Low-dimensional dynamics of two coupled biological oscillators

Droin, Colas; Paquet, Éric R.; Naef, Félix

doi:10.1038/s41567-019-0598-1

Cited by 32 publications

(16 citation statements)

References 48 publications

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“…Such coupling between the circadian clock and cell cycle has been studied extensively, both experimentally as well as theoretically (e.g. [ 77 , 78 ]). Here, we use the fact that the expression of the Wee1 kinase is not only affected by DNA damage but also tightly regulated by the Clock-Bmal1 transcription factor complex, a master regulator of the circadian clock ( Fig 8G ) [ 79 ].…”

Section: Resultsmentioning

confidence: 99%

“…It should be emphasized that the unidirectional coupling between circadian clock and cell cycle as discussed here, merely functions as a conceptual example of our phenomenological modeling approach. Indeed, in reality, the situation is much more complex, as coupling happens in a bidirectional manner [ 77 , 78 ] and also the circadian clock itself includes bistable switches [ 82 ]. Nevertheless, as with the other examples discussed, certain key aspects of the system’s dynamical behavior can be described using the approach proposed here.…”

Section: Resultsmentioning

confidence: 99%

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A modular approach for modeling the cell cycle based on functional response curves

2021

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Modeling biochemical reactions by means of differential equations often results in systems with a large number of variables and parameters. As this might complicate the interpretation and generalization of the obtained results, it is often desirable to reduce the complexity of the model. One way to accomplish this is by replacing the detailed reaction mechanisms of certain modules in the model by a mathematical expression that qualitatively describes the dynamical behavior of these modules. Such an approach has been widely adopted for ultrasensitive responses, for which underlying reaction mechanisms are often replaced by a single Hill function. Also time delays are usually accounted for by using an explicit delay in delay differential equations. In contrast, however, S-shaped response curves, which by definition have multiple output values for certain input values and are often encountered in bistable systems, are not easily modeled in such an explicit way. Here, we extend the classical Hill function into a mathematical expression that can be used to describe both ultrasensitive and S-shaped responses. We show how three ubiquitous modules (ultrasensitive responses, S-shaped responses and time delays) can be combined in different configurations and explore the dynamics of these systems. As an example, we apply our strategy to set up a model of the cell cycle consisting of multiple bistable switches, which can incorporate events such as DNA damage and coupling to the circadian clock in a phenomenological way.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

A modular approach for modeling the cell cycle based on functional response curves

2021

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“…The short answer is a surprising yes . For instance, our discussion on the coupling between circadian clock and cell cycle has focused mostly on their 1:1 phase-locking, yet a recent study has experimentally demonstrated that both 1:1 and 1:2 phase-locking ratios can mutually exist even among the same population of cells ( Droin et al, 2019 ). In other words, cells can couple every ~24 hr of the circadian turn to either one (1:1) or half (1:2) a division cycle.…”

Section: The Logic and Potential Evolutionary Origins Of Autonomous Clocksmentioning

confidence: 99%

Autonomous clocks that regulate organelle biogenesis, cytoskeletal organization, and intracellular dynamics

Mofatteh

Iturra

Alamban

et al. 2021

eLife

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How do cells perceive time? Do cells use temporal information to regulate the production/degradation of their enzymes, membranes, and organelles? Does controlling biological time influence cytoskeletal organization and cellular architecture in ways that confer evolutionary and physiological advantages? Potential answers to these fundamental questions of cell biology have historically revolved around the discussion of ‘master’ temporal programs, such as the principal cyclin-dependent kinase/cyclin cell division oscillator and the circadian clock. In this review, we provide an overview of the recent evidence supporting an emerging concept of ‘autonomous clocks,’ which under normal conditions can be entrained by the cell cycle and/or the circadian clock to run at their pace, but can also run independently to serve their functions if/when these major temporal programs are halted/abrupted. We begin the discussion by introducing recent developments in the study of such clocks and their roles at different scales and complexities. We then use current advances to elucidate the logic and molecular architecture of temporal networks that comprise autonomous clocks, providing important clues as to how these clocks may have evolved to run independently and, sometimes at the cost of redundancy, have strongly coupled to run under the full command of the cell cycle and/or the circadian clock. Next, we review a list of important recent findings that have shed new light onto potential hallmarks of autonomous clocks, suggestive of prospective theoretical and experimental approaches to further accelerate their discovery. Finally, we discuss their roles in health and disease, as well as possible therapeutic opportunities that targeting the autonomous clocks may offer.

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“…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.…”

Section: Discussionmentioning

confidence: 99%

The circadian oscillator analysed at the single‐transcript level

Phillips

Hugues

Yeung

et al. 2021

Molecular Systems Biology

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The circadian clock is an endogenous and self-sustained oscillator that anticipates daily environmental cycles. While rhythmic gene expression of circadian genes is well-described in populations of cells, the single-cell mRNA dynamics of multiple core clock genes remain largely unknown. Here we use single-molecule fluorescence in situ hybridisation (smFISH) at multiple time points to measure pairs of core clock transcripts, Rev-erbα (Nr1d1), Cry1 and Bmal1, in mouse fibroblasts. The mean mRNA level oscillates over 24 h for all three genes, but mRNA numbers show considerable spread between cells. We develop a probabilistic model for multivariate mRNA counts using mixtures of negative binomials, which accounts for transcriptional bursting, circadian time and cell-to-cell heterogeneity, notably in cell size. Decomposing the mRNA variability into distinct noise sources shows that clock time contributes a small fraction of the total variability in mRNA number between cells. Thus, our results highlight the intrinsic biological challenges in estimating circadian phase from single-cell mRNA counts and suggest that circadian phase in single cells is encoded post-transcriptionally.

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Low-dimensional dynamics of two coupled biological oscillators

Cited by 32 publications

References 48 publications

A modular approach for modeling the cell cycle based on functional response curves

A modular approach for modeling the cell cycle based on functional response curves

Autonomous clocks that regulate organelle biogenesis, cytoskeletal organization, and intracellular dynamics

The circadian oscillator analysed at the single‐transcript level

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