Combinatorial dynamics of protein synthesis time delay and negative feedback loop in NF-κB signalling pathway

The transcription factor NF-κB links immune response and inflammatory reaction and its different oscillation patterns determine different cell fates. In this study, a mathematical model with IκBα protein synthesis time delay is developed based on the experimental evidences. The results show that time delay has the ability to drive oscillation of NF-κB via Hopf bifurcation. Meanwhile, the amplitude and period are sensitive to the time delay. Moreover, the time delay threshold is a function of four parameters characterising the negative feedback loop. Likewise, the parameters also have effects on the amplitude and period of NF-κB oscillation induced by time delay. Therefore, the oscillation patterns of NF-κB are collaborative results of time delay coupled with the negative feedback loop. These results not only enhance the understanding of NF-κB biological oscillation but also provide clues for the development of anti-inflammatory or anti-cancer drugs.