Na+/Ca2+ exchanger mediates cold Ca2+ signaling conserved for temperature-compensated circadian rhythms.

Circadian rhythms are based on biochemical oscillations generated by clock genes/proteins, which independently evolved in animals, fungi, plants, and cyanobacteria. Temperature compensation of the oscillation speed is a common feature of the circadian clocks, but the evolutionary-conserved mechanism has been unclear. Here, we show that Na+/Ca2+ exchanger (NCX) mediates cold-responsive Ca2+ signaling important for the temperature-compensated oscillation in mammalian cells. In response to temperature decrease, NCX elevates intracellular Ca2+, which activates Ca2+/calmodulin-dependent protein kinase II and accelerates transcriptional oscillations of clock genes. The cold-responsive Ca2+ signaling is conserved among mice, Drosophila, and Arabidopsis The mammalian cellular rhythms and Drosophila behavioral rhythms were severely attenuated by NCX inhibition, indicating essential roles of NCX in both temperature compensation and autonomous oscillation. NCX also contributes to the temperature-compensated transcriptional rhythms in cyanobacterial clock. Our results suggest that NCX-mediated Ca2+ signaling is a common mechanism underlying temperature-compensated circadian rhythms both in eukaryotes and prokaryotes.

Theoretical study on the regulation of circadian rhythms by RNA methylation.

Messenger RNAs are often destabilized by methylation, suggesting that mRNA methylation alters mRNA and protein dynamics. This may indicate that the gene regulatory system is reflected by the metabolic system through mRNA methylation because methylation substrates are components of the metabolic system. Elucidating the mechanisms by which mRNA methylation regulates gene regulatory systems has posed considerable challenges due to the numerous targets of mRNA methylation. Recent studies have demonstrated that inhibition of mRNA N6-methyladenosine methylation elongates circadian periods. The aim of this study was to understand the mechanisms by which mRNA methylation regulates circadian rhythms. Using a detailed realistic model and a simple model, we demonstrated that period elongation of circadian rhythms by decreasing mRNA methylation can be achieved by two possibilities, i.e., decreasing mRNA methylation stabilizes nonoscillatory mRNAs such as Ck1δ and/or stabilizes oscillatory mRNAs of clock genes such as Per and Cry. In addition, we predicted that period elongation by stabilizing nonoscillatory mRNA (Ck1δ) should always be accompanied by the distortion of the circadian waveform. Finally, we discuss the validity of the two possible mechanisms on the regulation of circadian rhythms by mRNA methylation by quantifying waveform distortion of circadian gene activity data with or without mRNA methylation inhibitors.

Non-sinusoidal Waveform in Temperature-Compensated Circadian Oscillations.

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 transcriptional-translational 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.

Two Ck1δ transcripts regulated by m6A methylation code for two antagonistic kinases in the control of the circadian clock.

The N6-methylation of internal adenosines (m6A) in mRNA has been quantified and localized throughout the transcriptome. However, the physiological significance of m6A in most highly methylated mRNAs is unknown. It was demonstrated previously that the circadian clock, based on transcription-translation negative feedback loops, is sensitive to the general inhibition of m6A. Here, we show that the Casein Kinase 1 Delta mRNA (Ck1δ), coding for a critical kinase in the control of circadian rhythms, cellular growth, and survival, is negatively regulated by m6A. Inhibition of Ck1δ mRNA methylation leads to increased translation of two alternatively spliced CK1δ isoforms, CK1δ1 and CK1δ2, uncharacterized until now. The expression ratio between these isoforms is tissue-specific, CK1δ1 and CK1δ2 have different kinase activities, and they cooperate in the phosphorylation of the circadian clock protein PER2. While CK1δ1 accelerates the circadian clock by promoting the decay of PER2 proteins, CK1δ2 slows it down by stabilizing PER2 via increased phosphorylation at a key residue on PER2 protein. These observations challenge the previously established model of PER2 phosphorylation and, given the multiple functions and targets of CK1δ, the existence of two isoforms calls for a re-evaluation of past research when CK1δ1 and CK1δ2 were simply CK1δ.

Time-lapse imaging of microRNA activity reveals the kinetics of microRNA activation in single living cells.

