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From 2010.igem.org

Derivation

Discussion of how we derived GRN model....

GRN Models

A Gene Regulatory Network (GRN) model is an established way of representing the biochemical reactions within a bacterial cell (7). Representing a network of interacting components using differential equations can be very useful, mainly because one can make analytical and qualitative assessments of a system’s behaviour with very limited information on parameters. This GRN represents a protein called NsrR that represses the production of mRNA encoding GFP, and so indirectly repressing the production of GFP. NsrR can bind to nitrates, effectively destroying its ability to repress the system.

The most interesting relationship in this system of equations is the relationship between the concentration of NsrR repressor protein and the concentration of GFP in the system. A useful way of visualising and analysing the system’s dynamics is using a phase plane portrait in 2 dimensions. However, this means eliminating one of the variables. This can be done by making an equilibrium assumption about the amount of mRNA encoding GFP (mGFP for short). To do this, we set Equation 2 equal to 0. Rearranging in terms of [mGFP], this gives: