The vertex model is a useful mathematical model to describe the dynamics of epithelial cell sheets. However, existing vertex models do not distinguish contraction forces on the cell boundary from adhesion between cells, employing a single parameter to express both. In this paper, we introduce the rest length of the cell boundary and its dynamics into the existing vertex model, giving a novel formulation of the model that treats separately the contraction force and the strength of adhesion between cells. We apply this vertex model to the phenomenon of compartment boundary in the fruit fly pupa, recapturing the observation that increasing the strength of adhesion between cells straightens the compartment boundary, even though contraction forces at cell boundaries remain unchanged. We also discuss possibilities of the present vertex models by considering the stretching of a cell sheet by external forces.

中文翻译：

---

一种新的细胞顶点模型公式，可区分细胞边界处的收缩力和粘附强度

顶点模型是描述上皮细胞片动态的有用数学模型。然而，现有的顶点模型没有区分细胞边界上的收缩力和细胞之间的粘附力，使用单个参数来表达两者。在本文中，我们将细胞边界的静止长度及其动力学引入现有的顶点模型，给出了一种新的模型公式，该模型将收缩力和细胞之间的粘附强度分开处理。我们将此顶点模型应用于果蝇蛹中的隔室边界现象，重新观察到增加细胞之间的粘附强度会使隔室边界变直，即使细胞边界的收缩力保持不变。