Geometry of membrane fission

• Proteins employ shallow membrane wedging to create local “molecular” geometry of membrane fission.
• Protein complexes coordinate localized membrane wedging to produce highly curved membrane intermediates.
• Neck and hemifission intermediates adapt their shapes to minimize elastic stresses in lipid monolayers.
• Geometric catalysis is a synergistic action of protein and lipids in search for an optimal geometrical pathway of fission.

Cellular membranes define the functional geometry of intracellular space. Formation of new membrane compartments and maintenance of complex organelles require division and disconnection of cellular membranes, a process termed membrane fission. Peripheral membrane proteins generally control membrane remodeling during fission. Local membrane stresses, reflecting molecular geometry of membrane-interacting parts of these proteins, sum up to produce the key membrane geometries of fission: the saddle-shaped neck and hour-glass hemifission intermediate. Here, we review the fundamental principles behind the translation of molecular geometry into membrane shape and topology during fission. We emphasize the central role the membrane insertion of specialized protein domains plays in orchestrating fission in vitro and in cells. We further compare individual to synergistic action of the membrane insertion during fission mediated by individual protein species, proteins complexes or membrane domains. Finally, we describe how local geometry of fission intermediates defines the functional design of the protein complexes catalyzing fission of cellular membranes.