Team:Paris/Analysis/Construction2

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| 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).
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*To model the quorum sensing dynamics, we consider:
*To model the quorum sensing dynamics, we consider:
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the production of HSL as:
 
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eqHSL 1,
 
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the transport of HSL is given by:
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<center>
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{|WIDTH=70%
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|[[Image:final_HSL_int.gif|center]]
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| the production of HSL as:
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| the transport of HSL is given by:
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| [[Image:HSLext_sum_2.jpg|center]]
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<center> [[Image:HSLext_sum_2.jpg]],</center>
 
where...
where...

Revision as of 00:32, 26 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:
Final chemostat.gif
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 αcell and at high population density, the population reaches a maximum concentration, cmax.
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 (Drenewal) and cell death (d).
  • To model the quorum sensing dynamics, we consider:


Final HSL int.gif
the production of HSL as:
the transport of HSL is given by:
HSLext sum 2.jpg


where...

when in...:

HSLext final 2.jpg,          where     Cell number volume.jpg;

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 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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