Team:Imperial College London/Drylab/M1/Protein production/Analysis

=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:
 * We also assume that the concentration of IPTG we put in is below the threshold of toxicity that could significantly start killing our cells.
 * Literature review on IPTG
 * 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.


 * In the absence of IPTG the system becomes:

[Introduce system in the absence of IPTG here] click here for explanation of the equations and parameters or click here

[Introduce full system with IPTG included] and expansion to the model. [link]
 * When IPTG is introduced the system becomes: