Our gene circuit is made of six different variables: the concentrations of three proteins (cI, VIP and GFP) and their respective mRNA inside a cell. In table 1, the symbols for each variable are shown. Proteins are represented by a single letter and their mRNAs are represented by that same letter with a lowercase "m" before it.

To parameterize our model, we chose to follow the approach of team Beijing 2009; they propose a relationship between the gene length in base pairs and the maximum transcription rate and, similarly, between the protein length in amino acid numbers and the maximum translation rate. Assuming that the number of polymerases and ribosomes are the average values determined for E. coli, the following equations are used:

For all the variables the degradation rate is expressed by the formula (ln(2)/half life)+(ln(2)/division time), with the same division time of e. coli (30 min), because all the process occurs within it. The only thing that change is the half time; for cI, VIP and GFP (mRNA) is 6.8 minutes and for cI (Selinger, GW, et al., 2003), VIP and GFP protein is more than 10 hours (Varshavsky, (1997) and Tobias et al., 1991).