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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We have <span style="color:#0000FF;">[OmpR<sup>*</sup>]<sub>''real''</sub> = {coef<sub>omp</sub>}''expr(pTet)'' = {coef<sub>omp</sub>} &#131;1([aTc]<sub>i</sub>)</span>
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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,
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and <span style="color:#0000FF;">[FliA]<sub>''real''</sub> = {coef<sub>FliA</sub>}''expr(pBad)'' = {coef<sub>FliA</sub>} &#131;2([arab]<sub>i</sub>)</span>
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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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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;">[arab]<sub>i</sub> = Inv_&#131;2( [FliA] ) </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 ''' [aTc]<sub>i</sub> = Inv_&#131;1( [OmpR<sup>*</sup>] ) '''
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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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