On Robust Stability And Sensitivity Of Circadian Rhythms
On Robust Stability And Sensitivity Of Circadian Rhythms
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DOI：
10.1111/j.1934-6093.2006.tb00279.x
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发表时间：
2006-09
影响因子：
2.4
通讯作者：
K. Ogawa;N. Takekawa;K. Uchida;S. Shibata
中科院分区：
文献类型：
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作者：
K. Ogawa;N. Takekawa;K. Uchida;S. Shibata
我们基于数学模型，从周期性轨迹的（局部）鲁棒稳定性及其周期敏感性的角度，开发了一种昼夜节律的鲁棒性分析方法。我们的注意力集中在由 Goldbeter [1] 提出的在果蝇中产生昼夜节律的核心分子模型，以说明我们的方法。我们考虑两种情况，即昼夜节律受到光/暗（LD）循环的周期性强迫以及昼夜节律处于持续黑暗（DD）下。首先，我们提出了（局部）鲁棒稳定性的条件/算法，并表明核心分子模型生成的昼夜节律在 LD 和 DD 情况下都是（局部）鲁棒稳定的。其次，在 DD 情况下，我们推导了周期敏感性公式，并评估（无穷小）参数变化对昼夜节律周期的影响。
We develop an approach to robustness analysis of circadian rhythms from the viewpoints of (local) robust stability of periodic trajectories and their period‐sensitivity, based on mathematical models. Our attention is directed to the core molecular model generating circadian rhythms in Drosophila, proposed by Goldbeter [1], for our approach to be illustrated. We consider two cases when the circadian rhythms are subjected to periodic forcing by light/dark (LD) cycles and when the circadian rhythms are under continuous darkness (DD). First, we propose conditions/algorithms for (local) robust stability, and show that the circadian rhythms generated by the core molecular model are (locally) robustly stable, in both LD and DD cases. Second, in DD case, we derive a formula of period sensitivity, and assess effects of (infinitesimal) parameter‐variations on the period of the circadian rhythms.