Necks are features of lipid membranes characterized by an uniquley large curvature, functioning as bridges between different compartments. These features are ubiquitous in the life-cycle of the cell and instrumental in processes such as division, extracellular vesicles uptake and cargo transport between organelles, but also in life-threatening conditions, as in the endocytosis of viruses and phages. Yet, the very existence of lipid necks challenges our understanding of membranes biophysics: their curvature, often orders of magnitude larger than elsewhere, is energetically prohibitive, even with the arsenal of molecular machineries and signalling pathways that cells have at their disposal. Using a geometric triality, namely a correspondence between three different classes of geometric objects, here we demonstrate that lipid necks are in fact metastable, thus can exist for finite, but potentially long times even in the absence of stabilizing mechanisms. This framework allows us to explicitly calculate the forces a corpuscle must overcome in order to penetrate cellular membranes, thus paving the way for a predictive theory of endo/exo-cytic processes.
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