Cell movement is crucial for morphogenesis in multicellular organisms. Growing embryos or tissues often expand isotropically, i.e., uniformly, in all dimensions. On the surfaces of these expanding environments, which we call "fields," cells are subjected to frictional forces and move passively in response. However, the potential roles of isotropically expanding fields in morphogenetic events have not been investigated well. Our previous mathematical simulations showed that a tissue was elongated on an isotropically expanding field (Imuta et al., 2014). However, the underlying mechanism remains unclarified, and how cells behave during tissue elongation was not investigated. In this study, we mathematically analyzed the effect of isotropically expanding fields using a vertex model, a standard type of multi-cellular model. We found that cells located on fields were elongated along a similar direction each other and exhibited a columnar configuration with nearly single-cell width. Simultaneously, it was confirmed that the cell clusters were also elongated, even though field expansion was absolutely isotropic. We then investigated the mechanism underlying these counterintuitive phenomena. In particular, we asked whether the dynamics of elongation was predominantly determined by the properties of the field, the cell cluster, or both. Theoretical analyses involving simplification of the model revealed that cell clusters have an intrinsic ability to asymmetrically deform, leading to their elongation. Importantly, this ability is effective only under the non-equilibrium conditions provided by field expansion. This may explain the elongation of the notochord, located on the surface of the growing mouse embryo. We established the mechanism underlying tissue elongation induced by isotropically expanding external environments, and its involvement in collective cell alignment with cell elongation, providing key insight into morphogenesis involving multiple adjacent tissues.

中文翻译：

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外部环境的各向同性扩张诱导组织伸长和集体细胞排列。

细胞运动对于多细胞生物的形态发生至关重要。生长中的胚胎或组织通常在所有维度上各向同性地、即均匀地膨胀。在我们称之为“场”的这些不断扩张的环境的表面上，细胞受到摩擦力的影响并被动地作为响应移动。然而，各向同性扩展场在形态发生事件中的潜在作用尚未得到很好的研究。我们之前的数学模拟表明，组织在各向同性扩展的场上被拉长（Imuta 等，2014）。然而，潜在的机制仍未阐明，并且没有研究细胞在组织伸长过程中的行为。在这项研究中，我们使用顶点模型（一种标准类型的多细胞模型）从数学上分析了各向同性扩展场的影响。我们发现位于场上的细胞沿彼此相似的方向被拉长，并呈现出接近单细胞宽度的柱状结构。同时，证实细胞簇也被拉长，即使场扩展是绝对各向同性的。然后，我们研究了这些违反直觉的现象背后的机制。特别是，我们询问了伸长的动力学是否主要由场、细胞簇或两者的性质决定。涉及模型简化的理论分析表明，细胞簇具有不对称变形的内在能力，从而导致它们的伸长。重要的是，这种能力仅在场扩展提供的非平衡条件下有效。这可以解释脊索的伸长，位于正在生长的小鼠胚胎表面。我们建立了由各向同性扩展的外部环境诱导的组织伸长的潜在机制，及其参与细胞伸长的集体细胞排列，为涉及多个相邻组织的形态发生提供了关键见解。