Modeling Cdc42 GTPase dynamics in the control of polarized growth
The conserved GTPase Cdc42 is a key regulator of cell polarity and morphogenesis that controls processes such as actin-cable polymerization and exocyst localization. In fission yeast, Cdc42 activation exhibits oscillatory dynamics at the two polar growth zones. Anticorrelated oscillations at the cell tips result from positive and delayed negative feedbacks and competition for Cdc42 activators. One of these activators, the guanine nucleotide exchange factor (GEF) Gef1, undergoes a phosphorylation–dephosphorylation cycle that regulates its localization to its site of action at the cell cortex. Cortical localization of Gef1 is hypothesized to be dependent on microtubule-based delivery of a phosphatase to the cell tips.
In this work, I used XPP to model the ordinary differential equations that describe the positive and negative feedbacks and the contribution of a constant level of active Gef1 to Cdc42 activation. Model parameters were tuned to generate oscillations that were dependent on achieving a threshold level of Gef1, which is consistent with experimental observations. At these parameters, phase plane analysis revealed the existence of stable, unstable,
and saddle point nodes and a limit cycle. Bifurcation analysis showed that the system exhibits saddle homoclinic orbit bifurcations that begin at a Hopf bifurcation point and end at the saddle node bifurcation.
To model the role of microtubules in Cdc42 oscillations, I included expressions generating a periodic source of phosphatase to activate Gef1 at the cell tips. The period during which microtubules contact and shrink away from the cell tips was approximated based on published data. The model showed that microtubule contact could maintain Gef1 levels at the cell tips sufficiently for oscillations to occur, and the oscillations were driven by the microtubule period. Changing the microtubule period and amplitude resulted in irregularities in the oscillations. These predictions can be experimentally studied by observing oscillations of active Cdc42 in mutants that have altered microtubule dynamics.