Microtubes and nanotubes of a phospholipid bilayer membrane

We propose a theory describing the stable structure of a phospholipid bilayer in pure water involving a spherical mother vesicle with long thin tubular protrusion. It is considered that the phospholipid molecules are in general anisotropic with respect to the axis normal to the membrane and can orient in the plane of the membrane if the curvature field is strongly anisotropic. Taking this into account, the membrane free energy is derived starting from a single-molecule energy and using methods of statistical mechanics. By linking the description on the microscopic level with the continuum theory of elasticity we recover the expression for the membrane bending energy and obtain an additional (deviatoric) contribution due to the orientational ordering of the phospholipid molecules. It is shown that the deviatoric contribution may considerably decrease the phospholipid vesicle membrane free energy if the vesicle involves regions where the difference between the two principal curvatures is large (thin cylindrical protrusions and/or thin finite necks) and thereby yields a possible explanation for the stability of the long thin tubular protrusions of the phospholipid bilayer vesicles. We report on the experiment exhibiting a stable shape of the spherical phospholipid vesicle with a long thin tubular protrusion in pure water.