The topology design principles that determine the spatiotemporal dynamics of G-protein cascades

Small monomeric G-proteins control cellular behavior, cycling between inactive GDP-bound and active GTP-bound states. Activating and deactivating transitions are regulated by guanine nucleotide exchange factors (GEFs) and GTPase activating proteins (GAPs), respectively. G-proteins can control different GEF and GAP activities, thereby creating GTPase signaling cascades. Here, we characterize all 128 different wiring topologies of two-layer cascades, which include feedforward/feedback interactions and an auto-regulatory loop. Exclusion of "mirror" designs leaves 64 topologies, which are classified into eight groups. We demonstrate that eight different cascades in each group generate the same number of steady states and similar spatiotemporal dynamics. Two groups (featuring 16 topologies) can generate three distinct dynamics: (i) bistable switches, (ii) excitable behavior, and (iii) sustained oscillations, giving rise to propagating waves of G-protein activation switches and pulses. Four other groups can produce switch-like, bistable behaviors and trigger waves. The remaining two groups have a single steady state. This first, complete classification of all possible interaction circuitries systematically links topological design to the spatiotemporal dynamics of G-protein cascades, predicting and explaining experimentally observed behavior.