IGEM:IMPERIAL/2009/M1/Modelling/Analysis

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Protein Production

Model Assumptions

  • 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:
II09 M1 reaction.jpg
  • 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.

The model

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.

Click here for a detailed explanation of the equations

Enzymatic reactions

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