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From 2010.igem.org

Yildirim N et al model

In a series of 5 equations, They proposed dynamics for mRNA production, β-galactosidase production, Allolactose, Lactose for Lac operon. In their model they also considered transcriptional and translational delays (ie. β-galactosidase and β-galactoside permease production from mRNA is not instant and takes time). [Here model for yildirim et al will come]

Simplified model

This model can be simplified. Ahmadzadeh et al. 2005 proposed a simplified model of Yildirim N et al 2002, where they ignored time delays for transcription and translation. For more simplification they also assumed that β-galactosidase and β-galactoside permease reach their steady state values instantly, ending up with 3 equations just for mRNA, Lactose and Allolactose dynamics.