This work considers an expansion of a dense monolayer of cells: a collective multicellular phenomenon, where cells divide, grow, and maintain contacts with their neighbors. During migration, cells display complex behavior, adjusting both their division rate and their growth after division to the local mechanical environment. Experimental observations show that cells near the edge of the expanding monolayer are larger and move faster than cells deep inside the colony. To explain these observations and describe cell migration patterns, we formulate a spatio-temporal theoretical model for multicellular dynamics in terms of the cell area distribution; the model includes cell growth after division and effective pressure. Numerical simulations of the model predict both the speed of invasion and the width of the outer proliferative rim; these predictions are in a good agreement with experimental observations. Theoretical analysis yields the equation for density of cells and reveals a novel type of propagating front with compact support. The velocity of front propagation (monolayer expansion) is derived analytically and its dependence on all the relevant parameters is determined.

这项工作考虑了密集单层细胞的扩展：一种集体多细胞现象，其中细胞分裂、生长并保持与其邻居的联系。在迁移过程中，细胞表现出复杂的行为，根据局部机械环境调整其分裂率和分裂后的生长。实验观察表明，靠近扩张单层边缘的细胞比集落深处的细胞更大，移动速度更快。为了解释这些观察结果并描述细胞迁移模式，我们根据细胞面积分布为多细胞动力学制定了一个时空理论模型；该模型包括分裂后的细胞生长和有效压力。该模型的数值模拟预测了侵袭速度和外增殖边缘的宽度；这些预测与实验观察非常吻合。理论分析产生了细胞密度方程，并揭示了一种具有紧凑支撑的新型传播前沿。前向传播（单层膨胀）的速度通过分析推导出来，并确定其对所有相关参数的依赖性。