Regulation mechanisms of the dual ATPase in KaiC.

KaiC is a dual adenosine triphosphatase (ATPase), with one active site in its N-terminal domain and another in its C-terminal domain, that drives the circadian clock system of cyanobacteria through sophisticated coordination of the two sites. To elucidate the coordination mechanism, we studied the contribution of the dual-ATPase activities in the ring-shaped KaiC hexamer and these structural bases for activation and inactivation. At the N-terminal active site, a lytic water molecule is sequestered between the N-terminal domains, and its reactivity to adenosine triphosphate (ATP) is controlled by the quaternary structure of the N-terminal ring. The C-terminal ATPase activity is regulated mostly by water-incorporating voids between the C-terminal domains, and the size of these voids is sensitive to phosphoryl modification of S431. The up-regulatory effect on the N-terminal ATPase activity inversely correlates with the affinity of KaiC for KaiB, a clock protein constitutes the circadian oscillator together with KaiC and KaiA, and the complete dissociation of KaiB from KaiC requires KaiA-assisted activation of the dual ATPase. Delicate interactions between the N-terminal and C-terminal rings make it possible for the components of the dual ATPase to work together, thereby driving the assembly and disassembly cycle of KaiA and KaiB.

[Changes in the residence of elderly people after hospitalization in the Integrated Community Care Ward].

AIM: When elderly people return to their daily lives after inpatient treatment, they may be offered a chance to change the residence to which they are accustomed. The present study clarified the changes in the residence of elderly patients through an Integrated Community Care Ward (ICCW). SUBJECTS AND METHODS: Patients were admitted to and discharged from the ICCW (53 beds) of Hospital A, located in a city with a population of 30,000 and an aging rate of 37%, for 2 years from April 1, 2018, to March 31, 2020. Patients ≥65 years old were included in the study. We conducted a retrospective survey of information recorded in the electronic medical record system and collected information on activities of daily living, medical procedures at the time of discharge, residence before and after hospitalization, and intentions regarding discharge destination within seven days of hospitalization. RESULTS: Of the 735 patients ≥65 years old who were admitted to the ICCW, 608 were included, excluding 127 patients admitted for scheduled surgeries. The average age was 82.9 years old, with 52% being over 85 years and 26% being over 90 years old. Of the 465 people hospitalized from home, 64% were discharged, 23% changed to a facility or hospital, and the remaining 13% died. More than 80% of the 143 discharged from facilities or hospitals returned to facilities, but 36 (25%) were discharged to a different facility from before admission. Of the 404 patients who were admitted from home and discharged alive, independence in eating, independence in movement, and having family members living with them were independently related factors for achieving discharge home. Regarding the intended discharge destination within 7 days after hospitalization, of the 246 hospitalized patients who wished to be discharged home, 56 said they wanted to be discharged to a facility or hospital, showing a discrepancy of 23%. CONCLUSIONS: Many elderly people changed their residences after admission to the ICCW. While coordinating disagreements within families as well as navigating medical and nursing care constraints, dialogue across multiple professions should be continued to help elderly patients live their own lives.

IL-1ß promotes osteoclastogenesis by increasing the expression of IGF2 and chemokines in non-osteoclastic cells.

Bone remodeling mediated by bone-forming osteoblasts (OBs) and bone-resorbing osteoclasts (OCs) maintains bone structure and function. Excessive OC activation leads to bone-destroying diseases such as osteoporosis and bone erosion of rheumatoid arthritis (RA). Differentiation of OCs from bone marrow cells (BMCs) is regulated by the bone microenvironment. The proinflammatory cytokine interleukin (IL)-1ß reportedly enhances osteoclastogenesis and plays important roles in RA-associated bone loss. The present study investigated the effect of IL-1ß on OC formation via microenvironmental cells. Treating mouse BMCs with IL-1ß in the presence of receptor activator of NF-κB ligand and macrophage colony-stimulating factor increased the number of OCs. Real-time RT-PCR revealed increased expression of the IL-1ß, IL-1RI, and IL-1RII genes in non-OCs compared with OCs. Removing CD45- cells which cannot differentiate into OCs, from mouse BMCs reduced the IL-1ß-mediated enhancement of osteoclastogenesis. IL-1ß treatment upregulated the expression of inducible nitric oxide synthase, insulin-like growth factor 2 (IGF2), and the chemokines stromal cell derived factor 1, C-X3-C motif ligand 1 (CX3CL1), and CXCL7 in non-OCs. Neutralizing antibodies against these chemokines and IGF2 suppressed osteoclastogenesis in the presence of IL-1ß. These results suggest that IL-1ß enhances osteoclastogenesis by upregulating IGF2 and chemokine expression in non-OCs.

