# Boundary behaviours of open vesicles in axisymmetric case

## TL;DR

This paper analytically investigates the boundary behaviors of axisymmetric open vesicles, revealing conditions under which a vesicle can transition from closed to open states, emphasizing the roles of spontaneous curvature and boundary parameters.

## Contribution

It provides an analytic expression for boundary edges of open vesicles and identifies key parameters influencing the open-closed transition.

## Key findings

- Boundary radius and line tension are strongly constrained by bending moduli.
- A minimal nonzero boundary radius exists in some cases.
- Spontaneous curvature is essential for continuous vesicle opening.

## Abstract

A continuous transformation from a closed vesicle to an open vesicle needs that the area of open hole enlarge from zero. Since the shape equation and boundary conditions of lipid open vesicles with free edges have been obtained, we want know whether this process can be archived with valid parameters. By study the boundary conditions in the axisymmetric case, the analytic expression of the boundary edges is obtained generally. It reveals that the radius and line tension of boundary edges are confined strongly by bending moduli. In some cases, there is the minimal nonzero boundary radius and the line tension needs to surmount the maxim following the increase of boundary radius. Without the spontaneous curvature, the line tension will trend to infinite when the boundary radius shrinks to zero. The continuous opening process from a closed vesicle to an open vesicle needs that the spontaneous curvature is nonzero and the ratio between the bending moduli of Gauss curvature and mean curvature satisfies $k\leq-4$. Besides the line tension, a closed vesicle can be opened through changing the spontaneous curvature.