Equatorial deformation of homogeneous spherical fluid vesicles by a rigid ring

TL;DR

This study investigates how a rigid ring deforms spherical fluid vesicles, revealing shape transitions and force expressions, with implications for understanding vesicle mechanics under constraints.

Contribution

It introduces a detailed analysis of vesicle deformation by a rigid ring, including force expressions and shape transition behaviors under fixed area or volume constraints.

Findings

Vesicles transition from prolate to dumbbell shapes with a small neck.

Force expressions involve curvature discontinuities and global vesicle properties.

Bifurcations occur near spontaneous curvature values, affecting energy states.

Abstract

We examine the deformation of homogeneous spherical fluid vesicles along their equator by a circular rigid ring. We consider deformations preserving the axial and equatorial mirror symmetries of the vesicles. The configurations of the vesicle are determined employing the spontaneous curvature model subject to the constraints imposed by the ring as well as of having constant area or volume. We determine two expressions of the force exerted by the ring, one involving a discontinuity in the derivative of the curvature of the membrane across the ring, and another one in terms of the global quantities of the vesicle. For small enough values of the spontaneous curvature there is only one sequence of configurations for either fixed area or volume. The behavior of constricted vesicles is similar for both constraints, they follow a transition from prolate to dumbbell shapes, which culminates in two quasispherical vesicles connected by a small catenoid-like neck. We analyze the geometry and the force of the small neck employing a perturbative analysis about the catenoid. A stretched vesicle initially adopts an oblate shape for either constraint. If the area is fixed the vesicle increasingly flattens until it attains a disclike shape, which we examine using an asymptotic analysis. If the volume is fixed the poles approach until they touch and the vesicle adopts a discocyte shape. When the spontaneous curvature of the vesicle is close to the mean curvature of the constricted quasispherical vesicles, the sequences of configurations of both constraints develop bifurcations, and some of the configurations corresponding to one of their branches have the lowest energy.