Principles that govern competition or co-existence in Rho-GTPase driven polarization
Rho-GTPases are master regulators of polarity establishment and cell morphology. Positive feedback enables concentration of Rho-GTPases into clusters at the cell cortex, from where they regulate the cytoskeleton. Different cell types reproducibly generate either one (e.g. the front of a migrating cell) or several clusters (e.g. the multiple dendrites of a neuron), but the mechanistic basis for uni-polar or multi-polar outcomes is unclear. The design principles of Rho-GTPase circuits are captured by reaction-diffusion models based on conserved aspects of Rho-GTPase biochemistry. Some such models display rapid winner-takes-all competition between clusters, yielding a unipolar outcome. Other models allow prolonged co-existence of clusters. We derive a \"saturation rule\" general to all relevant models that governs the timescale of competition, and thereby predicts whether the system will generate uni-polar or multi-polar outcomes. We suggest that the saturation rule is a fundamental property of the Rho-GTPase polarity machinery, regardless of the specific feedback mechanism.