Low-dimensional Dynamics of Two Coupled Biological Oscillators

Abstract

The circadian clock and the cell cycle are two biological oscillatory processes that coexist within individual cells. These two oscillators were found to interact, which can lead to their synchronization. Here, we develop a method to infer their coupling and non-linear dynamics from thousands of mouse and human single-cell microscopy traces. This coupling predicts multiple phase-locked states showing different degrees of robustness against molecular fluctuations inherent to cellular scale biological oscillators. Moreover, the phase–locked states were temperature-independent and evolutionarily conserved from mouse to human, hinting at a common underlying dynamical mechanism. Finally, we detected a signature of the coupled dynamics in a physiological context, where tissues with different proliferation states exhibited shifted circadian clock phases.

Multi-synchronization and other patterns of multi-rhythmicity in oscillatory biological systems

“…The evolution towards either one of the stable modes of entrainment depends on initial conditions. These results are supported by experimental [80] and numerical evidence [86] for the coexistence between different patterns of entrainment of the cell cycle by the circadian clock in mammalian cells.…”

“…the cell cycle network, is coupled unidirectionally to a second oscillator, such as the circadian clock. Synchronization of the cell cycle and the circadian clock can occur at 1 : 1 or 1 : 2 ratios of frequencies [79,85,86]. Numerical simulations indicate the possible coexistence between different modes of entrainment of the cell cycle by the circadian clock [85].…”

Cell size homeostasis under the circadian regulation of cell division in cyanobacteria

“…Circadian control of cell division was first observed in cyanobacteria under LL [12], and later found in eukaryotes including mammalian cells [22][23][24][25][26]. Mori et al 1996 proposed that the circadian clock gates cell division at early subjective night [12].…”

“…In this study, we adopted a phenomenological model of the circadian gating. Although the current model only considers the influence of the circadian clock on cell division, cell division could also affect the phase of the circadian clock [22,36,37]. For example, because gene copy number increases during DNA replication, cell divisions can cause temporal changes in the transcription rate of kaiABC genes and shift the phase of the circadian clock [37].…”

The circadian oscillator analysed at the single‐transcript level

“…The fact that circadian time captures only a low contribution to total mRNA variability may be surprising given that clear circadian oscillations of a single‐cell reporter ( Rev‐Erbα ‐YFP) are observed in the same NIH 3T3 cells (Nagoshi et al , 2004; Bieler et al , 2014) and in human U2OS cells (Droin et al , 2019). It should be noted that the reporter used in these cells is probably present in many copies, since the cells are typically selected for high signals.…”