Membrane Viscosity And Lipid Diffusion In A Model Bilayer Measured At Molecular Scales

In a two-dimensional biological membrane, constituent molecules such as lipids, sterols, and proteins, must be delivered to specific functional sites in time to accommodate biological functions. This specific functionality is characterized as transport properties in membranes. Hydrodynamic models accurately describe the diffusion behavior in membranes as long as the inclusion is relatively large compared to the constituent lipid molecules within the membrane. However, when the inclusion size is smaller than a certain threshold, less than about 1 nm, such a continuum picture breaks down. In order to understand the diffusion behavior at molecular scales smaller than captured by hydrodynamics, it is crucial to experimentally measure both the molecular diffusion constant D and the membrane viscosity ηm at length and time scales of the constituent molecules. Here, we employ both incoherent and coherent quasi-elastic neutron scattering techniques to access ps to ns dynamics at molecular size scales, and to quantify D and ηm in large unilamellar vesicles composed of saturated phosphocholine lipid molecules. A direct comparison between D and ηm is performed to compare with the two-dimensional hydrodynamic model proposed by Saffman and Delbrück. Although this theory predicts an almost linear dependence of the drag kBT/D with respect to ηm, the experimental data show a clear deviation from the linear relation, where kBT is the thermal energy. These data support theoretical predictions beyond the hydrodynamic models that suggest that are additional contributions to the drag at the molecular length scale, such as the molecular order parameter or interactions.