Numerical Modeling of Tether Formation in Viscous Lipidic Membranes

Abstract

We present a finite element formulation to study the behavior of biological membranes governed by viscous and bending forces and subjected to area and volume constraints. The membrane is discretized by a surface mesh made up of planar triangles over which the Boussinesq-Scriven operator is solved to account for the viscous effects. A Laplace-Beltrami identity is used to compute the membrane curvature. A semi-implicit approach in which curvature and velocity are coupled, is used to improve stability of simulations. The area and volume constraints are accounted by considering suitable Lagrange multipliers. We focus on the formation of tethers in lipidic vesicles by means of externally applied forces.
The simulation of a tether formation by pulling a small parcel of an originally spherical membrane was performed. The results were compared to the analytical solution of a cylindrical membrane under the influence of an external axial force. The agreement of the overall dynamics of the 3D tether with the exact solution of the idealized cylindrical tether is quite remarkable, indicating that the fundamental relaxation processes are adequately captured. Due to the large deformations suffered along the process a suitable adaptive re-meshing strategy is needed to preserve the mesh quality and thus robustness of computations, and to capture the tether’s geometrical features. In our re-meshing procedure the new and the original meshes do not maintain a topological relation.