SignificanceThe most abundant modification in mRNA is the N6-methylation of internal adenosines (m6A), but m6A’s physiological function is unknown for most mRNAs. Here we show that Casein Kinase 1 Delta mRNA (Ck1δ), coding for a critical kinase in the control of circadian rhythms, is regulated by m6A. When m6A is inhibited, the expression of two CK1δ isoforms, uncharacterized until now, increases due to enhanced translation. This increase in CK1δs leads to a slower clock because of increased phosphorylation of the clock protein PER2 at a key residue, leading to the stabilization of PER2 protein.

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Time series of biological rhythms are of various shapes. Here, we investigated the waveforms of circadian rhythms in gene-protein dynamics using a newly developed, to our knowledge, index to quantify the degree of distortion from a sinusoidal waveform. In general, most biochemical reactions accelerate with increasing temperature, but the period of circadian rhythms remains relatively stable with temperature change, a phenomenon known as ''temperature compensation.'' Despite extensive research, the mechanism underlying this remains unclear. To understand the mechanism, we used transcriptionaltranslational oscillator models for circadian rhythms in the fruit fly Drosophila and mammals. Given the assumption that reaction rates increase with temperature, mathematical analyses revealed that temperature compensation required waveforms that are more nonsinusoidal at higher temperatures. We then analyzed a post-translational oscillator (PTO) model of cyanobacteria circadian rhythms. Because the structure of the PTO is different from that of the transcriptional-translational oscillator, the condition for temperature compensation would be expected to differ. Unexpectedly, the computational analysis again showed that temperature compensation in the PTO model required a more nonsinusoidal waveform at higher temperatures. This finding held for both models even with a milder assumption that some reaction rates do not change with temperature, which is consistent with experimental evidence. Together, our theoretical analyses predict that the waveform of circadian gene-activity and/or protein phosphorylation rhythms would be more nonsinusoidal at higher temperatures, even when there are differences in the network structures.

Mammalian hibernators decrease basal metabolism and body temperature (Tb) to minimize energy expenditure in harsh seasons. During hibernation, Tb drops to low temperature (<10 °C) and remains constant for days, known as deep torpor. Spontaneous interbout arousals interrupt torpor bouts, when Tb recovers to euthermic state ∼37 °C. Torpor-interbout arousal event repeats during hibernation. Little is known about mechanisms governing Tb fluctuation during hibernation. Here, we analyzed Tb fluctuation across Syrian hamsters’ hibernation cycle using generalized harmonic analysis and discovered a model with frequency modulation quantitatively reproducing Tb fluctuation. This analysis identified that an unexpectedly longer period of 120–430 days modulates period of several days, generating Tb fluctuation. We propose that concerted action of two endogenous periods governs torpor-interbout arousal cycles during hibernation.