Rigidity transitions in simple models of confluent cells have been a powerful organizing principle in understanding the dynamics and mechanics of dense biological tissue. In this work we explore the interplay between geometry and rigidity in two-dimensional vertex models confined to the surface of a sphere. By considering shapes of cells defined by perimeters whose magnitude depends on geodesic distances and areas determined by spherical polygons, the critical shape index in such models is affected by the size of the cell relative to the radius of the sphere on which it is embedded. This implies that cells can collectively rigidify by growing the size of the sphere, i.e., by tuning the curvature of their domain. Finite-temperature studies indicate that cell motility is affected well away from the zero-temperature transition point.

中文翻译：

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基于形状的融合组织模型中曲率和刚度的相互作用

简单的汇合细胞模型中的刚性转变已成为理解致密的生物组织的动力学和力学的强有力的组织原理。在这项工作中，我们探索了局限于球体表面的二维顶点模型中几何和刚度之间的相互作用。通过考虑由周长定义的像元形状，其大小取决于测地距离和球形多边形确定的面积，此类模型中的临界形状指数受像元尺寸相对于其所嵌入的球体半径的影响。这意味着细胞可以通过增大球体的大小（即通过调整其域的曲率）来集体硬化。有限温度研究表明，远离零温度转变点时，细胞运动受到很大影响。