MicroRNAs (miRNAs) are small, non-coding RNAs that play critical roles in the post-transcriptional regulation of gene expression. Although the molecular mechanisms of the biogenesis and activation of miRNA have been extensively studied, the details of their kinetics within individual living cells remain largely unknown. We developed a novel method for time-lapse imaging of the rapid dynamics of miRNA activity in living cells using destabilized fluorescent proteins (dsFPs). Real-time monitoring of dsFP-based miRNA sensors revealed the duration necessary for miRNA biogenesis to occur, from primary miRNA transcription to mature miRNA activation, at single-cell resolution. Mathematical modeling, which included the decay kinetics of the fluorescence of the miRNA sensors, demonstrated that miRNAs induce translational repression depending on their complementarity with targets. We also developed a dual-color imaging system, and demonstrated that miR-9-5p and miR-9-3p were produced and activated from a common hairpin precursor with similar kinetics, in single cells. Furthermore, a dsFP-based miR-132 sensor revealed the rapid kinetics of miR-132 activation in cortical neurons under physiological conditions. The timescale of miRNA biogenesis and activation is much shorter than the median half-lives of the proteome, suggesting that the degradation rates of miRNA target proteins are the dominant rate-limiting factors for miRNA-mediated gene silencing.

Temperature-amplitude coupling for stable biological rhythms at different temperatures.

Most biological processes accelerate with temperature, for example cell division. In contrast, the circadian rhythm period is robust to temperature fluctuation, termed temperature compensation. Temperature compensation is peculiar because a system-level property (i.e., the circadian period) is stable under varying temperature while individual components of the system (i.e., biochemical reactions) are usually temperature-sensitive. To understand the mechanism for period stability, we measured the time series of circadian clock transcripts in cultured C6 glioma cells. The amplitudes of Cry1 and Dbp circadian expression increased significantly with temperature. In contrast, other clock transcripts demonstrated no significant change in amplitude. To understand these experimental results, we analyzed mathematical models with different network topologies. It was found that the geometric mean amplitude of gene expression must increase to maintain a stable period with increasing temperatures and reaction speeds for all models studied. To investigate the generality of this temperature-amplitude coupling mechanism for period stability, we revisited data on the yeast metabolic cycle (YMC) period, which is also stable under temperature variation. We confirmed that the YMC amplitude increased at higher temperatures, suggesting temperature-amplitude coupling as a common mechanism shared by circadian and 4 h-metabolic rhythms.

Dynamics and control at feedback vertex sets. II: a faithful monitor to determine the diversity of molecular activities in regulatory networks.

Modern biology provides many networks describing regulations between many species of molecules. It is widely believed that the dynamics of molecular activities based on such regulatory networks are the origin of biological functions. However, we currently have a limited understanding of the relationship between the structure of a regulatory network and its dynamics. In this study we develop a new theory to provide an important aspect of dynamics from information of regulatory linkages alone. We show that the "feedback vertex set" (FVS) of a regulatory network is a set of "determining nodes" of the dynamics. The theory is powerful to study real biological systems in practice. It assures that (i) any long-term dynamical behavior of the whole system, such as steady states, periodic oscillations or quasi-periodic oscillations, can be identified by measurements of a subset of molecules in the network, and that (ii) the subset is determined from the regulatory linkage alone. For example, dynamical attractors possibly generated by a signal transduction network with 113 molecules can be identified by measurement of the activity of only 5 molecules, if the information on the network structure is correct. Our theory therefore provides a rational criterion to select key molecules to control a system. We also demonstrate that controlling the dynamics of the FVS is sufficient to switch the dynamics of the whole system from one attractor to others, distinct from the original.

Circadian regulation of food-anticipatory activity in molecular clock-deficient mice.

In the mammalian brain, the suprachiasmatic nucleus (SCN) of the anterior hypothalamus is considered to be the principal circadian pacemaker, keeping the rhythm of most physiological and behavioral processes on the basis of light/dark cycles. Because restriction of food availability to a certain time of day elicits anticipatory behavior even after ablation of the SCN, such behavior has been assumed to be under the control of another circadian oscillator. According to recent studies, however, mutant mice lacking circadian clock function exhibit normal food-anticipatory activity (FAA), a daily increase in locomotor activity preceding periodic feeding, suggesting that FAA is independent of the known circadian oscillator. To investigate the molecular basis of FAA, we examined oscillatory properties in mice lacking molecular clock components. Mice with SCN lesions or with mutant circadian periods were exposed to restricted feeding schedules at periods within and outside circadian range. Periodic feeding led to the entrainment of FAA rhythms only within a limited circadian range. Cry1(-/-) mice, which are known to be a "short-period mutant," entrained to a shorter period of feeding cycles than did Cry2(-/-) mice. This result indicated that the intrinsic periods of FAA rhythms are also affected by Cry deficiency. Bmal1(-/-) mice, deficient in another essential element of the molecular clock machinery, exhibited a pre-feeding increase of activity far from circadian range, indicating a deficit in circadian oscillation. We propose that mice possess a food-entrainable pacemaker outside the SCN in which canonical clock genes such as Cry1, Cry2 and Bmal1 play essential roles in regulating FAA in a circadian oscillatory manner.

