Cellular timing heterogeneity regulates phase transitions in living matter

Rigidity transitions govern tissue organization in ways reminiscent of inert materials. Yet, living tissues are composed of active units with autonomous timing mechanisms, raising the question whether microscopic cellular timing distribution influences collective mechanical states. Here we identify heterogeneity in cellular timescales as a heritable parameter, regulating rigidity transitions in embryonic tissues. Lineage tracking and quantitative mechanical analysis reveal that zebrafish morphogenesis starts with a tissue rigidity collapse occurring at maximal cell cycle length heterogeneity. This heterogeneity arises from size-dependent stochastic differences in resource allocation, with resource availability defining the cell cycle length. Such differences are inherited across generations, amplifying and structuring tissue-wide cell cycle length heterogeneity. Experiments and large-scale 3D simulations identify an optimum level of cellular timing variability at which cell-cell contact remodelling is spatially coordinated driving timely and robustly the rigidity transition. These findings demonstrate that embryos exploit microscopic temporal disorder for timing and tuning tissue morphogenesis.