Team:Paris/Analysis/Construction2

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== Model Construction ==
== Model Construction ==
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* First of all, it seems important at this stage to present the way we interpret the evolution of the population in the 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. Hence a logistic model of the population, where c denotes the concentration of cells in the medium:
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[[Image:population_evolution_2.jpg|center]]
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* Then, we need to add the death term, and a dilution term cause by the renewal of the chemostat. Finally we get :
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[[Image:population_evolution_full_2.jpg|center]]
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where c<sub>max</sub> is  the carrying capacity for cell growth, and
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[[Image:D_renewal.jpg]] the dilution rate, d the death rate constant
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why use a chemostat
why use a chemostat

Revision as of 20:53, 25 October 2008

Model Construction

  • First of all, it seems important at this stage to present the way we interpret the evolution of the population in the 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. Hence a logistic model of the population, where c denotes the concentration of cells in the medium:


Population evolution 2.jpg


  • Then, we need to add the death term, and a dilution term cause by the renewal of the chemostat. Finally we get :


Population evolution full 2.jpg


where cmax is the carrying capacity for cell growth, and D renewal.jpg the dilution rate, d the death rate constant


why use a chemostat

which model of chemostat we choose


equations

d[c]/dt=alpha_cell*[c]*(c_max-[c])/c_max-(D_renewal+death)*[c] d[LasI]/dt=beta_FlhDC*theta_FlhDC^n_FlhDC/(theta_FlhDC^n_FlhDC+[TetR]^n_FlhDC)-gamma*[LasI] d[TetR]/dt=beta_TetR*[HSL]^n_TetR/(theta_TetR^n_TetR+[HSL]^n_TetR)-gamma*[TetR] d[HSL::ext]/dt=eta*v_cell*[c]*([HSL]-[HSL::ext])-(D_renewal+gamma_HSLext)*[HSL::ext] d[HSL]/dt=beta_HSL*[LasI]+eta*[HSL::ext]-(gamma+gamma_HSLint+eta)*[HSL]


parameters

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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