A mathematical model for genetic regulation of the lactose operon

In this paper we construct a mathematical model for the genetic regulatory network of the lactose operon. This mathematical model contains transcription and translation of the lactose permease (LacY) and a reporter gene GFP. The probability of transcription of LacY is determined by 14 binding states out of all 50 possible binding states of the lactose operon based on the quasi-steady-state assumption for the binding reactions, while we calculate the probability of transcription for the reporter gene GFP based on 5 binding states out of 19 possible binding states because the binding site O2 is missing for this reporter gene. We have tested different mechanisms for the transport of thio-methylgalactoside (TMG) and the effect of different Hill coefficients on the simulated LacY expression levels. Using this mathematical model we have realized one of the experimental results with different LacY concentrations, which are induced by different concentrations of TMG.