A Symmetric Dual Feedback System Provides a Robust and Entrainable Oscillator

Maeda, Kazuhiro; Kurata, Hiroyuki

doi:10.1371/journal.pone.0030489

Cited by 12 publications

(11 citation statements)

References 49 publications

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“…In the RCO, the robust period and amplitude were simultaneously realized with high entrainability to the day-night cycle. This result is consistent with some previous works that the robustness increases flexibility or entrainability [16,21,49].…”

Section: Discussionsupporting

confidence: 93%

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Coupling protocol of interlocked feedback oscillators in circadian clocks

Rashid

Kurata

2020

J. R. Soc. Interface.

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Circadian rhythms (approx. 24 h) show the robustness of key oscillatory features such as phase, period and amplitude against external and internal variations. The robustness of Drosophila circadian clocks can be generated by interlocked transcriptional–translational feedback loops, where two negative feedback loops are coupled through mutual activations. The mechanisms by which such coupling protocols have survived out of many possible protocols remain to be revealed. To address this question, we investigated two distinct coupling protocols: activator-coupled oscillators (ACO) and repressor-coupled oscillators (RCO). We focused on the two coupling parameters: coupling dissociation constant and coupling time-delay. Interestingly, the ACO was able to produce anti-phase or morning–evening cycles, whereas the RCO produced in-phase ones. Deterministic and stochastic analyses demonstrated that the anti-phase ACO provided greater fluctuations in amplitude not only with respect to changes in coupling parameters but also to random parameter perturbations than the in-phase RCO. Moreover, the ACO deteriorated the entrainability to the day–night master clock, whereas the RCO produced high entrainability. Considering that the real, interlocked feedback loops have evolved as the ACO, instead of the RCO, we first proposed a hypothesis that the morning–evening or anti-phase cycle is more essential for Drosophila than achieving robustness and entrainability.

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Section: Discussionsupporting

confidence: 93%

“…It can provide robust oscillations in constant condition, but they are inflexible in a precise sense. Typically, simple negative feedback models alone cannot generate robustness with respect to various genetic and environmental perturbations [8,20,21].…”

Section: Introductionmentioning

confidence: 99%

Coupling protocol of interlocked feedback oscillators in circadian clocks

Rashid

Kurata

2020

J. R. Soc. Interface.

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“…In addition to system analysis, we developed the DDM-based DS simulator that solves the exact value of the DS without approximation, while the IDMs use approximate sensitivity values [ 22 , 23 ]. In principle, the accuracy of DDM outperforms IDM.…”

Section: Discussionmentioning

confidence: 99%

Robustness analysis of the detailed kinetic model of an ErbB signaling network by using dynamic sensitivity

et al. 2017

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The ErbB receptor signaling pathway plays an important role in the regulation of cellular proliferation, survival and differentiation, and dysregulation of the pathway is linked to various types of human cancer. Mathematical models have been developed as a practical complementary approach to deciphering the complexity of ErbB receptor signaling and elucidating how the pathways discriminate between ligands to induce different cell fates. In this study, we developed a simulator to accurately calculate the dynamic sensitivity of extracellular-signal-regulated kinase (ERK) activity (ERK*) and Akt activity (Akt*), downstream of the ErbB receptors stimulated with epidermal growth factor (EGF) and heregulin (HRG). To demonstrate the feasibility of this simulator, we estimated how the reactions critically responsible for ERK* and Akt* change with time and in response to different doses of EGF and HRG, and predicted that only a small number of reactions determine ERK* and Akt*. ERK* increased steeply with increasing HRG dose until saturation, while showing a gently rising response to EGF. Akt* had a gradual wide-range response to HRG and a blunt response to EGF. Akt* was sensitive to perturbations of intracellular kinetics, while ERK* was more robust due to multiple, negative feedback loops. Overall, the simulator predicted reactions that were critically responsible for ERK* and Akt* in response to the dose of EGF and HRG, illustrated the response characteristics of ERK* and Akt*, and estimated mechanisms for generating robustness in the ErbB signaling network.

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“…Use of MPS has revealed that negative feedback loops with multiple phosphorylations produce oscillators robust to parameter uncertainty [ 8 ]. The dual feedback model, a simplified version of the Drosophila PER-TIM feedback model [ 12 ], was found to be the most robust and entrainable among many feedback models with various connection logics [ 13 ].…”

Section: Introductionmentioning

confidence: 99%

“…A number of numerical studies have been reported for the biological oscillators and many of mathematical models are available from databases such as JWS Online [ 14 ], BioModels [ 15 , 16 ] and BioFNet [ 17 ]. Numerical analyses have revealed the mechanisms of how a variety of feedback structures produce robust oscillators [ 8 , 13 ] and identified critical kinetic parameters that are related to changes in the period and amplitude [ 9 , 11 ]. Although numerical simulations are useful for a quantitative understanding of how complicated biological oscillators behave, they do not provide explicit information on how the period, amplitude and their robustness depend on kinetic parameters.…”

Section: Introductionmentioning

confidence: 99%

Analytical study of robustness of a negative feedback oscillator by multiparameter sensitivity

Maeda

Kurata

2014

BMC Syst Biol

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BackgroundOne of the distinctive features of biological oscillators such as circadian clocks and cell cycles is robustness which is the ability to resume reliable operation in the face of different types of perturbations. In the previous study, we proposed multiparameter sensitivity (MPS) as an intelligible measure for robustness to fluctuations in kinetic parameters. Analytical solutions directly connect the mechanisms and kinetic parameters to dynamic properties such as period, amplitude and their associated MPSs. Although negative feedback loops are known as common structures to biological oscillators, the analytical solutions have not been presented for a general model of negative feedback oscillators.ResultsWe present the analytical expressions for the period, amplitude and their associated MPSs for a general model of negative feedback oscillators. The analytical solutions are validated by comparing them with numerical solutions. The analytical solutions explicitly show how the dynamic properties depend on the kinetic parameters. The ratio of a threshold to the amplitude has a strong impact on the period MPS. As the ratio approaches to one, the MPS increases, indicating that the period becomes more sensitive to changes in kinetic parameters. We present the first mathematical proof that the distributed time-delay mechanism contributes to making the oscillation period robust to parameter fluctuations. The MPS decreases with an increase in the feedback loop length (i.e., the number of molecular species constituting the feedback loop).ConclusionsSince a general model of negative feedback oscillators was employed, the results shown in this paper are expected to be true for many of biological oscillators. This study strongly supports that the hypothesis that phosphorylations of clock proteins contribute to the robustness of circadian rhythms. The analytical solutions give synthetic biologists some clues to design gene oscillators with robust and desired period.

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A Symmetric Dual Feedback System Provides a Robust and Entrainable Oscillator

Cited by 12 publications

References 49 publications

Coupling protocol of interlocked feedback oscillators in circadian clocks

Coupling protocol of interlocked feedback oscillators in circadian clocks

Robustness analysis of the detailed kinetic model of an ErbB signaling network by using dynamic sensitivity

Analytical study of robustness of a negative feedback oscillator by multiparameter sensitivity

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