Abstract
Any cellular fission process is completed when the neck connecting almost-separate membrane compartments is severed. This crucial step is somehow accomplished by proteins from the dynamin family, which polymerize into helical spirals around such necks. Much research has been devoted to elucidating the specifics of that somehow, but despite no shortage of ideas, the question is not settled. Pictorially obvious notions of strangling or pushing are difficult to render in mechanically precise terms. Moreover, because dynamin is a GTPase, it is tempting to speculate that it has a motor activity that assists the necessary severing action, but again the underlying mechanics is not obvious. We believe the difficulty to be the mechanically nontrivial nature of confining elastic filaments onto curved surfaces, for which efficient methods to conceptualize the associated forces and torques have only recently appeared. Here we investigate the implications of a conceptually simple yet mechanically challenging model: consider an elastic helical filament confined to a surface mimicking the neck between two membrane compartments, which we assume to take the shape of a catenoid. What can we say about the expected length of such adsorbed filaments, their shapes, and the forces they exert, as a function of the key parameters in the model? While real dynamin is surely more complex, we consider such a minimal model to be the indispensable baseline. Without knowing what such a model can and cannot explain, it is difficult to justify more complex mechanisms, or understand the constraints under which this machinery evolved in the first place.