Cell Polarity — Wave-Pinning (Mori-Jilkine-Edelstein-Keshet)

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Wave-Pinning Model of Cell Polarity

The Mori-Jilkine-Edelstein-Keshet (2008) model describes cell polarity via a bistable reaction-diffusion system with mass conservation. Active GTPase u (membrane-bound) and inactive v (cytosolic) interconvert: ∂u/∂t = Du·∇²u + f(u,v), ∂v/∂t = Dv·∇²v - f(u,v). The cubic kinetics f(u,v) = (k₀+u²/(K²+u²))·v - δu create bistability. A wave initiated at one end pins when mass depletion halts propagation, creating stable polarity — front half active (Cdc42/Rac), back half inactive.