Precision measurements of lipid membrane hydrodynamic drag

The hydrodynamic drag at a lipid bilayer determines, among other things, the flow properties of suspensions of cells and liposomes. For spherical liposomes or lipid vesicles, the Stokes equation relates the drag coefficient ζ to the radius r and the fluid viscosity η by ζ = Cπηr, where the dimensionless C depends on the hydrodynamic boundary between the sphere and the fluid. For solid spheres C=6 and for liquid spheres C=4. This constant has been assumed to be 6 for lipid membranes, but we have found no direct measurements of it, and given the fluidity of lipid membranes it is not obvious that the solid-sphere value applies. The Stokes-Einstein relationship D = k_BT/(Cπηr), where D is the diffusion coefficient, k_B is Boltzmann's constant, and T is the temperature allows determination of C provided D can be determined precisely. We use light sheet fluorescence microscopy to image lipid vesicles far from surfaces that complicate application of the Stokes-Einstein relationship. Combined with high-accuracy image localization, this allows us to measure C, finding that it closely matches the C=6 value of a solid sphere. We comment on deviations from C=6 for non-spherical vesicles with thermally driven undulations.