Pattern formation in a coupled membrane-bulk reaction-diffusion model for intracellular polarization and oscillations

•A membrane-bulk model for cell polarization is analyzed in 3 different geometries.•In 1D, a PDE-ODE system exhibits pole-to-pole oscillations of polarity molecule Cdc42.•On the disk, symmetry-breaking instabilities cause rotating waves and Turing patterns.•Assuming a well-mixed bulk leads to a nonlocal PDE system on a 1D circular domain.•The effects of bulk and surface diffusion on spatio-temporal patterning are described.