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- | [[Image:f5DCA.png|thumb]]
| + | {{Paris/Menu}} |
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- | We have [FlhDC] = {coef<sub>flhDC</sub>}''expr(pTet)'' = {coef<sub>flhDC</sub>} ƒ1([aTc]<sub>i</sub>)
| + | {{Paris/Header|Method & Algorithm : ƒ5}} |
| + | <center> = act_''pFliL'' </center> |
| + | <br> |
| | | |
- | and [FliA] = {coef<sub>FliA</sub>}''expr(pBad)'' = {coef<sub>FliA</sub>} ƒ2([arab]<sub>i</sub>) | + | [[Image:f5DCA.png|thumb|Specific Plasmid Characterisation for ƒ5]] |
| + | |
| + | According to the characterization plasmid (see right) and to our modeling, in the '''exponential phase of growth''', at the steady state, |
| + | |
| + | we have ''' [''FlhDC'']<sub>''real''</sub> = {coef<sub>''flhDC''</sub>} ƒ1([aTc]<sub>i</sub>) ''' |
| + | and ''' [''FliA'']<sub>''real''</sub> = {coef<sub>''fliA''</sub>} ƒ2([arab]<sub>i</sub>) ''' |
| + | |
| + | but we use ''' [aTc]<sub>i</sub> = Inv_ƒ1( [''FlhDC''] ) ''' |
| + | and ''' [arab]<sub>i</sub> = Inv_ƒ2( [''FliA''] ) ''' |
| | | |
| So, at steady-states, | | So, at steady-states, |
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| [[Image:F5.jpg|center]] | | [[Image:F5.jpg|center]] |
| | | |
- | <br><br>
| + | we use this analytical expression to determine the parameters : |
| | | |
- | <center> | + | <div style="text-align: center"> |
- | {|border="1" style="text-align: center"
| + | {{Paris/Toggle|Table of Values|Team:Paris/Modeling/More_f5_Table}} |
- | |param
| + | </div> |
- | |signification
| + | |
- | |unit
| + | |
- | |value
| + | |
- | |comments
| + | |
- | |-
| + | |
- | |[expr(pFlhDC)]
| + | |
- | |expression rate of <br> pFlhDC '''with RBS E0032'''
| + | |
- | |nM.min<sup>-1</sup>
| + | |
- | | | + | |
- | |need for 20 mesures with well choosen values of [aTc]<sub>i</sub> <br> and for 20 mesures with well choosen values of [arab]<sub>i</sub> <br> and 5x5 measures for the relation below?
| + | |
- | |- | + | |
- | |γ<sub>GFP</sub>
| + | |
- | |dilution-degradation rate <br> of GFP(mut3b)
| + | |
- | |min<sup>-1</sup>
| + | |
- | |0.0198
| + | |
- | |
| + | |
- | |-
| + | |
- | |[GFP]
| + | |
- | |GFP concentration at steady-state
| + | |
- | |nM
| + | |
- | |
| + | |
- | |need for 20 + 20 measures <br> and 5x5 measures for the relation below?
| + | |
- | |-
| + | |
- | |(''fluorescence'')
| + | |
- | |value of the observed fluorescence
| + | |
- | |au
| + | |
- | |
| + | |
- | |need for 20 + 20 measures <br> and 5x5 measures for the relation below?
