Periodicity, Mixed-Mode Oscillations, and Multiple Timescale in a Phosphoinositide-Rho GTPase Network

While rhythmic contractile behavior is prevalent on the cortex of living cells, current experimental observation and mechanistic understanding primarily tackle a small subset of dynamical behavior including excitable or periodic events that can be described by simple activator-delayed inhibitor mechanisms. In this work we found that the oscillatory activation of Rho GTPase in nocodazole-treated mitotic rat basophilic leukemia (RBL) cells exhibited both simple and complex mixed-mode oscillations, with periodicity ranging from 30 sec to 5 min. Complex mixed-mode oscillations require at least two instability-generating mechanisms. We show that Rho oscillations at the fast timescale (20-30 sec) is regulated by phosphatidylinositol (3,4,5)-trisphosphate (PIP3) via an activator-delayed inhibitor mechanism, while the period of the slow reaction (minutes) is regulated by phosphatidylinositol 4-phosphate (PI(4)P) via an activator-substrate depletion mechanism where replenishment of phosphatidylinositol (4,5)-bisphosphate (PI(4,5)P2) is rate-limiting. Conversion from simple to complex oscillations could be induced by modulating PIP3 metabolism or membrane contact site dynamics. In particular, a period-doubling intermediate can be captured by PTEN depletion. Both period doubling and mixed-mode oscillations are intermediate states towards chaos. Collectively, these results suggest that phosphoinositide-Rho GTPase signaling network is poised at the edge of chaos and small parameter changes in the phosphoinositide metabolism network could confer cells the flexibility to rapidly transit into a number of ordered states with different periodicities.