Team:Imperial College London/Drylab/Protein production/Analysis

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:

• We also assume that the concentration of IPTG we put in is below the threshold of toxicity that could significantly start killing our cells. ([http://openwetware.org/wiki/IGEM:IMPERIAL/2009/M1/Modelling/Analysis/literatureIPTG Literature review on IPTG])
• In this model we have neglected the degradation rate of IPTG and also of the [IPTG-LacI] complex.

Model Predictions Taking these assumptions into account, we can predict what the overall Qualitative behavior of the system will be.

• In the absence of IPTG, the output amount of our protein of interest will depend on the steady state of LacI protein.
  • If the levels of LacI at steady state are low, we get a relatively high basal production of protein of interest, as the steady state is dependent on the lac promoter strength and its degradation. A weak promoter does not repress sufficiently the production of protein of interest.
  • If the levels of LacI at steady state are high, we are repressing more the production of protein of interest, so we will get a lower initial rate of protein production as the Lac promoter is stronger (higher PoPs output)
• If we take into account leakiness of the Lac promoter, we will see a higher basal amount of protein of interest initially than in the non-leaky case.
• When IPTG is added in, it will undergo a secondary reaction with LacI, thus, de-repressing the pathway, so we will see a bump in production of the protein of interest.
  • These effects are transient. LacI has a constitutive equilibrium, so after sometime, it will return to its original state and repress production of protein of interest once again.
  • The more IPTG we add in, the more LacI we will remove initially from the system, so the more output protein produced for a given period of time.

The actual model... We can describe the behavior of the system with ODEs: Click here for details