Introduction

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

bcp de données bibliographique + gros effort de normalisation dou détermination de tous les parametre et pas de pipo

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).

We did a lot of bibliography work and found many interesting expressions found in S.Kalir and U. Alon article. We also kept the parameters values. When we did not find relevant information, we chose a classical Hill function.

We normalized every concentration, so that their value would range between 0 and 1. Indeed, we found it necessary because we needed to be able to compare the respective influences of these concentrations.

Furthermore, 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. Thus, every degradation rates are equal. We kept the designation “degradation rate” for convenience, so as not to mix up with the dilution that might occur elsewhere.

We therefore wanted to have a proper time scale. We then set the degradation rates, γ ,to 1. Since we can know easily the value of the real half-time, we may know the real timescale out of our computations. Then we have:

We finally obtained the following equations :

and the following parameters :

Parameter Table
Parameter	Parameter in code	Meaning	Original Value	Normalized Value	Unit	Source
γ		Degradation rate	0.0198	1	min^-1	wet-lab
β_FlhDC		Maximum production rate		1	min^-1	∅
β_FliA		FlhDC activation coefficient	50	0.1429	min^-1	[1]
β'_FliA		FliA activation coefficient	300	0.8571	min^-1	[1]
β_CFP		FlhDC activation coefficient	1200	0.8276	min^-1	[1]
β'_CFP		FliA activation coefficient	250	0.1724	min^-1	[1]
β_YFP		FlhDC activation coefficient	150	0.3333	min^-1	[1]
β'_YFP		FliA activation coefficient	300	0.6667	min^-1	[1]
β_RFP		FlhDC activation coefficient	100	0.2222	min^-1	[1]
β'_RFP		FliA activation coefficient	350	0.7778	min^-1	[1]
n_envZ		Hill coefficient		4	¤	∅
θ_envZ		Hill characteristic concentration		0.5	c.u	∅
β_envZ			Maximum production rate		1	min^-1	∅

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

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