Cell strain-stiffening drives cell breakout from embedded spheroids

Understanding how cells escape from embedded spheroids requires a mechanical framework linking stress generation within cells, across cells, and between cells and the surrounding extracellular matrix (ECM). We develop such a framework by coupling a 3D vertex model of a spheroid to a fibrous ECM network and deriving a 3D Cauchy stress tensor for deformable polyhedral cells, enabling direct cell-level stress quantification in three dimensions. We analyze maximum shear stress in solid-like and fluid-like spheroids: solid-like spheroids exhibit broader stress distributions and radial stress gradients, while fluid-like spheroids show lower stresses with weak spatial organization. Cell shape anisotropy is not generically aligned with principal stress directions, indicating that morphology alone is an unreliable proxy for mechanical state. We further demonstrate strain stiffening at the single-cell level, where elongation produces nonlinear increases in maximum shear stress, allowing boundary cells in otherwise low-stress, fluid-like spheroids to transiently generate forces sufficient to remodel the matrix. To connect strain-induced stress amplification to invasion modes, we introduce an extended 3D vertex model with explicit, tunable cell-cell adhesion springs. In this minimal mechanical framework, single-cell breakout results from strain stiffening combined with reduced adhesion, whereas multi-cell streaming additionally requires anisotropic adhesion strengthened along the elongation axis and weakened orthogonally. Together, these results identify distinct mechanical pathways coupling cell strain, stress amplification, and adhesion organization to spheroid invasion.