Team:Paris/Modeling/f7

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{{Paris/Header|Method & Algorithm : ƒ7}}
{{Paris/Header|Method & Algorithm : ƒ7}}
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<center> = act_''pTet'' </center>
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<br>
[[Image:f7DCA.png|thumb|Specific Plasmid Characterisation for &#131;7]]
[[Image:f7DCA.png|thumb|Specific Plasmid Characterisation for &#131;7]]
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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,
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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_f7_Table}}  
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{{Paris/Toggle|Table of Values|Team:Paris/Modeling/More_f7_Table}}  
</div>
</div>

Latest revision as of 02:10, 30 October 2008

Method & Algorithm : ƒ7


= act_pTet


Specific Plasmid Characterisation for ƒ7

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,

F7a.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.
ƒ7 activity of
pFlgB with RBS E0032 		nM.min-1



param signification
corresponding parameters in the equations 		unit value comments
β28 total transcription rate of
FlhDC><pFlgB with RBS E0032
β28 		nM.min-1
(K4/{coeffliA}) activation constant of FlhDC><pFlgB
K4 		nM
n4 complexation order of FlhDC><pFlgB
n4 		no dimension
β29 total transcription rate of
FlhDC><pFlgB with RBS E0032
β29 		nM.min-1
(K10/{coefflhDC}) activation constant of FlhDC><pFlgB
K10 		nM
n10 complexation order of FlhDC><pFlgB
n10 		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

SumpFlgB.jpg


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<Back - to "Protocol Of Characterization" |

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