= 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 time resetting

• Classically we use the following equation to model gene interactions (see for example in [5]) :

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.

Sum effect and linear modelling

• Yet, the flagella gene network has been thoroughly studied in [1]. We used two major results presented in this study. Firstly, Shiraz Kalir and Uri Alon came up with the fact that the promoters of class 2 genes, among which fliL, flgA and flhB, behaved like SUM-gate functions with flhDC and fliA inputs. Secondly, their experiments proved that these influences could be considered as linear. Thus the following model:

β and β’ represent the relative influence of flhDC and fliA respectively, the units of β and β’ being time^-1.

• Furthermore, they came up with numerical values of β and β’ for each gene, which fitted quite well to their experiments. We then decided that we could use those values as well in our model.

Use Hill quand on ne sait pas

Conclusion

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.