Complementary Phase Responses Via Functional Differentiation Of Dual Negative Feedback Loops

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.Author summaryGene regulatory networks underlie various cellular functions and often include multiple feedback regulations. Multiple feedback loops confer robustness on cellular systems, but whether and how they can obtain different functions is unclear. To address this question, we analyze the phase responses of mammalian circadian rhythms to light signals. In mammals, dual negative feedback loops (NFLs) of Period1 (Per1) and Period2 (Per2) genes are responsible for rhythm generation. Light signals induce transcription of both Pers mRNAs, shifting the phase of clocks. We show that the time difference between expression peaks of two repressors, as in expression of Per genes, leads to functional differentiation: the NFL with an earlier expression peak of repressor, as Per1, contributes mainly to advancing the clock, whereas the other NFL with a later peak of repressor, as Per2, contributes to delaying the clock. These complementary contributions suggest that the ratio of light-induced transcription rates between two Per genes underlies the differences in phase responses between different mammalian species. Furthermore, the relation between the circadian and light-dark periods determines the ratio of light-induced transcription rates required for entrainment. Our study reveals a mechanism for functional differentiation of dual NFLs and its significance in circadian clock systems.