Modelling the repression of the promoter before IPTG is introduced to the reaction

IPTG is an inducer which binds to LacI. LacI is a repressor that is constitutively expressed. It binds to the promoter preventing the promoter from expressing an output, in this case GFP.

In the absence of IPTG , LacI is constitutively expressed. Hence the constitutive expression model from the previous characterisation step can be assumed. At the same time, it can bind to the promoter to repress it.

Evolution of LacI concentration

The repressor only binds to the promoter when it is in its unbound form.

Evolution of promoter concentration

Evolution of the promoter-LacI complex

Evolution of GFP

d_GFP[GFP] is the basal rate of GFP. This is caused by the leakiness of the LacI-PLac complex when LacI does not repress the promoter completely.