The emerging collective behaviors during embryogenesis play an important role in precise and reproducible morphogenesis. An important question in the study of collective behavior is what rule underlies the emerging pattern. Here we use the Drosophila embryo as a test tube to study this question. We focus on the nuclear array without membrane separation on the embryo periphery from the nuclear cycle (NC) 11 to NC14. After live imaging with light sheet microscopy, we extract the nuclear trajectory, speed, and internuclear distance with an automatic nuclear tracing method. We find that the nuclear speed shows a period of standing waves along the anterior-posterior (AP) axis after each metaphase as the nuclei collectively migrate towards the embryo poles and partially move back. And the maximum nuclear speed dampens by 38% in the second half of the standing wave. Moreover, the nuclear density is 35% higher in the middle than the pole region of the embryo during the S phase of NC11-NC14. To find mechanical rules controlling the collective motion and packing patterns of the nuclear array, we use the deep neural network (DNN) to learn the force field from data. We find two potential strong nuclear-age-dependent force fields, i.e., the repulsive or attractive force field. Simulations with the particle-based model indicate that only if the net internuclear force is attractive and increases with distance, the pseudo-synchronous mitotic wave in a nuclear array with lower nuclear density in embryo poles can drive the collective motion with the damped standing wave of the nuclear speed, and the collective nuclear motion, in turn, maintains the non-uniform nuclear density.

中文翻译：

---

有吸引力的核间作用力驱动果蝇胚胎中核阵列的集体行为

胚胎发生过程中出现的集体行为在精确和可再现的形态发生中起重要作用。集体行为研究中的一个重要问题是，什么规则是新兴模式的基础。在这里，我们使用果蝇胚胎作为试管来研究这个问题。我们专注于从核周期（NC）11到NC14在胚胎外围没有膜分离的核阵列。在用光片显微镜进行实时成像后，我们使用自动核示踪方法提取了核轨迹，速度和核间距离。我们发现，在每个中期之后，随着核共同朝着胚胎极移并部分向后移动，核速显示出沿前后轴（AP）轴的驻波周期。在驻波的后半段，最大核速度衰减了38％。此外，在NC11-NC14的S期，中部的核密度比胚胎的极区高35％。为了找到控制核阵列集体运动和堆积模式的机械规则，我们使用深度神经网络（DNN）从数据中学习力场。我们发现了两个潜在的依赖核年龄的强力场，即排斥力场或吸引力场。基于粒子模型的仿真表明，只有净核间力具有吸引力并且随着距离的增加而增加，胚极中核密度较低的核阵列中的伪同步有丝分裂波才能够通过阻尼的驻波来驱动集体运动。核速和集体核运动，