Living systems exhibit an unmatched complexity, due to countless and entangled interactions across scales. Here we aim to understand and gain control of a complex system, such as the segmentation timing of a developing mouse embryo, without a reference to these detailed interactions. To this end, we develop a coarse-grained approach in which theory guides the experimental identification of the system-level responses to entrainment, in the context of a network of coupled cellular oscillators that constitute the embryonic somite segmentation clock. We demonstrate period- and phase-locking of the embryonic system across a wide range of entrainment parameters, including higher-order coupling. These experimental quantifications allow to derive the phase response curve (PRC) and Arnold tongues of the system, revealing the essential dynamical properties of the embryonic segmentation clock. Our results indicate that at the macro-scale, the somite segmentation clock has characteristics of a highly non-linear oscillator close to a saddle-node on invariant cycle (SNIC) bifurcation and suggests the presence of long-term feedbacks. Combined, this coarse-grained theoretical-experimental approach reveals how we can derive simple, essential features of a highly complex dynamical system and hereby provides precise experimental control over the pace and rhythm of the somite segmentation clock.

Living systems exhibit an unmatched complexity, due to countless, entangled interactions across scales. Here, we aim to understand a complex system, that is, segmentation timing in mouse embryos, without a reference to these detailed interactions. To this end, we develop a coarse-grained approach, in which theory guides the experimental identification of the segmentation clock entrainment responses. We demonstrate period- and phase-locking of the segmentation clock across a wide range of entrainment parameters, including higher-order coupling. These quantifications allow to derive the phase response curve (PRC) and Arnold tongues of the segmentation clock, revealing its essential dynamical properties. Our results indicate that the somite segmentation clock has characteristics reminiscent of a highly non-linear oscillator close to an infinite period bifurcation and suggests the presence of long-term feedbacks. Combined, this coarse-grained theoretical-experimental approach reveals how we can derive simple, essential features of a highly complex dynamical system, providing precise experimental control over the pace and rhythm of the somite segmentation clock.

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