
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<div style="text-align: center">
<div style="text-align: center">
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{{Paris/Toggle|Table|Team:Paris/Modeling/More_f3_Table}}  
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{{Paris/Toggle|Table of Values|Team:Paris/Modeling/More_f3_Table}}  
</div>
</div>
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<div style="text-align: center">
<div style="text-align: center">

Latest revision as of 02:12, 30 October 2008

Method & Algorithm : ƒ3


= act_pFlhDC


Specific Plasmid Characterisation for ƒ3

According to the characterization plasmid (see right) and to our modeling, in the exponential phase of growth, at the steady state,

we have [OmpR*]real = {coefompR} ƒ1([aTc]i) and [FliA]real = {coefFliA} ƒ2([arab]i)

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

So, at steady-states,

F3ompfinal.jpg

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.
ƒ3 activity of
pFlhDC with RBS E0032 		nM.min-1



param signification
corresponding parameters in the equations 		unit value comments
β22 total transcription rate of
FliA><pFlhDC with RBS B0034
β22 		nM.min-1
(K6/{coeffliA}) activation constant of FliA><pFlhDC
K6 		nM
n6 complexation order of FliA><pFlhDC
n6 		no dimension
β17 basal activity of
pFlhDC with RBS B0034
β17 		nM.min-1
(K15/{coefompR}) activation constant of OmpR><pFlhDC
K15 		nM
n15 complexation order of OmpR><pFlhDC
n15 		no dimension
↓ Algorithm ↑


find_ƒ3 ( FliA ) 

function optimal_parameters = find_f3_FliA(X_data, Y_data, initial_parameters)
% gives the 'best parameters' involved in f3 with OmpR = 0 by least-square optimisation
% -> USE IT AFTER find_f3_OmpR
 
% X_data = vector of given values of ( [FliA]i ) (experimentally
% controled)
% Y_data = vector of experimentally measured values f3 corresponding of
% the X_data
% initial_parameters = values of the parameters proposed by the literature
%                       or simply guessed
%                    = [beta22, K6 -> (K6)/(coefOmp), n6]
 
global beta17; % parameter GIVEN BY find_f3_OmpR
 
     function output = act_pFlhDC(parameters, X_data)
         for k = 1:length(X_data)
                 output(k) = beta17*(1 - hill( X_data(k), parameters(2), parameters(3))) ...
                     + 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_pFlhDC(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

find_ƒ3 ( OmpR* ) 

function optimal_parameters = find_f3_OmpR(X_data, Y_data, initial_parameters)
% gives the 'best parameters' involved in f3 with FliA = 0 by least-square optimisation
% -> USE IT BEFORE find_f3_FliA
 
% X_data = vector of given values of ( [OmpR]i ) (experimentally
% controled)
% Y_data = vector of experimentally measured values f3 corresponding of
% the X_data
% initial_parameters = values of the parameters proposed by the literature
%                       or simply guessed
%                    = [beta17, K15 -> (K15)/(coefOmp), n15]
 
     function output = act_pFlhDC(parameters, X_data)
         for k = 1:length(X_data)
                 output(k) =(1 - hill( X_data(k), parameters(2), parameters(3) )) * parameters(1);
         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_pFlhDC(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

SumFlhDC1.jpg


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

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