Supporting Information for Collective transitions from orbiting to matrix invasionin three-dimensional multicellular spheroids

Coordinated cell rotation along a curved matrix interface can sculpt epithelial tissues into spherical morphologies. Subsequently, radially oriented invasion of multicellular strands or branches can occur by local remodeling of the confining matrix. These symmetry-breaking transitions emerge from the dynamic reciprocity between cells and matrix but remain poorly understood. Here, we show that epithelial cell spheroids collectively transition from circumferential orbiting to radial invasion via bidirectional interactions with the surrounding matrix curvature. Initially, spheroids exhibit an ellipsoidal shape but become rounded as orbiting occurs. In turn, orbiting along sharper curvature results in locally stronger contractile tractions, which gradually align collagen fibers in the radial direction. Thus, the initially elongated morphology primes the matrix towards subsequent invasion of two to four strands that are roughly aligned with the major axis. We then show that orbiting can be arrested and invasion can be reversed using osmotic pressure. We also investigate coordinated orbiting in mosaic spheroids, showing a small fraction of cells with weakened cell-cell adhesions can impede collective orbiting but still invade into the matrix. Altogether, this work elucidates how symmetry-breaking in tissue morphogenesis is governed by the interplay of collective migration and the local curvature of the cell-matrix, with relevance for embryonic development and tumor progression.