Team:EPF-Lausanne/ODEmodeling

 

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



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



3. lovTAP* --> TetR



4. TetR --> RFP



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



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]


 * [[Image:Theta.png]] is the function of light exposure


 * [[Image: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


 * [[Image:gamma.png]] is the molecule degradation rate [min -1]


 * [[Image:delta.png]] is the dilution rate [min -1]

Parameters values
The values used for these parameters are listed  below:


 * L = 7 [um]


 * [[Image: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


 * [[Image:gamma.png]] = 0.069 [min -1] for LovTAP, 0.069  [min -1] for TetR and 0.012 [min -1] for RFP


 * [[Image:delta.png]] = log(2)/20, since a division occurs every 20 min for E. Coli

