Team:EPF-Lausanne/ODEmodeling

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Modeling with differential equations


The model

The simulation of the expression of the RFP protein activated by the lovTAP in the Read Out 2 circuit was obtained by the following model:

1. LacI --> LovTAP

DLdt.png


2. LovTAP --> LovTAP* (activated form of LovTAP due to a light-induced conformational change)

Lstar.png


3. lovTAP* --> TetR

DTdt.png

4. TetR --> RFP

DRdt.png

5. RFP --> RFP* (activated, fluorescent)

DRstardt.png


Where:

  • L is the concentration of lovTAP [um]
  • L* is the concentration of the activated lovTAP (all lovTAP molecules become activated when exposed to light stimulation) [um]
  • T is the concentration of TetR [um]
  • R is the concentration of RFP [um]
  • R* is the concentration of activated RFP [um]
  • Theta.png is the function of light exposure
  • Alpha 0.png is the basal expression of the given promoter
  • K is the affinity of the given repressor for its target promoter [um]
  • n is the cooperativity coefficient of the Hill function
  • Gamma.png is the molecule degradation rate [min -1]
  • Delta.png is the dilution rate [min -1]



The values of these parameters are listed in the table below:


  • Alpha 0.png = 0.05 for TetR and 0.3 for RFP
  • K = 7 [um] for L*, 7 [um] for TetR and 7 [um] for RFP [um]
  • n = 2 for L, 2 for TetR and 2 for RFP
  • Gamma.png = 0.069 [min -1] for LovTAP, 0.069 [min -1] for TetR and 0.012 [min -1] for RFP
  • Delta.png = log(2)/20, since a division occurs every 20 min for E. Coli
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