Team:Paris/Modeling/f8

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[[Image:f8DCA.png|thumb]] At the steady-state, we have
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{{Paris/Menu}}
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<center>[[Image:FlhDCeq.jpg]]</center>
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{{Paris/Header|Method & Algorithm : &#131;8}}
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and
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<center> = act_''pTet'' </center>
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<center>[[Image:FliAeq.jpg]]</center>
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<br>
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so the expression
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[[Image:f6DCA.png|thumb|Specific Plasmid Characterisation for &#131;8]]
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<center>[[Image:f8expr.jpg]]</center>
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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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gives
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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 ''' [''FliA'']<sub>''real''</sub> = {coef<sub>''fliA''</sub>} &#131;2([arab]<sub>i</sub>) '''
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<center>[[Image:f8FlhDC.jpg]]</center>
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but we use ''' [aTc]<sub>i</sub> = Inv_&#131;1( [''FlhDC''] ) '''
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and
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and       ''' [arab]<sub>i</sub> = Inv_&#131;2( [''FliA''] ) '''
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<center>[[Image:f8FliA.jpg]]</center>
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and for ''calculated values of the TF'',
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So, at steady-states,
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<center>[[Image:f8FlhDCCalc.jpg]]</center>
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[[Image:F8.jpg|center]]
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and
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<center>[[Image:f8FliACalc.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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{|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|Table of Values|Team:Paris/Modeling/More_f8_Table}}
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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(pFlhB)]
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|expression rate of <br> pFlhB '''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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|-
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|γ<sub>GFP</sub>
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|dilution-degradation rate <br> of GFP(mut3b)
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|s<sup>-1</sup>
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|ln(2)/3600
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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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|-
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|''conversion''
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|conversion ration 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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|}
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<br><br>
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<div style="text-align: center">
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{{Paris/Toggle|Algorithm|Team:Paris/Modeling/More_FP_Algo}}
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</div>
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{|border="1" style="text-align: center"
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Then, if we have time, we want to verify the expected relation
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|param
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|signification <br> corresponding parameters in the [[Team:Paris/Modeling/Oscillations#Resulting_Equations|equations]]
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|unit
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|value
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|-
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|β<sub>6</sub>
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|production rate of FlhDC-pFlhB '''with RBS E0032''' <br> β<sub>6</sub>
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|nM.s<sup>-1</sup>
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|
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|-
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|(K<sub>4</sub>/{coef<sub>flhDC</sub>}<sup>n<sub>4</sub></sup>)
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|activation constant of FlhDC-pFlhB <br> K<sub>4</sub>
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|nM<sup>n<sub>4</sub></sup>
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|
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|-
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|n<sub>4</sub>
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|complexation order of FlhDC-pFlhB <br> n<sub>4</sub>
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|no dimension
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|
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|-
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|-
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|β<sub>14</sub>
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|production rate of FliA-pFlhB '''with RBS E0032''' <br> β<sub>14</sub>
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|nM.s<sup>-1</sup>
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|
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|-
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|(K<sub>10</sub>/{coef<sub>fliA</sub>}<sup>n<sub>10</sub></sup>)
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|activation constant of FliA-pFlhB <br> K<sub>10</sub>
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|nM<sup>n<sub>10</sub></sup>
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|
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|-
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|n<sub>10</sub>
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|complexation order of FliA-pFlhB <br> n<sub>10</sub>
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|no dimension
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|
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|}
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<br><br>
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[[Image:SumpFlhB.jpg|center]]
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Then, if we have time, we want to verify the expected relation
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<br>
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<center>[[Image:SumpFlhB.jpg]]</center>
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<center>
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[[Team:Paris/Modeling/Implementation| <Back - to "Implementation" ]]| <br>
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[[Team:Paris/Modeling/Protocol_Of_Characterization| <Back - to "Protocol Of Characterization" ]]|
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</center>

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


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

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