Collective dynamics in lipid membranes: The continuum is that which is divisible into indivisibles that are infinitely divisible (Aristotle, Physics)

In solid-state NMR of biomolecules, the average structure and dynamics are addressed by combining experimental results with theory. Relaxation rates exhibit a functional dependence on order parameters because of molecular motions and/or collective excitations of liquid-crystalline membranes. Mixtures of phospholipids with cholesterol or nonionic surfactants allow the experimental correspondence of 2H NMR observables to be quantitatively tested. For cholesterol-stiffened bilayers, the spin-lattice relaxation rate profile is reduced together with an increased order profile. Bilayer softening due to nonionic surfactants gives an opposite relaxation enhancement accompanied by reduced order parameters. In both cases a square-law functional dependence (Fermi's Golden Rule) explains the relaxation and order profiles in terms of mean-square amplitudes of the lipid fluctuations. Model-free analysis reveals an ω^-1/2 frequency law for three-dimensional (3D) fluctuations of the membrane, whereas for two-dimensional (2D) elastic sheets an ω^-1 dependence is expected. Collective segmental or molecular modes emerge on the mesoscale of the bilayer thickness and smaller that are formulated with continuum elastic theory. Furthermore, the bilayer core resembles a hydrocarbon fluid with a viscosity of only a few centipoises (cP). Magnetic resonance spectroscopy thus reveals properties of the membrane lipids described by a hierarchical energy landscape that affects their polymorphism, phase behavior, and lipid-protein interactions.