The role of spontaneous curvature in the formation of cell membrane necks

TL;DR

This paper investigates how inhomogeneous spontaneous curvature and surface tension influence the formation of membrane necks in cells, providing analytical solutions and energetic insights into the mechanics of membrane constriction.

Contribution

It introduces an analytical framework for membrane neck formation considering inhomogeneous spontaneous curvature and surface tension within the Canham-Helfrich model.

Findings

Analytic solutions for spontaneous curvature and surface tension are derived.

A constrictive force expression at the membrane neck is obtained.

Energy barriers between different membrane configurations are identified.

Abstract

The mechanical effects of membrane compositional inhomogeneities are analyzed in a process analogous of neck formation in cellular membranes. We cast on the Canham-Helfrich model of fluid membranes with both the spontaneous curvature and the surface tension being non-homogeneous functions along the cell membrane. The inhomogeneous distribution is determined by the equilibrium mechanical equations, and, in order to establish the role played by the inhomogeneity, we focus on the catenoid, a surface of zero mean curvature, which can be described in terms of the catenary curve parameterized by arc length. We show that analytic solutions exist for the spontaneous curvature, as well as for both, the surface tension and the radial elastic force. An analytic expression for the constrictive force at the neck, is obtained. From the energetic analysis, it is found that, if we fix the value of the constrictive force at the neck, the set of solutions lies on two branches separated by an energetic barrier. This barrier corresponds to the energy of the maximum catenoid. If instead we fix the axial force, the solution has access to catenoid of any size