Solvent hydrodynamics enhances the collective diffusion of membrane lipids

The collective motion of membrane lipids over hundred of nanometers and nanoseconds is essential for the formation of submicron complexes of lipids and proteins in the cell membrane. These dynamics are difficult to access experimentally and are currently poorly understood. One of the conclusions of the celebrated Saffman-Debr\"uck (SD) theory is that lipid disturbances smaller than the Saffman length (microns) are not affected by the hydrodynamics of the embedding solvent. Using molecular dynamics and coarse-grained models with implicit hydrodynamics we show that this is not true. Hydrodynamic interactions between the membrane and the solvent strongly enhance the short-time collective diffusion of lipids at all scales. The momentum transferred between the membrane and the solvent in normal direction (not considered by the SD theory) propagates tangentially over the membrane inducing long-ranged repulsive forces amongst lipids. As a consequence the lipid collective diffusion coefficient increases proportionally to the disturbance wavelength. We find quantitative agreement with the predicted anomalous diffusion in quasi-two-dimensional dynamics, observed in colloids confined to a plane but embedded in 3D solvent.