Team:Paris/Modeling/f3bis

From 2008.igem.org

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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;6}}
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and [EnvZ]<sub>total</sub> = [EnvZ]<sub>b</sub> + [EnvZ]<sub>produced</sub>
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[[Image:f6DCA.png|thumb|Specific Plasmid Characterisation for &#131;6]]
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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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We have <span style="color:#0000FF;">[''FlhDC'']<sub>''real''</sub> = {coef<sub>''flhDC''</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>} &#131;2([arab]<sub>i</sub>)</span>
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So, if we denote phosphorylated OmpR by ''OmpR<sup>*</sup>'', we have
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but we use <span style="color:#0000FF;">[aTc]<sub>i</sub> = Inv_&#131;1( [''FlhDC''] ) </span>
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and        <span style="color:#0000FF;">[arab]<sub>i</sub> = Inv_&#131;2( [''FliA''] ) </span>
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[[Image:F3ompfromenv.jpg|center]]
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So, at steady-states,
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that we can then introduce in the previous expression ([[Team:Paris/Modeling/f3|see &#131;3]]) :
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[[Image:F6.jpg|center]]
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[[Image:F3ompfinalenv.jpg|center]]
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<br>
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<br><br>
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<div style="text-align: center">
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{{Paris/Toggle|Table|Team:Paris/Modeling/More_f6_Table}}
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</div>
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{|border="1" style="text-align: center"
 
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|param
 
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|signification
 
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|unit
 
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|value
 
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|comments
 
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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.min<sup>-1</sup>
 
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|
 
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|need for 20 mesures with well choosen values of [aTc]<sub>i</sub>
 
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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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|min<sup>-1</sup>
 
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|0.0198
 
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|
 
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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 mesures
 
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|(''fluorescence'')
 
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|value of the observed fluorescence
 
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|au
 
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|
 
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|need for 20 mesures
 
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|-
 
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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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|
 
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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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[[Image:SumpFlgA.jpg|center]]
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|unit
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|value
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<br>
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|comments
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|-
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<center>
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|K<sub>21</sub><sup>eff</sup>
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[[Team:Paris/Modeling/Implementation| <Back - to "Implementation" ]]| <br>
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|dissociation constant OmpR_-_EnvZ <br> K<sub>21</sub><sup>eff</sup>
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[[Team:Paris/Modeling/Protocol_Of_Characterization| <Back - to "Protocol Of Characterization" ]]|
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|nM
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</center>
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|
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|the literature [[Team:Paris/Modeling/Bibliography|[?] ]] gives K<sub>21</sub> =
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|n<sub>21</sub>
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|complexation order OmpR_-_EnvZ <br> n<sub>21</sub>
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|no dimension
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|the literature [[Team:Paris/Modeling/Bibliography|[?] ]] gives n<sub>21</sub> =
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|{coef<sub>env</sub>}
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|coefficient due to the difference of the RBS and degradation rate between EnvZ and GFP <br> ! not precised in the equations !
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|no dimension
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|! not precised in the equations ! watch out when writing the corresponding simulating program
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|[EnvZ]<sub>b</sub>
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|"basal" presence of EnvZ <br> [EnvZ]<sub>b</sub>
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|nM
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|the literature [[Team:Paris/Modeling/Bibliography|[?] ]] gives, under high osmolarity, [EnvZ]<sub>b</sub> =
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|[OmpR]<sub>b</sub>
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|"basal" presence of OmpR <br> [OmpR]<sub>b</sub>
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|nM
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|the literature [[Team:Paris/Modeling/Bibliography|[?] ]] gives, under high osmolarity, [OmpR]<sub>b</sub> =
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|}
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Revision as of 14:26, 29 October 2008

Method & Algorithm : ƒ6


Specific Plasmid Characterisation for ƒ6

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,

F6.jpg


↓ Table ↑


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.
ƒ6 activity of
pFlgA with RBS E0032 		nM.min-1



param signification
corresponding parameters in the equations 		unit value comments
β26 total transcription rate of
FlhDC><pFlgA with RBS E0032
β26 		nM.min-1
(K3/{coeffliA}) activation constant of FlhDC><pFliL
K3 		nM
n3 complexation order of FlhDC><pFliL
n3 		no dimension
β27 total transcription rate of
FliA><pFliL with RBS E0032
β27 		nM.min-1
(K9/{coefflhDC}) activation constant of FliA><pFliL
K9 		nM
n9 complexation order of FliA><pFliL
n9 		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

SumpFlgA.jpg


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

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