Team:Paris/Analysis/Construction2

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Revision as of 21:52, 25 October 2008

Model Construction

Description

We chose to use a chemostat. We want to impose to our model the fact that the rate of production has to be proportional to the existing population and to the amount of available resources.

We assume a logistic model for the population kinetics in the chemostat (reference).

To archieve synchronization we use QS. Explain the principle?

Kinetics

Following a logistic model of the population in the chamostat, the concentration of cells in the medium can be expressed in terms of a production (positive) term and degradation (negative) terms, as:

On the one hand, the concentration of cells (c) increase exponentialy with a velocity given by the growth rate (α_cell). After a certain time, the population reaches a maximum concentration (c_max). On the other hand, c is reduced due to the dilution (D_renewal) and the cell death (d).

Then, we need to add the death term, and a dilution term cause by the renewal of the chemostat. Finally we get :

where c_max is the carrying capacity for cell growth, and the dilution rate, d the death rate constant

Production of HSL:

eqHSL 1

Transport of HSL:

eqHSL 2

Activation of envZ depends of the concentration of HSL:

eqHSL 3

Parameters Search

manly from literature but also from S0 analysis.

Parameters

Chemostat	Parameter	Meaning	Original Value	Normalized Value	Unit	Source
figure / equations of Chemostat	α_cell	Growth rate	0.0198	1	min^-1	wet-lab
	c_max	Carrying capacity for cell growth	0.1	0.1	µm³	[3]
	D_renewal	Dilution rate	0.00198	0.1	min^-1	wet-lab ([3])
	d	Death rate	0.0099	0.5	min^-1	wet-lab

Quorum Sensing	Parameter	Meaning	Original Value	Normalized Value	Unit	Source
figure / equations of Quorum Sensing	γ_HSL	Degradation rate	0.0053	0.2690	min^-1	wet-lab
	γ_{HSL_ext}	Degradation rate	0.0106	0.5380	min^-1	[6]
	β_HSL	Production rate	0.3168	16	min^-1	∅
	η	Diffusion rate	10	505	min^-1	[2]
	n_HSL	Hill coefficient		4		[3]
	θ_HSL	Hill characteristic concentration for the second operator		0.5	c.u	[3]

@@ Line 12: / Line 12: @@
 == Kinetics ==
-* Following a logistic model of the population in the chamostat, the concentration of cells in the medium can be expressed in terms of a production term and a degradation term, as:
+* Following a logistic model of the population in the chamostat, the concentration of cells in the medium can be expressed in terms of a production (positive) term and degradation (negative) terms, as:
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 [[Image:population_evolution_full_2.jpg|center]]