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Abstract

The cells of our body are compartmentalized by biomembranes and vesicles, which consist of molecular bilayers with a thickness of a few nanometers and represent two-dimensional fluids. Due to their fluidity, the bilayer membranes can easily remodel their composition, shape, and topology. Here, we focus on their topology and transformations between different topologies via fission and fusion processes. In general, these topological transformations can be characterized by changes in the Euler characteristic and in the topological genus. Fission processes proceed via the closure and cleavage of membrane necks as recently demonstrated for giant unilamellar vesicles (GUVs) and for unilamellar nanovesicles assembled in silico. Neck cleavage is controlled by constriction forces that compress the neck and provide a general physical mechanism for membrane fission. Fusion processes proceed via the adhesion of two membranes and by the formation of a fusion pore, which has the same shape as a membrane neck. In fact, when two membranes fuse, they undergo the same sequence of shapes as during fission but in reversed order. However, the ‘local surgery,’ necessary to form the fusion pore, involves alternative molecular pathways as reviewed here for tension-induced fusion. Multispherical vesicles, doped with membrane proteins that drive homotypic fusion, can be used to form high genus vesicles, which are accessible to experimental studies.