(757k) Irreversible Thermodynamics of Lipid Membranes: Theory and Computation

We develop an irreversible thermodynamic framework for arbitrarily curved and deforming lipid membranes to determine their dynamical equations of motion. Using this framework, we study the coupling between elastic membrane bending and the irreversible processes of intramembrane lipid flow, intramembrane lipid--lipid phase transitions, and protein binding and diffusion. With the equations governing lipid membrane dynamics, we develop an arbitrary Lagrangian--Eulerian (ALE) finite element method to simulate the evolution of lipid membranes in several biologically relevant situations. An ALE theory is developed by endowing the membrane surface with a mesh whose in-plane velocity is independent of the in-plane material velocity, and can be specified arbitrarily. A new physical insight is obtained by applying the ALE developments to lipid membrane tubes, which are computationally and analytically found to be unstable with respect to long-wavelength perturbations when there is a large pressure drop across the membrane surface.