Method & Algorithm : 5
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
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