Fast Simulation of Lipid Vesicle Deformation Using Spherical Harmonic Approximation. (5th December 2016)

• Record Type: Journal Article
• Authors: Mikucki, Michael; Zhou, Yongcheng
• Is Part Of: Communications in computational physics. Volume 21:Number 1(2017:Jan.)
• Page Start: 40
• Page End: 64
• Publication Date: 2016-12-05
• Subjects: 35Q92, -- 92C40, -- 65M70; Lipid bilayer, -- curvature energy, -- surface harmonics, -- fast algorithm; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.OA-2015-0029
• Languages: English
• ISSNs: 1815-2406

Abstract

Abstract: Lipid vesicles appear ubiquitously in biological systems. Understanding how the mechanical and intermolecular interactions deform vesicle membranes is a fundamental question in biophysics. In this article we develop a fast algorithm to compute the surface configurations of lipid vesicles by introducing surface harmonic functions to approximate themembrane surface. This parameterization 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.