Modeling light adaptation in circadian clock: prediction of the response that stabilizes entrainment.

Periods of biological clocks are close to but often different from the rotation period of the earth. Thus, the clocks of organisms must be adjusted to synchronize with day-night cycles. The primary signal that adjusts the clocks is light. In Neurospora, light transiently up-regulates the expression of specific clock genes. This molecular response to light is called light adaptation. Does light adaptation occur in other organisms? Using published experimental data, we first estimated the time course of the up-regulation rate of gene expression by light. Intriguingly, the estimated up-regulation rate was transient during light period in mice as well as Neurospora. Next, we constructed a computational model to consider how light adaptation had an effect on the entrainment of circadian oscillation to 24-h light-dark cycles. We found that cellular oscillations are more likely to be destabilized without light adaption especially when light intensity is very high. From the present results, we predict that the instability of circadian oscillations under 24-h light-dark cycles can be experimentally observed if light adaptation is altered. We conclude that the functional consequence of light adaptation is to increase the adjustability to 24-h light-dark cycles and then adapt to fluctuating environments in nature.

Positive autoregulation delays the expression phase of mammalian clock gene Per2.

In mammals, cellular circadian rhythms are generated by a transcriptional-translational autoregulatory network that consists of clock genes that encode transcriptional regulators. Of these clock genes, Period1 (Per1) and Period2 (Per2) are essential for sustainable circadian rhythmicity and photic entrainment. Intriguingly, Per1 and Per2 mRNAs exhibit circadian oscillations with a 4-hour phase difference, but they are similarly transactivated by CLOCK-BMAL1. In this study, we investigated the mechanism underlying the phase difference between Per1 and Per2 through a combination of mathematical simulations and molecular experiments. Mathematical analyses of a model for the mammalian circadian oscillator demonstrated that the slow synthesis and fast degradation of mRNA tend to advance the oscillation phase of mRNA expression. However, the phase difference between Per1 and Per2 was not reproduced by the model, which implemented a 1.1-fold difference in degradation rates and a 3-fold difference in CLOCK-BMAL1 mediated inductions of Per1 and Per2 as estimated in cultured mammalian cells. Thus, we hypothesized the existence of a novel transcriptional activation of Per2 by PER1/2 such that the Per2 oscillation phase was delayed. Indeed, only the Per2 promoter, but not Per1, was strongly induced by both PER1 and PER2 in the presence of CLOCK-BMAL1 in a luciferase reporter assay. Moreover, a 3-hour advance was observed in the transcriptional oscillation of the delta-Per2 reporter gene lacking cis-elements required for the induction by PER1/2. These results indicate that the Per2 positive feedback regulation is a significant factor responsible for generating the phase difference between Per1 and Per2 gene expression.

A temperature-compensated model for circadian rhythms that can be entrained by temperature cycles.

From the viewpoint that reaction rates will change with temperature, we present a general method to build circadian clock models that generate circadian oscillations with almost constant period under different constant ambient temperature, and propose an algorithm estimating the parameter condition for compensated period against the change of temperature based on the PER single-feedback loop model of Goldbeter [1995. A model for circadian oscillations in the Drosophila period protein (PER). Proc. R. Soc. London Ser. B 261, 319-324] for Drosophila. We show that the model with derived parameters can realize the temperature compensation over a wide range of temperature, and simultaneously can realize the entrainment to temperature cycles.

A model for the circadian rhythm of cyanobacteria that maintains oscillation without gene expression.

