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

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Assumptions

  • LacI assumptions:
    • The lac operon represses by constitutively synthesizing the LacI gene product [1].
    • Here we have assumed that all the other complicated dynamical pathways are at dynamic equilibrium [2], 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. ([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... Click here for details. Genetic circuit models are explained extensively in [3].

References

[1] Patrick Wong, Stephanie Gladney, and J. D. Keasling*. Mathematical Model of the lac Operon: Inducer Exclusion, Catabolite Repression, and Diauxic Growth on Glucose and Lactose. Biotechnol. Prog. 1997, 13, 132-143
[2]3.Kuhlman T, Zhang Z, Saier MH Jr, & Hwa T (2007) Combinatorial transcriptional control of the lactose operon of Escherichia coli. - PNAS 104 (14) 6043-6048
[3]2.Alon, U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits - Chapman & Hall/Crc Mathematical and Computational Biology

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