A kinematic equation for the morphogenetic reproducibility of an animal
摘要
It is intriguing how cell positioning is regulated during animal development to achieve reproducible morphogenesis under genetic or environmental perturbations. In this study, we track single-cell spatiotemporal dynamics in over 2,000 C. elegans embryos subjected to diverse perturbations. By analyzing the inheritance of cell position along developmental lineages, we uncover ubiquitous negative-feedback “canals” that prevent the propagation of positional noise, thereby ensuring morphogenetic reproducibility. Examining cell kinematic parameters reveals that cell migration velocity underlies the negative-feedback regulation. The velocity dynamics across cell generations are described by a self-similar equation characterized by a single parameter φ (the golden ratio) that quantifies velocity adjustment, suggesting an inherent program recurrently employed by cells to attain their expected positions. Further analysis shows that φ = 0.618 represents the theoretical optimum, enabling an expected zero net noise accumulation and thus along-lineage conservation of cell velocity. Deviation from this self-similar equation predicts hatching failure (AUC = 0.89), and reveals a set of cytoskeleton-enriched genes required for its maintenance. In summary, by revealing a conservation principle of cell kinematics in C. elegans embryos, this study establishes a novel kinematic-mechanical framework for investigating animal morphogenesis, highlighting a golden-ratio-embedded natural design adaptable to general dynamic systems for noise control.
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