Vesicle deformation by an axial load: From elongated shapes to tethered vesicles

A sufficiently large force acting on a;single point of the fluid membrane o f a flaccid phospholipid vesicle is known to cause the formation of-a narro w bilayer tube (tether). We analyze this;phenomenon by means of general mat hematical methods allowing us to determine the shapes of strongly deformed; vesicles including their stability. Starting from a free vesicle with an ax isymmetric, prolate equilibrium shape, we consider an axial load that pulls (or pushes) the poles of the vesicle apart. Arranging the resulting shapes of strained vesicles in dependence of the axial deformation and of the are a difference of monolayers, phase diagrams of stable shapes are presented c omprising prolate shapes with or without equatorial mirror symmetry. For re alistic values of membrane parameters, we study the force-extension relatio n of strained vesicles,and we demonstrate in detail, how the initially elon gated shape of an axially stretched vesicle transforms into a shape involvi ng a membrane tether, This tethering. transition may be continuous or disco ntinuous. If the free vesicle is mirror symmetric, the mirror symmetry is b roken as the tether forms. The stability analysis of tethered shapes reveal s that, for the considered vesicles,:the stable shape is always asymmetric (polar), i.e., it involves only a single tether on one side of the main ves icle body. Although a bilayer tube formed from a closed vesicle is not an i deal cylinder, We show that, for most practical purposes, it is safe to ass ume a cylindrical geometry of tethers, This analysis is supplemented by the documentation of a prototype experiment supporting our theoretical predict ions; It shows that::the currently accepted model for the description of li pid-bilayer elasticity (generalized bilayer: couple model) properly account s for the tethering phenomenon.