Tubular lipid membranes pulled from vesicles: Dependence of system equilibrium on lipid bilayer curvature

Conditions of joint equilibrium and stability are derived for a spherical lipid vesicle and a tubular lipid membrane (TLM) pulled from this vesicle. The obtained equations establish relationships between the geometric and physical characteristics of the system and the external parameters, which have been found to be controllable in recent experiments. In particular, the proposed theory shows that, in addition to the pressure difference between internal and external regions of the system, the variable spontaneous average curvature of the lipid bilayer (forming the TLM) also influences the stability of the lipid tube. The conditions for stability of the cylindrical phase of TLMs after switching off the external force that initially formed the TLM from a vesicle are discussed. The loss of system stability under the action of a small axial force compressing the TLM is considered.