Theoretical analysis of the formation of membrane microtubes on axially strained vesicles

Abstract

The formation of membrane microtubes (tethers) was analyzed by a theoretical study of the shape changes of an axisymmetrical phospholipid vesicle caused by a pulling axial force applied at the vesicle poles. Equilibrium vesicle shapes were obtained by variationally seeking the minimum of the sum of membrane local and nonlocal bending energies at constant vesicle volume, membrane area, and the distance between the vesicle poles. The effect of axial force on vesicle shapes was studied by examining the shape behavior of prolate axisymmetrical vesicles with equatorial mirror symmetry. For a vesicle with a given relative volume, the resulting shapes reside within a given region of the phase diagram for this vesicle as a function of the distance between vesicle poles and the relative difference between the areas of the membrane layers. The upper limit of this region was obtained by a variational procedure for the determination of vesicle shapes that correspond, at given vesicle volume, membrane area, and difference between the areas of membrane layers, to the maximum distance between the vesicle poles. It was shown that for finite values of the ratio between the nonlocal and local bending moduli, at high enough axial force the vesicle shape exhibits an elongated tubular ending at each pole. The equation for the radius of such a tubular ending obtained by the rigorous treatment presented matches the equation that has previously been used as an approximation in analyses of tether formation methods for the determination of membrane bending moduli. Furthermore, it is predicted that below a certain critical value of the ratio between the two bending moduli that depends on the vesicle volume, the shape characterized by the tubular endings is attained, with continuously increasing the axial force, by a discontinuous shape transformation.