Team:Stockholm/Modelling/Final eq

Which model?

Here we will introduce the model proposed by [http://www.ncbi.nlm.nih.gov/pubmed/12719218 Yildirim N et al 2002] a brief introduction to their model, then we will try to simplify it, declare some of our assumptions, apply our assumptions 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, eq. (2) is the dynamics for mRNA, eq. (3) is dynamics for β-galactosidase, eq. 4 is dynamics of allolactose, eq. (5) is dynamics of Lactose, and finally eq. (6) is the equation for premease. For more detailed explanation for the terms look in: [http://www.ncbi.nlm.nih.gov/pubmed/12719218 Yildirim N et al 2002]. Until this point we have the same assumption as [http://www.ncbi.nlm.nih.gov/pubmed/12719218 Yildirim N et al 2002].

Simplified model

This model can be simplified. Ahmadzadeh et al. 2005 proposed a simplified model of [http://www.ncbi.nlm.nih.gov/pubmed/12719218 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. Full description of the assumptions behind this simplification can be found at Ahmadzadeh et al. 2005 .