MODELING AND COMPUTING OF DEFORMATION DYNAMICS OF INHOMOGENEOUS BIOLOGICAL SURFACES~?

摘要

Thin elastic surfaces frequently contain molecules influencing their mechanical properties. Such structures occur at different scales in biological systems. Prominent examples are bilayer membranes and cell tissues. We introduce a continuous dynamical model of deformation of lateral inhomogeneous surfaces, using the example of artificial membranes. In agreement with experimental observations, the membrane consists of different molecular species undergoing lateral phase separation and influencing the mechanical properties of the membrane. The model is based on minimization of free energy leading to a nonlinear PDE system of fourth order, related to the Willmore flow and the Cahn-Hilliard equation. The novelty of our work is in modeling and computing of time-dependent dynamics of the system, which requires local mass conservation. Parametric finite element simulations show how dynamics result in diverse equilibrium patterns. The presented simulations are in good agreement with recent theoretical and experimental observations. We investigate how each of the four elastic model parameters (line tension, spontaneous curvature, bending rigidity, and Gaussian rigidity) influences velocity and minimum shape of membrane budding.