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- | [[Image:f2.jpg|thumb]] According to previous consideration on pBad, we have
| + | {{Paris/Menu}} |
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- | <center>[[Image:f2expr.jpg]]</center> | + | {{Paris/Header|Method & Algorithm : ƒ2}} |
| + | <center> = act_''pBad'' </center> |
| + | <br> |
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- | so, with the complexation between Arabinose and AraC, and after reducing the equation
| + | [[Image:f2.jpg|thumb|Specific Plasmid Characterisation for ƒ2]] |
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- | <center>[[Image:f2exprRedu.jpg]]</center>
| + | According to the characterization plasmid (see right) and to our modeling, in the '''exponential phase of growth''', at the steady state, the experiment would give us |
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| + | [[Image:f2expr.jpg|center]] |
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- | {|border="1" style="text-align: center"
| + | and at steady-state and in the exponential phase of growth, we expect : |
- | |param
| + | |
- | |signification
| + | |
- | |unit
| + | |
- | |value
| + | |
- | |-
| + | |
- | |[expr(pBad)]
| + | |
- | |expression rate of <br> pBad '''with RBS E0032'''
| + | |
- | |nM.s<sup>-1</sup>
| + | |
- | |see [[Team:Paris/Modeling/Programs|"findparam"]] <br> need for 20 measures
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- | |-
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- | |γ<sub>GFP</sub>
| + | |
- | |dilution-degradation rate <br> of GFP(mut3b)
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- | |s<sup>-1</sup>
| + | |
- | |ln(2)/3600
| + | |
- | |-
| + | |
- | |[GFP]
| + | |
- | |GFP concentration at steady-state
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- | |nM
| + | |
- | |need for 20 measures
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- | |-
| + | |
- | |(''fluorescence'')
| + | |
- | |value of the observed fluorescence
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- | |au
| + | |
- | |need for 20 measures
| + | |
- | |-
| + | |
- | |''conversion''
| + | |
- | |conversion ration between <br> fluorescence and concentration
| + | |
- | |nM.au<sup>-1</sup>
| + | |
- | |(1/79.429)
| + | |
- | |}
| + | |
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- | <br><br>
| + | [[Image:Exprpbad.jpg|center]] |
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- | {|border="1" style="text-align: center"
| + | we use this analytical expression to determine the parameters : |
- | |param | + | |
- | |signification <br> corresponding parameters in the [[Team:Paris/Modeling/Oscillations#Resulting_Equations|equations]] | + | <div style="text-align: center"> |
- | |unit
| + | {{Paris/Toggle|Table of Values|Team:Paris/Modeling/More_f2_Table}} |
- | |value
| + | </div> |
- | |-
| + | |
- | |β<sub>bad</sub>
| + | <div style="text-align: center"> |
- | |production rate of pBad '''with RBS E0032''' <br> not in the system
| + | {{Paris/Toggle|Algorithms|Team:Paris/Modeling/More_f2_Algo}} |
- | |nM.s<sup>-1</sup>
| + | </div> |
- | | | + | |
- | |- | + | That will give us directly ƒ2([arab]) |
- | |(K<sub>bad</sub>/[AraC<sub>tot</sub>]<sup>n<sub>bad</sub></sup>)
| + | |
- | |activation constant of pBad <br> not in the system
| + | <br> |
- | |nM<sup>n<sub>bad</sub></sup>
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- | |
| + | <center> |
- | |-
| + | [[Team:Paris/Modeling/Implementation| <Back - to "Implementation" ]]| <br> |
- | |n<sub>bad</sub> | + | [[Team:Paris/Modeling/Protocol_Of_Characterization| <Back - to "Protocol Of Characterization" ]]| |
- | |complexation order of pBad<br> not in the system
| + | </center> |
- | |no dimension
| + | |
- | |
| + | |
- | |-
| + | |
- | |K<sub>ara</sub> | + | |
- | |complexation constant Arabinose-AraC <br> not in the system
| + | |
- | |nM<sup>n<sub>ara</sub></sup>
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- | |
| + | |
- | |- | + | |
- | |n<sub>ara</sub> | + | |
- | |complexation order Arabinose-AraC <br> n<sub>17</sub>
| + | |
- | |no dimension
| + | |
- | |
| + | |
- | |}
| + | |
Method & Algorithm : 2
= act_pBad
Specific Plasmid Characterisation for 2
According to the characterization plasmid (see right) and to our modeling, in the exponential phase of growth, at the steady state, the experiment would give us
and at steady-state and in the exponential phase of growth, we expect :
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 measures with well choosen [arab]i
|
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
| Only Dilution Time Cell Disvision : 35 min.
|
2
| activity of pBad with RBS E0032
| nM.min-1
|
|
|
param
| signification corresponding parameters in the equations
| unit
| value
| comments
|
βbad
| total transcription rate of pBad with RBS E0032 not in the Core System
| nM.min-1
|
|
|
(γ Kbad/const.expr(pBad))
| activation constant of pBad not in the Core System
| nM
|
|
|
nbad
| complexation order of pBad not in the Core System
| no dimension
|
| The literature [?] gives nbad =
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Kara
| complexation constant Arabinose><AraC not in the Core System
| nM
|
| The literature [?] gives Kara =
|
nara
| complexation order Arabinose><AraC not in the Core System
| no dimension
|
| The literature [?] gives nara =
|
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↓ Algorithms ↑
find_2
function optimal_parameters = find_f2(X_data, Y_data, initial_parameters)
function output = expr_pBad(parameters, X_data)
for k = 1:length(X_data)
output(k) = parameters(1) * ( hill( ...
(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);
optimal_parameters = lsqcurvefit( @(parameters, X_data) expr_pBad(parameters, X_data), ...
initial_parameters, X_data, Y_data, 1/10*initial_parameters, 10*initial_parameters, options );
end
Inv_2
function quant_ara = Inv_f2(inducer_quantity)
function equa = F(x)
equa = f2( x ) - inducer_quantity;
end
options=optimset('LevenbergMarquardt','on','TolX',1e-10,'MaxFunEvals',1e10,'TolFun',1e-10,'MaxIter',1e4);
quant_ara = fsolve(F,1,options);
end
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That will give us directly 2([arab])
<Back - to "Implementation" |
<Back - to "Protocol Of Characterization" |
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