Arnold tongue entrainment reveals dynamical principles of the embryonic 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.

Imaging the onset of oscillatory signaling dynamics during mouse embryo gastrulation.

A fundamental requirement for embryonic development is the coordination of signaling activities in space and time. A notable example in vertebrate embryos is found during somitogenesis, where gene expression oscillations linked to the segmentation clock are synchronized across cells in the presomitic mesoderm (PSM) and result in tissue-level wave patterns. To examine their onset during mouse embryo development, we studied the dynamics of the segmentation clock gene Lfng during gastrulation. To this end, we established an imaging setup using selective plane illumination microscopy (SPIM) that enables culture and simultaneous imaging of up to four embryos ('SPIM- for-4'). Using SPIM-for-4, combined with genetically encoded signaling reporters, we detected the onset of Lfng oscillations within newly formed mesoderm at presomite stages. Functionally, we found that initial synchrony and the first ∼6-8 oscillation cycles occurred even when Notch signaling was impaired, revealing similarities to previous findings made in zebrafish embryos. Finally, we show that a spatial period gradient is present at the onset of oscillatory activity, providing a potential mechanism accounting for our observation that wave patterns build up gradually over the first oscillation cycles.

ES cell-derived presomitic mesoderm-like tissues for analysis of synchronized oscillations in the segmentation clock.

Somites are periodically formed by segmentation of the anterior parts of the presomitic mesoderm (PSM). In the mouse embryo, this periodicity is controlled by the segmentation clock gene Hes7, which exhibits wave-like oscillatory expression in the PSM. Despite intensive studies, the exact mechanism of such synchronous oscillatory dynamics of Hes7 expression still remains to be analyzed. Detailed analysis of the segmentation clock has been hampered because it requires the use of live embryos, and establishment of an in vitro culture system would facilitate such analyses. Here, we established a simple and efficient method to generate mouse ES cell-derived PSM-like tissues, in which Hes7 expression oscillates like traveling waves. In these tissues, Hes7 oscillation is synchronized between neighboring cells, and the posterior-anterior axis is self-organized as the central-peripheral axis. This method is applicable to chemical-library screening and will facilitate the analysis of the molecular nature of the segmentation clock.