= Introduction = biblio A FAIRE We wished to build a model that could be used to help us design our biological system. We shall hereby describe the asumptions we made

Classical model and temporal rescaling

• Classically we use the following equation to model gene interactions (see for example in [1]) :

where [Y] denotes the concentration of Y protein and γ its degradation rate (which unit is time^-1).

• Then, we wanted to have a proper time scale. We then set the degradation rates, γ ,to 1. It is important to note that this degradation rate represents both the influence of the degradation and dilution. We assume that the degradation can be neglected compared to the dilution caused by the cell growth. Then we have:

• Since we can know easily the value of the real half-time, we may know the real timescale out of our computations. We kept the designation “degradation rate” for convenience, so as not to mix up with the dilution that occurs with the HSL in the synchronisation step.

Conclusion

This finally gave the following equations :

Now you have had a good overlook of our model, go see a more detailed justification!

Liens

Bibliography

• [1] Shiraz Kalir, Uri Alon. Using quantitative blueprint to reprogram the dynamics of the flagella network. Cell, June 11, 2004, Vol.117, 713-720.