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Team:Paris/Production modeling
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As a first approximation, we assumed that : | As a first approximation, we assumed that : | ||
*When the pBad promoter is induced, the concentration of arabinose in the medium is very high and constant during he whole study ; as a consequence, we will consider that the creation rate of Protein and LacI* is constant during the experiment : | *When the pBad promoter is induced, the concentration of arabinose in the medium is very high and constant during he whole study ; as a consequence, we will consider that the creation rate of Protein and LacI* is constant during the experiment : | ||
| - | [[Image:Constant rate copie.png|350px|center| | + | [[Image:Constant rate copie.png|350px|center| Arabinose constant]] |
| - | *We | + | *We considered that all the binding constants are identical and of an average of 40nM which correspond to approximately 40 monomers per cell ; we can write that : |
| + | [[Image:Constant rate copie.png|350px|center| Binding constants]] | ||
Revision as of 13:24, 2 September 2009
iGEM > Paris > Production > Modeling
Modeling
A. Genetic Network Regulation
The first thing that we wanted to study in modeling was the efficiency of the construction chosen to create a delay. Our first approach was a deterministic analysis of the system using differential equations. The regulation of promoters was described using the Hill functions and the methods described by U. Alon in his book An Introduction to Systems Biology.
When the system is activated, there is Arabinose in the medium and the pBad promoters are activated. And the system can be described by this system of differential equations :
| Differential System |
 |
As a first approximation, we assumed that :
- When the pBad promoter is induced, the concentration of arabinose in the medium is very high and constant during he whole study ; as a consequence, we will consider that the creation rate of Protein and LacI* is constant during the experiment :
- We considered that all the binding constants are identical and of an average of 40nM which correspond to approximately 40 monomers per cell ; we can write that :
- As the Plac promoter is leaking, we tried to model this behaviour by introducing a constant rate K in the activation coefficient of PLac.
