The periodic transcription output is ubiquitously observed in an isogenic cell population. To understand mechanisms of cyclic behavior in transcription, we extend the gene activation process in the two-state model by assuming that the synthesis rate is periodic. We derive the analytical forms of the mean transcript level and the noise. The limits of them indicate that the mean level and the noise display periodic behaviors. Numerical examples strongly suggest that the transcription system with a periodic synthesis rate generates more noise than that with a constant rate but maintains transcription homeostasis in each period. It is also suggested that if the periodicity is not considered, the calculated noise may be greater than the real value.

在同基因细胞群中普遍观察到周期性转录输出。为了理解转录中循环行为的机制，我们通过假设合成速率是周期性的来扩展二态模型中的基因激活过程。我们推导出平均转录水平和噪声的分析形式。它们的限制表明平均水平和噪声显示出周期性行为。数值例子强烈表明，具有周期性合成速率的转录系统比具有恒定速率的转录系统产生更多的噪音，但在每个时期都保持转录稳态。还建议如果不考虑周期性，计算出的噪声可能会大于实际值。