Math Biology Seminar: Leah Keshet

A mutually inhibitory Rac-Rho circuit is emerging as a central, regulatory hub that can affect the shape and of eukaryotic cells. Rac and Rho are members of the Rho-family GTPases that regulate cell polarization and motility by controlling assembly and contraction of the cytoskeleton. Recent experimental manipulation of the amounts of Rac and Rho or their regulators (GEFs, GAPs, GDIs) have been shown to bias the prevalence of typical cell shapes and transitions between those shapes. 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 correspond to 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, in principle, take on any of these discrete fates depending on its environment or stimuli. Our methods are based on local perturbation analysis (a kind of nonlinear stability analysis), and an approximation of nonlinear feedback by sharp switches (step functions). 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, not just network topology. (Joint work with William R Holmes, Vanderbilt University)