Viscous modes of quasi-spherical fluid bilayer membranes*

Membrane viscosity is usually assumed to only affect short-wavelength undulations of lipid bilayers [Seifert and Langer, Europhys. Lett. (1993)]. Here, we show that  fluctuation dynamics about a curved shape such as a quasi-spherical vesicle is sensitive to the membrane viscosity even at long-wavelengths, if the Saffman-Debruck length is larger than the radius of curvature. The theory predicts a relaxation rate of ~1/q^4 for a spherical harmonic mode of order q, a drastic change from the classic result ~ 1/q^3. Accordingly, the stretched exponential in the Dynamic Structure Factor (DSF) becomes ~ t^{1/2} instead of the commonly used  ~t^{2/3} [Zilman and Granek, Phys. Rev. Lett. (1996)]. Experimental measurements of the shape fluctuations of giant vesicles made of DPPC:Chol  confirm the theoretical results and for the first time quantify the effect of membrane viscosity in the bilayer bending dynamics.  The new DSF scaling implies that the data analysis in methods that utilize DSF of liposomes, e.g., neutron spin-echo, need to be reassessed.