延迟负循环反馈中的生化振荡：谐波平衡分析及其应用
Biochemical Oscillations in Delayed Negative Cyclic Feedback: Harmonic Balance Analysis with Applications
AI总结：
提出基于多变量谐波平衡的理论框架，解析负循环反馈基因调控网络中振荡蛋白浓度的频率、相位和振幅，并应用于Pentilator和Hes7自抑制网络验证。
摘要：
振荡化学反应通常作为活细胞中细胞过程的计时时钟。因此，蛋白质浓度水平的时间动态在生物学中具有重要意义。本文提出了一个理论框架，用于分析具有负循环反馈的基因调控网络中振荡蛋白浓度的频率、相位和振幅。我们首先基于多变量谐波平衡建立了振荡轮廓的分析框架。利用该框架，尽管动力学具有非线性，但频率、相位和振幅可以解析地表示为反应动力学常数的函数。这些结果通过Pentilator和Hes7自抑制网络进行了验证，表明所开发的分析方法确实预测了振荡轮廓。所呈现结果的一个显著特征是，对于一大类生化系统，振荡波形可以解析获得。因此，很容易看出波形如何由系统参数和结构决定。我们提出了适用于任何具有负循环反馈的基因调控网络的通用生物学见解。
英文摘要：
Oscillatory chemical reactions often serve as a timing clock of cellular processes in living cells. The temporal dynamics of protein concentration levels is thus of great interest in biology. Here we propose a theoretical framework to analyze the frequency, phase and amplitude of oscillatory protein concentrations in gene regulatory networks with negative cyclic feedback. We first formulate the analysis framework of oscillation profiles based on multivariable harmonic balance. With this framework, the frequency, phase and amplitude are obtained analytically in terms of kinetic constants of the reactions despite the nonlinearity of the dynamics. These results are demonstrated with the Pentilator and Hes7 self-repression network, and it is shown that the developed analysis method indeed predicts the profiles of the oscillations. A distinctive feature of the presented result is that the waveform of oscillations is analytically obtained for a broad class of biochemical systems. Thus, it is easy to see how the waveform is determined from the system's parameters and structures. We present general biological insights that are applicable for any gene regulatory networks with negative cyclic feedback.
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