Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China.
Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China.
J Chem Phys. 2019 Nov 7;151(17):175101. doi: 10.1063/1.5125046.
Recently, a "mode-hopping" phenomenon has been observed in a NF-κB gene regulatory network with oscillatory tumor necrosis factor (TNF) inputs. It was suggested that noise facilitates the switch between different oscillation modes. However, the underlying mechanism of this noise-induced "cellular mode-hopping" behavior remains elusive. We employed a landscape and flux approach to study the stochastic dynamics and global stability of the NF-κB regulatory system. We used a truncated moment equation approach to calculate the probability distribution and potential landscape for gene regulatory systems. The potential landscape of the NF-κB system exhibits a "double ring valley" shape. Barrier heights from landscape topography provide quantitative measures of the global stability and transition feasibility of the double oscillation system. We found that the landscape and flux jointly govern the dynamical "mode-hopping" behavior of the NF-κB regulatory system. The landscape attracts the system into a "double ring valley," and the flux drives the system to move cyclically. As the external noise increases, relevant barrier heights decrease, and the flux increases. As the amplitude of the TNF input increases, the flux contribution, from the total driving force, increases and the system behavior changes from one to two cycles and ultimately to chaotic dynamics. Therefore, the probabilistic flux may provide an origin of chaotic behavior. We found that the height of the peak of the power spectrum of autocorrelation functions and phase coherence is correlated with barrier heights of the landscape and provides quantitative measures of global stability of the system under intrinsic fluctuations.
最近，在具有振荡肿瘤坏死因子（TNF）输入的 NF-κB 基因调控网络中观察到一种“模态跃迁”现象。有人认为噪声有助于在不同的振荡模式之间切换。然而，这种噪声诱导的“细胞模态跃迁”行为的潜在机制仍不清楚。我们采用景观和通量方法研究了 NF-κB 调控系统的随机动力学和全局稳定性。我们使用截断矩方程方法来计算基因调控系统的概率分布和势景观。NF-κB 系统的势景观呈现出“双环谷”形状。来自地形景观的势垒高度为双振荡系统的全局稳定性和跃迁可行性提供了定量度量。我们发现，景观和通量共同控制 NF-κB 调控系统的动力学“模态跃迁”行为。景观将系统吸引到“双环谷”中，而通量则驱动系统循环运动。随着外部噪声的增加，相关势垒高度降低，通量增加。随着 TNF 输入幅度的增加，来自总驱动力的通量贡献增加，系统行为从一个周期变为两个周期，最终变为混沌动力学。因此，概率通量可能为混沌行为提供了起源。我们发现，自相关函数和相位相干性的功率谱峰值的高度与景观的势垒高度相关，并为系统在固有波动下的全局稳定性提供了定量度量。
