- LacI assumptions:
- The lac operon represses by constitutively synthesizing the LacI gene product [ref1].
- Here we have assumed that all the other complicated dynamical pathways are at dynamic equilibrium [ref2], and we are only considering the LacI gene.
- If these effects were included, the dynamics of the entire system will be more complicated, and the outcome of the model will be different.
- In a culture grown overnight, levels of LacI expression will have reached steady state. We can assume that this is the case before we add in IPTG.
- IPTG assumptions:
- LacI and IPTG undergo a secondary set of reactions when IPTG is added in. We assume that 1 molecule of IPTG binds to 1 molecule of LacI, creating an intermediate reaction complex:
- We also assume that the concentration of IPTG we put in is below the threshold of toxicity that could significantly start killing our cells.
- In this model we have neglected the degradation rate of IPTG and also of the [IPTG-LacI] complex.
We can describe the behavior of the system with 4 ODEs. In this system, the first two equations describe the expression of LacI protein, and these will be linked to how it represses production of the protein of interest.