Mechanical forces are critical for the emergence of diverse three-dimensional morphologies of multicellular systems. However, it remains unclear what kind of mechanical parameters at cellular level substantially contribute to tissue morphologies. This is largely due to technical limitations of live measurements of cellular forces. Here we developed a framework for inferring and modeling mechanical forces of cell-cell interactions. First, by analogy to coarse-grained models in molecular and colloidal sciences, we approximated cells as particles, where mean forces (i.e. effective forces) of pairwise cell-cell interactions are considered. Then, the forces were statistically inferred by fitting the mathematical model to cell tracking data. This method was validated by using synthetic cell tracking data resembling various in vivo situations. Application of our method to the cells in the early embryos of mice and the nematode Caenorhabditis elegans revealed that cell-cell interaction forces can be written as a pairwise potential energy in a manner dependent on cell-cell distances. Importantly, the profiles of the pairwise potentials were quantitatively different among species and embryonic stages, and the quantitative differences correctly described the differences of their morphological features such as spherical vs. distorted cell aggregates, and tightly vs. non-tightly assembled aggregates. We conclude that the effective pairwise potential of cell-cell interactions is a live measurable parameter whose quantitative differences can be a parameter describing three-dimensional tissue morphologies.

中文翻译：

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细胞间相互作用的有效机械势解释了早期胚胎发生过程中的三维形态

机械力对于多细胞系统的多种三维形态的出现至关重要。然而，目前尚不清楚细胞水平上什么样的机械参数对组织形态有显着贡献。这主要是由于细胞力实时测量的技术限制。在这里，我们开发了一个用于推断和建模细胞与细胞相互作用的机械力的框架。首先，通过类比分子和胶体科学中的粗粒度模型，我们将细胞近似为粒子，其中考虑成对细胞-细胞相互作用的平均力（即有效力）。然后，通过将数学模型拟合到细胞跟踪数据来统计推断力。该方法通过使用类似于各种体内情况的合成细胞跟踪数据进行了验证。将我们的方法应用于小鼠早期胚胎和线虫秀丽隐杆线虫中的细胞表明，细胞间相互作用力可以以依赖于细胞间距离的方式写成成对势能。重要的是，成对电位的分布在物种和胚胎阶段之间存在定量差异，并且定量差异正确地描述了它们形态特征的差异，例如球形与扭曲的细胞聚集体，以及紧密与非紧密组装的聚集体。我们得出的结论是，细胞与细胞相互作用的有效成对电位是一个实时可测量的参数，其定量差异可以是描述三维组织形态的参数。