The transcription factor NF- κ B links immune response and inflammatory reaction and its different oscillation patterns determine different cell fates. In this study, a mathematical model with I κ B α 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- κ B 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- κ B oscillation induced by time delay. Therefore, the oscillation patterns of NF- κ B are collaborative results of time delay coupled with the negative feedback loop. These results not only enhance the understanding of NF- κ B biological oscillation but also provide clues for the development of anti-inflammatory or anti-cancer drugs.

中文翻译：

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NF-κB信号通路中蛋白质合成时间延迟与负反馈回路的组合动力学

转录因子NF- κ B将免疫反应和炎症反应联系起来，其不同的振荡模式决定了不同的细胞命运。在这项研究中，我建立了一个数学模型 κ 乙 α蛋白质合成时间延迟是根据实验证据开发的。结果表明，时间延迟具有驱动NF-振荡的能力。 κ B 通过 Hopf 分岔。同时，幅度和周期对时间延迟很敏感。此外，时间延迟阈值是表征负反馈回路的四个参数的函数。同样，这些参数也对 NF- 的幅度和周期有影响。 κ B 由时间延迟引起的振荡。因此，NF-的振荡模式 κ B 是时间延迟加上负反馈循环的协同结果。这些结果不仅增强了对 NF- κ B生物振荡也为开发抗炎或抗癌药物提供线索。