Tuning the circadian period of cyanobacteria up to 6.6 days by the single amino acid substitutions in KaiC.

The circadian clock of cyanobacteria consists of only three clock proteins, KaiA, KaiB, and KaiC, which generate a circadian rhythm of KaiC phosphorylation in vitro. The adenosine triphosphatase (ATPase) activity of KaiC is the source of the 24-h period and temperature compensation. Although numerous circadian mutants of KaiC have been identified, the tuning mechanism of the 24-h period remains unclear. Here, we show that the circadian period of in vitro phosphorylation rhythm of mutants at position 402 of KaiC changed dramatically, from 15 h (0.6 d) to 158 h (6.6 d). The ATPase activities of mutants at position 402 of KaiC, without KaiA and KaiB, correlated with the frequencies (1/period), indicating that KaiC structure was the source of extra period change. Despite the wide-range tunability, temperature compensation of both the circadian period and the KaiC ATPase activity of mutants at position 402 of KaiC were nearly intact. We also found that in vivo and in vitro circadian periods and the KaiC ATPase activity of mutants at position 402 of KaiC showed a correlation with the side-chain volume of the amino acid at position 402 of KaiC. Our results indicate that residue 402 is a key position of determining the circadian period of cyanobacteria, and it is possible to dramatically alter the period of KaiC while maintaining temperature compensation.

The Inducible Nitric Oxide Synthase Pathway Promotes Osteoclastogenesis under Hypoxic Culture Conditions.

Bone homeostasis depends on the balance between bone resorption by osteoclasts (OCs) and bone formation by osteoblasts. Bone resorption can become excessive under various pathologic conditions, including rheumatoid arthritis. Previous studies have shown that OC formation is promoted under hypoxia. However, the precise mechanisms behind OC formation under hypoxia have not been elucidated. The present study investigated the role of inducible nitric oxide synthase (iNOS) in OC differentiation under hypoxia. Primary bone marrow cells obtained from mice were stimulated with receptor activator of NF-κB ligand and macrophage colony-stimulating factor to induce OC differentiation. The number of OCs increased in culture under hypoxia (oxygen concentration, 5%) compared with that under normoxia (oxygen concentration, 20%). iNOS gene and protein expression increased in culture under hypoxia. Addition of an iNOS inhibitor under hypoxic conditions suppressed osteoclastogenesis. Addition of a nitric oxide donor to the normoxic culture promoted osteoclastogenesis. Furthermore, insulin-like growth factor 2 expression was significantly altered in both iNOS inhibition experiments and nitric oxide donor experiments. These data might provide clues to therapies for excessive osteoclastogenesis under several hypoxic pathologic conditions, including rheumatoid arthritis.

Insulin-like growth factor 2 promotes osteoclastogenesis increasing inflammatory cytokine levels under hypoxia.

Osteoporosis is caused by an imbalance in bone remodeling due to abnormal osteoclast (OC) formation and activation. Hypoxia at the site of inflammation promotes OC formation and activation in various species, including humans. We previously reported that insulin-like growth factor 2 (IGF2) plays an important role in osteoclastogenesis under hypoxia. In our present study, we focused on the mechanism of osteoclastogenesis in regard to IGF2 signaling under hypoxia. We confirmed that the addition of IGF2 promoted osteoclastogenesis under normoxic conditions. Conversely, IGF2-neutralizing antibodies inhibited osteoclastogenesis under both normoxic and hypoxic conditions. IGF2 addition increased levels of phosphorylated Akt (Thr308 and Ser473) and NF-κB (Ser536), indicating activation of the Akt-NF-κB pathway. IGF2 also increased the expression of inducible nitric oxide synthase, which promotes osteoclastogenesis via nitric oxide production. Expression levels of genes encoding inflammatory cytokines, such as tumor necrosis factor-α, interleukin (IL)-1ß, and IL-6, were upregulated, indicating that IGF2 promotes osteoclastogenesis by increasing the expression of inflammatory cytokines via activation of the Akt-NF-κB pathway. These results suggest that IGF2 is a promising therapeutic target for osteoporosis and rheumatoid arthritis.

Low temperature nullifies the circadian clock in cyanobacteria through Hopf bifurcation.

