Positive feedback system can be found in everywhere, which exists widely in creatures ranging from Lac operon of prokaryotes to human beings. It has been used to construct various attractive circuits such bistable state, oscillators and other inconceivable systems. In our project this year, the significant performance of sensitivity would be developed in the positive feedback loop established by LuxR/LuxI quorum sensing system. But this loop can be opened up because of its background expression. The AiiA, which can hydrolyze the AHL, together with the Lac operon, will control the background expression. Furthermore, the input defined by user will have a negative correlation to the opening time. Hence, there is a need to establish a model to describe this relation and even realize quantitative determination.