Arnold tongue entrainment reveals dynamical principles of the embryonic segmentation clock

Abstract

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.