Standard biological parts (pTet-LacI-pLac-LacY-GFP) from the iGEM Registry were used to design a synthetic circuit operated by IPTG as an extracellular stimulus to trigger gene transcription. The circuit was designed to work as a Schmitt trigger (a switch with hysteresis). A genetic program without the LacY gene (open-loop configuration) was first cloned into a high-copy-number plasmid and was used in E. coli to identify a mathematical model of the molecular circuit. Then, the model was used to predict the behaviour in closed loop and to assess the existence of a switch with hysteresis.