Team:BUAP Mexico/Model
Theoretical foundation: Toggle Switch
The Toggle switch is one of the synthetic gene-regulatory network designed by Gardner, Cantor and collins at the beginning of 2000. This network was constructed using two repressors and two constitutive promoters and each promoter is inhibited by the repressor that is transcribed by the opposing promoter. Toggle switch shows bistability over a wide range of parameter values, this bistability arises from the mutually inhibitory arrangement of the genes repressors. In absence of inducers, two states are possible: First one: The promoter 1 transcribes repressor 2 Second one: The promoter 2 transcribes repressor 1 Switching is activated introducing an inducer in the environment which inactivate one of the currently active repressor. The inducer allows the opposing repressor to be maximally transcribed until it stably represses the originally active promoter.
Theoretically toggle design does not require any specialized promoters, whit this in mind we decided to use the Pyruvate Dehydrogenase Complex (pdh) promoter containing a site which is recognized by RNA polymerase and a binding site for pdh repressive protein combined with arcA gene and the ompW promoter containing a binding site for RNA polymerase and ArcA repressive protein combined with pdhR gene. The inducer to pdhR is the pyruvate and the inducer to arcA is the aerobic condition, in which arcB loses its kinase activity allowing the dephosphorylation of ArcA inactivating this protein and leading the gene expression. Furthermore curiously, in many bacteria the ArcA protein is activated not only in anaerobic conditions then is activated by the addition of H2O2 to the environment showing a response to oxidative stress, but this phenomenon have not been demonstrated in E. coli.
Modeling
First, we are going to define the variables that we’ll use along the equations: Ktranscription (constant rate of transcription from DNA to mRNA) Ktranslation (constant rate of translation from mRNA to protein) γm (constant rate of degradation of mRNA) γp (constant rate of degradation of protein) KR (dissociation constant for a repressor) KI (dissociation constant for an inducer) N (Hill coefficient for a repressor) M (Hill coeffcient for an inducer)
Inspiration
Here are a few examples from previous teams: