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

NCX is a new clock component common to eukaryotes and prokaryotes.


INTRODUCTION
Among a wide variety of biological functions, the circadian clock is of particular interest because of its unique property, i.e., temperaturecompensated oscillation with a period of approximately 24 hours (1). Generally, an increase in temperature by 10°C accelerates rates of biochemical reactions by two-to threefold (Q 10 = 2 to 3), whereas Q 10 of the oscillation speed of the clock is 0.8 to 1.2. The property was originally termed temperature independence, but later termed temperature compensation on the basis of the finding of overcompensation for the effect of temperature on the period length in photosynthetic dinoflagellates (Lingulodinium polyedra) (1). The temperature compensation is a common property of the circadian clocks, implicating that a mechanism underlying the compensation is tightly associated with machinery for cell-autonomous oscillation.
Most of the overt circadian rhythms are based on biochemical oscillations generated by clock genes and their encoded proteins (2)(3)(4)(5). Homologies of the clock genes are limited among animals, fungi, plants, and cyanobacteria, suggesting that the clock genes independently evolved after divergence of the lineages. In cyano bacteria, KaiC phosphorylation rhythms constitute a core circadian oscillator termed posttranslational oscillator (PTO) (5). The phosphorylation rhythms of KaiC in the KaiA-KaiB-KaiC protein complex are temperature compensated in vitro. In eukaryotes, clock genes and their encoded proteins constitute transcriptional/translational feedback loops (TTFLs) (2)(3)(4). Because a HES (Hairy and Enhancer of Split)based TTFL in segmentation clock is temperature sensitive (Q 10 = 2 to 3) (6), temperature compensation is not a general property intrinsic to TTFLs. This suggests the existence of an important mechanism regulating the circadian oscillation of the TTFLs.
Historically, before the discovery of the clock genes, a feedback system involving ions and ion regulators in plasma membranes was proposed as the oscillation mechanism of the circadian clock (7). This "membrane model" is based on the observation that the circadian rhythms are notably affected by manipulating ion concentrations or ion regulator activities in various eukaryotes (7). To date, several ions, especially Ca 2+ , have been shown to play an essential role for oscillation of the TTFLs in mammals (8), insects (9), and plants (10). In mice and Drosophila, intracellular Ca 2+ levels were shown to exhibit robust circadian oscillations (11)(12)(13), which elicit rhythmic activation of Ca 2+ /calmodulin-dependent protein kinase II (CaMKII) (14)(15)(16). CaMKII phosphorylates CLOCK to activate CLOCK-BMAL1 heterodimer, a key transcriptional activator in the animal TTFLs (3). The upstream regulator of the Ca 2+ -dependent phosphorylation signaling has been a missing link between the TTFL and the membrane model. compounds targeting protein kinases or ion regulators (table S1) on cellular rhythms of Rat-1 fibroblasts stably expressing Bmal1luciferase reporter (14,17). A Q 10 value was calculated from the period lengths of the bioluminescence rhythms recorded at 32° and 37°C (figs. S1, A and B, and S2A). All the screening results were evaluated by using a Q 10 value, which was defined as a difference of the Q 10 values between drug-treated cells and control [0.1% dimethyl sulfoxide (DMSO)-treated] cells (Fig. 1A). We found a remarkable increase in Q 10 by CaMKII inhibitor KN-93 (Fig. 1A) in a dose-dependent manner (Fig. 1, B and C). The treatment with 10 M KN-93 shortened the period at 37°C, whereas it lengthened the period at 32°C (Fig. 1D). Such a temperature-dependent bidirectional effect of KN-93 was unique in that many compounds showed a unidirectional period-modifying effect at 32° and 37°C ( fig. S1C). KN-92, an inactive analog of KN-93, had no significant effect on Q 10 value ( Fig. 1E and fig. S2B), supporting the specific effect of KN-93 on CaMKII.
In detailed analysis of the effects of the compounds, we noticed that the treatment with KB-R7943, an inhibitor of Na + /Ca 2+ exchanger (NCX) (18), increased the Q 10 value in a dose-dependent manner ( Fig. 1, B and C). Similar to the CaMKII inhibitor, KB-R7943 exhibited the temperature-dependent bidirectional effect on the circadian period (Fig. 1D). Another NCX inhibitor, SEA0400 (18), also showed the bidirectional period-modifying effect (Fig. 1D) and the Q 10increasing effect (Fig. 1E). On the other hand, none of these effects were observed after treatment of Rat-1 cells with nifedipine and verapamil, blockers of L-type Ca 2+ channel, or with IC261, a periodlengthening inhibitor of casein kinase I (Fig. 1, C and D, and fig.  S3) (15).
The period-modifying effects of KN-93 and KB-R7943 were further analyzed at various temperatures between 32° and 37°C ( fig. S4). As a control, Rat-1 cells treated with DMSO showed shorter periods at lower temperatures ( Fig. 2A), a phenomenon termed overcompensation observed in a wide range of species (1)(2)(3)(4)(5). In contrast, the oscillation speed was slowed down by decreasing the temperature in the presence of KN-93 or KB-R7943 ( Fig. 2A), and this periodlengthening effect was particularly obvious below 35°C (Fig. 2B). The Q 10 value calculated from the circadian periods at 32° and 35°C was 0.89 (vehicle), 1.49 (20 M KB-R7943), or 2.01 (10 M KN-93). It is evident that the overcompensated oscillation becomes temperature sensitive by inhibiting CaMKII or NCX activity. These results together demonstrate that CaMKII and NCX are key players for temperature compensation in the mammalian cellular clock.

NCX-Ca 2+ -CaMKII signaling is important for cellular circadian oscillation
Note that the KB-R7943 treatment of Rat-1 fibroblasts decreased the amplitude of the cellular rhythms (Fig. 1B). Among the chemicals targeting ion channels and transporters, only KB-R7943 suppressed the relative amplitude of the rhythms (Fig. 3A), suggesting an important role of NCX in the cell-autonomous oscillation mechanism, in addition to the temperature compensation.
NCX exchanges 3 Na + for 1 Ca 2+ across the plasma membrane. NCX is a unique bidirectional regulator of cytosolic Ca 2+ concentration because it can mediate both Ca 2+ influx and efflux, depending on not only the membrane potential but also local concentrations of Na + and Ca 2+ (18). In response to an increase in cytoplasmic Ca 2+ levels, NCX mediates Ca 2+ efflux, while NCX can maintain steadystate levels of intracellular Ca 2+ by promoting Ca 2+ influx in several types of cells (18). We examined roles of NCX in regulation of intracellular Ca 2+ levels in NIH3T3 fibroblasts. Fluo-4 acetoxymethyl ester (Fluo-4 AM)-based Ca 2+ imaging revealed that the basal fluorescence level in the cultured cells was remarkably reduced by the addition of 5 to 20 M NCX inhibitor KB-R7943 to the culture medium ( Fig. 3B), indicating that NCX contributes to net Ca 2+ influx in the quiescent state. Then, we evaluated the effect of KB-R7943 on cellular CaMKII activity, which reflects intracellular Ca 2+ level (14). One-day treatment of NIH3T3 cells with 20 M KB-R7943 significantly decreased the CaMKII activity toward syntide-2, a model substrate specific to CaMKII (Fig. 3C) (14). These results reveal an important role of NCX in the maintenance of the activity level of Ca 2+ -CaM-KII signaling in the fibroblasts.
To address the role of NCX-Ca 2+ -CaMKII signaling in cellautonomous oscillation, we investigated effects of chronic inhibition of the signaling on circadian rhythms in Rat-1 reporter cells (14,17). The relative amplitude of the cellular bioluminescence rhythm detected by Bmal1-luc was markedly reduced by chronic treatment with KN-93, trifluoperazine (calmodulin antagonist), 1,2-bis(2aminophenoxy)ethane-N,N,N′,N′-tetraacetic acid (BAPTA)-AM (intracellular Ca 2+ chelator), or KB-R7943 (Fig. 3D). The amplitudereducing effect by chronic treatment with KB-R7943 or SEA0400 was also observed in Per2-luc reporter cells (Fig. 3E). The severe damping of the transcriptional rhythms was reversed by washing out the drug-containing medium (Fig. 3E). On the other hand, a pulse treatment (for 1 to 2 hours) of Rat-1-Bmal1-luc cells with KN-93, KB-R7943, or SEA0400 caused a phase-dependent phase shift of the bioluminescence rhythms with their maximal responses at circadian time (CT)21 (Fig. 3F). The amplitude-reducing effects (Fig. 3, D and E) and the overt phase-resetting actions of the inhibitors (Fig. 3F) together suggest that NCX-dependent Ca 2+ -CaMKII signaling functions as a state variable of the circadian oscillator in a limit cycle interpretation ( fig. S5) (14,19).

Lowering temperature activates NCX-Ca 2+ -CaMKII signaling
In the experiments examining the relationship between temperature and the cellular rhythms, we found that the amplitude of the rhythm was decreased by lowering temperature particularly below 34°C ( Note that hypothermia is clinically defined as a drop in core body temperature below 35°C (20). We hypothesized that Ca 2+ signaling may be activated for cold response in mammalian cells, as reported for cold tolerance mechanism of insects and plant cells (21). This idea was tested by investigating intracellular Ca 2+ levels in cultured fibroblasts. In Fluo-4 AM-based Ca 2+ imaging, lowering of the temperature from 37° to 25°C significantly increased free Ca 2+ levels in NIH3T3 cells (Q 10 = 0.73) (Fig. 4C). The hypothermic response was blocked by treatment with SEA0400 or KB-R7943 (Fig. 4D). We found that the CaMKII activity of lysates prepared from the cells cultured at 27°C was higher than that at 37°C (Q 10 = 0.78) (Fig. 4E, DMSO). In addition, the hypothermic activation of CaMKII was inhibited in the cells cultured with 20 M KB-R7943 (Fig. 4E). These results indicate that NCX enhances Ca 2+ influx and activates CaMKII signaling in response to the temperature decrease in the mammalian cells.
We then examined how intracellular Ca 2+ levels affect the clock gene expression rhythms. In Rat-1-Bmal1-luc cells, 1-hour treatment     4G). In addition, E4bp4, which is regulated by Ca 2+ -NFAT signaling (22), is also up-regulated by the temperature decrease (Fig. 4G). Consistent with the decrease in relative amplitude of the bioluminescence rhythms at lower temperatures (Fig. 4A), a peak-trough ratio of Bmal1 expression rhythm was reduced by lowering the temperature (Fig. 4G). We found that the hypothermic up-regulation of Per1 and Per2 transcripts was significantly attenuated in the presence of NCX inhibitor KB-R7943 or CaMKII inhibitor KN-93 (Fig. 4H). These results together indicate that the temperature changes have a marked influence on the clock gene expression levels through NCX-Ca 2+ -CaMKII signaling.
Cold-responsive Ca 2+ signaling compensates for slowdown of TTFL at lower temperature In 1957, Hastings and Sweeney (1) hypothesized that temperature compensation of the circadian clock is based on a combination of temperature-sensitive period-shortening and period-lengthening processes. Most biochemical reactions in the TTFL are slowed down by decreasing the temperature (table S2). In an in vitro assay, kinase activity of purified CaMKII toward a CLOCK peptide (Ser/ Pro-rich region of CLOCK) (15) was reduced by lowering the temperature (Q 10 = 2.9) (Fig. 5A). In contrast, as described above (Fig. 4E), CaMKII activity in the cultured cells was enhanced by lowering the temperature (Q 10 = 0.78), indicating that Ca 2+ influx is a key factor for accelerating CaMKII-mediated processes in the circadian clock at lower temperatures. Overexpression of CaMKII-T286D, a constitutive active form of CaMKII (14), accelerated the oscillation speed (shortened the period) and increased the amplitude of Bmal1-luc rhythms in cultured NIH3T3 cells (Fig. 5, B and C). To understand the experimental results theoretically, we simulated the effect of phosphorylation-dependent activation of CLOCK-BMAL1 on the gene expression rhythm by using a previously published mathematical model (23). In the horizontal axis of this simulation (Fig. 5D), a standard phosphorylation rate of CLOCK-BMAL1 estimated from previous experimental results was set to 1 (23). We found that an increase in the phosphorylation rate of CLOCK-BMAL1 accelerated the oscillation speed (shortened the period) and increased the amplitude of Bmal1 mRNA rhythm (Fig. 5D). These theoretical analysis and experimental data collectively indicate that the cold-responsive Ca 2+ signaling compensates for the period lengthening and amplitude reduction of the TTFL caused by lowering the temperatures.
Considering the roles of intracellular Ca 2+ in the circadian oscillation of the TTFL (Fig. 3) and in its temperature compensation (Figs. 1, 2, 4, and 5, A to D), we propose an oscillation model in which the TTFL couples with a Ca 2+ oscillator for temperature-compensated circadian rhythms (Fig. 5E). We then examined responses of the Ca 2+ oscillator to temperature changes. Circadian rhythms of intracellular Ca 2+ levels in cultured slices of the mouse suprachiasmatic nucleus (SCN) were monitored by using adeno-associated virusmediated gene transfer of GCaMP6s (11). Lowering the temperature from 35° to 28°C caused upward shifts of both the peak and trough levels of the intracellular Ca 2+ (Fig. 5, F and G) with no significant change in the period length of the Ca 2+ oscillation (Q 10 = 1.02).
These results together suggest that the circadian Ca 2+ oscillator is highly responsive to temperature changes to maintain constant period lengths of cellular circadian rhythms.

Cold-responsive phosphorylation signaling is conserved among animals and plants
The cold-responsive Ca 2+ signaling was investigated in vivo in several organisms. Cold exposure of mice to 4°C for 10 min remarkably decreased the temperatures of the body surface (Fig. 6A) without a large change in the core body temperature ( fig. S7A). Infrared thermography revealed that the temperatures of the ear and tail dropped by 12.0° and 16.5°C, respectively (Fig. 6A). We found that CaMKII activities (toward syntide-2) in the tissue lysates were enhanced by 1.34-fold (ear) and 2.25-fold (tail) after 90-min exposure at 4°C (Fig. 6B). The cold response of CaMKII was also analyzed in Drosophila melanogaster. CaMKII activities in the fly heads were enhanced by 1.57-fold (Fig. 6B), when the flies (maintained at 25°C) were exposed to 4°C for 90 min. In plants, Ca 2+ -dependent protein kinases (CDPKs) are the major transducers of Ca 2+ signaling (24). Catalytic domains of CDPKs are highly homologous to animal CaMKII, and syntide-2 is a model substrate of CDPKs (24). The enzymatic activities phosphorylating syntide-2 in the shoot (leaf and stem) lysates of Arabidopsis thaliana (kept at 22°C) were remarkably enhanced by 90-min exposure at 4°C (Fig. 6B). These results suggest that activation   of Ca 2+ -dependent phosphorylation signaling is a conserved mechanism underlying the cold responses.

Roles of NCX in circadian clockworks are conserved in eukaryotes and prokaryotes
Mammalian NCXs form a multigene family composed of three members: NCX1, NCX2, and NCX3. NCX1 is ubiquitously expressed in a variety of tissues, while NCX2 and NCX3 are expressed in the brain and muscle (18,25,26). A previous study demonstrated that homozygous knockout of NCX1 or NCX2 results in lethality (18,25). We examined wheel-running activity rhythms of NCX2 +/− mice and NCX2 +/− NCX3 −/− double-mutant mice. In constant dark condition, NCX2 +/− and NCX2 +/− NCX3 −/− mice showed free-running rhythms with circadian periods significantly longer than that of wild-type mice (Fig. 7, A and B). One double-mutant mouse exhibited unstable coordination between onset and offset of the wheel-running activity bouts under constant darkness (Fig. 7C), a phenotype similar to that observed for CaMKIIK42R kinase-dead knock-in mice (14).
These results indicate that NCX2 and NCX3 play important roles in maintaining normal behavioral rhythms in mice.
In D. melanogaster, NCX is encoded by a single gene, calx. We analyzed behavioral rhythms of two different lines of calx mutants, calx A deficient for Na + /Ca 2+ exchange currents and calx B deficient for CALX protein expression (27). Both calx A and calx B homozygous mutants showed severely weakened rhythmicity in locomotor activities at 25°C under constant darkness (Fig. 7D). Fast Fourier transform (FFT) analysis revealed a significant reduction in the behavioral rhythmicity in the calx mutants (Fig. 7, D and E), indicating an essential role of CALX in the Drosophila clock governing the behavioral rhythms.
Roles of Ca 2+ in plant clocks were investigated in A. thaliana expressing CCA1::LUC reporter. Because Arabidopsis has 13 NCX genes (28), it is difficult to evaluate roles of NCXs genetically. Instead, we investigated effects of Ca 2+ depletion in a growth medium on the bioluminescence rhythms. The Ca 2+ depletion resulted in significant shortening of the free-running period in constant light condition at 22°C (Fig. 7, F and G), whereas the period-shortening effect was undetectable at 17°C. The Ca 2+ depletion caused an increase in the Q 10 value from 0.80 (in the normal medium) to 0.95 (Fig. 7H), indicating that Ca 2+ signaling is required for accelerating the oscillation speed at lower temperatures in the plant as well.
Roles of NCX in prokaryotic circadian clocks were investigated by generating a cyanobacterial strain lacking yrbG, a bacterial homolog of NCX (28). The circadian rhythms in the yrbG strain were monitored with P KaiBC ::luxAB reporter under constant light condition (Fig. 7I). We found that yrbG deficiency caused significant shortening of the period length at 30°C, whereas the period was lengthened at 25°C when compared with the wild-type strain (Fig. 7, I and J). Hence, the Q 10 value of the bioluminescence rhythms was increased from 1.19 to 1.49 by the depletion of yrbG (Fig. 7K). These results demonstrate that NCX-dependent Ca 2+ signaling plays a conserved role in both the TTFL-based eukaryotic clock and the PTO-based prokaryotic clock systems.

DISCUSSION
Circadian TTFLs are an elaborate system that drives a wide range of overt rhythms with various phase angles and amplitudes. The oscillation speed of the TTFLs is temperature compensated, although many of the biochemical reactions in TTFLs are slowed down by decreasing temperature (table S2). The present study demonstrates that the temperature compensation of the TTFL in mammalian cells was compromised when Ca 2+ -dependent phosphorylation signaling was inhibited ( Fig. 2A). We found an important role of NCX-CaMKII activity as the state variable of the circadian oscillator (Fig. 3, D to F,  and fig. S5). The present study and a series of preceding works demonstrate that the Ca 2+ oscillator plays essential roles in the circadian oscillation mechanism (Fig. 5E) (8-16). Functional studies clearly demonstrated essential roles of NCX-dependent Ca 2+ signaling in the three important properties of the circadian clock, i.e., cellautonomous oscillation (Figs. 3, A to E, and 7, A to C), temperature compensation (Figs. 1, 2, 4, and 5), and entrainment (Fig. 3F). The circadian Ca 2+ oscillation is observed in mice lacking Bmal1 or Cry1/ Cry2 (11,12), implicating that the Ca 2+ oscillator is an upstream regulator of the TTFL in mammals.
The effects of NCX2 and NCX3 deficiencies on the regulation of mouse behavioral rhythms (Fig. 7, A to C) suggest involvement of Na + /Ca 2+ exchanging activity in the Ca 2+ dynamics of the SCN. Previous studies showed that L-type Ca 2+ channel (LTCC) and voltage-gated Na + channel (VGSC) are required for high-amplitude Ca 2+ rhythms in the SCN (11,12). Because NCX activities are regulated by local concentrations of Na + /Ca 2+ and the membrane potential (18), cooperative actions of LTCC, VGSC, and NCX seem to play important roles in generation mechanism of the robust Ca 2+ oscillations in the SCN.
It should be emphasized that the role of Ca 2+ /calmodulin-dependent protein kinases is conserved among clockworks in insects (9,13,16), fungi (29), and plants (10,24), suggesting that the Ca 2+ oscillator might be a core timekeeping mechanism in their common ancestor (Fig. 8, Eukaryota). After divergence of each lineage, a subset of clock genes should have independently evolved in association with the Ca 2+ oscillator. It is noteworthy that NCX is also required for temperature compensation of PTO-based cyanobacterial clock (Fig. 7, I to K). Because intracellular Ca 2+ in cyanobacteria is elevated in response to temperature decrease (30), YrbG-mediated Ca 2+ signaling may regulate the PTO in vivo. Conservation of NCX among eukaryotes, eubacteria, and archaea ( Fig. 8) (31) suggests that NCX-dependent temperature signaling is essential for adaptation of a wide variety of organisms to environment. Further studies on NCX-regulated Ca 2+ flux will provide evolutionary insights into the origin of the circadian clocks.
For normalization of dish-to-dish variation of the bioluminescence levels, the raw data were divided by the mean bioluminescence signals recorded for 7 days. The normalized rhythms were detrended by subtracting 24-hour centered moving averages, and the areas under the curves (arbitrary units) were used for calculating the relative amplitudes of the rhythms (14). Period lengths were calculated using the average value of peak-to-peak periods and trough-to-trough periods 1 day after the dexamethasone treatment of cultured cells. Q 10 value was calculated by the following equation where 1 and 2 are the periods at temperature T1 and T2, respectively.

Real-time monitoring of gene expression rhythms in plants
Monitoring of bioluminescence rhythms of A. thaliana (ecotype Columbia-0) expressing CCA1::LUC was performed as described previously (32). The plants were grown on a growth medium containing 10 mM KCl, 0.6 mM NH 4

Real-time monitoring of gene expression rhythms in cyanobacteria
A strain that harbored a P kaiBC ::luxAB reporter cassette with a chloramphenicol resistance gene at the targeting site (neutral site I) on the genome (ILC 976) was used as a wild-type strain. To disrupt the yrbG gene, a plasmid (pIL 1000) was constructed to harbor upstream and downstream regions of yrbG (Synpcc7942_0242) with a gentamicin resistance gene in the pGEM-T Easy backbone (Promega). The ∆yrbG strain (ILC 1383) was generated by transformation of ILC 976 with pIL 1000. Cells were grown in BG-11 media in the absence of calcium source (250 M CaCl 2 ). The bioluminescence profiles were measured with photomultiplier tubes under continuous light (LL, 40 mol/m 2 s) conditions after 2 days of 12-hour light/12-hour dark cycles (33).

Reverse transcription polymerase chain reaction analysis
Total RNA was prepared from cultured cells using TRIzol reagent (Invitrogen) according to the manufacturer's protocol. Reverse transcription polymerase chain reaction analysis was performed as described previously (14,17).

Intracellular Ca 2+ imaging
For Ca 2+ imaging in cultured cells, NIH3T3 cells were plated on 35-mm dishes (1.0 × 10 6 cells per dish) and cultured at 37°C under 5% CO 2 in the culture medium. One day after the plating, the medium was replaced by an imaging buffer of Hanks' balanced salt solution (Sigma-Aldrich, catalog no. H8264) containing 0.04% Pluronic F-127 and 1.25 mM probenecid. One hour after loading of 2 M Fluo-4 AM at 37°C, the fluorescence intensity of the cells was monitored by a fluorescence microscope (Olympus, BX51W1) equipped with an electron multiplying charge-coupled device digital camera (Hamamatsu Photonics, C9100-13 ImagEM) in the imaging buffer. The buffer was perfused by using a peristatic pump (Gilson, MINIPULS 3) for control of the buffer temperature, which is continuously monitored by thermoelectric couple and controlled by a dual automatic temperature controller (Warner, TC-344B).
Circadian Ca 2+ imaging in the SCN was performed as described previously (11). Briefly, the SCN slices were prepared from neonate mice (C57BL/6, 5 days old, both male and female). Ca 2+ indicator protein GCaMP6s and control fluorescence protein mRuby were expressed under the control of the human synapsin-1 promoter by using adeno-associated virus (Addgene, 50942-AAV1).

Measurement of CaMKII activity
For analysis of CaMKII activities in cultured cells, NIH3T3 cells were plated on 100-mm dishes (1.0 × 10 7 cells per dish) and cultured at 37°C under 5% CO 2 in the culture medium. One day after the plating, the medium was replaced by the recording medium containing the NCX inhibitor or 0.1% DMSO (vehicle), and the cells were cultured at 27° or 37°C. One day after the culture, cells were harvested by a cell scraper with 2 ml of a sampling buffer [20 mM tris-HCl, 5 mM EDTA, 1 mM EGTA, 10 mM sodium pyrophosphate, 50 mM NaF, 1 mM Na 3 VO 4 , 1 mM dithiothreitol (DTT), 0.1 mM phenylmethylsulfonyl fluoride, leupeptin (0.04 mg/ml), and aprotinin (0.04 mg/ml), pH 7.5]. For analysis of tissues, the tails or ears of C57BL/6 mice (7 weeks old, male), the heads of D. melanogaster (W 1118 , male), or the shoots of A. thaliana (ecotype Columbia-0, 14 days old) were prepared at ZT5, and 1 mg of the tissue was homogenized in 1 ml of the sampling buffer. The cells or tissues were homogenized by using a glass/ Teflon homogenizer (20 strokes). CaMKII activity levels of the lysates phosphorylating syntide-2 were measured by using CaM-kinase II Assay kit (CycLex, catalog no. CY-1173) according to the manufacturer's protocol.
For analysis of purified CaMKII activity phosphorylating a CLOCK peptide (GST-SP), CaM and rat brain CaMKII were prepared as described previously (15,34). The assay was carried out at 5°, 10°, 15°, or 20°C in a reaction mixture (10 l) composed of 40 mM tris-HCl (pH 8.0), 2 mM DTT, 5 mM MgCl 2 , 0.5 mM CaCl 2 , 1 mM [-32 P] ATP, 1 M CaM, 100 ng of rat brain CaMKII, and 500 ng of GST-SP peptide. After incubation for 30 min, the reaction was stopped by the addition of 10 l of 2× SDS sample buffer. Phosphorylated proteins or peptides were resolved by SDS-polyacrylamide gel electrophoresis and detected by autoradiography. We found that CaMKII activity purified from the rat brain was inactivated by incubation above 30°C, as reported by the previous study (34). Thus, the activity levels of the purified CaMKII were analyzed in the range of 5° to 20°C.

Animal experiments
The animal experiments were conducted in accordance with the guidelines of the University of Tokyo. NCX2 heterozygous knockout mice (NCX2 +/− ) were produced as described previously (25). NCX3 homozygous knockout mice (NCX3 −/− ) were generated as follows: The targeting vector was constructed by replacing the 1.9 kilo-base pairs Eco RI-Mun I fragment containing exon 2 of the NCX3 gene with a PGK (Phosphoglycerate kinase promoter)-neo cassette. The targeted ES (embryonic stem cell) clones were confirmed by Southern blot analysis and used for the generation of germline chimeras. Chimeric male mice were crossed with female C57BL/6 mice to establish the germline transmission and backcrossed to C57BL/6 mice for more than 10 generations. The mutant mice (C57BL/6 background, male, 6 to 8 weeks old) were housed individually at 23°C in cages (13 × 23 × 15 cm) equipped with a running wheel (diameter, 10 cm) with food and water available ad libitum. Wheel-running rhythms were monitored under constant dark condition after housing under 12-hour light/12-hour dark cycles for at least 2 weeks. The numbers of wheel revolution were collected every minute into a computer system. All the behavioral data were analyzed by using ClockLab software (Actimetrics). For measurement of the internal body temperature, the activity-and temperature-measuring device, nano tag (KISSEI COMTEC Co. Ltd.), was implanted into the peritoneal cavity or subcutaneous site in mice (C57BL/6 background, male, 8 weeks old). For measurement of the surface body temperature, an infrared camera (FLIR, E6) was used, and the image data were analyzed by FLIR Tools software (FLIR).
Locomotor activity rhythms of D. melanogaster were monitored as described previously (35). Male flies (2 to 5 days old) were individually housed in glass tubes (length, 65 mm; inside diameter, 3 mm) containing sucrose-agar (1% agar supplemented with 5% sucrose) food at one end and a cotton plug on the other end. The glass tubes were placed in the Drosophila activity monitor system (TriKinetics), and the locomotor activity of each fly was recorded as the numbers of infrared beam crossing in 1-min bin. Free-running rhythms were recorded under constant dark condition after housing under 12-hour light/12-hour dark cycles for at least 3 days. calx A or calx B mutant flies were obtained from the Bloomington Drosophila Stock Center.

Mathematical analysis
By using a previously published mathematical model (23), we investigated an effect of CaMKII activation on the TTFL of the mammalian circadian clock. Because CaMKII phosphorylates CLOCK to activate transcriptional activity of the CLOCK-BMAL1 complex (14)(15)(16)(17), we varied the corresponding parameter, which was represented as "phos" in the original model (23). Ordinary differential equations were solved numerically by using the Euler method with delta t = 0.001.

SUPPLEMENTARY MATERIALS
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