||Murayama Y, Kori H, Oshima C, Kondo T, Iwasaki H, Ito H, Low temperature nullifies the circadian clock in cyanobacteria through Hopf bifurcation, Proceedings of National Academy of Sciences, 114, 5641-5646, 2017.05, 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..
||Shingo Gibo, Hiroshi Ito, Discrete and ultradiscrete models for biological rhythms comprising a simple negative feedback loop, Journal of Theoretical Biology, 2015.05.
||Nakajima M*, Ito H*, Kondo T.(*Equally contributed), In vitro regulation of circadian phosphorylation rhythm of cyanobacterial clock protein KaiC by KaiA and KaiB , FEBS Letters, 10.1016/j.febslet.2010.01.016, 584, 898-902 , , 2010.01.
||Ito H*, Mutsuda M, Murayama Y, Tomita J, Hosokawa N, Terauchi K, Sugita C, Sugita M, Kondo T, Iwasaki H*. (*Equally contributed), Cyanobacterial daily life with Kai-based circadian and diurnal genome-wide transcriptional control in Synechococcus elongatus., Proceedings of National Academy of Sciences , 10.1073/pnas.0902587106, 106 (2009), 14168-14173, 2011.07.
||Ito H, Kageyama H, Mutsuda M, Nakajima M, Oyama T, Kondo T., Autonomous synchronization of the circadian KaiC phosphorylation rhythm, Nature Structural and Molecular Biology, 10.1038/nsmb1312, 14, 1084-1088, 2007.11.
||Yoshida T*, Murayama Y*, Ito H*, Kageyama H, Kondo T. (*Equally contributed), Non-parametric entrainment of the in vitro circadian phosphorylation rhythm of cyanobacterial KaiC by temperature cycle
, Proceedings of National Academy of Sciences, 10.1073/pnas.0806741106, 106, 1648-1653, 2009.01.