Collective motion of epithelial cells along a wrinkled 3D-buckled hydrogel

Abstract

Epithelial cells migrate autonomously by aligning and inducing a collective motion. Controlling the collective motion of epithelial cells in geometrically confined environments is important for understanding physiological processes such as wound healing and self-organized morphogenesis. However, collective migration under a three-dimensional (3D) curved surface resembling living epithelial tissue has not yet been explored. In this study, we investigated the collective motion of a 3D-buckled polyacrylamide (PAAm) gel that mimics the shape of folds and wrinkles of epithelial tissue to understand the geometric effects of collective motion. We found that the velocity correlation in the space near the hydrogel boundary showed a periodic change that correlated with the wrinkled folding of the hydrogel pattern. Furthermore, the characteristic length of the velocity correlation increased proportionally with the wavelength of wrinkled folding. These observations indicated that the hydrogel pattern could steer the collective motion of epithelial cells over long distances. Our study also suggests that the wrinkled design of the hydrogel is a versatile platform for studying the geometric effect of a curved surface on complex epithelial cell dynamics.

Fig. 1. Epithelial cell monolayer on 3D-buckled hydrogel. (a) Schematic of a 3D-buckled hydrogel. (b) Mechanical properties of PAAm gel. (b, left) Schematic of tensile testing and tensile stress–strain curves of PAAm gel. (b, right) Young’s modulus was calculated from the initial slope of the plot for each sample. (c–e) Fluorescent microscopic images of the 3D-buckled hydrogel. Representative folded pattern with a peeling width of 600 μm and crosslinking density of 1 mol%. The wavelength λ is defined as the peak-to-peak distance. (f) The mean curvature of the concave (blue) and convex (red) sides of the wrinkled patterns with various wavelengths λ. (g) Microscopic image of MDCK epithelial cell monolayer far from the wrinkled patterns (white line) and near the wrinkled patterns (green line). Scale bars: 200 μm. (h) Velocity field of collective motion of MDCK cells near the wrinkled patterns. Green arrows indicate the velocity field v(x,t). (i) Power spectrum density (PSD) of the velocity field of MDCK cells, analyzed using the velocity field at a point far from the wrinkled pattern of the hydrogel. The data from three independent experiments are shown as different colored curves.

Fig. 2. Velocity field of epithelial cell monolayer along the tangential direction and the normal direction of 3D-buckled hydrogel. (a) Schematic of tangential direction along the wrinkle pattern. The wave-like deformation of the folded hydrogel has a wavelength (λ) of 1008.4 μm. (b) Schematic of normal direction along the hydrogel pattern. (c and d) Tangential velocity v_T(x,t) near the wrinkle pattern (c) and far from the wrinkle pattern (d). The white arrowhead in (c) indicates the position showing the greater speed of v_T locally on the concave side. (e and f) Normal velocity v_N(x,t) near the wrinkle pattern (e) and far from the wrinkle pattern (f).

Fig. 3. The autocorrelation function of velocity in the tangential direction and normal direction along the 3D-buckled hydrogel. (a–d) The ACF of tangential velocity v_T(x,t) near the wrinkled pattern (a and b) and far from the wrinkle pattern (c and d). (a and c) The ACF of v_T(x,t) and (b and d) the plot of the ACF extracted at Δt = 0. (e–h) The ACF of normal velocity v_N(x,t) near the wrinkle pattern, near the wrinkled pattern (e and f), and far from the wrinkle pattern (g and h). (e and g) The ACF of v_N(x,t) and (f and h) the plot of the ACF extracted at Δt = 0.

Fig. 4. The linear dependence of velocity correlation length on the wavelength of folded hydrogel pattern. (a) The characteristic length of the tangential velocity (k⁻¹_T) and (b) the characteristic length of the normal velocity (k⁻¹_N) at various wrinkled patterns. In each figure, from left to right, k⁻¹_T and k⁻¹_N in the vicinity of the pattern (near the wrinkle pattern, left), 500 μm farther away (intermediate region, middle) and 1 mm farther away (far from the wrinkle pattern, right) are shown. The statistical analysis was carried out using λ = 500–550 μm as the standard, and significant differences were found when λ = 1100–1150 μm was reached. The p-value was determined by Student's t-test (*p < 0.05, n.s. represents no significant difference). The black line is drawn by the least-square fitting.