Team:Paris/Analysis/Construction2

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Revision as of 22:40, 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

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 cause by the renewal of the chemostat (D_renewal) and the cell death (d). As a consequence, the concentration of cells in the medium can be expressed in terms of a production (positive) term and degradation (negative) terms, as:

To model the quorum sensing dynamics, we use:

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]

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 == 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<sub>cell</sub>). After a certain time, the population reaches a maximum concentration (c<sub>max</sub>).
+On the other hand, c is reduced due to the dilution cause by the renewal of the chemostat (D<sub>renewal</sub>) and the cell death (d). As a consequence, the concentration of cells in the medium can be expressed in terms of a production (positive) term and degradation (negative) terms, as:
 <br>
 [[Image:population_evolution_full_2.jpg|center]]
 <br>
-On the one hand, the concentration of cells (c) increase exponentialy with a velocity given by the growth rate (α<sub>cell</sub>). After a certain time, the population reaches a maximum concentration (c<sub>max</sub>).
-On the other hand, c is reduced due to the dilution cause by the renewal of the chemostat (D<sub>renewal</sub>) and the cell death (d).