Cell Stiffness-Mediated Mechanochemical Waves in Three-Dimensional Tissues

Tissue development, physiological or pathological, commonly involves stiffness alterations in the constituent cells. Here, we develop a three-dimensional (3D) active vertex model incorporating mechanical feedback from extracellular signal-regulated kinase (ERK) to explore mechanochemical waves in tissues with varying cell stiffness. Combining theory and simulations, we show that rich cell oscillations, mediated by cell stiffness and its spatial heterogeneity, can arise from mechanochemical instability. Increasing cell stiffness promotes the long-range force transmission and synchronization of collective waves, which exhibit robustness against cell heterogeneity of both size and stiffness. These mechanochemical waves can propagate around the locally stiffened inclusions or traverse stiff walls but retain their intrinsic modes. We further generate and interpret the ERK edge wave in 3D multicellular spheroids with stiffness variation, consistent with previous experiments. Our work uncovers the multifaceted roles of mechanics in self-organized mechanochemical dynamics within 3D multicellular tissues.