Oscillatory dynamics mechanism induced by protein synthesis time delay in quorum-sensing system

Recent experimental evidence reports that the oscillatory behavior of quorum sensing plays an extremely important role in the process of bacterial synthesis and release drug to fight cancer. As we know, the six substances AiiA, LuxI, internal AHL, external AHL, AHL substrate, and H_{2}O_{2} are the core parts of the quorum-sensing system. Here, the effects of several important factors, including time delay, variable H_{2}O_{2}, AHL synthesis rate induced by LuxI, and AHL degradation rate induced by AiiA on the oscillatory behavior of the quorum-sensing system are studied theoretically based on a part of mathematical model describing the interaction of the above six substances proposed by Prindle et al. [Nature 508, 387 (2014)10.1038/nature13238]. The results show that the time delay is a prerequisite for inducing oscillation of the quorum-sensing system. Furthermore, the length of time delay can determine the amplitude and period of oscillation. As a further matter, the change of H_{2}O_{2} concentration can induce the oscillatory behavior of the quorum-sensing system. In addition, under the regulation of H_{2}O_{2}, the period robustness of the quorum-sensing system is increased. Similarly, the quorum-sensing system exhibits periodic oscillation when AHL synthesis rate induced by LuxI less than a certain critical value, unless it displays a steady state. Additionally, a too-high or too-low level of AHL degradation rate induced by AiiA will fail to generate oscillation of the quorum-sensing system, only the intermediate level will cause oscillation. Finally, the two and three parameter regions in which the quorum-sensing system exhibits oscillation behavior are generated.