Small equatorial deformation of homogeneous spherical fluid vesicles

TL;DR

This paper analytically investigates how a homogeneous spherical fluid vesicle deforms under a localized equatorial force, revealing the initial response and the force needed to induce deformation.

Contribution

It provides an analytical solution for the linear deformation of spherical vesicles under localized forces, including the force threshold for membrane deformation.

Findings

Derived the first-order perturbations of the vesicle shape.

Calculated the force required to initiate membrane deformation.

Identified the discontinuity in membrane curvature across the ring.

Abstract

We examine the reaction of a homogeneous spherical fluid vesicle to the force exerted by a rigid circular ring located at its equator in the linear regime. We solve analytically the linearized first integral of the Euler-Lagrange equation subject to the global constraints of fixed area and volume, as well as to the local constraint imposed by the ring. We determine the first-order perturbations to the generating curve of the spherical membrane, which are characterized by the difference of the radii of the membrane and the ring, and by a parameter depending on the physical quantities of the membrane. We determine the total force that is required to begin the deformation of the membrane, which gives rise to a discontinuity in the curvature of the membrane across the ring.