A Continuum Variational Approach to Vesicle Membrane Modeling

Abstract

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. Membrane mechanics is a conservative, equilibrium theory and so cannot, a priori, describe the time course, flows and dissipations of a real system. Over the past few decades, physical scientists and mathematicians have developed global multi-physics field equations that describe the time course of processes for condensed matter in a thermodynamically consistent way. We use these equations to describe the membrane during lipid bilayer membrane remodelings. We analyze the vesicle membrane and its lipid layers as a bulk continuum variable in a Hamiltonian. The Hamiltonian includes the surface tension and curvature effects of the classical Helfrich model. The representations are, however, more flexible and can readily account for multicomponent systems, inhomogeneities, and changes in topology. 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. Numerical schemes, designed specifically for this field theory, provide the position, velocity and forces of the fluid--vesicle system at each point in space and time. Classical models assume a specific shape for the vesicle (e.g., a sphere). The assumed shape will occur in the real world, however, only if it is a self-consistent solution of the equations. Our calculations yield values of all key variables and energies over time-the shape is an output. 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.