Synthetic biology aims to the rational design of gene circuits with predictable behaviours. Great efforts have been done so far to introduce in the field mathematical models that could facilitate the design of synthetic networks. Here we present a mathematical model of a synthetic gene-circuit with a negative feedback. The closed loop configuration allows the control of transcription by an inducer molecule (IPTG). Escherichia coli bacterial cells were transformed and expression of a fluorescent reporter (GFP) was measured for different inducer levels. Computer model simulations well reproduced the experimental induction data, using a single fitting parameter. Independent genetic components were used to assemble the synthetic circuit. The mathematical model here presented could be useful to predict how changes in these genetic components affect the behaviour of the synthetic circuit.