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In vertebrate embryos, a posterior unsegmented tissue called the presomitic mesoderm (PSM) becomes rhythmically and sequentially segmented into transient multicellular blocks called somites. A population of cellular oscillators locally coupled by Notch signalling generates waves of gene expression that sweep through the PSM from posterior to anterior. An opposing moving wavefront records each temporally periodic signal and converts it into permanent spatially periodic patterns, prefiguring the position of each new somite boundary. Signaling gradients regulate the position of the moving wavefront and thereby somite length. How these three elements interact at the molecular level to drive boundary formation and cell specification remains incompletely understood. In this work, single-cell genomics technologies, in particular gene expression and chromatin accessibility modalities, were exploited using zebrafish as a model organism. Custom experimental methods were developed to produce sequencing data of posterior embryonic tissues. The PSM exhibits continuous tissue dynamics in which cells are advected through space while undergoing progressive molecular changes, naturally coupling spatial position with developmental time. To place the reconstructed gene expression changes obtained in the sequencing data in a spatial context, we developed a Bayesian variational inference framework that uses gene expression profiles to infer a latent tissue-referenced spatial coordinate. Low-dimensional representations of the sequencing data revealed a putative coupling between cell cycle progression and somitogenesis. Cell-cycle phase analysis showed a reduction in S-phase proportions and a concomitant increase in G1 along the PSM, linking cell cycle progression with PSM maturation. An additional cell cycle regulation was observed in nascent somites coupled to cell specification. Analysis on mutant embryos for the wavefront gene tbx6 showed that somite formation machinery modulates cell cycle progression in the anterior PSM in concert with cell specification. Previous perturbations of signaling gradients suggested the existence of a spatially defined location of irreversible somite commitment within the PSM. Chromatin accessibility analysis along the inferred spatial axis revealed progressive and overlapping chromatin modules, suggesting a combinatorial regulatory grammar underlying PSM maturation. A mid-PSM transition toward anterior somitic programs was identified, consistent with experimental observations. A dissection of the regulatory logic of the wavefront gene ripply1 was performed. CRISPR-mediated deletions of accessible regions at the ripply1 locus, combined with motif profiling, supports a model in which ripply1 expression emerges from the coordinated activity of chromatin regulatory elements that integrate oscillatory signal from the clock, positional information from gradients, and commitment cues from the wavefront, enabling precise and robust somite bou