An intriguing property of the cyanobacterial circadian clock is that endogenous rhythm persists when protein abundances are kept constant either in the presence of translation and transcription inhibitors or in the constant dark condition. Here we propose a regulatory mechanism of KaiC phosphorylation for the generation of circadian oscillations in cyanobacteria. In the model, clock proteins KaiA and KaiB are assumed to have multiple states, regulating the KaiC phosphorylation process. The model can explain 1), the sustained oscillation of gene expression and protein abundance when the expression of the kaiBC gene is regulated by KaiC protein, and 2), the sustained oscillation of phosphorylated KaiC when transcription and translation processes are inhibited and total protein abundance is fixed. Results of this work suggest that KaiA and KaiB strengthen the nonlinearity of KaiC phosphorylation, thereby promoting the circadian rhythm in cyanobacteria.

Amplitude of circadian oscillations entrained by 24-h light-dark cycles.

An intriguing property of circadian clocks is that their free-running period is not exactly 24h. Using models for circadian rhythms in Neurospora and Drosophila, we determine how the entrainment of these rhythms is affected by the free-running period and by the amplitude of the external light-dark cycle. We first consider the model for Neurospora, in which light acts by inducing the expression of a clock gene. We show that the amplitude of the oscillations of the clock protein entrained by light-dark cycles is maximized when the free-running period is smaller than 24h. Moreover, if the amplitude of the light-dark cycle is very strong, complex oscillations occur when the free-running period is close to 24h. In the model for circadian rhythms in Drosophila, light acts by enhancing the degradation of a clock protein. We show that while the amplitude of circadian oscillations entrained by light-dark cycles is also maximized if the free-running period is smaller than 24h, the range of entrainment is centered around 24h in this model. We discuss the physiological relevance of these results in regard to the setting of the free-running period of the circadian clock.

Temperature compensation in circadian clock models.

Circadian clock of organisms has a free-running period that does not change much with ambient temperature. This property "temperature compensation" is studied when the rate of all reaction steps increase with temperature in the biochemical network generating the rhythm. The period becomes shorter when all the rate parameters are enhanced by the same factor. However, the period becomes longer as degradation rate of proteins and/or transcription rate of the clock gene increase (their elasticity is positive). This holds for a wide range of models, including N-variable model, and PER-TIM double oscillator model, provided that (1) branch reactions (e.g. degradation of proteins or mRNAs) are strongly saturated, and that (2) the cooperativity of transcription inhibition by nuclear proteins is not very large. A strong temperature sensitivity of degradation of PER proteins and/or temperature-sensitive alternative splicing of per gene, known for Drosophila, can be mechanisms for the temperature compensation of circadian clock.

Saturation of enzyme kinetics in circadian clock models.

From the mathematical study of simple models for circadian rhythm, the authors identified a clear effect of saturation in the enzyme kinetics on the promotion or suppression of a sustained oscillation. In the models, a clock gene (per gene) is transcribed to produce mRNAs, which are translated to produce proteins in the cytosol which are then transported to the nucleus and suppress the transcription of the gene. The negative feedback loop with a long time delay creates sustained oscillation. All the enzymatic reactions (e.g., degradation, translation, and modification) are assumed to be of Michaelis-Menten type. The reaction rate increases with the amount of substrate but saturates when it is very large. The authors prove mathematically that the saturation in any of the reactions included in the feedback loop (in-loop reaction steps) suppresses the oscillation, whereas the saturation of both degradation steps and the back transport of the protein to cytosol (branch reaction steps) makes the oscillation more likely to occur. In the experimental measurements of enzyme kinetics and in published circadian clock simulators, in-loop reaction steps have a small saturation index whereas branch reaction steps have a large saturation index.

Comparative study of circadian clock models, in search of processes promoting oscillation.

We study simple models for circadian rhythm, and examine the condition in which the equilibrium is unstable, generating a sustained oscillation. In the models, a clock gene(s) is transcribed to produce mRNAs, which are translated to produce proteins that suppress the transcription of the clock gene(s). First, using a Lyapunov function, we prove under very general conditions that two-variable models cannot generate a stable oscillation, implying that additional structures are needed for the model to generate a sustainable rhythm. By comparing several models of different complexities using the Routh-Hurwitz criteria of stability, we show that a sustained oscillation is more likely to occur if the cell is compartmentalized and the proteins need to be transported from the cytosol to the nucleus, if the proteins have to be modified before entering the nucleus, if the kinetics of transcription inhibition or the transport to the nucleus have cooperativity with a nonlinear dependence on the substrate concentration, or if the products of two clock genes form a heterodimer that suppresses both of their own genes. We discuss the implications of these results.