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Fast Simulation of Lipid Vesicle Deformation Using Spherical Harmonic Approximation

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Physiological, cellular and medical topics Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  05 December 2016

Michael Mikucki  and
Yongcheng Zhou
Michael Mikucki*
Affiliation:
Department of Applied Mathematics & Statistics, Colorado School of Mines, Golden, Colorado, 80401, USA
Yongcheng Zhou*
Affiliation:
Department of Mathematics, Colorado State University, Fort Collins, Colorado, 80523, USA
*
*Corresponding author. Email addresses:[email protected] (M. Mikucki), [email protected] (Y. Zhou)
*Corresponding author. Email addresses:[email protected] (M. Mikucki), [email protected] (Y. Zhou)
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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.

Keywords

Lipid bilayercurvature energysurface harmonicsfast algorithm

MSC classification

Secondary: 35Q92: PDEs in connection with biology and other natural sciences 92C40: Biochemistry, molecular biology 65M70: Spectral, collocation and related methods
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 1 , January 2017 , pp. 40 - 64
Copyright
Copyright © Global-Science Press 2016 

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