Tumor invasion as non-equilibrium phase separation

Tumor invasion depends upon properties of both cells and of the extracellular matrix (ECM). Despite ample evidence that cancer cells can modulate their material state during invasion, underlying biophysical mechanisms remain unclear. Here, we show the potential for coexistence of - and transition between - solid-like, fluid-like, and gas-like phases in invading breast cancer spheroids. Epithelial spheroids are nearly jammed and solid-like in the core but unjam at the periphery to invade as a fluid-like collective. Conversely, post-metastatic spheroids are unjammed and fluid-like in the core and - depending on ECM density - can further unjam and invade as gas-like single cells, or re-jam to invade as a fluid-like collective. A novel jamming phase diagram predicts material phases that are superficially similar to inanimate systems at thermodynamic equilibrium, but here arising in living systems, which exist far from equilibrium. We suggest that non-equilibrium phase separation may provide a unifying physical picture of tumor invasion. TWO-SENTENCE SUMMARYUsing tumor spheroids invading into an engineered three-dimensional matrix, we show here that the cellular collective exhibits coexistent solid-like, fluid-like, and gas-like phases. The spheroid interior develops spatial and temporal heterogeneities in material phase which, depending upon cell type and matrix density, ultimately result in a variety of phase separation patterns at the invasive front, as captured by a jamming phase diagram.