Team:Paris/Modeling/f8

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(Difference between revisions)
 
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{{Paris/Header|Method & Algorithm : ƒ8}}
{{Paris/Header|Method & Algorithm : ƒ8}}
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<center> = act_''pTet'' </center>
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<br>
[[Image:f6DCA.png|thumb|Specific Plasmid Characterisation for &#131;8]]
[[Image:f6DCA.png|thumb|Specific Plasmid Characterisation for &#131;8]]
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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;">[''FlhDC'']<sub>''real''</sub> = {coef<sub>''flhDC''</sub>} &#131;1([aTc]<sub>i</sub>)</span>
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we have ''' [''FlhDC'']<sub>''real''</sub> = {coef<sub>''flhDC''</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( [''FlhDC''] ) </span>
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but we use ''' [aTc]<sub>i</sub> = Inv_&#131;1( [''FlhDC''] ) '''
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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,

Latest revision as of 02:11, 30 October 2008

Method & Algorithm : ƒ8


= act_pTet


Specific Plasmid Characterisation for ƒ8

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] )

So, at steady-states,

F8.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.
ƒ8 activity of
pFlhB with RBS E0032 		nM.min-1



param signification
corresponding parameters in the equations 		unit value comments
β30 total transcription rate of
FlhDC><pFlhB with RBS E0032
β30 		nM.min-1
(K5/{coeffliA}) activation constant of FlhDC><pFlhB
K5 		nM
n5 complexation order of FlhDC><pFlhB
n5 		no dimension
β31 total transcription rate of
FlhDC><pFlhB with RBS E0032
β31 		nM.min-1
(K11/{coefflhDC}) activation constant of FlhDC><pFlhB
K11 		nM
n11 complexation order of FlhDC><pFlhB
n11 		no dimension
↓ 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

SumpFlhB.jpg


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