A literature search revealed two models of IPTGinduced expression through the Plac promoter. Both models assume constitutive expression of LacI. Before IPTG is added, a steadystate is reached comprising basal (leaky) expression of GFP.
Simpler model
In the simpler model (2) IPTG competes with free promoter for LacI binding, but does not itself bind to the LacIpromoter complex.
>>> Details >>>
Under this model, with all other parameters constant, the steadystate concentration of free promoter and hence the steadystate concentration of GFP are independent of the initial concentration of IPTG. (See time evolution of GFP expression assuming different concentrations of IPTG are used for induction, right.)
The presteadystate dynamic behaviour of the GFP concentration will differ with different initial concentrations of IPTG (but the steadystate behaviour will not). Hence, accurate data collection during the presteadystate phase is crucial for parameter estimation.
More complex model
A more sophisticated model allows for interaction between IPTG and the promoterLacI complex (3). IPTG can bind to the promoterLacI complex to form IPTGLacI and free promoter. This eases the repression by LacI and allows transcription of GFP.
Under this model, the dynamic behaviour (whether or not [GFP] attains a maximum higher than its steadystate value) depends on the relative strengths of the kinetic constants describing the interactions underlying the model. Either way, the steadystate [GFP] will vary as a Hillfunction dependent on the initial concentration of IPTG; this characteristic can be used to discriminate between the two models.
ODEs and simulation mfiles for further exploration of the properties of these models can, again, be found in the appendices.
>>> Details of equilibria and equations and qualitative discussion of parameter effects >>>
