Team:Paris/Modeling/Programs
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* ''Prot'' is a protein, produce by a ''promoter'' | * ''Prot'' is a protein, produce by a ''promoter'' | ||
* ''expr_prom'' is the given expression of this ''promoter'' (production rate of ''Prot'') | * ''expr_prom'' is the given expression of this ''promoter'' (production rate of ''Prot'') | ||
- | * ''γ'' is the degradation/dilution rate of the proteins and complexes in the cell (especially due to cell division) | + | * ''γ'' is the degradation/dilution rate of the proteins and complexes in the cell (especially due to cell division, we made so far the hypothesis that it is the same for all the proteins) |
* ''SM<sub>int</sub>'' binds to ''Prot'', with a cooperativity ''n'' and a dissociation constant ''K<sub>d</sub>'', to form the complex ''Compl'' | * ''SM<sub>int</sub>'' binds to ''Prot'', with a cooperativity ''n'' and a dissociation constant ''K<sub>d</sub>'', to form the complex ''Compl'' | ||
* The cell culture is in a chemostat : the cell population is N; The renewal rate (flow of the medium, in L.min<sup>-1</sup>) is ''rnw''; The Volume of a cell is ''V<sub>int</sub>''; and of the outer medium is ''V<sub>ext</sub>'' ( = ''Volume(chemostat)'' - ''N'' * ''V<sub>int</sub>'') | * The cell culture is in a chemostat : the cell population is N; The renewal rate (flow of the medium, in L.min<sup>-1</sup>) is ''rnw''; The Volume of a cell is ''V<sub>int</sub>''; and of the outer medium is ''V<sub>ext</sub>'' ( = ''Volume(chemostat)'' - ''N'' * ''V<sub>int</sub>'') | ||
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+ | ===Induction for the caracterisations=== | ||
+ | see [[https://2008.igem.org/Team:Paris/Modeling/estimation#How_to_control_the_concentration_of_the_transcription_factor_.3F|details on the induction]] | ||
+ | |||
+ | In this experimental conditions, the input medium has a constant (controlled) concentration [''SM'']<sub>i</sub>. So, we can easily make the hypothesis that it impose the [''SM'']<sub>ext</sub> in the outer medium ; and, under the hypothesis of a "quick enough" diffusion, we get at steady-state : | ||
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+ | [[Image:EquaConc.jpg|center]] | ||
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+ | Then, considering the previous complexations equations, and by the equilibrium of ''Prot'', we have at steady states | ||
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+ | [[Image:ProtSt.jpg|center]] | ||
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+ | and by the definition of the dissociation constant | ||
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+ | [[Image:Kd.jpg|center]] | ||
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+ | that leads to the following expression of the complexes and proteins : | ||
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+ | [[Image:ComplProt.jpg]] | ||
==Finding Parameters== | ==Finding Parameters== |
Revision as of 12:43, 25 September 2008
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