Fast Algorithm for Simulating Lipid Vesicle Deformation I: Spherical Harmonic Approximation

TL;DR

This paper introduces a fast, surface harmonic-based algorithm for simulating lipid vesicle deformation, significantly reducing computational complexity while accurately modeling vesicle shapes and interactions.

Contribution

The authors developed a novel surface harmonic approximation method that simplifies vesicle surface modeling and enables efficient energy minimization, outperforming traditional finite element and finite difference approaches.

Findings

Accurately approximates vesicle shapes with fewer harmonic functions.

Reduces computational cost for simulating multiple vesicle interactions.

Effective for vesicles with reduced volume > 0.65.

Abstract

Lipid vesicles appear ubiquitously in biological systems. Understanding how the mechanical and intermolecular interations deform vesicle membrane is a fundamental question in biophysics. In this article we developed a fast algorithm to compute the surface configurations of lipid vesicles by introducing the surface harmonic functions to approximate the surfaces. This parameterization of the surfaces allows an analytical computation of the membrane curvature energy and its gradient for the efficient minimization of the curvature energy using a nonlinear conjugate gradient method. Our approach drastically reduces the degrees of freedom for approximating the membrane surfaces compared to the previously developed finite element and finite difference methods. Vesicle deformations with a reduced volume larger than 0.65 can be well approximated by using as small as 49 surface harmonic functions. The method thus has a great potential to reduce the computational expense of tracking multiple vesicles which deform for their interaction with external fields.