| + | |
- | |-
| + | |
- | |''conversion''
| + | |
- | |conversion ratio between <br> fluorescence and concentration
| + | |
- | |nM.au<sup>-1</sup>
| + | |
- | |(1/79.429)
| + | |
- | |
| + | |
- | |}
| + | |
| | | |
- | <br><br> | + | <div style="text-align: center"> |
- | | + | {{Paris/Toggle|Algorithm|Team:Paris/Modeling/More_FP_Algo}} |
- | {|border="1" style="text-align: center"
| + | </div> |
- | |param | + | |
- | |signification <br> corresponding parameters in the [[Team:Paris/Modeling/Oscillations#Resulting_Equations|equations]] | + | |
- | |unit
| + | |
- | |value
| + | |
- | |comments
| + | |
- | |-
| + | |
- | |β<sub>52</sub>
| + | |
- | |production rate of FlhDC-pFliL '''with RBS E0032''' <br> β<sub>52</sub>
| + | |
- | |nM.min<sup>-1</sup>
| + | |
- | |
| + | |
- | |
| + | |
- | |-
| + | |
- | |(K<sub>46</sub>/{coef<sub>fliA</sub>})
| + | |
- | |activation constant of FlhDC-pFliL <br> K<sub>46</sub>
| + | |
- | |nM
| + | |
- | |
| + | |
- | |
| + | |
- | |-
| + | |
- | |n<sub>46</sub>
| + | |
- | |complexation order of FlhDC-pFliL <br> n<sub>46</sub>
| + | |
- | |no dimension
| + | |
- | |
| + | |
- | |
| + | |
- | |-
| + | |
- | |β<sub>53</sub>
| + | |
- | |production rate of FliA-pFliL '''with RBS E0032''' <br> β<sub>53</sub>
| + | |
- | |nM.min<sup>-1</sup>
| + | |
- | |
| + | |
- | |
| + | |
- | |-
| + | |
- | |(K<sub>47</sub>/{coef<sub>omp</sub>})
| + | |
- | |activation constant of FliA-pFliL <br> K<sub>47</sub>
| + | |
- | |nM
| + | |
- | |
| + | |
- | |
| + | |
- | |-
| + | |
- | |n<sub>47</sub>
| + | |
- | |complexation order of FliA-pFliL <br> n<sub>47</sub>
| + | |
- | |no dimension
| + | |
- | |
| + | |
- | |
| + | |
- | |}
| + | |
- | </center>
| + | |
- | <br><br>
| + | |
| | | |
| Then, if we have time, we want to verify the expected relation | | Then, if we have time, we want to verify the expected relation |
| | | |
| [[Image:SumpFliL.jpg|center]] | | [[Image:SumpFliL.jpg|center]] |
| + | |
| + | <br> |
| + | |
| + | <center> |
| + | [[Team:Paris/Modeling/Implementation| <Back - to "Implementation" ]]| <br> |
| + | [[Team:Paris/Modeling/Protocol_Of_Characterization| <Back - to "Protocol Of Characterization" ]]| |
| + | </center> |
Method & Algorithm : 5
= act_pFliL
Specific Plasmid Characterisation for 5
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} 1([aTc]i)
and [FliA]real = {coeffliA} 2([arab]i)
but we use [aTc]i = Inv_1( [FlhDC] )
and [arab]i = Inv_2( [FliA] )
So, at steady-states,
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.
|
5
| activity of pFliL with RBS E0032
| nM.min-1
|
|
|
param
| signification corresponding parameters in the equations
| unit
| value
| comments
|
β24
| total transcription rate of FlhDC><pFliL with RBS E0032 β24
| nM.min-1
|
|
|
(K2/{coeffliA})
| activation constant of FlhDC><pFliL K2
| nM
|
|
|
n2
| complexation order of FlhDC><pFliL n2
| no dimension
|
|
|
β25
| total transcription rate of FliA><pFliL with RBS E0032 β25
| nM.min-1
|
|
|
(K8/{coefflhDC})
| activation constant of FliA><pFliL K8
| nM
|
|
|
n8
| complexation order of FliA><pFliL n8
| no dimension
|
|
|
|
↓ Algorithm ↑
find_P
function optimal_parameters = find_FP(X_data, Y_data, initial_parameters)
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);
optimal_parameters = lsqcurvefit( @(parameters, X_data) act_pProm(parameters, X_data),...
initial_parameters, X_data, Y_data, options );
end
|
Then, if we have time, we want to verify the expected relation
<Back - to "Implementation" |
<Back - to "Protocol Of Characterization" |
|