Beyond the creeping viscous flow limit for lipid bilayer membranes: Theory of single-particle microrheology, domain flicker spectroscopy, and long-time tails

Recent experiments suggest that lipid bilayer membranes may be viscoelastic. We present a generalized "Saffman-Einstein" relation that may be used to determine the linear viscoelastic shear modulus from single-bead microrheology experiments on membranes. We show that viscoelastic parameters can also be extracted from membrane domain flicker spectroscopy experiments. Contributions from fluid inertia are expected to be negligible in both microrheology and domain flicker spectroscopy experiments, but can create a "long-time tail" in the membrane velocity autocorrelation function. In a viscous membrane, this tail crosses over from t(-1) at intermediate times, as in a two-dimensional fluid, to t(-3/2) at long times, as in a three-dimensional fluid. If the membrane is viscoelastic, the velocity autocorrelation function may be negative at intermediate times.