Speaker
Description
Vertex models have been widely used to study mechanical phase transitions in confluent tissues. In the classical formulation, the normalized cell perimeter, or shape index, serves as a key geometric control parameter: increasing the shape index drives a transition from solid-like to fluid-like tissue behavior as cells become more elongated. Here, we extend the passive energy of the vertex model by introducing an average curvature-energy contribution for each cell.
The local curvature at each vertex is estimated by fitting a circle through the vertex and its two neighboring vertices, with curvature defined as the inverse radius of this circle. The resulting curvature is weighted by the area of the triangle formed by the three vertices, providing a local measure of cell-boundary bending.
Our simulations show that curvature energy strongly modifies tissue phase behavior. Increasing the curvature contribution fluidizes the tissue, as reflected by enhanced cell diffusion, and gives rise to a distinct dynamical regime beyond the conventional shape-index-controlled transition. This new regime is characterized by increased heterogeneity in cell morphology and the emergence of long-range bent structures across the tissue.
These results suggest that curvature is not merely a local geometric descriptor, but can act as an additional mechanical control parameter governing collective tissue organization and dynamics. Our work provides a generalized vertex-model framework in which curvature-mediated mechanics can drive emergent tissue-scale structures and alter the solid–fluid transition in epithelial tissues.