Cold temperatures lead to nullification of circadian rhythms in many organisms. Two typical scenarios explain the disappearance of rhythmicity: the first is oscillation death, which is the transition from self-sustained oscillation to damped oscillation that occurs at a critical temperature. The second scenario is oscillation arrest, in which oscillation terminates at a certain phase. In the field of nonlinear dynamics, these mechanisms are called the Hopf bifurcation and the saddle-node on an invariant circle bifurcation, respectively. Although these mechanisms lead to distinct dynamical properties near the critical temperature, it is unclear to which scenario the circadian clock belongs. Here we reduced the temperature to dampen the reconstituted circadian rhythm of phosphorylation of the recombinant cyanobacterial clock protein KaiC. The data led us to conclude that Hopf bifurcation occurred at ∼19 °C. Below this critical temperature, the self-sustained rhythms of KaiC phosphorylation transformed to damped oscillations, which are predicted by the Hopf bifurcation theory. Moreover, we detected resonant oscillations below the critical temperature when temperature was periodically varied, which was reproduced by numerical simulations. Our findings suggest that the transition to a damped oscillation through Hopf bifurcation contributes to maintaining the circadian rhythm of cyanobacteria through resonance at cold temperatures.

Development and Optimization of Expression, Purification, and ATPase Assay of KaiC for Medium-Throughput Screening of Circadian Clock Mutants in Cyanobacteria.

The slow but temperature-insensitive adenosine triphosphate (ATP) hydrolysis reaction in KaiC is considered as one of the factors determining the temperature-compensated period length of the cyanobacterial circadian clock system. Structural units responsible for this low but temperature-compensated ATPase have remained unclear. Although whole-KaiC scanning mutagenesis can be a promising experimental strategy, producing KaiC mutants and assaying those ATPase activities consume considerable time and effort. To overcome these bottlenecks for in vitro screening, we optimized protocols for expressing and purifying the KaiC mutants and then designed a high-performance liquid chromatography system equipped with a multi-channel high-precision temperature controller to assay the ATPase activity of multiple KaiC mutants simultaneously at different temperatures. Through the present protocol, the time required for one KaiC mutant is reduced by approximately 80% (six-fold throughput) relative to the conventional protocol with reasonable reproducibility. For validation purposes, we picked up three representatives from 86 alanine-scanning KaiC mutants preliminarily investigated thus far and characterized those clock functions in detail.

Exchange of ADP with ATP in the CII ATPase domain promotes autophosphorylation of cyanobacterial clock protein KaiC.

The cyanobacterial circadian oscillator can be reconstituted in vitro. In the presence of KaiA and KaiB, the phosphorylation state of KaiC oscillates with a periodicity of ∼24 h. KaiC is a hexameric P-loop ATPase with autophosphorylation and autodephosphorylation activities. Recently, we found that dephosphorylation of KaiC occurs via reversal of the phosphorylation reaction: a phosphate group attached to Ser431/Thr432 is transferred to KaiC-bound ADP to generate ATP, which is subsequently hydrolyzed. This unusual reaction mechanism suggests that the KaiC phosphorylation rhythm is sustained by periodic shifts in the equilibrium of the reversible autophosphorylation reaction, the molecular basis of which has never been elucidated. Because KaiC-bound ATP and ADP serve as substrates for the forward and reverse reactions, respectively, we investigated the regulation of the nucleotide-bound state of KaiC. In the absence of KaiA, the condition in which the reverse reaction proceeds, KaiC favored the ADP-bound state. KaiA increased the ratio of ATP to total KaiC-bound nucleotides by facilitating the release of bound ADP and the incorporation of exogenous ATP, allowing the forward reaction to proceed. When both KaiA and KaiB were present, the ratio of ATP to total bound nucleotides exhibited a circadian rhythm, whose phase was advanced by several hours relative to that of the phosphorylation rhythm. Based on these findings, we propose that the direction of the reversible autophosphorylation reaction is regulated by KaiA and KaiB at the level of substrate availability and that this regulation sustains the oscillation of the phosphorylation state of KaiC.

Tracking and visualizing the circadian ticking of the cyanobacterial clock protein KaiC in solution.

