Team:Paris/Modeling/More From2Ode Expl

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Polymere of Transcription Factor
As it is explained in the introduction for the case of "FlhDC", instead of considering every polymere and complexes of proteins, we simplify those phenomenon by dealing with "abstract" proteins which represents the real transcription factors. It is the case for :

It is actually an hexamere [?]
 * FlhDC &larr; FlhD4C2

TetR dimerizes before acting on pTet [?]
 * TetR &larr; TetR2

aTC dimerizes before binding on TetR [?]
 * aTc &larr; aTc2

OmpR acts on pFlhDC only if phosphorylated (OmpR><EnvZ

Transcription
We suppose that the transcription rate is proportional to the amount of "effecive promoter" in the cell. An effective promoter is either a induced promoter bound to its transcription factor, either a free constitutive promoter. We use the following notations : transcription rate = bpromoter * Nb(effective_promoter) transcription constant = &beta;promoter = bpromoter * Nb(total_promoter)

Competition Between Transcription Factors
If several transcription factors bind to a given promoter, those several complexations are in competition. To treat this phenomenon, we must know if a reaction is predominant, or if all the steady-states are reached "at the same time", oother rules of order. We made the following hypothesis :


 * The contribution of the two inducers FliA and FlhDC on the promoters of "class 2 genes" (pFliL,pFlgA,pFlgB,pFlhB ; U. Alon demonstated it for pFliL in [?] ) are synthetised by a SUM logical gate : that corresponds to the biological hypothesis that the promoter has got two specific sites of binding, one for each TF, and that we can sum the probabilities of binding between the RNAase and the adequat sites.
 * It seems obvious that the binding sites of OmpR* and of FliA on pFlhDC are completly different. We made the hypothesis that any pFlhDC bound to OmpR is inactivated, whether it is bound to FliA or not.

Dilution/Degradation &gamma;
As we want the cells to remain in "exponential phase of growth", we assume that every protein involved in the system and for the characterisation has a half-life time far superior than the time of cell division. In that way, we consider that every protein in the cell disappears only by dilution, whose value would be estimated in the wet-lab.

Translation : RBS issue
We use the GFPgenerator (E0240) in association with its RBS (B0032), to caracterise the "expression of the gene behind a given promoter". However, the Ribosome Binding Site of the gene influence it's expression. By considering that  the translation rate depends near linearly of the Ribosome Binding Site (as we guess ; it gives the affinity between the mRNA and the ribosome !), we introduce a constant factor between the expected value of a protein and its real value.

Moreover, we observe that at the steady state, the "disappearance rate" &gamma; has got a linear effect on the concentration of the protein at equilibrium, too.

For instance, if we consider a protein prot coded by its corresponding gene, put behind one of our "characterized promoters", with its natural RBS, we will have between our construction (expected value, given by GFP) and the real expression of prot the following relation

where

It does not invalid our will of "systematic characterization", because this error is reported once prot is considered as transcription factor for the next step in which it is involved...

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