Dynamical characteristics of the LEGI, Turing-like and Wave-pining polarity models.

(A) Top: topology of interaction of LEGI model. Color coding and arrows as in Fig 1A. Bottom: corresponding bifurcation diagram and the respective parameter organization in signal absence. Simulations have been performed using Eq 18, and ku = k−u = 2s−1, kv = k−v = 1s−1, kw = k−w = 1μM−1s−1. (B), (C) same as in (A) but for Turing and Wave-pinning models, respectively. The simulations of the Turing model correspond to Eqs (16) and (20), with a1 = 2.5, a2 = 0.7, and for the Wave-pinning model, Eqs (2) and (16) and parameters as in Fig 1B. In (A)-(C), shaded region: parameter organization, TC: Transcritical bifurcation, PB: pitchfork bifurcation, SNPB: saddle-node; u/w are membrane bound, and v—cytosolic component, ulocal: local variable associated with u from LPA analysis, line description as in Fig 1B. (D) Quasi-potential landscapes calculated for the LEGI model (Eq 19) subjected to a transient signal. Landscapes in absence and maximal signal strength are shown. Transitions in signal presence/absence: green/black arrows. Coloured contour maps: landscape projection in uL-uR plane. (E) Corresponding instantaneous phase portraits and system’s trajectory (as in Fig 1G). Black circles: stable steady states. Transitions in signal presence/absence: green/black arrows. (F) Same as in (E) only for the Wave-pinning model. Grey circles: saddles; black squares: IHSS.