Fast Simulation of Lipid Vesicle Deformation Using Spherical Harmonic Approximation (Communications in Computational Physics, 2018)
Lipid vesicles appear ubiquitously in biological systems. Understandinghow the mechanical and intermolecular interactions deform vesicle membranes is afundamental question in biophysics. In this article we develop a fast algorithm tocompute the surface configurations of lipid vesicles by introducing surface harmonicfunctions to approximate the membrane surface. This parameterization allows an analyticalcomputation of the membrane curvature energy and its gradient for the efficientminimization of the curvature energy using a nonlinear conjugate gradient method.Our approach drastically reduces the degrees of freedom for approximating the membranesurfaces compared to the previously developed finite element and finite differencemethods. Vesicle deformations with a reduced volume larger than 0.65 can bewell approximated by using as small as 49 surface harmonic functions. The methodthus has a great potential to reduce the computational expense of tracking multiplevesicles which deform for their interaction with external fields.