Cell-level mechanical heterogeneity promotes rigidity in confluent tissues

Intra-tumor heterogeneity is one of the hallmarks of cancer, which describes the phenotypic differences among cells in a tumor or cellular collective. While genetic heterogeneity has been an intense focus of study, how mechanical variations among cells influence tissue mechanics is not well understood. Here, we investigate the effect of cell-to-cell mechanical heterogeneity on the overall bulk mechanics of a confluent 2d tissue using a vertex model-based approach. We find that the rigidity of a confluent tissue depends on overall statistical properties of single-cell properties such as mean and variance, rather than the specific functional form of its distribution. A single universal parameter - the fraction of mechanically rigid cells, f_r, can be used to characterize the tissue mechanical state. As f_r is tuned, the tissue undergoes a rigidity percolation at a critical threshold of f_r. Remarkably, this rigidity percolation occurs at a much lower value than what is required for rigid-cell to form a spanning cluster. A mean field model is proposed to explain the discrepancy between rigidity and contact percolations.