  Plasma membrane tubes are ubiquitous in cellular membranes and in the
membranes of intracellular organelles. They play crucial roles in trafficking,
ion transport, and cellular motility. The formation of plasma membrane tubes
can be due to localized forces acting on the membrane or by curvature-induced
by membrane-bound proteins. Here, we present a mathematical framework to model
cylindrical tubular protrusions formed by proteins that induce anisotropic
spontaneous curvature. Our analysis revealed that the tube radius depends on an
effective tension that includes contributions from the bare membrane tension
and the protein-induced curvature. We also found that the length of the tube
undergoes an abrupt transition from a short, dome-shaped membrane to a long
cylinder and this transition is characteristic of a snapthrough instability.
Finally, we show that the snapthrough instability depends on the different
parameters including coat area, bending modulus, and extent of protein-induced
curvature. Our findings have implications for tube formation due to BAR-domain
proteins in processes such as endocytosis, t-tubule formation in myocytes, and
cristae formation in mitochondria.
