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The collective motion of membrane lipids over hundred of nanometers andnanoseconds is essential for the formation of submicron complexes of lipids andproteins in the cell membrane. These dynamics are difficult to accessexperimentally and are currently poorly understood. One of the conclusions ofthe celebrated Saffman-Debr\"uck (SD) theory is that lipid disturbances smallerthan the Saffman length (microns) are not affected by the hydrodynamics of theembedding solvent. Using molecular dynamics and coarse-grained models withimplicit hydrodynamics we show that this is not true. Hydrodynamic interactionsbetween the membrane and the solvent strongly enhance the short-time collectivediffusion of lipids at all scales. The momentum transferred between themembrane and the solvent in normal direction (not considered by the SD theory)propagates tangentially over the membrane inducing long-ranged repulsive forcesamongst lipids. As a consequence the lipid collective diffusion coefficientincreases proportionally to the disturbance wavelength. We find quantitativeagreement with the predicted anomalous diffusion in quasi-two-dimensionaldynamics, observed in colloids confined to a plane but embedded in 3D solvent.

Solvent hydrodynamics enhances the collective diffusion of membrane lipids