Developmental Biology Unit, European Molecular Biology Laboratory, Heidelberg 69117, Germany.
Department of Physics, McGill University, Montreal, QC H3A 2T8, Canada.
Proc Natl Acad Sci U S A. 2024 Sep 3;121(36):e2401604121. doi: 10.1073/pnas.2401604121. Epub 2024 Aug 27.
Synchronization of coupled oscillators is a universal phenomenon encountered across different scales and contexts, e.g., chemical wave patterns, superconductors, and the unison applause we witness in concert halls. The existence of common underlying coupling rules defines universality classes, revealing a fundamental sameness between seemingly distinct systems. Identifying rules of synchronization in any particular setting is hence of paramount relevance. Here, we address the coupling rules within an embryonic oscillator ensemble linked to vertebrate embryo body axis segmentation. In vertebrates, the periodic segmentation of the body axis involves synchronized signaling oscillations in cells within the presomitic mesoderm (PSM), from which somites, the prevertebrae, form. At the molecular level, it is known that intact Notch-signaling and cell-to-cell contact are required for synchronization between PSM cells. However, an understanding of the coupling rules is still lacking. To identify these, we develop an experimental assay that enables direct quantification of synchronization dynamics within mixtures of oscillating cell ensembles, for which the initial input frequency and phase distribution are known. Our results reveal a "winner-takes-it-all" synchronization outcome, i.e., the emerging collective rhythm matches one of the input rhythms. Using a combination of theory and experimental validation, we develop a coupling model, the "Rectified Kuramoto" (ReKu) model, characterized by a phase-dependent, nonreciprocal interaction in the coupling of oscillatory cells. Such nonreciprocal synchronization rules reveal fundamental similarities between embryonic oscillators and a class of collective behaviors seen in neurons and fireflies, where higher-level computations are performed and linked to nonreciprocal synchronization.
耦合振荡器的同步是一种普遍存在于不同尺度和背景下的现象，例如化学波模式、超导体以及我们在音乐厅中看到的齐鸣掌声。共同的基础耦合规则的存在定义了普遍性类别，揭示了看似不同的系统之间的基本共性。因此，确定任何特定环境中的同步规则都至关重要。在这里，我们研究了与脊椎动物胚胎体轴分割相关的胚胎振荡器集合内的耦合规则。在脊椎动物中，周期性的体轴分割涉及到前体节中细胞内同步的信号振荡，前体节是未来的脊椎骨。在分子水平上，已知完整的 Notch 信号和细胞间接触对于 PSM 细胞之间的同步是必需的。然而，对于耦合规则的理解仍然缺乏。为了识别这些规则，我们开发了一种实验测定方法，该方法能够直接定量振荡细胞混合物中的同步动力学，对于这些混合物，初始输入频率和相位分布是已知的。我们的结果揭示了一种“胜者通吃”的同步结果，即出现的集体节奏与输入节奏之一匹配。通过理论和实验验证的结合，我们开发了一种耦合模型，即“整流 Kuramoto”（ReKu）模型，其特征是在振荡细胞的耦合中存在相位依赖的、非互易相互作用。这种非互易同步规则揭示了胚胎振荡器和一类在神经元和萤火虫中看到的集体行为之间的基本相似性，其中更高层次的计算是在非互易同步的基础上进行的。
