Pulsating Voronoi tissue ●

A confluent cell monolayer as a periodic Voronoi tessellation (Li, Lei & Ma, PNAS 2025). Each cell carries a pulsating phase φ that breathes its preferred area a₀ = 1 + α·sin φ; cells move by overdamped descent of the shape energy. Raise the coupling J to synchronize the phases and watch the ±1 topological defects of the phase field annihilate.

Tissue shape

Target shape p₀ 3.90 Perimeter modulus ξ 1.00 Mobility μ 1.0

Pulsation

Mode Strength α 0.40 Period T₀ 20 Coupling J 0.080 Phase noise T_φ 0.05

Integration

Time step dt 0.020 Steps/frame 2 Cells N

Display

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Model

Cells are Voronoi regions of N points in a periodic box (L = √N, mean area 1). Energy E = Σ (aᵢ−a₀ᵢ)² + ξ(pᵢ−p₀ᵢ)²; overdamped motion ṙᵢ = μFᵢ with analytic Voronoi forces; phases by Kuramoto on the Voronoi graph. Forward Euler; defects = ±1 phase winding around Delaunay triangles. The rigidity transition sits near p₀ ≈ 3.81; synchronization near J* ≈ 0.06.