Effects of the period mismatch on entrainment properties in two coupled genetic oscillators are studied. The entrainment is calculated with a phase reduction approach and a Floquet multiplier analysis, and their dependencies on coupling strength and the period ratio are investigated in two genetic oscillator models (smooth and relaxation oscillators). We find that the existence of the period  mismatch induces an enhancement of entrainment in both smooth and relaxation oscillators. By calculating Floquet multipliers, we show that the enhancement mechanism is based on the coupled oscillators which are in the vicinity of  bifurcation on limit cycle  .
Biological oscillators coordinate individual cellular components to function coherently and collectively. They are typically composed of multiple feedback loops, and period mismatch between them is unavoidable in biological implementations. We investigated the advantageous effect of the period mismatch in terms of synchronization against external stimuli (or trainability). Specifically, we numerically analyzed two fundamental genetic models, smooth and relaxation oscillators, on their trainability for different coupling strength and period ratio by the phase reduction and the Floquet multiplier analysis. We found that the period mismatch induces better entrainment in both oscillators; the enhancement occurred in the vicinity of the bifurcation on limit cycle . The optimal period ratio in the smooth oscillator for the enhanced trainability coincided with the experimentally observed ratio, which suggested the biological exploitation of the period mismatch. Although the origin of multiple feedback loops is often accounted for by the notion of passive robustness against perturbation, we here studied active benefits of the period mismatch on the efficiency of genetic oscillators. Our findings show qualitatively different perspective on the essentiality and inherent advantage of multiple loops in genetic oscillators .
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Effects of the period mismatch on entrainment properties in two coupled genetic oscillators are studied. The entrainment is calculated with a phase reduction approach and a Floquet multiplier analysis, and their dependencies on
Biological oscillators coordinate individual cellular components to function coherently and collectively. They are typically composed of multiple feedback loops, and period mismatch between them is unavoidable in biological implementations. We investigated the advantageous effect of the period mismatch in terms of synchronization against external stimuli (or trainability). Specifically, we numerically analyzed two fundamental genetic models, smooth and relaxation oscillators, on their trainability for different
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the period ratio are investigated in two genetic oscillator models (smooth and relaxation oscillators). We find that the existence of the
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ratio by the phase reduction and the Floquet multiplier analysis. We found that the period
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an enhancement of
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smooth and relaxation oscillators. By calculating Floquet multipliers, we show that the enhancement mechanism is based on the coupled oscillators which are
oscillators; the enhancement occurred
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the
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. The optimal period ratio in the smooth oscillator for the enhanced trainability coincided with the experimentally observed ratio, which suggested the biological exploitation of the period mismatch. Although the origin of multiple feedback loops is often accounted for by the notion of passive robustness against perturbation, we here studied active benefits of the period mismatch on the efficiency of genetic oscillators. Our findings show qualitatively different perspective on the essentiality and inherent advantage of multiple loops in genetic oscillators