Biological oscillators are present in nearly all self-regulating systems, from individual cells to entire organisms. In any oscillator structure, a negative feedback loop is necessary, but not sufficient to guarantee the emergence of periodic behaviors. The likelihood of oscillations can be improved by careful tuning of the system time constants and by increasing the loop gain, yet it is unclear whether there is any general relationship between optimal time constants and loop gain. This issue is particularly relevant in genetic oscillators resulting from a chain of different subsequent biochemical events, each with distinct (and uncertain) kinetics. Using two families of genetic oscillators as model examples, we show that the loop gain required for oscillations is minimum when all elements in the loop have the same time constant. On the contrary, we show that homeostasis is ensured if a single element is considerably slower than the others.

中文翻译：

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均匀的时间常数会在负反馈回路中引起振荡。

从单个细胞到整个生物，几乎所有的自我调节系统都存在生物振荡器。在任何振荡器结构中，负反馈环路都是必要的，但不足以保证周期性行为的出现。仔细调整系统时间常数并增加环路增益可以提高振荡的可能性，但尚不清楚最佳时间常数与环路增益之间是否存在任何一般关系。这个问题在由一系列不同的后续生化事件产生的遗传振荡器中尤为重要，每个后续生化事件都有不同的（且不确定的）动力学。使用两个家族的遗传振荡器作为模型示例，我们表明，当环路中的所有元素都具有相同的时间常数时，振荡所需的环路增益最小。相反，