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First-order synchronization transition in a large population of strongly coupled relaxation oscillators.

ABSTRACT: Onset and loss of synchronization in coupled oscillators are of fundamental importance in understanding emergent behavior in natural and man-made systems, which range from neural networks to power grids. We report on experiments with hundreds of strongly coupled photochemical relaxation oscillators that exhibit a discontinuous synchronization transition with hysteresis, as opposed to the paradigmatic continuous transition expected from the widely used weak coupling theory. The resulting first-order transition is robust with respect to changes in network connectivity and natural frequency distribution. This allows us to identify the relaxation character of the oscillators as the essential parameter that determines the nature of the synchronization transition. We further support this hypothesis by revealing the mechanism of the transition, which cannot be accounted for by standard phase reduction techniques.

SUBMITTER: Calugaru D

PROVIDER: S-EPMC7531889 | biostudies-literature | 2020 Sep

REPOSITORIES: biostudies-literature

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First-order synchronization transition in a large population of strongly coupled relaxation oscillators.

Călugăru Dumitru D Totz Jan Frederik JF Martens Erik A EA Engel Harald H

Science advances 20200923 39

Onset and loss of synchronization in coupled oscillators are of fundamental importance in understanding emergent behavior in natural and man-made systems, which range from neural networks to power grids. We report on experiments with hundreds of strongly coupled photochemical relaxation oscillators that exhibit a discontinuous synchronization transition with hysteresis, as opposed to the paradigmatic continuous transition expected from the widely used weak coupling theory. The resulting first-or ...[more]

PMID: 32967828

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Project description:BackgroundThe biochemical oscillator that controls periodic events during the Xenopus embryonic cell cycle is centered on the activity of CDKs, and the cell cycle is driven by a protein circuit that is centered on the cyclin-dependent protein kinase CDK1 and the anaphase-promoting complex (APC). Many studies have been conducted to confirm that the interactions in the cell cycle can produce oscillations and predict behaviors such as synchronization, but much less is known about how the various elaborations and collective behavior of the basic oscillators can affect the robustness of the system. Therefore, in this study, we investigate and model a multi-cell system of the Xenopus embryonic cell cycle oscillators that are coupled through a common complex protein, and then analyze their synchronization ability under four different external stimuli, including a constant input signal, a square-wave periodic signal, a sinusoidal signal and a noise signal.ResultsThrough bifurcation analysis and numerical simulations, we obtain synchronization intervals of the sensitive parameters in the individual oscillator and the coupling parameters in the coupled oscillators. Then, we analyze the effects of these parameters on the synchronization period and amplitude, and find interesting phenomena, e.g., there are two synchronization intervals with activation coefficient in the Hill function of the activated CDK1 that activates the Plk1, and different synchronization intervals have distinct influences on the synchronization period and amplitude. To quantify the speediness and robustness of the synchronization, we use two quantities, the synchronization time and the robustness index, to evaluate the synchronization ability. More interestingly, we find that the coupled system has an optimal signal strength that maximizes the synchronization index under different external stimuli. Simulation results also show that the ability and robustness of the synchronization for the square-wave periodic signal of cyclin synthesis is strongest in comparison to the other three different signals.ConclusionsThese results suggest that the reaction process in which the activated cyclin-CDK1 activates the Plk1 has a very important influence on the synchronization ability of the coupled system, and the square-wave periodic signal of cyclin synthesis is more conducive to the synchronization and robustness of the coupled cell-cycle oscillators. Our study provides insight into the internal mechanisms of the cell cycle system and helps to generate hypotheses for further research.

Dataset Information

First-order synchronization transition in a large population of strongly coupled relaxation oscillators.

Publications

First-order synchronization transition in a large population of strongly coupled relaxation oscillators.

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