Table 1. List of parameters, variables and their definitions.

The parameters with their values mentioned are held fixed throughout the paper. The control parameters, i.e. the geometric disorder ϵ₀, the length scale of the cooperative interactions λ, and the magnitude of elongation $\mathcal{E}$, are to be varied to explore the behavior of polarization in different regimes.

Parameters	Definition
f0 = 1	total concentration of F
g0 = 1	total concentration of G
κ = 10	formation rate
γ = 1	dissociation rate
α = 5	magnitude of cooperative formation
β = 5	magnitude of cooperative dissociation
η0 = 0.1	magnitude of stochastic noise
ℓ0 = 1	average length of cell-cell junctions
ϵ0: control param.	magnitude of geometric disorder
λ: control param.	lengthscale of cooperative interactions
$\mathcal{E}$: control param.	magnitude of elongation
Dynamical Variables	Definition
uij(t) & vji(t)	concentration of [Fi − Gj]
$\overline{P}\left(t\right)$	magnitude of average polarity
$\overline{Q}\left(t\right)$	average of the dipoles’ magnitudes
$\mathcal{O}\left(t\right)$	$\overline{P}\left(t\right)/\overline{Q}\left(t\right)$
ξ(t)	correlation length