标题： 顶点模型中的曲线边增加组织流动性 显示英文标题

标题： Curved edges in the vertex model increase tissue fluidity

摘要： 顶点模型对上皮组织的顶面进行建模，通过镶嵌来表示组织的顶面，多边形代表细胞，边代表细胞间的连接。 力学特性由一个能量描述，该能量受每个细胞的目标面积和周长偏离的影响。 已经证明，目标周长 p0 控制着固体到流体的相变：当目标周长较小时，重排存在能量障碍，而当目标周长较大时，细胞可以自由重排，组织可以像液体一样流动。 一种常见的简化方法是使用直线边来模拟连接。 然而，杨-拉普拉斯方程指出，界面应为圆弧，曲率等于相邻细胞之间压力差除以界面张力。 在此，我们研究了包含曲线边如何改变顶点模型的力学特性和单个细胞的平衡形状。 重要的是，我们展示了曲线边如何将固液相变点从$p0 = 3.81$移动到$p0 = 3.73$，使得组织在传统模型中使用直线边的情况下更早发生流体化。 显示英文摘要

摘要： The Vertex Model for epithelia models the apical surface of the tissue by a tiling, with polygons representing cells and edges representing cell-cell junctions. The mechanics are described by an energy governed by deviations from a target area and perimeter for each cell. It has been shown that the target perimeter, p0, governs a solid-to-fluid phase transition: when the target perimeter is low there is an energy barrier to rearrangement, and when it is high cells may rearrange for free and the tissue can flow like a liquid. One simplification often made is modelling junctions using straight edges. However, the Young-Laplace equation states that interfaces should be circular arcs, with the curvature being equal to the pressure difference between the neighbouring cells divided by the interfacial tension. Here, we investigate how including curved edges alters the mechanical properties of the vertex model and equilibrium shape of individual cells. Importantly, we show how curved edges shift the solid-to-fluid transition point, from $p0 = 3.81$ to $p0 = 3.73$, allowing tissues to fluidise sooner than in the traditional model with straight edges.