We analyze the mechanical properties of three epithelial/mesenchymal cell lines (MCF-10A, MDA-MB-231, MDA-MB-436) that exhibit a shift in E-, N-and P-cadherin levels characteristic of an epithelial−mesenchymal transition associated with processes such as metastasis, to quantify the role of cell cohesion in cell sorting and compartmentalization. We develop a unique set of methods to measure cell-cell adhesiveness, cell stiffness and cell shapes, and compare the results to predictions from cell sorting in mixtures of cell populations. We find that the final sorted state is extremely robust among all three cell lines independent of epithelial or mesenchymal state, suggesting that cell sorting may play an important role in organization and boundary formation in tumours. We find that surface densities of adhesive molecules do not correlate with measured cell-cell adhesion, but do correlate with cell shapes, cell stiffness and the rate at which cells sort, in accordance with an extended version of the differential adhesion hypothesis (DAH). Surprisingly, the DAH does not correctly predict the final sorted state. This suggests that these tissues are not behaving as immiscible fluids, and that dynamical effects such as directional motility, friction and jamming may play an important role in tissue compartmentalization across the epithelial−mesenchymal transition. transgress even the strong lineage boundaries, invading adjacent tissues. Therefore, a question of immediate practical importance is what changes allow metastatic cells to break through these boundaries, or conversely, what prevents non-metastatic tumour cells from leaving the compartment? Moreover, it is a fundamental question if a solid tumour behaves sufficiently like a fluid that surface tension-like effects hold cancer cells back at the tumour boundary.Metastasis has been attributed to tumour cells losing epithelial characteristics and acquiring a more migratory mesenchymal phenotype [9][10][11]. This change known as the epithelial−mesenchymal transition (EMT) is typically accompanied by a loss of specific types of cellular adhesion. While epithelial cells are closely connected via various types of cell junctions such as adherens junctions and desmosomes that allow them to form organized cell layers in vivo and cell clusters in vitro, mesenchymal cells are less constrained, contacting only through focal points [11]. During EMT, the expression of E-cadherin decreases while the expression of N-cadherin and other cadherins increases [12][13][14]. This might be the molecular origin for the change in adhesiveness, although recent work highlights that different cadherins play vastly different roles in regulating intercellular forces and adhesion [15]. In addition, EMT also causes a down-regulation of the keratin cytoskeleton and a replacement with vimentin [16], which also hinders desmosome formation. This leads to secondary effects that modulate cell-cell adhesion. However, it remains unclear how these processes interact with boundary formation and compartment m...