Modeling circadian clocks: From equations to oscillations

Gonze, Didier

doi:10.2478/s11535-011-0061-5

Cited by 35 publications

(45 citation statements)

References 104 publications

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“…3) Rhythms can be entrained or reset by external cues such as light or temperature [7,8]. These dynamic features of circadian rhythms have provided a natural setting for mathematical modeling and led to the publication of more than 600 theoretical studies about circadian rhythms [9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

“…cell division) [29,30]. See [10][11][12] for a detailed review of this type of abstract phase-based models.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, intracellular transcriptional/translational negative feedback loops (NFLs) between activators and repressors have been uncovered as the key oscillatory mechanisms in many organisms including Neurospora, Drosophila and mammals. These exciting discoveries have spurred the development of molecular-based models in which individual molecular reactions are described by ordinary differential equations [9][10][11][12][13]. Because the typical simulation outputs of such models are time-courses of the rise and fall of specific molecular components, model predictions can be tested directly by experiments.…”

Section: Introductionmentioning

confidence: 99%

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Protein sequestration versus Hill‐type repression in circadian clock models

Kim¹

2016

IET syst. biol.

107

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Circadian (~24hr) clocks are self-sustained endogenous oscillators with which organisms keep track of daily and seasonal time. Circadian clocks frequently rely on interlocked transcriptionaltranslational feedback loops to generate rhythms that are robust against intrinsic and extrinsic perturbations. To investigate the dynamics and mechanisms of the intracellular feedback loops in circadian clocks, a number of mathematical models have been developed. The majority of the models use Hill functions to describe transcriptional repression in a way that is similar to the Goodwin model. Recently, a new class of models with protein sequestration-based repression has been introduced. Here, we discuss how this new class of models differs dramatically from those based on Hill-type repression in several fundamental aspects: conditions for rhythm generation, robust network designs and the periods of coupled oscillators. Consistently, these fundamental properties of circadian clocks also differ among Neurospora, Drosophila, and mammals depending on their key transcriptional repression mechanisms (Hill-type repression or protein sequestration). Based on both theoretical and experimental studies, this review highlights the importance of careful modeling of transcriptional repression mechanisms in molecular circadian clocks.

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Section: Introductionmentioning

confidence: 99%

“…cell division) [29,30]. See [10][11][12] for a detailed review of this type of abstract phase-based models.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Protein sequestration versus Hill‐type repression in circadian clock models

Kim¹

2016

IET syst. biol.

107

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“…With these discoveries, computational models became even more critical to determining how a proposed mechanism would behave. Computational models proposed by Goldbeter (2003, 2008), (Gonze, 2011), and others provided support for the claim that a mechanism of this type could generate sustained oscillations. Computational models can show that a proposed mechanism is adequate to generate the specific feature of the phenomenon in question-sustained oscillation.…”

Section: Abstractly Representing a Mechanism To Explain Why It Producmentioning

confidence: 79%

Explaining features of fine-grained phenomena using abstract analyses of phenomena and mechanisms: two examples from chronobiology

Bechtel

2017

Synthese

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Explanations of biological phenomena such as cell division, protein synthesis or circadian rhythms commonly take the form of models of the responsible mechanisms. Recently philosophers of science have attempted to analyze this practice, presenting mechanisms as organized collections of parts performing operations that together produce the phenomenon. But in some cases what researchers seek to explain is not a general phenomenon, but a specific feature of a more fine-grained phenomenon. In some of these cases, it is not the model of the mechanism that performs the explanatory work. I consider a case in which the investigator offered an abstract representation of a fine-grained phenomenon to show why in had the feature in question. I consider a second case in which a researcher abstracted from the mechanism to identify a design principle that explains why the functioning mechanism exhibits a specific feature.

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“…In the accompanying paper, I have described mathematical models developed in the circadian field [25] and explained how these models are derived and how they are analyzed. I have shown how to compute bifurcation diagrams, entrainment, and phase response curves.…”

Section: Figurementioning

confidence: 99%

Modeling circadian clocks: Roles, advantages, and limitations

Gonze¹

2011

Open Life Sciences

Self Cite

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Circadian rhythms are endogenous oscillations characterized by a period of about 24h. They constitute the biological rhythms with the longest period known to be generated at the molecular level. The abundance of genetic information and the complexity of the molecular circuitry make circadian clocks a system of choice for theoretical studies. Many mathematical models have been proposed to understand the molecular regulatory mechanisms that underly these circadian oscillations and to account for their dynamic properties (temperature compensation, entrainment by light dark cycles, phase shifts by light pulses, rhythm splitting, robustness to molecular noise, intercellular synchronization). The roles and advantages of modeling are discussed and illustrated using a variety of selected examples. This survey will lead to the proposal of an integrated view of the circadian system in which various aspects (interlocked feedback loops, inter-cellular coupling, and stochasticity) should be considered together to understand the design and the dynamics of circadian clocks. Some limitations of these models are commented and challenges for the future identified.

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Modeling circadian clocks: From equations to oscillations

Cited by 35 publications

References 104 publications

Protein sequestration versus Hill‐type repression in circadian clock models

Protein sequestration versus Hill‐type repression in circadian clock models

Explaining features of fine-grained phenomena using abstract analyses of phenomena and mechanisms: two examples from chronobiology

Modeling circadian clocks: Roles, advantages, and limitations

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