Team:Paris/Analysis/Construction2

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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 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).
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).
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*To model the quorum sensing dynamics, we use:
*To model the quorum sensing dynamics, we use:

Revision as of 22:38, 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:


Population evolution full 2.jpg


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


  • 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 αcell Growth rate 0.0198 1 min-1 wet-lab
cmax Carrying capacity for cell growth 0.1 0.1 µm3 [3]
Drenewal 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 γHSL Degradation rate 0.0053 0.2690 min-1 wet-lab
γHSLext

Degradation rate 0.0106 0.5380 min-1 [6]
βHSL Production rate 0.3168 16 min-1 ∅
η Diffusion rate 10 505 min-1 [2]
nHSL Hill coefficient   4   [3]
θHSL Hill characteristic concentration for the second operator   0.5 c.u [3]
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