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Sensitivity to external signals and synchronization properties of a non-isochronous auto-oscillator with delayed feedback.

ABSTRACT: For auto-oscillators of different nature (e.g. active cells in a human heart under the action of a pacemaker, neurons in brain, spin-torque nano-oscillators, micro and nano-mechanical oscillators, or generating Josephson junctions) a critically important property is their ability to synchronize with each other. The synchronization properties of an auto oscillator are directly related to its sensitivity to external signals. Here we demonstrate that a non-isochronous (having generation frequency dependent on the amplitude) auto-oscillator with delayed feedback can have an extremely high sensitivity to external signals and unusually large width of the phase-locking band near the boundary of the stable auto-oscillation regime. This property could be used for the development of synchronized arrays of non-isochronous auto-oscillators in physics and engineering, and, for instance, might bring a better fundamental understanding of ways to control a heart arrythmia in medicine.

SUBMITTER: Tiberkevich VS

PROVIDER: S-EPMC3902486 | biostudies-literature | 2014

REPOSITORIES: biostudies-literature

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Sensitivity to external signals and synchronization properties of a non-isochronous auto-oscillator with delayed feedback.

Tiberkevich Vasil S VS Khymyn Roman S RS Tang Hong X HX Slavin Andrei N AN

Scientific reports 20140127

For auto-oscillators of different nature (e.g. active cells in a human heart under the action of a pacemaker, neurons in brain, spin-torque nano-oscillators, micro and nano-mechanical oscillators, or generating Josephson junctions) a critically important property is their ability to synchronize with each other. The synchronization properties of an auto oscillator are directly related to its sensitivity to external signals. Here we demonstrate that a non-isochronous (having generation frequency d ...[more]

PMID: 24464086

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Project description: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.

Dataset Information

Sensitivity to external signals and synchronization properties of a non-isochronous auto-oscillator with delayed feedback.

Publications

Sensitivity to external signals and synchronization properties of a non-isochronous auto-oscillator with delayed feedback.

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