A Continuum Variational Approach to Vesicle Membrane Modeling

Biological membranes remodel in lipid pore formation, fusion, endocytosis and other processes. Traditionally, continuum membrane mechanics has been used to describe the physics of these remodelings. We analyze the vesicle membrane and its lipid layers as a bulk continuum variable in a Hamiltonian defined in terms of phase field labeling functions. The Hamiltonian includes the surface tension and curvature effects of the classical Helfrich model. Coupling the Hamiltonian to the motion of the aqueous medium with Rayleigh dissipation leads to a complicated, self-consistent system of partial differential equations that is solved numerically. Movies that precisely illustrate the time evolution of the membrane configuration are generated. Changes over time are appreciated visually without reference to the equations—or even to the physics—of the remodeling processes.