Local sensitivity analysis of the `Membrane shape equation' derived from the Helfrich energy

TL;DR

This paper investigates the sensitivity of the membrane shape equations derived from Helfrich energy, combining analytical and numerical methods to understand parameter effects on membrane morphology, including vesicle shape formations.

Contribution

It provides a detailed analysis of parameter sensitivity in Helfrich-based membrane models, especially focusing on the spontaneous curvature parameter, with simulations illustrating shape transformations.

Findings

Parameter choices significantly influence membrane shapes.

Sensitivity analysis clarifies the role of spontaneous curvature.

Simulations demonstrate formation of spherical buds and pearled shapes.

Abstract

The Helfrich energy is commonly used to model the elastic bending energy of lipid bilayers in membrane mechanics. The governing differential equations for certain geometric characteristics of the shape of the membrane can be obtained by applying variational methods (minimization principles) to the Helfrich energy functional and are well-studied in the axisymmetric framework. However, the Helfrich energy functional and the resulting differential equations involve a number of parameters, and there is little explanation of the choice of parameters in the literature, particularly with respect to the choice of the "spontaneous curvature" term that appears in the functional. In this paper, we present a careful analytical and numerical study of certain aspects of parametric sensitivity of Helfrich's Using simulations of specific model systems, we demonstrate the application of our scheme to the formation of spherical buds and pearled shapes in membrane vesicles.