Mathematical Modeling of Bistable Toggle Switch

Thermodynamic Model of Cooperative Repression

A thermodynamic approach was used to model the cooperative repression by transcription factors (iTAL and CRISPR) binding to multiple binding sites. The model was largely based on the models shown in "Transcriptional regulation by the numbers: models" (Bintu, 2005), which base on the reasoning that gene expression level is related to the probabilities of various molecules--such as transcription factors (TFs) and RNA Polymerase (RNAP)--binding to the DNA of interest. The key concept in this model is using the "probability that RNAP occupies the promoter of interest" instead of using "concentration of protein" produced. One of the most important assumptions of this model is that promoter occupancy by RNAP is directly proportional to the level of gene expression.