Lipid membrane viscosities from molecular simulations via time-correlation formulas

Biological lipid membranes make up the boundary of the cell, as well as many of the cell's internal organelles. Such membranes play a dynamic role in cellular processes, and are unique materials: lipids flow in-plane as a two-dimensional viscous fluid, while the membrane bends out-of-plane as an elastic shell. Though the continuum equations governing membrane dynamics are known, experimental measurements of membrane viscosities often vary significantly. As a consequence, it is often difficult to compare experimental observations of membrane dynamics with theoretical predictions.

In this talk, we discuss recent efforts to calculate the two-dimensional membrane shear and dilational viscosities via molecular dynamics simulations. In particular, we use the established continuum theory to solve for the dynamical evolution of planar membrane modes in configurations that are amenable to molecular simulation. We find the relaxation of height and density variations is governed by several parameters, including both membrane viscosities. We then employ the Onsager regression hypothesis, and assume membrane fluctuations—and thus membrane time-correlations—are governed by this same relaxation. In doing so, we demonstrate how the shear and dilational viscosities of the membrane can be extracted from molecular simulations.