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Description
The active vertex model is a widely used framework for studying mechanical properties, phase transitions, cell topology, and tissue organization in developmental biology. In this work, we extend the classical formulation by introducing a curvature energy term that captures bending at cell edges through interactions between neighboring vertices. By assigning different target curvature values to cells, we investigate how curvature influences both tissue phase behavior and cell morphology.
Our simulations demonstrate that cellular curvature can strongly modulate tissue mechanics: it can fluidize solid tissues, solidify fluid-like tissues, and give rise to heterogeneous intermediate states. These findings highlight curvature as a mechanical regulator, capable of reorganizing tissue architecture and dynamics. This approach opens new directions for understanding the role of membrane bending and geometric constraints in tissue morphogenesis.