Team:Paris/Analysis/Construction2

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Revision as of 23:34, 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

The concentration variation of cells in the chemostat over time can be expressed in terms of a production (positive) term and degradation (negative) terms:

,

For the production term, we use a logistic equation to model cell growth, according to standard assumptions [Garcia-Ojalvor--ref]. The behaiviour obtained is as follows: at low population density, the concentration of cells in the chemostat (c) increase exponentialy with a growth rate α_cell and at high population density, the population reaches a maximum concentration, c_max.

For the degradation term, it is considered that c decrease proportionaly to both a dilution phenomena cause by the renewal of the chemostat (D_renewal) and cell death (d).

To model the quorum sensing dynamics, we consider the production of HSL as:

eqHSL 1,

the transport of HSL is given by:

,

where...

when in...:

, where

;

and the activation of envZ depends of the concentration of HSL according to:

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 standard assumptions, We use a logistic equation for representing cell growth [Garcia-Ojalvor--ref]. This captures the fact that at low population density, the concentration of cells in the chemostat (c) increase exponentialy with a growth rate α<sub>cell</sub> and at high population density, the population reaches a maximum concentration c<sub>max</sub>. 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 follows:
+* The concentration variation of cells in the chemostat over time can be expressed in terms of a production (positive) term and degradation (negative) terms:
 <br>
 <center>[[Image:population_evolution_full_2.jpg]],</center>
 <br>
-where...
+For the production term, we use a logistic equation to model cell growth, according to standard assumptions [Garcia-Ojalvor--ref]. The behaiviour obtained is as follows: at low population density, the concentration of cells in the chemostat (c) increase exponentialy with a growth rate α<sub>cell</sub> and at high population density, the population reaches a maximum concentration, c<sub>max</sub>.
+For the degradation term, it is considered that c decrease proportionaly to both a dilution phenomena cause by the renewal of the chemostat (D<sub>renewal</sub>) and cell death (d).
 *To model the quorum sensing dynamics, we consider the production of HSL as: