We found evidence of dynamic scaling in the spreading of Madin-Darby canine kidney (MDCK) cell monolayer, which can be characterized by the Hurst exponent $\alpha =0.86$ and the growth exponent $\beta =0.73$, and theoretically and experimentally clarified the mechanism that governs the contour shape dynamics. Dynamic scaling refers to the roughness of the surface scales, both spatially and temporally. During the spreading of the monolayer, it is known that so-called leader cells generate the driving force and lead the other cells. Our time-lapse observations of cell behavior showed that these leader cells appeared at the early stage of the spreading and formed the monolayer protrusion. Informed by these observations, we developed a simple mathematical model that included differences in cell motility, cell-cell adhesion, and random cell movement. The model reproduced the quantitative characteristics obtained from the experiment, such as the spreading speed, the distribution of the increment, and the dynamic scaling law. Analysis of the model equation shows that the model can reproduce different scaling laws from $(\alpha =0.5,\beta =0.25)$ to $(\alpha =0.9,\beta =0.75)$, where the exponents $\alpha$ and $\beta$ are determined by two dimensionless quantities determined by the microscopic cell behavior. From the analytical result, parameter estimation from the experimental results was achieved. The monolayer on the collagen-coated dishes showed a different scaling law, $\alpha =0.74,\beta =0.68$, suggesting that cell motility increased ninefold. This result was consistent with the assay of the single-cell motility. Our study demonstrated that the dynamics of the contour of the monolayer were explained by the simple model, and we propose a mechanism that exhibits the dynamic scaling property.

中文翻译：

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在扩散上皮单层的轮廓中观察到的动态缩放特性的机制

我们发现了 Madin-Darby 犬肾 (MDCK) 细胞单层扩散过程中动态缩放的证据，其特征在于 Hurst 指数 $\alpha =0.86$ 和增长指数 $\beta =0.73$，并从理论上和实验上阐明了控制轮廓形状动力学的机制。动态缩放是指表面尺度在空间和时间上的粗糙度。在单层铺展期间，已知所谓的前导细胞产生驱动力并引导其他细胞。我们对细胞行为的延时观察表明，这些前导细胞出现在扩散的早期阶段并形成单层突起。根据这些观察结果，我们开发了一个简单的数学模型，其中包括细胞运动、细胞间粘附和随机细胞运动的差异。该模型再现了从实验中获得的定量特征，如铺展速度、增量分布和动态标度规律。$(\alpha =0.5,\beta =0.25)$ 到 $(\alpha =0.9,\beta =0.75)$，其中指数 $\alpha$ 和 $\beta$由微观细胞行为决定的两个无量纲量决定。根据分析结果，实现了根据实验结果的参数估计。涂有胶原蛋白的盘子上的单层显示出不同的缩放规律，$\alpha =0.74,\beta =0.68$，表明细胞运动增加了九倍。该结果与单细胞运动性的测定一致。我们的研究表明，单层轮廓的动力学可以通过简单的模型来解释，并且我们提出了一种表现出动态缩放特性的机制。