Onsager’s variational principle in soft matter: Introduction and application to the dynamics of adsorption of proteins onto fluid membranes

Abstract

Lipid bilayers are unique soft materials operating in general in the low Reynolds limit. While their shape is predominantly dominated by curvature elasticity as in a solid shell, their in-plane behavior is that of a largely inextensible viscous fluid. Furthermore, lipid membranes are extremely responsive to chemical stimuli. Because in their biological context they are continuously brought out-of-equilibrium mechanically or chemically, it is important to understand their dynamics. Here, we introduce Onsager’s variational principle as a general and transparent modeling tool for lipid bilayer dynamics. We introduce this principle with elementary examples, and then use it to study the sorption of curved proteins on lipid membranes.