  We develop theory and computational methods to investigate particle
inclusions embedded within curved lipid bilayer membranes. We consider the case
of spherical lipid vesicles where inclusion particles are coupled through (i)
intramembrane hydrodynamics, (ii) traction stresses with the external and
trapped solvent fluid, and (iii) intermonolayer slip between the two leaflets
of the bilayer. We investigate relative to flat membranes how the membrane
curvature and topology augment hydrodynamic responses. We show how both the
translational and rotational mobility of protein inclusions are effected by the
membrane curvature, ratio of intramembrane viscosity to solvent viscosity, and
inter-monolayer slip. For general investigations of many-particle dynamics, we
also discuss how our approaches can be used to treat the collective diffusion
and hydrodynamic coupling within spherical bilayers.
