## 2 Entrainment through the Input Pathway  
A mechanical clock has hands that come back to the same spot with a certain periodicity. _S. elongatus_' circadian clock, with its unusually high level of intricacy, seems to be equipped with this ability. Not only that, the time frame of natural competence can be shorter if the period of darkness becomes shorter, which is a condition that mimics longer days; the converse is also true for shorter days [30]. In addition, occasional cloudiness affects the gene expression pattern without affecting the KaiC phosphorylation profile [5]. These findings account for cyanobacteria's adaptation to the seasonal variance. Cyanobacteria do not have to deal with an extreme clock misalignment, such as in the case of jetlag. However, even the most accurate clock needs constant calibrations, and for that, a mechanical clock has a knob that can be turned to adjust to a new environmental time. Most organisms need to adjust their clock every day to maintain their internal physiological and behavioral activities in synchrony with the diurnal day/night cycle. Thus, one of the most crucial properties of the circadian clock is its ability to be entrained in response to an environmental cue. For cyanobacteria as well, the circadian clock's free-running period of oscillation is not always exactly 24 h. In order to guarantee survival in an oscillating environment, the temporal division of the two metabolic reactions must be able to constantly synchronize to the environmental time. Applying a dark period for 4 to 5 h (hereafter, a dark pulse) to a cyanobacterial culture causes the phase of the circadian oscillation to shift, and both a phase advance and delay can be generated depending on the time point of application (Figure 3b,c) [31]. How the information about light or darkness is passed down to the circadian clock and how cyanobacteria quickly shift their own phase in response to the environmental stimulus has intrigued a handful of scientists, although no  
Figure 3: The entrainment of a circadian rhythm with a dark pulse. The white part on the \(x\)-axis represents light or daytime; the dark area represents either the application of a dark pulse in vivo or the application of ADP or oxidized quinone in vitro. The \(y\)-axis represents the circadian gene expression pattern or KaiC phosphorylation rhythm in cyanobacteria. (**a**) A free-running rhythm that still runs even under a continuous light condition. (**b**) A phase advance that is caused by a dark-related cue during the rising phase of the clock. (**c**) A phase delay that is caused by a dark-related cue during the falling phase. direct light detection mechanism has been identified in cyanobacteria [32]. However, it was found that they use an indirect method of sensing the abundance of metabolites as a proxy for light/dark. Varying concentrations of ATP and adenosine diphosphate (ADP) shifted the circadian rhythm, both in vivo and in vitro [33]. During the day, the endogenous concentration of ATP becomes higher due to the superfluous influx of photosynthetic electrons, and more substrates become available to induce KaiC phosphorylation. Conversely, at night, ADP concentration gradually builds up, and it competes with ATP for the same binding site on KaiC, inducing its dephosphorylation as a result. This process was mimicked both in vivo and in vitro, and the presence of higher ATP and ADP induced premature phosphorylation and dephosphorylation, respectively, shifting the phase as a result [33]. The phase shift pattern matched with that of the in vivo dark pulse application; therefore, ATP/ADP was considered as the metabolite, where its periodic abundance aligns the peaking of the oscillatory phosphorylation of KaiC to the correct phase of the environmental cycle.