Biological oscillations are found ubiquitously in cells and are widely variable, with periods varying from milliseconds to months, and scales involving subcellular components to large groups of organisms. Interestingly, independent oscillators from different cells often show synchronization that is not the consequence of an external regulator. What is the underlying design principle of such synchronized oscillations, and can modeling show that the complex consequences arise from simple molecular or other interactions between oscillators? When biological oscillators are coupled with each other, we found that synchronization is induced when they are connected together through a positive feedback loop. Increasing the coupling strength of two independent oscillators shows a threshold beyond which synchronization occurs within a few cycles, and a second threshold where oscillation stops. The positive feedback loop can be composed of either double-positive (PP) or double-negative (NN) interactions between a node of each of the two oscillating networks. The different coupling structures have contrasting characteristics. In particular, PP coupling is advantageous with respect to stability of period and amplitude, when local oscillators are coupled with a short time delay, whereas NN coupling is advantageous for a long time delay. In addition, PP coupling results in more robust synchronized oscillations with respect to amplitude excursions but not period, with applied noise disturbances compared to NN coupling. However, PP coupling can induce a large fluctuation in the amplitude and period of the resulting synchronized oscillation depending on the coupling strength, whereas NN coupling ensures almost constant amplitude and period irrespective of the coupling strength. Intriguingly, we have also observed that artificial evolution of random digital oscillator circuits also follows this design principle. We conclude that a different coupling strategy might have been selected according to different evolutionary requirements.
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