### G$\beta$ mediated diffusive coupling synchronizes actin oscillators in cell motility

Alexandra Jilkine

Department of Applied & Computational Math & Statistics

University of Notre Dame

At the cortex of *Dictyostelium*, the actin cytoskeleton localizes in discrete patches which have been shown to oscillate at different phases. Recent findings suggest that the spatial coordination of actin oscillators is regulated by the G protein subunit G$\beta$, which diffuses rapidly throughout the cell. Upon G$\beta$ sequestration, the following phenomena are observed: (1) higher fraction of actin patches becomes oscillatory; (2) phase difference between different sectors becomes smaller. To understand these observations, we model each actin patch as a conditional oscillator, which is governed by an excitable activator-inhibitor model coupled by bulk diffusion of G$\beta$. Assuming that G$\beta$ promotes the actin activator Arp2/3 in each actin patch, we find that actin oscillations can emerge when the G$\beta$ concentration is low. We show that spatial heterogeneity of G$\beta$ can lead to phase differences in actin oscillators. We consider how additional spatial coupling by Arp2/3 can influence spatial patterning in this system.