Cellular Potts — Surface Tension Cell Sorting

Temperature T: 10

J(A-A) adhesion: 5

J(B-B) adhesion: 5

J(A-B) adhesion: 20

J(cell-medium): 15

Target area λ: 100

Area penalty κ: 1.0

Step: 0

Energy: —

High J(A-B) vs J(A-A),J(B-B)
→ cell sorting (DAH)

■ Type A ■ Type B
■ Medium

Differential Adhesion Hypothesis (Steinberg 1963): Cell sorting emerges purely from thermodynamic minimization of surface energy. Cells with stronger homotypic adhesion engulf cells with weaker.
Hamiltonian: H = Σ J(σᵢ,σⱼ)(1−δ) + κ Σₛ (aₛ−A₀)² — interface energy + area conservation.
Metropolis rule: copy spin with prob min(1, exp(−ΔH/T)). Higher T → more fluctuations, less sorting.
Key prediction: if J(A-B) > J(A-A), J(B-B) → A surrounds B (lower overall surface energy). Confirmed in zebrafish germ layers.

Cellular Potts Model — Surface Tension Cell Sorting