The circadian clock in cyanobacteria persists even without the transcription/translation feedbacks proposed for eukaryotic systems. The period of the cyanobacterial clock is tuned to the circadian range by the ATPase activity of a clock protein known as KaiC. Here, we provide structural evidence on how KaiC ticks away 24 h while coupling the ATPase activity in its N-terminal ring to the phosphorylation state in its C-terminal ring. During the phosphorylation cycle, the C-terminal domains of KaiC are repositioned in a stepwise manner to affect global expansion and contraction motions of the C-terminal ring. Arg393 of KaiC has a critical function in expanding the C-terminal ring and its replacement with Cys affects the temperature compensation of the period--a fundamental property of circadian clocks. The conformational ticking of KaiC observed here in solution serves as a timing cue for assembly/disassembly of other clock proteins (KaiA and KaiB), and is interlocked with its auto-inhibitory ATPase underlying circadian periodicity of cyanobacteria.

Synthesis of a chondroitin sulfate disaccharide library and a GAG-binding protein interaction analysis.

Chondroitin sulfate (CS), which belongs to the glycosaminoglycan (GAG) superfamily, is a linear sulfated polysaccharide involved in various biological processes. CS structure is very heterogeneous and contains various sulfation patterns owing to the multiple and random enzymatic modifications that occur during its biosynthesis. The resultant microdomain structure in the CS chain interacts with specific biomolecules to regulate biological functions. Therefore, an analysis of the structure-activity relationship of CS at the molecular level is necessary to clarify their biofunctions. In this study, we designed the common intermediate possessing an orthogonally removable protective group and systematically synthesized all 16 types of CS disaccharide structure generated by sulfation. In addition, we demonstrated the on-time analysis of the binding properties of GAG-binding proteins using 'Sugar Chip' immobilized CS disaccharide structures by surface plasmon resonance (SPR) imaging, indicating that our chip technology is effective for the evaluation of binding properties.

Melanopsin-dependent photo-perturbation reveals desynchronization underlying the singularity of mammalian circadian clocks.

Singularity behaviour in circadian clocks--the loss of robust circadian rhythms following exposure to a stimulus such as a pulse of bright light--is one of the fundamental but mysterious properties of clocks. To quantitatively perturb and accurately measure the dynamics of cellular clocks, we synthetically produced photo-responsiveness within mammalian cells by exogenously introducing the photoreceptor melanopsin and continuously monitoring the effect of photo-perturbation on the state of cellular clocks. Here we report that a critical light pulse drives cellular clocks into singularity behaviour. Our theoretical analysis consistently predicts and subsequent single-cell level observation directly proves that desynchronization of individual cellular clocks underlies singularity behaviour. Our theoretical framework also explains why singularity behaviours have been experimentally observed in various organisms, and it suggests that desynchronization is a plausible mechanism for the observable singularity of circadian clocks. Importantly, these in vitro and in silico findings are further supported by in vivo observations that desynchronization underlies the multicell-level amplitude decrease in the rat suprachiasmatic nucleus induced by critical light pulses.

Effects of adenylates on the circadian interaction of KaiB with the KaiC complex in the reconstituted cyanobacterial Kai protein oscillator.

Cyanobacteria are photosynthetic prokaryotes that possess circadian oscillators. Clock proteins, KaiA, KaiB, KaiC compose the central circadian oscillator, which can be reconstituted in vitro in the presence of ATP. KaiC has ATPase, autokinase, and autophosphatase enzymatic activities. These activities are modulated by protein-protein interactions among the Kai proteins. The interaction of KaiB with the KaiC complex shows a circadian rhythm in the reconstituted system. We previously developed a quantitative, real-time monitoring system for the dynamic behavior of the complex using fluorescence correlation spectroscopy. Here, we examined the effects of ATP and ADP on the rhythmic interaction of KaiB. We show that increased concentration of ATP or ADP shortened period length. Adding ADP to the Kai protein oscillation shifted its phase in a phase-dependent manner. These results provide insight into how circadian oscillation entrainment mechanism is linked to cellular metabolism.

Elucidation of the role of clp protease components in circadian rhythm by genetic deletion and overexpression in cyanobacteria.

In the cyanobacterium Synechococcus elongatus PCC7942, KaiA, KaiB, and KaiC are essential elements of the circadian clock, and Kai-based oscillation is thought to be the basic circadian timing mechanism. The Kai-based oscillator coupled with transcription/translation feedback and other intercellular factors maintains the stability of the 24-hour period in vivo. In this study, we showed that disruption of the Clp protease family genes clpP1, clpP2, and clpX and the overexpression of clpP3 cause long-period phenotypes. There were no significant changes in the levels of the clock proteins in these mutants. The overexpression of clpX led to a decrease in kaiBC promoter activity, the disruption of the circadian rhythm, and eventually cell death. However, after the transient overexpression of clpX, the kaiBC gene expression rhythm recovered after a few days. The rhythm phase after recovery was almost the same as the phase before clpX overexpression. These results suggest that the core Kai-based oscillation was not affected by clpX overexpression. Moreover, we showed that the overexpression of clpX sequentially upregulated ribosomal protein subunit mRNA levels, followed by upregulation of other genes, including the clock genes. Additionally, we found that the disruption of clpX decreased the expression of the ribosomal protein subunits. Finally, we showed that the circadian period was prolonged following the addition of a translation inhibitor at a low concentration. These results suggest that translational efficiency affects the circadian period and that clpX participates in the control of translation efficiency by regulating the transcription of ribosomal protein genes.

