标题： 3D顶点和Voronoi模型中边界行为的差异 显示英文标题

标题： Differences in boundary behavior in the 3D vertex and Voronoi models

摘要： 一个在生物组织建模中的重要开放问题是如何确定粗粒化的正确尺度，或者等价地，确定正确的自由度数量。对于融合的生物组织，顶点模型和Voronoi模型，它们仅在自由度的表示方式上有所不同，已被有效地用于预测行为，包括流体-固体相变和细胞组织分隔，这对生物功能很重要。然而，最近在二维系统中的工作表明，在两种组织类型之间的异型界面系统中，这两种模型可能存在差异，并且对三维组织模型的兴趣正在增长。因此，我们比较了三维顶点模型和Voronoi模型中两种细胞类型混合物的几何结构和动态排序行为。我们发现，尽管两种模型中的细胞形状指数表现出相似的趋势，但在边界处细胞中心与细胞取向之间的匹配在两种模型之间存在显著差异。我们证明这些宏观差异是由于边界处不同自由度表示引入的类似尖点的恢复力的变化造成的，并且Voronoi模型受到由自由度表示方式产生的力的更强约束。这表明顶点模型可能更适合具有异型接触的三维组织模拟。 显示英文摘要

摘要： An important open question in the modeling of biological tissues is how to identify the right scale for coarse-graining, or equivalently, the right number of degrees of freedom. For confluent biological tissues, both vertex and Voronoi models, which differ only in their representation of the degrees of freedom, have effectively been used to predict behavior, including fluid-solid transitions and cell tissue compartmentalization, which are important for biological function. However, recent work in 2D has hinted that there may be differences between the two models in systems with heterotypic interfaces between two tissue types, and there is a burgeoning interest in 3D tissue models. Therefore, we compare the geometric structure and dynamic sorting behavior in mixtures of two cell types in both 3D vertex and Voronoi models. We find that while the cell shape indices exhibit similar trends in both models, the registration between cell centers and cell orientation at the boundary are significantly different between the two models. We demonstrate that these macroscopic differences are caused by changes to the cusp-like restoring forces introduced by the different representations of the degrees of freedom at the boundary, and that the Voronoi model is more strongly constrained by forces that are an artifact of the way the degrees of freedom are represented. This suggests that vertex models may be more appropriate for 3D simulations of tissues with heterotypic contacts.