Analytical study of robustness of a negative feedback oscillator by multiparameter sensitivity.
Analytical study of robustness of a negative feedback oscillator by multiparameter sensitivity.
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DOI：
10.1186/1752-0509-8-s5-s1
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发表时间：
2014
影响因子：
--
通讯作者：
Kurata H
中科院分区：
文献类型：
--
作者：
Maeda K;Kurata H
生物振荡器（如生物钟和细胞周期）的显著特征之一是鲁棒性，即在面对不同类型的扰动时恢复可靠操作的能力。在以前的研究中，我们提出了多参数灵敏度（MPS）作为一个可理解的措施，动力学参数的波动的鲁棒性。解析解直接将机制和动力学参数与动力学性质（如周期、振幅及其相关MPS）联系起来。负反馈回路是生物振荡器的常见结构，但负反馈振荡器的一般模型的解析解至今尚未得到。本文给出了一般负反馈振子模型的周期、振幅及其相关MPs的解析表达式。通过与数值解的比较，验证了解析解的有效性.解析解明确地显示了动力学性质如何依赖于动力学参数。阈值与幅度的比率对周期MPS具有强烈影响。当比值接近1时，MPS增加，表明周期对动力学参数的变化变得更加敏感。我们提出的第一个数学证明，分布式的时间延迟机制有助于使振荡周期的参数波动鲁棒。MPS随着反馈回路长度的增加而减小（即，构成反馈回路的分子种类的数量）。由于采用了负反馈振荡器的一般模型，本文的结果可望对许多生物振荡器成立。这项研究有力地支持了时钟蛋白磷酸化有助于昼夜节律稳健性的假设。这些解析解为合成生物学家设计具有理想周期和鲁棒性的基因振荡器提供了线索。
One of the distinctive features of biological oscillators such as circadian clocks and cell cycles is robustness which is the ability to resume reliable operation in the face of different types of perturbations. In the previous study, we proposed multiparameter sensitivity (MPS) as an intelligible measure for robustness to fluctuations in kinetic parameters. Analytical solutions directly connect the mechanisms and kinetic parameters to dynamic properties such as period, amplitude and their associated MPSs. Although negative feedback loops are known as common structures to biological oscillators, the analytical solutions have not been presented for a general model of negative feedback oscillators. We present the analytical expressions for the period, amplitude and their associated MPSs for a general model of negative feedback oscillators. The analytical solutions are validated by comparing them with numerical solutions. The analytical solutions explicitly show how the dynamic properties depend on the kinetic parameters. The ratio of a threshold to the amplitude has a strong impact on the period MPS. As the ratio approaches to one, the MPS increases, indicating that the period becomes more sensitive to changes in kinetic parameters. We present the first mathematical proof that the distributed time-delay mechanism contributes to making the oscillation period robust to parameter fluctuations. The MPS decreases with an increase in the feedback loop length (i.e., the number of molecular species constituting the feedback loop). Since a general model of negative feedback oscillators was employed, the results shown in this paper are expected to be true for many of biological oscillators. This study strongly supports that the hypothesis that phosphorylations of clock proteins contribute to the robustness of circadian rhythms. The analytical solutions give synthetic biologists some clues to design gene oscillators with robust and desired period.