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In order to further probe the system, we performed a number of perturbations affecting both the circadian clock and the cell cycle. In all conditions the two oscillators remained synchronized, and the data were consistent with a scenario in which the coupling is predominantly from the cell cycle to the circadian clock. Moreover, we fitted a parametric form of the coupling functions to the data via maximum likelihood. This clearly identified an acceleration of circadian phase after the division, but the stochastic nature of the problem, the large number of parameters and the particular parametric form of the coupling functions made identifying further interaction points challenging.   Thus, contrary to our expectations, we found that the cell cycle progression exerts a predominant influence on the circadian clock. While fruitful, this analysis in term of peak and division times, implicitly assumes that the phase goes linearly between two events, and thus neglect fast components of the phase dynamic \cite{Kralemann_2008}.   In a recent study Feillet et al. \cite{Feillet2014} performed similar experiments in NIH-3T3 cells, using the same \revalphaYFP reporter with the notable advantage of adding the Fucci system in order to probe the state of the cell cycle. They found that the two oscillators are indeed synchronized, with distributions a distribution  of circadian phase at division consistent with our own findings, and also noted the effect of divisions on circadian intervals. Under dexamethasone treatment they found that a fraction of the cells was adopting a different mode of locking, in which a cell divides three times each two circadian cycles. Furthermore, they noted that in this condition cell divisions were clustered in time, a sign of the influence of the circadian clock on the cell cycle, and concluded that the coupling was bidirectional \cite{26029155}.   This interpretation contrasts with the conclusions inferred from our own dexamethasone experiment, although the experimental conditions for the synchronization were slightly different in the two studies. We indeed found that the timing of divisions was not showing a clear structure under dexamethasone-induced synchronization, suggesting that the cell cycle is not strongly affected by the clock. Despite these controversial evidences, both studies converged on the observation that the circadian gating of the cell cycle is not appreciable and that coupling governs this interaction.  
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