Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Japan.
PLoS Comput Biol. 2021 Mar 8;17(3):e1008774. doi: 10.1371/journal.pcbi.1008774. eCollection 2021 Mar.
Multiple feedback loops are often found in gene regulations for various cellular functions. In mammalian circadian clocks, oscillations of Period1 (Per1) and Period2 (Per2) expression are caused by interacting negative feedback loops (NFLs) whose protein products with similar molecular functions repress each other. However, Per1 expression peaks earlier than Per2 in the pacemaker tissue, raising the question of whether the peak time difference reflects their different dynamical functions. Here, we address this question by analyzing phase responses of the circadian clock caused by light-induced transcription of both Per1 and Per2 mRNAs. Through mathematical analyses of dual NFLs, we show that phase advance is mainly driven by light inputs to the repressor with an earlier expression peak as Per1, whereas phase delay is driven by the other repressor with a later peak as Per2. Due to the complementary contributions to phase responses, the ratio of light-induced transcription rates between Per1 and Per2 determines the magnitude and direction of phase shifts at each time of day. Specifically, stronger Per1 light induction than Per2 results in a phase response curve (PRC) with a larger phase advance zone than delay zone as observed in rats and hamsters, whereas stronger Per2 induction causes a larger delay zone as observed in mice. Furthermore, the ratio of light-induced transcription rates required for entrainment is determined by the relation between the circadian and light-dark periods. Namely, if the autonomous period of a circadian clock is longer than the light-dark period, a larger light-induced transcription rate of Per1 than Per2 is required for entrainment, and vice versa. In short, the time difference between Per1 and Per2 expression peaks can differentiate their dynamical functions. The resultant complementary contributions to phase responses can determine entrainability of the circadian clock to the light-dark cycle.
多个反馈回路通常存在于各种细胞功能的基因调控中。在哺乳动物的生物钟中，Period1（Per1）和 Period2（Per2）表达的振荡是由相互作用的负反馈回路（NFLs）引起的，其具有相似分子功能的蛋白质产物相互抑制。然而，在起搏组织中，Per1 的表达峰值早于 Per2，这就提出了一个问题，即峰时差是否反映了它们不同的动力学功能。在这里，我们通过分析光诱导的 Per1 和 Per2 mRNA 转录引起的生物钟的相位反应来解决这个问题。通过对双 NFLs 的数学分析，我们表明相位提前主要是由具有较早表达峰值的抑制剂的光输入驱动的，而相位延迟是由具有较晚峰值的另一个抑制剂驱动的。由于对相位反应的互补贡献，Per1 和 Per2 之间的光诱导转录速率比决定了每天每个时间的相移幅度和方向。具体来说，与 Per2 相比，Per1 的光诱导更强，会导致相位响应曲线（PRC）的相提前区大于相延迟区，如在大鼠和仓鼠中观察到的那样，而 Per2 的光诱导更强会导致相延迟区更大，如在小鼠中观察到的那样。此外，适应所需的光诱导转录速率比由生物钟和光暗周期之间的关系决定。也就是说，如果生物钟的自主周期长于光暗周期，则需要 Per1 的光诱导转录速率大于 Per2 才能适应，反之亦然。简而言之，Per1 和 Per2 表达峰值之间的时间差可以区分它们的动力学功能。对相位反应的互补贡献可以决定生物钟对光暗周期的适应能力。
