A Phase-Field Model for Vesicle Membranes Incorporating Area-Difference Elasticity
Yihong Liang, Emine Celiker, Ping Lin
TL;DR
This work develops a phase-field formulation for vesicle membranes that incorporates area-difference elasticity (ADE) under fixed volume and surface-area constraints. It employs a Fourier-spectral spatial discretization and a semi-implicit time-stepping scheme to efficiently simulate three-dimensional deformations driven by ADE. The results reveal a rich set of equilibrium shapes, from discocytes and toroids to gourds, cylinders, multi-armed, and nested morphologies, highlighting ADE as a key determinant of vesicle geometry. The approach provides a robust framework for exploring complex membrane morphologies and lays groundwork for studying processes like budding, fission, and cytoskeletal interactions in biomembranes.
Abstract
This paper presents a phase-field model for simulating the three-dimensional deformation of vesicle membranes, incorporating area-difference elasticity, with constraints on bulk volume and surface area. We develop efficient numerical schemes based on the Fourier-spectral method for spatial discretization and temporal evolution. The model successfully captures a wide variety of steady-state vesicle shapes. The numerical experiments demonstrate that by tuning the simulation parameters, the vesicle can transition from a simple discocyte shape to a complex, multi-armed starfish-like and nested configuration. These results highlight the crucial role of area-difference elasticity in determining vesicle morphology.