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

Marino Arroyo, Nikhil Walani, Alejandro Torres-Sánchez, Dimitri Kaurin. The Role of Mechanics in the Study of Lipid Bilayers (edited by David J. Steigmann) 287-332 (2018).

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.

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