Functioning and robustness of a bacterial circadian clock

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Abstract
Cyanobacteria are the simplest known cellular systems that regulate their biological activities in daily cycles. For the cyanobacterium Synechococcus elongatus , it has been shown by in vitro and in vivo experiments that the basic circadian timing process is based on rhythmic phosphorylation of KaiC hexamers. Despite the excellent experimental work, a full systems level understanding of the in vitro clock is still lacking. In this work, we provide a mathematical approach to scan different hypothetical mechanisms for the primary circadian oscillator, starting from experimentally established molecular properties of the clock proteins. Although optimised for highest performance, only one of the in silico ‐generated reaction networks was able to reproduce the experimentally found high amplitude and robustness against perturbations. In this reaction network, a negative feedback synchronises the phosphorylation level of the individual hexamers and has indeed been realised in S. elongatus by KaiA sequestration as confirmed by experiments. ### Synopsis In most eukaryotes, an internal clock drives numerous activities into daily cycles—a circadian clock, which is ticking with a periodicity of about 24 h. The period of this free‐running rhythm is highly robust against many changes in the natural environment, for example, in cyanobacteria the clock can compensate for variations in the ambient temperature. But for certain external stimuli (e.g. light, temperature, nutrients), the circadian rhythm is able to be entrained. The optimal temporal coordination of biological processes and the adaptation to daily fluctuations play a critical role in the survival of diverse organisms. Photoautotrophic organisms like plants and cyanobacteria are subjected to a daily light–dark rhythm during their photosynthetic activity and have been demonstrated to posses a free‐running circadian clock as well. In particular, for the cyanobacterium Synechococcus elongatus , a robust circadian rhythm has been observed under constant darkness conditions and even for complete suppression of the cellular transcription and translation activity ([Tomita et al , 2005][1]). Moreover, only three different cyanobacterial proteins (KaiA, KaiB, and KaiC) are sufficient to achieve a temperature‐compensated circadian rhythm of phosphorylation cycles in vitro ([Nakajima et al , 2005][2]). Despite numerous excellent experimental investigations, it remained unclear how a biochemical mechanism involving just three proteins can keep its timing so precisely over a long period, as biochemical events are known to be intrinsically stochastic. We used the in vitro clock of S. elongatus as an instructive model system for the circadian mechanism in a unicellular organism. The phosphorylation–dephosphorylation cycle of KaiC functions as a circadian oscillator by mixing the three Kai proteins and ATP in a test tube. Thereby, KaiA and KaiB are modulating KaiC phosphorylation state by forming complexes ([Kageyama et al , 2003][3]; [Garces et al , 2004][4]) with so far unknown stoichiometry. To identify the protein complex formation during a 24 h cycle, we monitored the molecular composition and weight of complexes by 2D gel separation experiments. Consistent with the recent observations, we demonstrated that KaiC forms stable hexamers. After incubation, the hexamers start to autophosphorylate, a process that is enhanced by KaiA. At maximum KaiC phosphorylation, KaiB dimers begin to associate and from stable complexes with KaiC, initiating the dephosphorylation of KaiC. Interestingly, at low phosphorylation levels of KaiC, KaiA is found in a complex with KaiC and KaiB. However, the exact molecular mechanism generating temperature‐compensated 24‐h oscillations is yet unknown. A novel mathematical approach was provided to generate different hypothetical mechanisms for a basic circadian oscillator. Starting from the biochemically defined reaction network known for the clock proteins and verified by our experiments, we introduced systematically different feedback interactions connecting different states of the KaiC phosphorylation cycle to achieve oscillatory behaviour ([Tyson et al , 2003][5]). We obtained 224 possible network topologies using a single feedback loop. A global optimisation of reaction constants for high amplitude was employed for each generated network topology based on experimental observations that in vivo phosphorylation is able to oscillate close to the maximum and minimum phosphorylation levels as found in vitro ([Nishiwaki et al , 2004][6]; [Tomita et al , 2005][1]). For the feedback mechanisms allowing oscillations, stability in phase and frequency was analysed as it has been shown that cyanobacterial cells possess a stable phase over several generations even under constant low‐light conditions ([Mihalcescu et al , 2004][7]). Finally, only one of the in silico ‐generated reaction networks ([Figure 1][8]) was able to reproduce the experimentally found high amplitude of oscillations and robustness against changes resulting from cell division, protein synthesis, and degradation. In this reaction network ([Figure 1C][8]), a negative feedback, which can be realised by KaiA sequestration to low‐phosphorylated KaiBC complexes ([Figure 2][9]), synchronises the phosphorylation level of the individual KaiC hexamers. Thus, our theoretical analysis suggests that the main oscillatory mechanism is a consequence of KaiA sequestration. Intriguingly, the experimentally observed behaviour can be simulated by our mathematical approach without the exact knowledge of the biochemical reaction constants. Moreover, our optimisation procedure revealed that for maximal oscillations of the found network only a small amount of KaiC hexamers is needed to form complexes with KaiA and KaiB and the remaining large fraction of phosphorylated KaiC never undergoes the complete cycle of our...