Modelling and analysing biological oscillations in quorum sensing networks.

Recent experiments have shown that the biological oscillation of quorum sensing (QS) system play a vital role not only in the process of bacterial synthesis but also in the treatment of cancer by releasing drugs. As known, these five substances TetR, CI, LacI, AiiA and AI are the core components of the QS system. However, the effects of AiiA and protein synthesis time delay on QS system are often ignored in the theoretical model, which is taken as a priority in the proposed research. Therefore, the authors developed a new mathematical model to explore the effects of AiiA and time delay on the dynamical behaviour of QS system theoretically and numerically. The results show that time delay can induce oscillation of QS system. Concretely, there exists a time delay threshold [inline-formula removed]. When time delay is less than [inline-formula removed], the system is stable. With the increasing of time delay and once it passes [inline-formula removed], oscillation behaviour occurs. Moreover, the length of time delay determines the amplitude and period of the QS oscillation. In addition, the value of [inline-formula removed] is sensitive to AiiA. These results may enhance the understanding of QS oscillations and provide new insights for bacterial release drugs to treat cancer.