Circadian oscillators, which provide internal daily periodicity, are found in a variety of living organisms, including mammals, insects, plants, fungi and cyanobacteria. Remarkably, these biochemical oscillators are resilient to external and internal modifications, such as temperature and cell division cycles. They have to be 'fluctuation (noise) resistant' because relative fluctuations in the number of messenger RNA and protein molecules forming the intracellular oscillators are likely to be large. In multicellular organisms, the strong temporal stability of circadian clocks, despite molecular fluctuations, can easily be explained by intercellular interactions. Here we study circadian rhythms and their stability in unicellular cyanobacteria Synechoccocus elongatus. Low-light-level microscopy has allowed us to measure gene expression under circadian control in single bacteria, showing that the circadian clock is indeed a property of individual cells. Our measurements show that the oscillators have a strong temporal stability with a correlation time of several months. In contrast to many circadian clocks in multicellular organisms, this stability seems to be ensured by the intracellular biochemical network, because the interactions between oscillators seem to be negligible.
Periodic forcing of nonlinear oscillators leads to a large number of dynamic behaviors. The coupling of the cell cycle to the circadian clock provides a biological realization of such forcing. A previous model of forcing leads to nontrivial relations between correlations along cell lineages. Here, we present a simplified two-dimensional nonlinear map for the periodic forcing of the cell cycle. Using high-throughput single-cell microscopy, we have studied the correlations between cell-cycle duration in discrete lineages of several different organisms, including those with known coupling to a circadian clock and those without known coupling to a circadian clock. The model reproduces the paradoxical correlations and predicts new features that can be compared with the experimental data. By fitting the model to the data, we extract the important parameters that govern the dynamics. Interestingly, the model reproduces bimodal distributions for * nathalie.balaban@mail.huji.ac.il PHYSICAL REVIEW X 8, 021035 (2018) 2160-3308=18=8(2)=021035 (15) 021035-1 Published by the American Physical Society cell-cycle duration, as well as the gating of cell division by the phase of the clock, without having been explicitly fed into the model. In addition, the model predicts that circadian coupling may increase cell-tocell variability in a clonal population of cells. In agreement with this prediction, deletion of the circadian clock reduces variability. Our results show that simple correlations can identify systems under periodic forcing and that studies of nonlinear coupling of biological oscillators provide insight into basic cellular processes of growth.
Accuracy in cellular function has to be achieved despite random fluctuations (noise) in the concentrations of different molecular constituents inside and outside the cell. The circadian oscillator in cyanobacteria is an example of resilience to noise. This resilience could be either the consequence of intercellular communication or the intrinsic property of the built-in biochemical network. Here we investigate the intercellular coupling hypothesis. A short theoretical depiction of interacting noisy phase oscillators, confirmed by numerical simulations, allows us to discriminate the effect of coupling from noise. Experimentally, by studying the phase of concurrent populations of different initial phases, we evaluate a very small upper limit of the intercellular coupling strength. In addition, in situ entrainment experiments confirm our ability to detect a coupling of the circadian oscillator to an external force and to describe explicitly the dynamic change of the mean phase. We demonstrate, therefore, that the cyanobacterial clock stability is a built-in property as the intercellular coupling effect is negligible.biological clock ͉ bioluminescence ͉ dynamics ͉ synechoccocus
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