Mechanism underlying bistability induced by large spatial extent of polarity patches

Determine the mechanistic reason that increasing the spatial width σ of the Gaussian polarity activation patches used to update the polarity field in the phase-field crawling cell model causes the deterministic acceleration footprint F(x, v) on the two-state micropattern (two square basins connected by a narrow bridge) to become nearly bistable, and ascertain whether this effect is driven by activation of a broader set of boundary contour points that reduces persistent single-front polarization.

Background

The model represents cell polarity as a field updated by stochastic Gaussian patches added at boundary points with width σ, frequency τf, and amplitude distribution characterized by μβ and σ_β. Varying these parameters alters the inferred deterministic acceleration footprint F(x, v) that summarizes simulated trajectories.

When σ is increased substantially, simulations on the two-state micropattern do not produce the usual limit cycle but instead exhibit nearly bistable dynamics, with streamlines terminating in either basin. The authors hypothesize this may be due to spatially-extended patches activating more contour points, increasing the likelihood of activity away from the leading front and disrupting persistent single-front polarization, but the precise mechanism is not established.