Team:Paris/Analysis/Construction2

(Difference between revisions)

Revision as of 00:19, 26 October 2008

Model Construction

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).

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 the following one: 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 medium in the chemostat (D_renewal) and cell death (d).

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.

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 16: / Line 16: @@
 <center>[[Image:final_chemostat.gif]]</center>
 <br>
-For the production term, we use a logistic equation to model cell growth, according to standard assumptions [Garcia-Ojalvor--ref]. The behaiviour obtained is the following one: 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 production term, we use a logistic equation to model cell growth, according to standard assumptions [Garcia-Ojalvor--ref]. The behaiviour obtained is the following one: 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 medium in the chemostat (D<sub>renewal</sub>) and cell death (d).
+**For the degradation term, it is considered that c decrease proportionaly to both a dilution phenomena cause by the renewal of the medium in the chemostat (D<sub>renewal</sub>) and cell death (d).
-*To model the quorum sensing dynamics, we consider the production of HSL as:
+*To model the quorum sensing dynamics, we consider:
+**the production of HSL as:
 eqHSL 1,