Fig. 1. Morphology of human mammary gland organoids depends on the mechanical interaction with the ECM.

a, Primary cells from reduction mammoplasty are seeded in collagen I gels and allowed to grow for up to 20 days. As a function of the attachment of the matrix, different morphologies are obtained. Scale bars, 100 μm. b, Organoids behave like liquids. After collagen hydrolysis by collagenase treatment, branches flow into the organoid body within a few minutes. Scale bar, 50 μm. c, Organoids grown in fluorescent collagen are completely surrounded by a layer of compacted collagen. Scale bar, 50 μm. d, To characterize the branch shape, we introduce the shape index α defined in terms of the axial and circumferential curvatures, namely, ${\kappa }_Z={\partial }_Z^{2}R/{\left[1+{\left({\partial }_{Z}R\right)}^2\right]}^{\frac{3}{2}}\text{and}{\kappa }_{\varphi }=-R^{-1}/{\left[1+{\left({\partial }_{Z}R\right)}^2\right]}^{\frac{1}{2}},$ respectively (Supplementary Section B1). Here, R ≡ R(z) refers to the local tube radius as a function of the axial coordinate z. To avoid irregular shapes of the branch tip, the integration region was taken at a distance of a = 30 μm from the tip. The upper bound b = 100 μm corresponds to the typical size of the alveoli on days 12–14. e, Effect of several biochemical perturbations on the development of organoids grown in floating gels. Calyculin A increases contractility, marimastat inhibits matrix metalloproteinases and HECD-1 antibody blocks cell–cell adhesion. f, Time evolution of average branch shape index α and overall organoid size (n_branches = 215, 95, 211 and 119 and n_organoids = 33, 23, 28 and 24 for control, marimastat, calyculin A and HECD-1, respectively). The shaded regions correspond to ±s.e. g, To determine the mechanical interaction between the branch tip and ECM, we ablate a 30-μm-high, 100-μm-wide and 1-μm-thick ECM region near the branch tip. Cylindrical branches recoil within 1 s away from the cut, revealing pulling tension (top); in contrast, round alveoli expand towards the cut, showing compressive ECM forces (bottom). The pink bar represents the ablated region (100 μm wide). Arrows, optical flow. Scale bar, 50 μm. Far right, recoil speed of the branch tip as a function of the shape index.