  "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.
