Team:Paris/Modeling/f3bis

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[[Image:f3env.png|thumb]] (see [[Team:Paris/Modeling/Oscillations#Biochemical_Assumptions|the considerations on the use of EnvZ]])
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{{Paris/Menu}}
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We have [EnvZ]<sub>produced</sub> = {coef<sub>env</sub>}''expr(pTet)'' = {coef<sub>env</sub>} &#131;1([aTc]<sub>i</sub>)
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{{Paris/Header|Method & Algorithm : &#131;3bis}}
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<center> = act_''pFlhDC'' </center>
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<br>
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and [EnvZ]<sub>total</sub> = [EnvZ]<sub>basal</sub> + [EnvZ]<sub>produced</sub>
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[[Image:f6DCA.png|thumb|Specific Plasmid Characterisation for &#131;3bis]]
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In this experiment, we have
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and [FliA] = {coef<sub>FliA</sub>}''expr(pBad)'' = {coef<sub>FliA</sub>} &#131;2([arab]<sub>i</sub>)
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''' [''EnvZ'']<sub>''real''</sub> = {coef<sub>''envZ''</sub>} &#131;1([aTc]<sub>i</sub>) '''
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So, if we denote phosphorylated OmpR by ''OmpR<sup>*</sup>'', we have
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but we use ''' [aTc]<sub>i</sub> = Inv_&#131;1( [''EnvZ''] ) '''
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[[Image:F3ompfromenv.jpg|center]]
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so, at steady-states, ''phosphorylated OmpR'' verify :
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that we can then introduce in the previous expression (&#131; 3) :
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[[Image:F3b.jpg|center]]
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[[Image:F3ompfinal.jpg|center]]
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We can then solve it, and reintroduce the result in the previously characterized ''' &#131;3( 0, [OmpR<sup>*</sup>] ) ''', to determine the parameters :
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<br><br>
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<div style="text-align: center">
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{{Paris/Toggle|Table of Values|Team:Paris/Modeling/More_f3bis_Table}}
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</div>
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{|border="1" style="text-align: center"
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<div style="text-align: center">
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|param
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{{Paris/Toggle|Algorithm|Team:Paris/Modeling/More_f3bis_Algo}}
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|signification
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</div>
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|unit
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|value
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|-
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|[expr(pFlhDC)]
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|expression rate of <br> pFlhDC '''with RBS E0032'''
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|nM.s<sup>-1</sup>
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|see [[Team:Paris/Modeling/Programs|"findparam"]] <br> need for 20 + 20 measures <br> and 5x5 measures for the ''SUM''?
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|γ<sub>GFP</sub>
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|dilution-degradation rate <br> of GFP(mut3b)
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|min<sup>-1</sup>
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|0.0198
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|[GFP]
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|GFP concentration at steady-state
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|nM
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|need for 20 + 20 measures <br> and 5x5 measures for the ''SUM''?
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|-
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|(''fluorescence'')
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|value of the observed fluorescence
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|au
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|need for 20 + 20 measures <br> and 5x5 measures for the ''SUM''?
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|''conversion''
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|conversion ratio between <br> fluorescence and concentration
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|nM.au<sup>-1</sup>
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|(1/79.429)
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<br><br>
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<br>
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{|border="1" style="text-align: center"
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<center>
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|param
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[[Team:Paris/Modeling/Implementation| <Back - to "Implementation" ]]| <br>
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|signification <br> corresponding parameters in the [[Team:Paris/Modeling/Oscillations#Resulting_Equations|equations]]
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[[Team:Paris/Modeling/Protocol_Of_Characterization| <Back - to "Protocol Of Characterization" ]]|
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|unit
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</center>
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|value
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|β<sub>12bis</sub>
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|production rate of FliA-pFlhDC '''with RBS E0032''' <br> replace β<sub>12</sub> (not written)
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|nM.min<sup>-1</sup>
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|(K<sub>11bis</sub>/{coef<sub>fliA</sub>})
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|activation constant of FliA-pFlhDC <br> K<sub>11bis</sub>
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|nM
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|n<sub>11bis</sub>
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|complexation order of FliA-pFlhDC <br> replace n<sub>11</sub> (not written)
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|no dimension
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|β<sub>2bis</sub>
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|production rate of EnvZ-pFlhDC '''with RBS E0032''' <br> β<sub>2bis</sub>
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|nM.min<sup>-1</sup>
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|(K<sub>19bis</sub>/{coef<sub>envZ</sub>})
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|activation constant of EnvZ-pFlhDC <br> replace K<sub>19</sub> (not written)
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|nM
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|n<sub>19bis</sub>
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|complexation order of EnvZ-pFlhDC <br> n<sub>19bis</sub>
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|no dimension
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|}
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<br><br>
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Then, if we have time, we want to verify the expected relation
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[[Image:SumpFlhDC2.jpg|center]]
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Latest revision as of 02:16, 30 October 2008

Method & Algorithm : ƒ3bis


= act_pFlhDC


Specific Plasmid Characterisation for ƒ3bis

In this experiment, we have

[EnvZ]real = {coefenvZ} ƒ1([aTc]i)

but we use [aTc]i = Inv_ƒ1( [EnvZ] )

so, at steady-states, phosphorylated OmpR verify :

F3b.jpg

We can then solve it, and reintroduce the result in the previously characterized ƒ3( 0, [OmpR*] ) , to determine the parameters :

↓ Table of Values ↑


Team:Paris/Modeling/More f3bis Table

↓ Algorithm ↑


function optimal_parameters = find_f3_EnvZ(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 ( [EnvZ]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
%                    = [EnvZ_b, OmpR_b, K14, n14]
 
global beta17 K15 n15; % parameters GIVEN BY find_f3_OmpR
 
     function output = act_pFlhDC(parameters, X_data)
         for k = 1:length(X_data)
             OmpR_P = complexes((parameters(1) + X_data(k)),parameters(2),parameters(3),parameters(4));
                 % complexes is a function that solve the "basical
                 % complexation equation"
             output(k) = beta17*(1 - hill( OmpR_P, K15, n15 ));
         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


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

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