Analysis of a minimal Rho-GTPase circuit regulating cell shape

Networks of Rho-family GTPases regulate eukaryotic cell polarization and motility by controlling assembly and contraction of the cytoskeleton. The mutually inhibitory Rac-Rho circuit is emerging as a central, regulatory hub that can affect the shape and motility phenotype of eukaryotic cells. Recent experimental manipulation of the amounts of Rac and Rho or their regulators (guanine nucleotide-exchange factors, GTPase-activating proteins, guanine nucleotide dissociation inhibitors) have been shown to bias the prevalence of these different states and promote transitions between them. Here we show that part of this data can be understood in terms of inherent Rac-Rho mutually inhibitory dynamics. We analyze a spatio-temporal mathematical model of Rac-Rho dynamics to produce a detailed set of predictions of how parameters such as GTPase rates of activation and total amounts affect cell decisions (such as Rho-dominated contraction, Rac-dominated spreading, and spatially segregated Rac-Rho polarization). We find that in some parameter regimes, a cell can take on any of these three fates depending on its environment or stimuli. We also predict how experimental manipulations (corresponding to parameter variations) can affect cell shapes observed. Our methods are based on local perturbation analysis (a kind of nonlinear stability analysis), and an approximation of nonlinear feedback by sharp switches. We compare the Rac-Rho model to an even simpler single-GTPase ('wave-pinning') model and demonstrate that the overall behavior is inherent to GTPase properties, rather than stemming solely from network topology.