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.Author summary: Cell morphology is a critical determinant of cell function, and the conserved Rho-family GTPases (Cdc42, Rac, Rho, or Rop in plants) are key regulators of cell morphology. Rho-GTPases self-organize by concentrating into clusters at the cortex, and several mathematical models have been proposed that capture the essential features of such pattern formation. However, it has been unclear how such systems reliably generate either a single cluster (unipolar outcome) or multiple clusters (multipolar outcome). In this paper, we show that a broad class of models for Rho-GTPase polarization all exhibit the ability to switch between a regime in which rapid winner-takes-all competition between clusters yields unipolar outcomes and a regime in which competition is so slow that multipolar outcomes occur at biologically relevant timescales. We find that the switch in model behavior follows a surprisingly simple rule, and elucidate the fundamental principles that underpin that rule. Our theoretical study explains how the same biochemical system can robustly yield unipolar or multipolar outcomes, and makes experimentally testable predictions.