Spherical Vesicles Distorted by a Grafted Latex Bead: An Exact Solution

TL;DR

This paper provides an exact mathematical solution for the shape of a spherical vesicle distorted by a grafted latex bead, using advanced elasticity techniques, revealing flattening opposite the bead and connecting to existing models.

Contribution

It introduces an exact solution to vesicle deformation by a grafted bead, employing Bogomol'nyi decomposition and elastic compatibility, extending previous approximate models.

Findings

The antipodal region flattens due to the grafted bead.

The solution recovers the hat-model approximation for small beads.

A shape equation is derived from variational principles.

Abstract

We present an exact solution to the problem of the global shape description of a spherical vesicle distorted by a grafted latex bead. This solution is derived by treating the nonlinearity in bending elasticity through the (topological) Bogomol'nyi decomposition technique and elastic compatibility. We recover the ``hat-model'' approximation in the limit of a small latex bead and find that the region antipodal to the grafted latex bead flattens. We also derive the appropriate shape equation using the variational principle and relevant constraints.