Many organs are formed through folding of an epithelium. This change in shape is usually attributed to tissue heterogeneities, for example, local apical contraction. In contrast, compressive stresses have been proposed to fold a homogeneous epithelium by buckling. While buckling is an appealing mechanism, demonstrating that it underlies folding requires measurement of the stress field and the material properties of the tissue, which are currently inaccessible in vivo. Here, we show that monolayers of identical cells proliferating on the inner surface of elastic spherical shells can spontaneously fold. By measuring the elastic deformation of the shell, we infer the forces acting within the monolayer and its elastic modulus. Using analytical and numerical theories linking forces to shape, we find that buckling quantitatively accounts for the shape changes of our monolayers. Our study shows that forces arising from epithelial growth in three-dimensional confinement are sufficient to drive folding by buckling.

许多器官是通过上皮折叠形成的。这种形状变化通常归因于组织异质性，例如局部心尖收缩。相比之下，已经提出压缩应力通过屈曲折叠均匀的上皮。虽然屈曲是一种吸引人的机制，但证明它是折叠的基础需要测量应力场和组织的材料特性，而这些特性目前在体内无法获得. 在这里，我们表明在弹性球壳内表面增殖的相同细胞的单层可以自发折叠。通过测量壳的弹性变形，我们推断作用在单层内的力及其弹性模量。使用将力与形状联系起来的分析和数值理论，我们发现屈曲定量地解释了我们单层的形状变化。我们的研究表明，三维约束中上皮生长产生的力足以通过屈曲驱动折叠。