Wrapping of a spherical colloid by a fluid membrane

TL;DR

This paper presents a theoretical analysis of how a spherical colloid induces elastic deformation in a fluid membrane, revealing continuous and discontinuous wrapping transitions with energy barriers, using both full optimization and analytical approximations.

Contribution

It introduces a comprehensive theoretical framework for membrane wrapping, including a full shape optimization and an analytical approximation for small deformations, clarifying phase boundaries.

Findings

Identification of continuous and discontinuous wrapping transitions

Discovery of a significant energy barrier in the envelopment process

Analytical approximation accurately predicts phase boundaries at low tension

Abstract

We theoretically study the elastic deformation of a fluid membrane induced by an adhering spherical colloidal particle within the framework of a Helfrich energy. Based on a full optimization of the membrane shape we find a continuous binding and a discontinuous envelopment transition, the latter displaying a potentially substantial energy barrier. A small gradient approximation permits membrane shape and complex energy to be calculated analytically. While this only leads to a good representation of the complex geometry for very small degrees of wrapping, it still gives the correct phase boundaries in the regime of low tension.