Active shape oscillations of giant vesicles with cyclic closure and opening of membrane necks

Reaction-diffusion systems encapsulated within giant unilamellar vesicles (GUVs) can lead to shape oscillations of these vesicles as recently observed for the bacterial Min protein system. This system contains two Min proteins, MinD and MinE, which periodically attach to and detach from the GUV membranes, with the detachment being driven by ATP hydrolysis. Here, we address these shape oscillations within the theoretical framework of curvature elasticity and show that they can be understood in terms of a spontaneous curvature that changes periodically with time. We focus on the simplest case provided by a attachment-detachment kinetics that is laterally uniform along the membrane. During each oscillation cycle, the vesicle shape is transformed from a symmetric dumbbell with two subcompartments of equal size to an asymmetric dumbbell with two subcompartments of different size, followed by the reverse, symmetry-restoring transformation. This sequence of shapes is first analyzed within the spontaneous curvature model which is then extended to the area-difference-elasticity model by decomposing the spontaneous curvature into a local and nonlocal component. For both symmetric and asymmetric dumbbells, the two subcompartments are connected by a narrow membrane neck with a circular waistline. The radius of this waistline undergoes periodic oscillations, the time dependence of which can be reasonably well fitted by a single Fourier mode with an average time period of 56 s.