标题： 自组织驱动干细胞衍生类器官的对称性破缺、尺度和临界生长转变 显示英文标题

标题： Self-organization drives symmetry-breaking, scaling, and critical growth transitions in stem cell-derived organoids

摘要： 发育组织中空间模式和有序生长的出现是一个显著特征。 虽然对称性破缺和尺度定律支配这些过程，但细胞如何协调空间模式与尺寸调节仍不清楚。 在这里，我们结合定量成像、具有自组织反应边界的一维激活子-抑制子模型以及早期小鼠发育的体外模型，研究二维（2D）原肠胚样结构中的中胚层模式形成。 我们表明，菌落大小决定了对称性：小菌落（半径约为100微米）会自发打破对称性，而较大的菌落保持中心对称，这与尺寸依赖的位置信息和模型预测一致。 中胚层区域面积随着菌落大小按幂律稳健地扩展，与细胞密度无关，表明细胞能够感知并响应原肠胚样结构的大小。 时间推移成像揭示了一种双相生长规律：早期的幂律扩张随后是指数停滞，标志着一种动力学相变。 这些动态在不同尺寸中是保守的，反映了物理系统中观察到的临界性特征，其中自组织、尺度和边界反馈汇聚在一起。 我们的发现揭示了一个尺寸依赖的模式形成和生长控制的最小机制。 这一框架使得能够对自组织组织中的对称性破缺和尺度进行定量研究，为多细胞组织背后的物理原理提供了见解。 显示英文摘要

摘要： The emergence of spatial patterns and organized growth is a hallmark of developing tissues. While symmetry-breaking and scaling laws govern these processes, how cells coordinate spatial patterning with size regulation remains unclear. Here, we combine quantitative imaging, a Turing activator-repressor model with self-organized reactive boundaries, and in vitro models of early mouse development to study mesodermal pattern formation in two-dimensional (2D) gastruloids. We show that colony size dictates symmetry: small colonies (radius approximately 100 micrometers) spontaneously break symmetry, while larger ones remain centro-symmetric, consistent with size-dependent positional information and model predictions. The mesodermal domain area scales robustly with colony size following a power law, independent of cell density, indicating that cells sense and respond to gastruloid size. Time-lapse imaging reveals a biphasic growth law: an early power-law expansion followed by exponential arrest, marking a dynamical phase transition. These dynamics, conserved across sizes, reflect features of criticality seen in physical systems, where self-organization, scaling, and boundary feedback converge. Our findings uncover a minimal mechanism for size-dependent pattern formation and growth control. This framework enables quantitative investigation of symmetry-breaking and scaling in self-organizing tissues, offering insights into the physical principles underlying multicellular organization.