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Mechanism underlying dynamic scaling properties observed in the contour of spreading epithelial monolayer

We found evidence of dynamic scaling in the spreading of MDCK 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. 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 revealed that the model could reproduce the different scaling law from ${\alpha} = 0.5, {\beta} = 0.25$ to ${\alpha} = 0.9, {\beta} = 0.75$, and the exponents ${\alpha}, {\beta}$ were determined by the two indices: $\rho t$ and $c$. Based on 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 by 9 folds. 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 proposed a new mechanism that exhibits the dynamic scaling property.

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