Circadian autodephosphorylation of cyanobacterial clock protein KaiC occurs via formation of ATP as intermediate.

The cyanobacterial circadian oscillator can be reconstituted in vitro; mixing three clock proteins (KaiA, KaiB, and KaiC) with ATP results in an oscillation of KaiC phosphorylation with a periodicity of ~24 h. The hexameric ATPase KaiC hydrolyzes ATP bound at subunit interfaces. KaiC also exhibits autokinase and autophosphatase activities, the latter of which is particularly noteworthy because KaiC is phylogenetically distinct from typical protein phosphatases. To examine this activity, we performed autodephosphorylation assays using (32)P-labeled KaiC. The residual radioactive ATP bound to subunit interfaces was removed using a newly established method, which included the dissociation of KaiC hexamers into monomers and the reconstitution of KaiC hexamers with nonradioactive ATP. This approach ensured that only the signals derived from (32)P-labeled KaiC were examined. We detected the transient formation of [(32)P]ATP preceding the accumulation of (32)P(i). Together with kinetic analyses, our data demonstrate that KaiC undergoes dephosphorylation via a mechanism that differs from those of conventional protein phosphatases. A phosphate group at a phosphorylation site is first transferred to KaiC-bound ADP to form ATP as an intermediate, which can be regarded as a reversal of the autophosphorylation reaction. Subsequently, the ATP molecule is hydrolyzed to form P(i). We propose that the ATPase active site mediates not only ATP hydrolysis but also the bidirectional transfer of the phosphate between phosphorylation sites and the KaiC-bound nucleotide. On the basis of these findings, we can now dissect the dynamics of the KaiC phosphorylation cycle relative to ATPase activity.

Fluorescence correlation spectroscopy to monitor Kai protein-based circadian oscillations in real time.

Dynamic protein-protein interactions play an essential role in cellular regulatory systems. The cyanobacterial circadian clock is an oscillatory system that can be reconstituted in vitro by mixing ATP and three clock proteins: KaiA, KaiB, and KaiC. Association and dissociation of KaiB from KaiC-containing complexes are critical to circadian phosphorylation and dephosphorylation of KaiC. We developed an automated and noninvasive method to monitor dynamic complex formation in real time using confocal fluorescence correlation spectroscopy (FCS) and uniformly labeled KaiB as a probe. A nanomolar concentration of the labeled KaiB for FCS measurement did not interfere with the oscillatory system but behaved similarly to the wild-type one during the measurement period (>5 days). The fluorescent probe was stable against repeated laser exposure. As an application, we show that this detection system allowed analysis of the dynamics of both long term circadian oscillations and short term responses to temperature changes (∼10 min) in the same sample. This suggested that a phase shift of the clock with a high temperature pulse occurred just after the stimulus through dissociation of KaiB from the KaiC complex. This monitoring method should improve our understanding of the mechanisms underlying this cellular circadian oscillator and provide a means to assess dynamic protein interactions in biological systems characterized by rates similar to those observed with the Kai proteins.

RpaB, another response regulator operating circadian clock-dependent transcriptional regulation in Synechococcus elongatus PCC 7942.

The circadian clock of cyanobacteria is composed of KaiA, KaiB, and KaiC proteins, and the SasA-RpaA two-component system has been implicated in the regulation of one of the output pathways of the clock. In this study, we show that another response regulator that is essential for viability, the RpaA paralog, RpaB, plays a central role in the transcriptional oscillation of clock-regulated genes. In vivo and in vitro analyses revealed that RpaB and not RpaA could specifically bind to the kaiBC promoter, possibly repressing transcription during subjective night. This suggested that binding may be terminated by RpaA to activate gene transcription during subjective day. Moreover, we found that rpoD6 and sigF2, which encode group-2 and group-3 σ factors for RNA polymerase, respectively, were also targets of the RpaAB system, suggesting that a specific group of σ factors can propagate genome-wide transcriptional oscillation. Our findings thus reveal a novel mechanism for a circadian output pathway that is mediated by two paralogous response regulators.

