Shapes of pored membranes

TL;DR

This paper investigates the shapes of pored membranes using Helfrich theory, revealing how curvature terms influence membrane morphology and proposing a method to measure Gaussian rigidity ratios through shape analysis.

Contribution

It introduces a novel approach to determine the Gaussian rigidity to bending rigidity ratio from membrane shape observations and extends findings to two-component membranes.

Findings

Mean curvature induces budding-like structures.

Gaussian curvature flattens membranes near pores.

Shape observations can estimate rigidity ratios.

Abstract

We study the shapes of pored membranes within the framework of the Helfrich theory under the constraints of fixed area and pore size. We show that the mean curvature term leads to a budding- like structure, while the Gaussian curvature term tends to flatten the membrane near the pore; this is corroborated by simulation. We propose a scheme to deduce the ratio of the Gaussian rigidity to the bending rigidity simply by observing the shape of the pored membrane. This ratio is usually difficult to measure experimentally. In addition, we briefly discuss the stability of a pore by relaxing the constraint of a fixed pore size and adding the line tension. Finally, the flattening effect due to the Gaussian curvature as found in studying pored membranes is extended to two-component membranes. We find that sufficiently high contrast between the components' Gaussian rigidities leads to budding which is distinct from that due to the line tension.