Relaxation dynamics in the self-propelled Voronoi model for epithelial monolayers

Cell monolayers and epithelial tissues display slow relaxation dynamics during the reversible transition between mesenchymal and epithelial cells, a phenomenon directly relevant to embryogenesis, tumor metastases, and wound healing. In active cells, persistent motion induces collective dynamics that significantly influence relaxation behavior. To better understand the role of persistence in cell relaxations, we perform extensive simulations and employ cage-relative measures to address the previously overlooked system size effects in model active cells. We identify the glass transition at various persistence values, demonstrating conventional near-equilibrium supercooled dynamics at low persistence. However, highly persistent cells exhibit distinctive intermittent dynamics associated with intermittent local T1 transitions, where cell velocity correlates over space with a characteristic length ζ. More significantly, we formulate a universal relationship predicting the global relaxation time based on the T1 transition and the spatial velocity correlation across a wide range of persistence values. Specifically, the relaxation time demonstrates a power-law dependence on the irreversible T1 transition rate, multiplied by exp(ζ). Here, ζ vanishes at small persistence in nearly equilibrated cells, and the irreversible T1 transition rate diminishes towards the mode-coupling glass transition point.