We study the influence of cell-level mechanical heterogeneity in epithelial tissues using a vertex-based model. Heterogeneity in single cell stiffness is introduced as a quenched random variable in the preferred shape index(p 0 ) for each cell. We uncovered a crossover scaling for the tissue shear modulus, suggesting that tissue collective rigidity is controlled by a single parameter f r , which accounts for the fraction of rigid cells. Interestingly, the rigidity onset occurs at f r = 0.21, far below the contact percolation threshold of rigid cells. Due to the separation of rigidity and contact percolations, heterogeneity can enhance tissue rigidity and gives rise to an intermediate solid state. The influence of heterogeneity on tumor invasion dynamics is also investigated. There is an overall impedance of invasion as the tissue becomes more rigid. Invasion can also occur in the intermediate heterogeneous solid state and is characterized by significant spatial-temporal intermittency.

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Inspired by how cells pack in dense biological tissues, we design 2D and 3D amorphous materials that possess a complete photonic bandgap. A physical parameter based on how cells adhere with one another and regulate their shapes can continuously tune the photonic bandgap size as well as the bulk mechanical properties of the material. The material can be tuned to go through a solid-fluid phase transition characterized by a vanishing shear modulus. Remarkably, the photonic bandgap persists in the fluid phase, giving rise to a photonic fluid that is robust to flow and rearrangements. Experimentally this design should lead to the engineering of self-assembled nonrigid photonic structures with photonic bandgaps that can be controlled in real time via mechanical and thermal tuning.

While it is known that cells with differential adhesion tend to segregate and preferentially sort, the physical forces governing sorting and invasion in heterogeneous tumors remain poorly understood. To investigate this, we develop a composite hydrogel that uncouples matrix stiffness and collagen fiber density, mimicking changes in the stiffness of the tumor microenvironment, to explore how physical confinement influences individual and collective cell migration in 3D spheroids. The mechanical properties of the hydrogel can be tuned through crosslinking and crosslink reversal. Using this hydrogel system and computational Self-Propelled Voronoi modeling, we show that spheroid sorting and invasion into the matrix depend on the balance between cell-generated forces and matrix resistance. Sorting is driven by high confinement and reducing matrix stiffness triggers a collective fluidization of cell motion. Cell sorting, which depends on cell-cell adhesion, is crucial to this phenomenon, and burst-like migration does not occur for unsorted spheroids irrespective of matrix stiffness. The findings support a model where matrix stiffness modulates 3D spheroid sorting and unjamming in an adhesion-dependent manner, providing insights into the mechanisms of cell sorting and migration in the primary tumor and toward distant metastatic sites.