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From 2010.igem.org

Choosing proper model for LacI/allolactose dynamics

With the above mentioned details, first step should be preparing a proper model for allolactose production, degradation and possible dilution. The reason to this is the binding of allolactose to LacI and inhibiting it from binding to operator, which will result in gene expression.

Yildirim N et al 2002 proposed a mathematical model for lac operon induction in E. Coli. The details that they considered in the model are what we are looking for: external lactose, internal lactose, conversion of lactose to allolactose and glucose, interaction of allolactose with LacI (Lac Repressor) and mRNA. Since the plasmid(?) that we are using to express our genes in bacteria have LacI as repressor, it is reasonable to use the same model as Yildirim N et al 2002.

Lac operon is responsible for transport and metabolism of lactose in e coli. It has a promoter site and three structural genes (LacZ, LacY and LacA). Availability of external Lactose and Glucose regulates this operon. In the absence of Lactose, the LacI gene (always expressed) ,which codes for the repressor , represses the expression the of Lac operon. When Lactose is available again for the bacteria, Allolactose (a β-galactosidase side reaction) binds to repressor and makes it impossible for the repressor to bind the operator on Lac operon. This will result in production of high levels of LacZ (β-galactosidase) , LacY (β-galactoside permease) and LacA, and these will lead to more production of Allolactose. Until this point we have the same assumption as Yildirim N et al 2002. Here we will introduce the model proposed by Yildirim N et al 2002 a brief introduction to their model, then we will try to simplify it and continue with our gene expression model in bacteria as final stage.

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.