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.

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.

Cyanobacterial daily life with Kai-based circadian and diurnal genome-wide transcriptional control in Synechococcus elongatus.

In the unicellular cyanobacterium Synechococcus elongatus PCC 7942, essentially all promoter activities are under the control of the circadian clock under continuous light (LL) conditions. Here, we used high-density oligonucleotide arrays to explore comprehensive profiles of genome-wide Synechococcus gene expression in wild-type, kaiABC-null, and kaiC-overexpressor strains under LL and continuous dark (DD) conditions. In the wild-type strains, >30% of transcripts oscillated significantly in a circadian fashion, peaking at subjective dawn and dusk. Such circadian control was severely attenuated in kaiABC-null strains. Although it has been proposed that KaiC globally represses gene expression, our analysis revealed that dawn-expressed genes were up-regulated by kaiC-overexpression so that the clock was arrested at subjective dawn. Transfer of cells to DD conditions from LL immediately suppressed expression of most of the genes, while the clock kept even time in the absence of transcriptional feedback. Thus, the Synechococcus genome seems to be primarily regulated by light/dark cycles and is dramatically modified by the protein-based circadian oscillator.

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.

Regulation of circadian clock gene expression by phosphorylation states of KaiC in cyanobacteria.

Three clock proteins--KaiA, KaiB, and KaiC--have been identified as essential components of the circadian oscillator in cyanobacteria, and Kai-based chemical oscillation is thought to be the basic circadian timing mechanism in Synechococcus elongatus PCC 7942. Transcription and translation of kaiBC in cyanobacterial cells was quantitatively studied to elucidate how these processes are coupled to the chemical oscillator using a strain in which circadian oscillation is under the control of IPTG (isopropyl-beta-D-thiogalactopyranoside). The kinetics of repression of kaiBC promoter triggered by IPTG allowed estimation of transient response at 10 h. This response time is suitable for cyanobacterial transcription and/or translation to match with the Kai-based oscillator. Interestingly, kaiBC promoter activity and KaiC phosphorylation showed robust circadian rhythms, whereas trc promoter-driven kaiBC mRNA levels and KaiC accumulation were almost arrhythmic. These results indicate that cyanobacterial circadian rhythms can be generated even if kaiBC expression is constitutive. Moreover, there was a positive correlation between activation of the kaiBC promoter and an increase in the KaiC phosphorylation ratio in three rhythmic conditions. Based on these observations, it is likely that the KaiC phosphorylation ratio is the main factor in the activation of kaiBC promoter. Finally, we quantitatively compared the threshold level of phosphorylated KaiC for the repression or derepression of kaiBC promoter and found that this parameter is an important factor in repressing the kaiBC promoter.

ATPase activity of KaiC determines the basic timing for circadian clock of cyanobacteria.

Self-sustainable oscillation of KaiC phosphorylation has been reconstituted in vitro, demonstrating that this cycle is the basic time generator of the circadian clock of cyanobacteria. Here we show that the ATPase activity of KaiC satisfies the characteristics of the circadian oscillation, the period length, and the temperature compensation. KaiC possesses extremely weak but stable ATPase activity (15 molecules of ATP per day), and the addition of KaiA and KaiB makes the activity oscillate with a circadian period in vitro. The ATPase activity of KaiC is inherently temperature-invariant, suggesting that temperature compensation of the circadian period could be driven by this simple biochemical reaction. Moreover, the activities of wild-type KaiC and five period-mutant proteins are directly proportional to their in vivo circadian frequencies, indicating that the ATPase activity defines the circadian period. Thus, we propose that KaiC ATPase activity constitutes the most fundamental reaction underlying circadian periodicity in cyanobacteria.

Reconstitution of circadian oscillation of cyanobacterial KaiC phosphorylation in vitro.

Kai proteins globally regulate circadian gene expression of cyanobacteria. The KaiC phosphorylation cycle, which persists even without transcription or translation, is assumed to be a basic timing process of the circadian clock. We have reconstituted the self-sustainable oscillation of KaiC phosphorylation in vitro by incubating KaiC with KaiA, KaiB, and adenosine triphosphate. The period of the in vitro oscillation was stable despite temperature change (temperature compensation), and the circadian periods observed in vivo in KaiC mutant strains were consistent with those measured in vitro. The enigma of the circadian clock can now be studied in vitro by examining the interactions between three Kai proteins.