Cellular Potts Model
Cell sorting via differential adhesion hypothesis (Steinberg 1963)
Cellular Potts Model (CPM) simulates cell sorting through the differential adhesion hypothesis.
The Hamiltonian penalizes unlike-cell contacts:
H = Σ J(τ,τ') δ(σᵢ≠σⱼ) + λ Σ (A−A₀)²
Cells minimize energy via Metropolis Monte Carlo moves. When J(A-B) > J(A-A), J(B-B) — cells prefer same-type neighbors and sort into separate domains (engulfment or complete separation depending on ratios).
This explains why dissociated embryonic cells spontaneously re-sort by tissue type.