# Bending models of lipid bilayer membranes: spontaneous curvature and area-difference elasticity

## TL;DR

This paper compares and extends computational models for the bending elasticity of lipid bilayer membranes, improving their accuracy and robustness in simulating vesicle shape transformations and related phenomena.

## Contribution

It evaluates four existing schemes for membrane bending energy computation, extends three of them to include spontaneous curvature and elasticity effects, and identifies the most effective scheme B.

## Key findings

- Extended scheme B outperforms others in accuracy and robustness.
- Proposed extensions enable modeling of budding, vesiculation, and non-axisymmetric shapes.
- Validated on benchmark problems including vesicle phase diagrams.

## Abstract

We preset a computational study of bending models for the curvature elasticity of lipid bilayer membranes that are relevant for simulations of vesicles and red blood cells. We compute bending energy and forces on triangulated meshes and evaluate and extend four well established schemes for their approximation: Kantor and Nelson 1987, Phys. Rev. A 36, 4020, J\"ulicher 1996, J. Phys. II France 6, 1797, Gompper and Kroll 1996, J. Phys. I France 6, 1305, and Meyer et. al. 2003 in Visualization and Mathematics III, Springer, p35, termed A, B, C, D. We present a comparative study of these four schemes on the minimal bending model and propose extensions for schemes B, C and D. These extensions incorporate the reference state and non-local energy to account for the spontaneous curvature, bilayer coupling, and area-difference elasticity models. Our results indicate that the proposed extensions enhance the models to account for shape transformation including budding/vesiculation as well as for non-axisymmetric shapes. We find that the extended scheme B is superior to the rest in terms of accuracy, and robustness as well as simplicity of implementation. We demonstrate the capabilities of this scheme on several benchmark problems including the budding-vesiculating process and the reproduction of the phase diagram of vesicles.