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 unipolar or multipolar outcomes is unclear. The design principles of Rho-GTPase circuits are captured by two-component 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 investigate the behavior of a simple class of models and show that while the timescale of competition varies enormously depending on model parameters, a single factor explains a large majority of this variation. The dominant factor concerns the degree to which the maximal active GTPase concentration in a cluster approaches a "saturation point" determined by model parameters. We suggest that both saturation and the effect of saturation on competition reflect fundamental properties of the Rho-GTPase polarity machinery, regardless of the specific feedback mechanism, which predict whether the system will generate unipolar or multipolar outcomes.