Onsager's Variational Principle in Soft Matter: Introduction and Application to the Dynamics of Adsorption of Proteins onto Fluid Membranes

摘要

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. These two behaviors, however, are tightly coupled through the membrane geometry. Indeed, shape transformations necessarily induce lipid flows that bring material from one part of the membrane to another (Evans and Yeung 1994). On the other hand, fluid flows in the presence of curvature generate out-of-plane forces, which modify the shape of the membrane and elicit elastic forces (Rahimi et al. 2013). This mechanical duality provides structural stability and adaptability, allowing membranes to build relatively stable structures that can nevertheless undergo dynamic shape transformations. These transformations are critical for the cell function; they are required in vesicular and cellular trafficking (Sprang et al. 2001; Rustom et al. 2004), cell motility and migration (Arroyo et al. 2012; Yamaguchi et al. 2015), or in the mechano-adaptation of cells to stretch and osmotic stress (Kosmalska et al. 2015).