Volume 21, Issue 1
Fast Simulation of Lipid Vesicle Deformation Using Spherical Harmonic Approximation

Michael Mikucki & Yongcheng Zhou

Commun. Comput. Phys., 21 (2017), pp. 40-64.

Published online: 2018-04

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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 the membrane 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.

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@Article{CiCP-21-40, author = {}, title = {Fast Simulation of Lipid Vesicle Deformation Using Spherical Harmonic Approximation}, journal = {Communications in Computational Physics}, year = {2018}, volume = {21}, number = {1}, pages = {40--64}, 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 the membrane 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2015-0029}, url = {http://global-sci.org/intro/article_detail/cicp/11231.html} }
TY - JOUR T1 - Fast Simulation of Lipid Vesicle Deformation Using Spherical Harmonic Approximation JO - Communications in Computational Physics VL - 1 SP - 40 EP - 64 PY - 2018 DA - 2018/04 SN - 21 DO - http://dor.org/10.4208/cicp.OA-2015-0029 UR - https://global-sci.org/intro/article_detail/cicp/11231.html KW - AB -

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 the membrane 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.

Michael Mikucki & Yongcheng Zhou. (2020). Fast Simulation of Lipid Vesicle Deformation Using Spherical Harmonic Approximation. Communications in Computational Physics. 21 (1). 40-64. doi:10.4208/cicp.OA-2015-0029
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