Team:Paris/Production modeling

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Modeling

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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 :

• We chose identical intrisinc promoter activities, β , all equal to 4000 proteins/cell cycle :

• All the time units were expressed in units of cell cycle (approximately half an hour) ; as a consequence we chose a dilution rate γ of 1 for protein without special tags. For the Laci protein with a LVA tag, the dilution rate is multiplied by 3: