Team:Paris/Analysis/Construction2

(Difference between revisions)

Revision as of 23:14, 25 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).

We use a logistic equation. This captures the fact that 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. 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:

,

where...

eqHSL 1,

the transport of HSL is given by:

,

which gives:

, 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 14: / Line 14: @@
 * We use a logistic equation. 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:
 <br>
-<center>[[Image:population_evolution_full_2.jpg]].</center>
+<center>[[Image:population_evolution_full_2.jpg]],</center>
 <br>
+where...
 *To model the quorum sensing dynamics, we consider the production of HSL as: