Shapes of nearly cylindrical, axisymmetric bilayer membranes

Shapes of nearly cylindrical sections of axisymmetric phospholipid membrane s are studied theoretically. Describing the shape of such sections by their deviation from a reference cylinder, the well-established shape equation f or axisymmetric bilayer membranes is expanded in terms of this deviation, a nd it is then solved analytically. The phase diagram shows the resulting st ationary shapes as functions of system parameters and external conditions, i.e., the pressure difference across the membrane, the membrane tension, th e difference between the tensions of the two monolayers, and the axial forc e acting on the vesicle. The accuracy of the approximate analytical solutio n is demonstrated by comparison with numerical results. The obtained analyt ical solution allows to extend the analysis to include shapes where numeric al methods have failed.