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

Mathematical models are useful in two ways:

• In the absence of experimental data they provide predictions about the behaviour of a system, and rely on a set of assumptions.
• When experimental data is available they can be refined and provide explanations about the results we see.

In this model, we made several assumptions, followed by predictions. These are listed below.

Model 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 the lacI gene product is the only repressing entity in the system. For more details on the theory see our section on |chemical induction.
    • 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... Click here for details. Genetic circuit models are explained extensively in [3].

References