Fig 4. Comparison of the polarization stability in systems with local and nonlocal upregulating interactions, but identical cellular geometries and initial conditions (for each value of the geometric disorder).

The magnitude of stochastic noise equals η₀ = 0.1 in all cases. (a1) illustrates a polarized initial condition in a tissue with small geometric disorder ϵ₀ = 0.45. (a2) and (a3) show the steady-state angular distributions of dipoles in the same tissue with LA-NLI and NLA-NLI mechanisms, respectively. The same quantities are depicted in (b1), (b2) and (b3), but in tissue with large geometric disorder ϵ₀ = 0.6. Loss of angular coherence in (b3), indicates that the absence of nonlocal upregulating interactions makes polarity susceptible to stochastic noises in disordered tissues.