Three major output pathways from the KaiABC-based oscillator cooperate to generate robust circadian kaiBC expression in cyanobacteria.

Circadian kaiBC expression in the cyanobacterium Synechococcus elongatus PCC 7942 is generated by temporal information transmission from the KaiABC-based circadian oscillator to RpaA, a putative transcriptional factor, via the SasA-dependent positive pathway and the LabA-dependent negative pathway which is responsible for feedback regulation of KaiC. However, the labA/sasA double mutant has a circadian kaiBC expression rhythm, suggesting that there is an additional circadian output pathway. Here we describe a third circadian output pathway, which is CikA-dependent. The cikA mutation attenuates KaiC overexpression-induced kaiBC repression and exacerbates the low-amplitude phenotype of the labA mutant, suggesting that cikA acts as a negative regulator of kaiBC expression independent of the LabA-dependent pathway. In the labA/sasA/cikA triple mutant, kaiBC promoter activity becomes almost arrhythmic, despite preservation of the circadian KaiC phosphorylation rhythm, suggesting that CikA largely accounts for the residual kaiBC expression rhythm observed in the labA/sasA double mutant. These results also strongly suggest that transcriptional regulation in the labA/sasA/cikA triple mutant is insulated from the circadian signals of the KaiABC-based oscillator. Based on these observations, we propose a model in which temporal information from the KaiABC-based circadian oscillator is transmitted to gene expression through three separate output pathways.

CmpR is important for circadian phasing and cell growth.

In the cyanobacterium Synechococcus elongatus PCC 7942, the circadian clock entrains to a daily light/dark cycle. The transcription factor Pex is abundant under dark conditions and represses kaiA transcription to fine-tune the KaiC-based core circadian oscillator. The transcription of pex also increases during exposure to darkness; however, its mechanism is unknown. We performed a molecular genetic study by constructing a pex expression bioluminescent reporter and screening for brightly luminescent mutants by random insertion of a drug resistance gene cassette in the reporter genome. One mutant contained an insertion of an antibiotic resistance cassette in the cmpR locus, a transcriptional regulator of inorganic carbon concentration. Insertions of the cassette in the remaining two mutant genomes were in the genes encoding flavodoxin and a putative partner of an ABC transporter with unknown function (ycf22). We further analyzed the cmpR mutant to examine whether CmpR directly or indirectly targeted pex expression. In the cmpR mutant, the pex mRNA level was 1.8-fold that of the wild type, and its circadian peak phase in bioluminescence rhythm occurred 5 h later. Moreover, a high-light stress phenotype was present in the colony. The abnormalities were complemented by ectopic induction of the native gene. However, the cmpR/pex double mutation partly suppressed the phase abnormality (2.5 h). In vitro DNA binding analysis of CmpR showed positive binding to the psbAII promoter, but not to any pex DNA. We postulate that the phenotypes of cmpR-deficient cells were attributable mainly to a feeble metabolic and/or redox status.

Nonparametric entrainment of the in vitro circadian phosphorylation rhythm of cyanobacterial KaiC by temperature cycle.

The three cyanobacterial Kai proteins and ATP are capable of generating an autonomous rhythm of KaiC phosphorylation in a test tube. As the period is approximately 24 hours and is stable in a wide temperature range, this rhythm is thought to function as the basic oscillator of the cyanobacterial circadian system. We have examined the rhythm under various temperature cycles and found that it was stably entrained by a temperature cycle of 20-28 hours. As the period length was not altered by temperature, entrainment by period change could be excluded from possible mechanisms. Instead, temperature steps between 30 degrees and 45 degrees C and vice versa shifted the phase of the rhythm in a phase-dependent manner. Based on the phase response curves of the step-up and step-down in temperature, phase shift by single temperature pulse was estimated using a nonparametric entrainment model (discontinuous phase jump by external stimuli). The predicted phase shift was consistent with the experimentally measured phase shift. Next, successive phase shifts caused by repeated temperature cycles were computed by two phase response curves and compared with actual entrainment of the rhythm. As the entrainment pattern observed after various combinations of temperature cycles matched the prediction, it is likely that nonparametric entrainment functions even in the simple three-protein system. We also analyzed entrainment of KaiC phosphorylation by temperature cycle in cyanobacterial cells and found both the parametric and the nonparametric models function in vivo.