Geometry of lipid vesicle adhesion

TL;DR

This paper analyzes the geometry of lipid vesicle adhesion to substrates using Helfrich Hamiltonian, deriving boundary conditions and force balances without symmetry assumptions, and discusses effects of strong bonding and curvature asymmetry.

Contribution

It provides a geometric framework for understanding vesicle adhesion, including boundary constraints and force balance, without relying on symmetry assumptions.

Findings

Derived boundary conditions for vesicle-substrate contact

Analyzed force balance at the adhesion boundary

Discussed effects of curvature asymmetry and strong bonding

Abstract

The adhesion of a lipid membrane vesicle to a fixed substrate is examined from a geometrical point of view. This vesicle is described by the Helfrich hamiltonian quadratic in mean curvature; it interacts by contact with the substrate, with an interaction energy proportional to the area of contact. We identify the constraints on the geometry at the boundary of the shared surface. The result is interpreted in terms of the balance of the force normal to this boundary. No assumptions are made either on the symmetry of the vesicle or on that of the substrate. The strong bonding limit as well as the effect of curvature asymmetry on the boundary are discussed.