Team:Paris/Modeling/f3

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We have [OmpR<sup>*</sup>] = {coef<sub>omp</sub>}''expr(pTet)'' = {coef<sub>omp</sub>} &#131;1([aTc]<sub>i</sub>)
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{{Paris/Header|Method & Algorithm : &#131;1}}
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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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[[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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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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and        <span style="color:#0000FF;">[ara]<sub>i</sub> = Inv_&#131;2( [FliA] ) </span>
So, at steady-states,
So, at steady-states,
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Also, this experiment will enable us to know the expression of &#131;1 :
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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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Revision as of 11:17, 29 October 2008

Method & Algorithm : ƒ1


Specific Plasmid Characterisation for ƒ3

We have [OmpR*]real = {coefomp}expr(pTet) = {coefomp} ƒ1([aTc]i) and [FliA]real = {coefFliA}expr(pBad) = {coefFliA} ƒ2([arab]i)

but we use [aTc]i = Inv_ƒ1( [OmpR*] ) and [ara]i = Inv_ƒ2( [FliA] )

So, at steady-states,

F3ompfinal.jpg




↓ Table ↑


param signification unit value comments
(fluorescence) value of the observed fluorescence au need for 20 values with well choosen [aTc]i
conversion conversion ration 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 Only dilution :
Time Cell Division : 35 min.
ƒ1 activity of
pTet with RBS E0032 		nM.min-1



param signification
corresponding parameters in the equations 		unit value comments
βtet basal activity of
pTet with RBS E0032
β16 		nM.min-1
(Ktet/{coeftetR}) activation constant of TetR><pTet
K13 		nM The optimisation program will give us (γ Ktet / {coeftet} ƒ0)
The literature [?] gives Ktet =
ntet complexation order of TetR><pTet
n13 		no dimension The literature [?] gives ntet =
KaTc complexation constant aTc><TetR
K12 		nM The literature [?] gives KaTc =
naTc complexation order aTc><TetR
n12 		no dimension The literature [?] gives naTc =


↓ Algorithm ↑


find_ƒ1 

function optimal_parameters = find_f1(X_data, Y_data, initial_parameters)
% gives the 'best parameters' involved in f1 by least-square optimisation
 
% X_data = vector of given values of a [aTc]i (experimentally
% controled)
% Y_data = vector of experimentally measured values f1 corresponding of
% the X_data
% initial_parameters = values of the parameters proposed by the literature
%                       or simply guessed
%                    = [beta16, (K13 -> (gamma.K13)/(coefTet.f0)), n13, K12, n12]
 
% Warning : in the global parameters, K20 -> K20/coefTet
 
     function output = expr_pTet(parameters, X_data)
         for k = 1:length(X_data)
                 output(k) = parameters(1) * (1 - ...
                     hill((1 - hill(X_data(k),parameters(4),parameters(5))),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) expr_pTet(parameters, X_data), ...
     initial_parameters, X_data, Y_data, 1/10*initial_parameters, 10*initial_parameters, options );
% search for the fittest parameters, between 1/10 and 10 times the initial
% parameters
 
end

Inv_ƒ1 

function quant_aTc = Inv_f1(inducer_quantity)
% gives the quantity of [aTc]i needed to get inducer_quantity of a protein
% throught a gene behind pTet
 
global gamma, f0;
% parameters
 
     function equa = F(x)
         equa = f1( (f0/gamma) , x ) - inducer_quantity;
     end
 
options=optimset('LevenbergMarquardt','on','TolX',1e-10,'MaxFunEvals',1e10,'TolFun',1e-10,'MaxIter',1e4);
 
quant_aTc = fsolve(F,1,options);
 
end

Also, this experiment will enable us to know the expression of ƒ1 :

ExprF1.jpg


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





param signification unit value comments
[expr(pFlhDC)] expression rate of
pFlhDC with RBS E0032 		nM.min-1 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?
γGFP dilution-degradation rate
of GFP(mut3b) 		min-1 0.0198
[GFP] GFP concentration at steady-state nM need for 20 + 20 measures
and 5x5 measures for the relation below?
(fluorescence) value of the observed fluorescence au need for 20 + 20 measures
and 5x5 measures for the relation below?
conversion conversion ratio between
fluorescence and concentration 		nM.au-1 (1/79.429)



param signification
corresponding parameters in the equations 		unit value comments
β13 production rate of FliA-pFlhDC with RBS E0032
β13 		nM.min-1
(K12/{coeffliA}) activation constant of FliA-pFlhDC
K12 		nM
n12 complexation order of FliA-pFlhDC
n12 		no dimension
β2 production rate of OmpR-pFlhDC with RBS E0032
β2 		nM.min-1
(K22/{coefomp}) activation constant of OmpR-pFlhDC
K22 		nM
n22 complexation order of OmpR-pFlhDC
n22 		no dimension



Then, if we have time, we want to verify the expected relation

SumFlhDC1.jpg
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